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  • 2016
    • Allstadt, Kate - Ph.D. Dissertation
      Surficial Seismology: Landslides, Glaciers, and Volcanoes in the Pacific Northwest through a Seismic Lens 2016, Allstadt,Kate,Kate Allstadt Surficial Seismology: Landslides Glaciers and Volcanoes in the Pacific Northwest through a Seismic Lens Kate Allstadt A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2013 Reading Committee: John Vidale Chair Juliet Crider Stephen Malone Ken Creager Program Authorized to Offer Degree: Earth and Space Sciences Copyright 2013 Kate Allstadt University of Washington Abstract Surficial Seismology: Landslides Glaciers and Volcanoes in the Pacific Northwest through a Seismic Lens Kate Allstadt Chair of the Supervisory Committee: Professor John Vidale Department of Earth and Space Sciences The following work is focused on the use of both traditional and novel seismological tools combined with concepts from other disciplines to investigate shallow seismic sources and hazards The study area is the dynamic landscape of the Pacific Northwest and its wide-ranging earthquake landslide glacier and volcano-related hazards The first chapter focuses on landsliding triggered by earthquakes with a shallow crustal earthquake in Seattle as a case study The study demonstrates that utilizing broadband synthetic seismograms and rigorously incorporating 3D basin amplification 1D site effects and fault directivity allows for a more complete assessment of regional seismically induced landslide hazard The study shows that the hazard is severe for Seattle and provides a framework for future probabilistic maps and near real-time hazard assessment The second chapter focuses on landslides that generate seismic waves and how these signals can be harnessed to better understand landslide dynamics This is demonstrated using two contrasting Pacific Northwest landslides The 2010 Mount Meager BC landslide generated strong long period waves New full waveform inversion methods reveal the time history of forces the landslide exerted on the earth that is used to quantify event dynamics Despite having a similar volume 107 m3 The 2009 Nile Valley WA landslide did not generate observable long period motions because of its smaller accelerations but pulses of higher frequency waves were valuable in piecing together the complex sequence of events The final chapter details the difficulties of monitoring glacier-clad volcanoes The focus is on small repeating low-frequency earthquakes at Mount Rainier that resemble volcanic earthquakes However based on this investigation they are actually glacial in origin: most likely stick-slip sliding of glaciers triggered by snow loading Identification of the source offers a view of basal glacier processes discriminates against alarming volcanic noises and has implications for repeating earthquakes in tectonic environments This body of work demonstrates that by combining methods and concepts from seismology and other disciplines in new ways we can obtain a better understanding and a fresh perspective of the physics behind the shallow seismic sources and hazards that threaten the Pacific Northwest Table of Contents Chapter 1: Landslides triggered by earthquakes: A scenario study of seismically induced landsliding in Seattle using broadband synthetic seismograms Chapter 2: Seismogenic landslides a new way to study landslide dynamics: Part a: Extracting source characteristics and dynamics of the August 2010 Mount Meager landslide from broadband seismograms Part b: The seismic story of the Nile Valley landslide Chapter 3: Glacier-quakes mimicking volcanic earthquakes: Swarms of repeating stick-slip glacial earthquakes triggered by snow loading at Mount Rainier Appendices Appendix 1 Representative Shear Wave Velocity Surficial Profiles for Seattle and Map of Units Chapter 1 Appendix 2 High resolution maps 2 of relative seismically induced landslide hazard for a Mw 7 0 Seattle fault earthquake for dry and saturated soil conditions Chapter 1 Appendix 3 Details of Inversion Methods Chapter 2a Chapter 1 - Landslides triggered by earthquakes: A Scenario Study of Seismically Induced Landsliding in Seattle using Broadband Synthetic Seismograms The content of this chapter was published in: Allstadt K Vidale J E and Frankel A D 2013 A Scenario Study of Seismically Induced Landsliding in Seattle Using Broadband Synthetic Seismograms Bull Seism Soc Am 103 No 6 doi: 10 1785 0120130051 with some added details from: Allstadt K and Vidale J E 2012 Seismically Induced Landsliding in Seattle: A Magnitude 7 Seattle Fault Earthquake Scenario USGS NEHRP Final Tech Report Grant : G11AP20012 39p 1-1 Table of Contents Summary 1-3 1 Introduction 1-4 2 Background 1-8 3 Methods 1-12 4 Synthetic Seismogram Generation 1-14 5 Incorporating Site Amplification 1-19 6 Model Outputs 1-23 7 Validation of Ground Motions 1-25 8 Validation of Landslide Simulation 1-29 9 Results of Landslide Simulation for Mw 7 0 Seattle Fault Earthquake 1-31 10 Infrastructure Impacts 1-36 11 Discussion 1-38 12 Conclusions 1-44 13 Data and Resources 1-46 14 Acknowledgements 1-47 15 References 1-48 1-2 Summary We demonstrate the value of utilizing broadband synthetic seismograms to assess regional seismically induced landslide hazard Focusing on a case study of an Mw 7 0 Seattle fault earthquake in Seattle WA we computed broadband synthetic seismograms that account for rupture directivity and 3D basin amplification We then adjusted the computed motions on a fine grid for 1D amplifications based on the site response of typical geologic profiles in Seattle and used these time series ground motions to trigger shallow landsliding using the Newmark method The inclusion of these effects was critical in determining the extent of landsliding triggered We found that for inertially triggered slope failures modeled by the Newmark method the ground motions used to simulate landsliding must have broadband frequency content in order to capture the full slope displacement We applied commonly used simpler methods based on ground motion prediction equations for the same scenario and found that they predicted far fewer landslides if only the mean values were used but far more at the maximum range of the uncertainties highlighting the danger of using just the mean values for such methods Our results indicate that landsliding triggered by a large Seattle fault earthquake will be extensive and potentially devastating causing direct losses and impeding recovery The high impact of landsliding predicted by this simulation shows that this secondary effect of earthquakes should be studied with as much vigor as other earthquake effects 1-3 1 Introduction Landslides triggered by earthquakes have caused significant damage and casualties worldwide For example seismically triggered landslides were responsible for more than half of the damage caused by the 1964 Good Friday Earthquake in Alaska Keefer 1984 and the 2008 Wenchuan earthquake in China triggered about 60 000 landslides that destroyed entire towns and caused tens of thousands of deaths about a third of the total Yin et al 2009 Huang and Fan 2013 Other recent examples include the 1999 Chi-chi earthquake Hung 2000 and the 1994 Northridge earthquake Harp and Jibson 1996 Despite these examples and calls for more focused attention to this secondary earthquake hazard e g Huang and Fan 2000 Wasowski et al 2000 seismically induced landslide hazard has not been quantitatively investigated or fully incorporated into seismic hazard assessments for many areas that are particularly at risk This is not for a lack of methods Researchers have been developing and implementing methods to assess seismically induced landslide hazard for years Some of these methods use soil and slope characteristics of landslides triggered by past earthquakes either qualitatively e g Stewart 2005 Keefer 1984 or through logistic regressions and neural network analysis e g Lee and Evangelista 2006 Keefer 2000 A limitation is that complete post-earthquake landslide distributions needed for many of these methods are rare Keefer 2002 and the applicability of these methods from one area to a different setting that does not have a similar dataset is an issue More sophisticated methods of estimating coseismic landslide triggering have also been developed such as those using dynamic finite-element modeling to simulate the permanent slope deformations induced by the input ground motion throughout the potential failure mass e g Seed et al 1973 Lee 1974 Prevost 1981 However these types of methods are both computationally intensive and require dense high-quality site-specific soil data in order 1-4 for the modeling efforts to be worthwhile Jibson 2011 Kramer 1996 As a result they are not feasible in most cases and certainly not for regional hazard mapping studies As a compromise between the empirical statistical approaches and detailed numerical models of slope performance the Newmark method Newmark 1965 has emerged as a dominant approach to seismically induced landslide hazard mapping and analysis e g Wilson and Keefer 1983 Jibson et al 2000 Miles and Ho 1999 Ambraseys and Menu 1988 Jibson and Michael 2009 Saygili and Rathje 2009 Variations abound but the core of the method is that slope displacements accumulate each time the ground acceleration exceeds a critical threshold value This threshold value depends on the slope geometry material properties and groundwater conditions The Newmark method is simple enough that it is well suited to regional seismically induced hazard mapping studies Jibson et al 2000 A major limitation to all of these methods of assessing seismically induced landsliding hazard is that they require ground motion information for future earthquakes Previous studies have gotten around this by using recordings of past earthquakes if they exist e g Peng et al 2009 Jibson et al 1998 or by using ground motion prediction equations to obtain a simplified ground motion parameter for a specific scenario earthquake such as peak ground acceleration PGA e g Ambraseys and Menu 1988 Lee and Evangelista 2006 or Arias intensity e g Jibson et al 1998 This is then coupled with regression equations to estimate the performance of slopes with various characteristics e g Jibson 2007 Rathje and Saygili 2009 Others take the peak ground acceleration for a specified return period straight from probabilistic seismic hazard maps e g Jibson and Michael 2009 Blake et al 2002 Saygili and Rathje 2009 More rigorous solutions include rescaling recordings of earthquakes in other locations or in the case of Miles and Ho 1999 producing simple stochastic synthetic seismograms for a specific event 1-5 Though some of these methods have ways of approximating site amplifications they are often generalized based on recordings of earthquakes all over the world in different settings not tailored to the peculiarities of a particular location This means variability and thus uncertainty is high and they are missing the characteristics in the time series such as coherent pulses from the finite fault rupture or increased duration due to basin amplification which can be important to landslide triggering Furthermore for studies that use a single ground motion parameter like PGA instead of a time series recording one more step of approximation with its own uncertainties is required to tie PGA to the slope displacement Fortunately seismological methods and computing power have advanced to the point where it is possible to generate realistic broadband synthetic seismograms for scenario earthquakes These methods are capable of accounting for finite fault rupture basin amplification coherent pulses and directivity effects specific to a particular event and locale that are poorly approximated by other methods In this study we used such methods to generate broadband synthetic seismograms on a fine grid 210-meter for a scenario earthquake striking the city of Seattle and rigorously adjusted these ground motions for site amplification due to soil layering on an even finer grid 5-meter using methods from geotechnical earthquake engineering and engineering geology Then we used these ground motions and pre-existing static slope stability data throughout the city to simulate seismically induced landsliding based on the Newmark method We show that using the full time-series recordings that account for the details of ground motion variability such as rupture directivity basin amplification and site response makes a substantial difference in determining the extent of landsliding triggered relative to simpler methods 1-6 We focus our efforts on simulating shallow landsliding triggered by a large crustal earthquake within the city limits of Seattle Washington in order to develop and test the methodology The reason we focus on Seattle is that it is a prime example of a city at risk of seismically induced landsliding that has not been thoroughly investigated The city is highly susceptible to landsliding in general Harp et al 2006 and is also located in an area of elevated seismic hazard that has been well quantified Frankel et al 2007 We simulate a magnitude 7 0 event on the Seattle fault a crustal reverse fault that lies directly below the city Blakely et al 2002 We focus on this fault because it is a primary contributor to the seismic hazard Around 900 A D an earthquake on this fault sent entire forested hillsides sliding into Lake Washington Jacoby et al 1992 and triggered lake-wide turbidity currents Karlin and Abella 1992 Karlin et al 2004 indicating that landsliding was widespread from both this most recent Seattle fault earthquake and previous earthquakes If such landsliding were to occur today the consequences could be dire: the steep hillsides along Lake Washington and Puget Sound are now densely populated In order to be prepared and to build a more resilient city such hazards must be quantified We use the methods described above and detailed in the methods section to demonstrate how they can be used to quantify the hazard posed by landsliding triggered by a scenario shallow crustal earthquake close to the city We map relative hazard but also take the scenario approach further and assign actual slope failures estimate areas in potential runout zones and look at potential intersections with infrastructure We address the critical questions of where landslides are most likely to occur how many might be triggered what effect soil saturation levels will have on the number of landslides triggered and how many buildings and critical infrastructure are at risk This scenario approach yields a tangible picture of the extent of landsliding and the 1-7 areas and infrastructure that could be at risk but represents just one of the countless scenarios that are possible However now that the framework is established for this scenario-based approach it can be used to run a suite of likely scenarios that could even eventually be compiled to develop a probabilistic seismically induced landslide hazard map similarly to how urban probabilistic seismic hazard maps are generated e g Frankel et al 2007 In the following sections we discuss the background of seismically induced landsliding in Seattle then present and validate the methods we used to simulate shallow landsliding triggered by a Seattle fault earthquake for the city of Seattle This is followed by the results of our seismically induced landslide simulation a discussion of the patterns and extent of landsliding triggered potential impacts on infrastructure the importance and sensitivity of various components of our methodology and a comparison to simpler methods Finally we conclude and discuss how broadband synthetic seismograms and these scenario-based methods could be refined for application to more scenarios to improve awareness of and preparedness for seismically induced landsliding in Seattle and other cities 2 Background Seattle s location near the convergence of the Juan de Fuca and North American plate Figure 1-1 inset leaves the city and surrounding region prone to three major earthquake sources: deep earthquakes within the subducted Juan de Fuca plate offshore megathrust earthquakes on the Cascadia subduction zone and shallow crustal earthquakes within the North American Plate Frankel et al 2007 Locally the latter type could be the most disastrous of the three if a large shallow crustal earthquake occurred close to the city The closest crustal fault that threatens Seattle is the Seattle fault which has not had a large earthquake since western settlement The zone of south-dipping reverse faults extends east-west across the Puget Lowland 1-8 just south of downtown Seattle Figure 1-1 forming the southern boundary of the Seattle basin Blakely et al 2002 Paleoseismic studies have revealed that the last major earthquake on this fault was around 900 A D Bucknam et al 1992 with an estimated magnitude of 7 5 ten Brink et al 2006 This event triggered some of the landslides preserved in Lake Washington and rock avalanches in the Olympic Mountains Jacoby et al 1992 Karlin and Abella 1992 Karlin et al 2004 Schuster et al 1992 If the 900 A D event is characteristic the next event could be thousands of years away Johnson et al 1999 Pratt et al 1997 but trenching of a backthrust of the Seattle Fault shows earthquake recurrence intervals in the fault zone range from 200 to 12 000 years Nelson et al 2003 and glacial loading and unloading could have disturbed the cycle Thorson 1996 Seattle itself is particularly prone to strong shaking because it was built directly over the Seattle Basin - a deep sedimentary basin that amplifies ground motion generates strong basin surface waves and tends to increase the duration of shaking Frankel et al 2002 On top of this deeper structure is a veneer of unconsolidated soils: layers of clay sands and till primarily deposited by retreating ice sheets at the end of the Pleistocene Troost et al 2005 These deposits compose steep slopes of unconsolidated material found throughout the city that have been further destabilized by human activity stream erosion and wave erosion along coastal bluffs Tubbs 1974 This steep unconsolidated surficial geology coupled with a wet climate make landsliding a frequent issue in Seattle most commonly triggered by some combination of human activity and heavy precipitation Landslides triggered by water have been the topic of many investigations specific to Seattle e g Tubbs 1974 Harp et al 2006 Baum et al 2005 Montgomery et al 2001 Coe et al 2004 Laprade et al 2000 Salciarini et al 2008 1-9 Figure 1-1 Map of Seattle showing location of Seattle Fault Zone dotted line frontal fault location used for rupture model for landslide simulation line of triangles and potential landsliding areas designated by the City of Seattle Neighborhoods and landmarks mentioned in the text are labeled Inset map shows regional tectonic setting and volcanoes triangles Earthquake-triggered landslides on the other hand occur only episodically and receive far less attention because of the long intervals between significant earthquakes in western Washington At least 15 earthquakes have triggered landsliding in the region since the mid1800 s Chleborad and Schuster 1998 Noson et al 1988 Keefer 1983 Hopper 1981 but nearly all of the historical examples were moderate earthquakes and the historical record is short in this part of the country All three major historical Puget Sound earthquakes Mw 7 1 in 1949 1-10 Mw 6 5 in 1965 and Mw 6 8 in 2001 caused ground failures throughout Western Washington and Northern Oregon Chleborad and Schuster 1998 Highland 2003 but not extensively because all three were deep Benioff zone earthquakes with relatively moderate ground motions and lower than normal or average antecedent rainfall Stewart 2005 Since its founding the city has yet to experience its most dangerous earthquakes: large crustal earthquakes on nearby faults and subduction megathrust earthquakes It is only when we look further back that we find that seismically induced landsliding has shown the potential to cause as much or more damage than other earthquake effects Oral traditions of the native Salish tribes report specific locations where earthquake-triggered landsliding or other earthquake effects occurred Ludwin et al 2005 Furthermore as mentioned earlier there is significant geologic evidence of seismically triggered landslides including sunken forests on giant block landslides submarine landslides and lake-wide turbidite layers preserved in Lake Washington Jacoby et al 1992 Karlin and Abella 1992 Karlin et al 2004 These deposits have been tied to landsliding triggered by as many as seven earthquakes in the last 3 500 years Karlin et al 2004 Despite this there are few rigorous studies of seismically induced landsliding in Seattle Of those that exist most characterize past seismically induced ground failures triggered by historical earthquakes in the area and identify the types of soils that failed e g Chleborad and Schuster 1998 Noson et al 1988 Keefer 1983 Hopper 1981 Stewart 2005 Highland 2003 McCalpin 1997 took a more quantitative approach and used ground motion prediction equations to calculate slope stability for some probabilistic and scenario earthquakes but did not include the level of detail that we have found to be necessary to accurately assess seismically induced landslide hazard in Seattle 1-11 3 Methods In this study we focus on shallow disrupted landslides which are generally the most abundant types of landslides triggered by earthquakes Keefer 1984 and are also the most common type of landslide in Seattle Baum et al 2005 The failure surface of this type of slide is within a few meters of the ground surface Deep-seated landsliding and liquefaction-related ground failure are also significant hazards that need to be addressed but are beyond the scope of this study We model co-seismic landslide movement using Newmark s method Newmark 1965 which approximates a slope as a rigid block sliding against friction down an inclined plane that is subjected to ground motion the block accumulates downslope displacement each time a threshold acceleration is exceeded The final displacement is termed the Newmark displacement Though the model is simplistic with some modifications it is currently the most widely used tool for looking at regional susceptibility of natural slopes to landsliding triggered by earthquakes e g Miles and Ho 1999 Ambraseys and Menu 1988 Jibson et al 1998 Peng et al 2009 Jibson and Michael 2009 For natural slopes the Newmark displacement is not the actual displacement that will occur but is instead considered an index for the likelihood of slope failure Jibson et al 2000 We take a similar approach Some have improved on the Newmark method to make it more realistic by allowing internal deformation within the failure mass e g Makdisi and Seed 1978 Bray and Rathje 1998 Rathje and Bray 2000 However we did not use these modifications because they are too computationally intensive to be applied on a citywide scale We discretized the city limits of Seattle into 5-meter cells To apply the Newmark method each cell was approximated as a rigid block sitting on a ramp with an incline equal to 1-12 the average slope within that cell The block is initially stable and has a threshold ground acceleration in the downslope direction above which the block starts to slide down the ramp This value is known as the critical acceleration ac sometimes referred to as the yield acceleration and is dependent on the slope the soil properties and the saturated thickness of the failure mass As the shaking progresses whenever the critical acceleration is exceeded the block accumulates displacement down the ramp The final Newmark displacement is calculated by integrating time intervals of the seismogram that exceed the threshold acceleration to determine the velocity time-history of the block when mobilized and then by integrating this result to determine the displacement history In this study after integrating once to velocity we assumed a symmetrical pulse shape in order to bring the velocity back to zero after each exceedance as in Goodman and Seed 1966 and then integrated once more to obtain displacement In order to speed up calculations we only calculated Newmark displacement for slopes equal to or greater than 15 the minimum slope for which shallow disrupted landslides typically occur Keefer 1984 We did not calculate Newmark displacement for slopes greater than 64 because only manmade structures are that steep at the resolution of our slope map 5m The factor of safety FS and slope angle of each cell was used to calculate the critical acceleration ac which is the acceleration in the downslope direction required to reduce the factor of safety to 1 This can be calculated by the relation ac FS-1 gsin where g is the acceleration due to gravity Newmark 1965 High-resolution 1 8 m slope information was available from the Puget Sound LIDAR Consortium The factor of safety is the ratio of resisting forces to driving forces thus a factor of safety of less than 1 means a slope is unstable Fortunately Harp et al 2006 conducted a detailed study of slope stability under static conditions in Seattle and calculated the factor of safety for dry and completely saturated soil 1-13 conditions on a 2-m grid for the entire city using typical engineering properties for each geologic unit They assumed a uniform failure thickness of 2 4 m to simulate shallow landslides of the same type we are investigating in this project so we were able to use their results The factor of safety reported by Harp et al 2006 was less than 1 for some cells because it was calculated on a large scale using a simple model For this study we assumed that all slopes were at least marginally stable prior to the simulated earthquake and raised all cells with a factor of safety below 1 to 1 01 4 Synthetic Seismogram Generation To accurately assess landslide hazard in Seattle it is necessary to use synthetic seismograms that account for rupture directivity and the effects of the Seattle basin The final input required for the simulation is a set of broadband synthetic seismograms generated on a fine grid throughout the city We chose to simulate an Mw 7 0 earthquake as a compromise between the estimated maximum magnitude the fault is capable of generating Mw 7 6 to 7 7 Pratt et al 1997 and the size of the earthquake that could be generated by the estimated slip accumulated since the last earthquake on the main fault 75-120 cm Johnson et al 1999 which would produce an Mw 6 6 to 6 7 earthquake if completely released Wells and Coppersmith 1994 We used the surface projection of the frontal fault Figure 1-2A from Blakely et al 2002 as the rupture plane We ruptured a 45-km segment from the middle of the fault from 315 km depth We assumed a rupture dip of 45 resulting in a rupture width of about 17 km The rupture plane was divided into 3 150 subevents that were spaced 500 m apart and had a mean Mw of 4 6 Figure 1-2b We used methods developed by Frankel et al 2007 to model the slip distribution and the moment distribution among the subevents as a spatial random field with a correlation length for asperities that corresponds to the magnitude of the earthquake Mai and 1-14 Beroza 2002 To simulate a finite fault rupture the point source subevents were set to break first at the lower eastern edge of the fault Then the rupture propagated updip and westward at rupture velocity that was set to 70% of the shear wave velocity so that it slows as the rupture approaches the surface The rupture velocity is randomized by 25% and constrained to never exceed the shear wave velocity in order to avoid unrealistically large directivity pulses Figure 12c In addition the rake of each subevent was varied randomly by 20 We deviate from the methods of Frankel et al 2007 slightly in the calculation of the rise time TD by making it dependent on the shear wave velocity at the point of rupture by TD 16Lf0 5 7 1 5 Stein and Wysession 2003 in which L is the length of the fault is the shear wave velocity and f is the ratio of width to length By doing so the source-time function at shallower depths was slightly longer than at greater depths which caused shallower subevents to radiate lower frequency energy than deeper ones This step helped maintain realistic ground acceleration levels We then used this fault rupture model to generate broadband seismograms by calculating long-period motion 1 Hz stochastically on a 210-meter grid throughout the city and combined them using methods developed by Frankel 2009 To compute the deterministic low-frequency ground motions we used the fault rupture model as input to a finite-difference code developed by Liu and Archuleta 2002 that propagates seismic waves through a 3D velocity model of the Seattle basin developed by Delorey and Vidale 2011 This simulates amplification and surface wave generation in the Seattle basin To isolate the influence of the Seattle basin on ground motions and consequently on the extent of landsliding triggered we also generated synthetic seismograms for a 1D velocity model 1-15 formulated from the out-of-basin velocities in Delorey and Vidale s 2011 3D model Both velocity models had a shear-wave velocity of 600 m s at the surface Figure 1-2 a The surface projection of fault rupture used to generate synthetic seismograms triangles corresponds to the frontal fault of the Seattle Fault Zone as defined by Blakely et al 2002 This is just one of the set of faults that make up the entire Seattle Fault Zone gray dotted lines b Contoured moment distribution of subevents on the fault rupture plane 0 km is westernmost end of ruptured segment c Rupture time in seconds from the start of the earthquake Higher frequency portions of the seismogram were computed stochastically using the constant stress-drop model proposed by Frankel 2009 derived from Boore 1983 1996 Subevents were assigned stress drops using a fractal distribution with a root-mean-square value of 10 MPa The assigned stress drops were used to calculate a theoretical spectrum for each subevent which was then multiplied by Gaussian white noise in the frequency domain so that 1-16 each subevent had a realistic seismogram when transformed into the time domain and tapered These subevent waveforms were then adjusted for attenuation geometrical spreading and travel times between each source and each station and summed up at each station The high- and lowfrequency components of the synthetics were combined with a crossover at 1 Hz using a matched filter to form broadband seismograms Figure 1-3 Examples of a North b East and c vertical component synthetic accelerograms starting from south of the surface trace of the fault at bottom moving northward toward the top of the plot Distance to the closest point on the frontal fault trace is shown to the left of each seismogram Locations of each synthetic seismometer used are shown as black dots on Figure 4 1-17 Figure 1-4 Maximum horizontal peak ground accelerations on a 210-m grid of broadband synthetic seismograms of the simulated Mw 7 0 Seattle fault earthquake generated using a a 1D velocity model of the Puget Lowland outside the Seattle basin compared with b a 3D velocity model Delorey and Vidale 2011 that simulates 3D basin amplification Triangles delineate the rupture used to generate seismograms dotted lines show the Seattle fault zone Sample synthetic seismograms are shown in Figure 1-3 These seismograms contain important features that would not be represented using ground-motion values from average ground-motion prediction equations For stations within about 5 km of the fault trace there is a forward rupture directivity pulse that greatly increases the peak acceleration The synthetics for stations in the Seattle basin also exhibit substantial basin surface waves generated at the edges of the Seattle basin These basin surface waves increase the amplitude and duration of long-period shaking The peak horizontal ground accelerations for this earthquake for the 3D velocity model and the 1D velocity model are shown in Figure 1-4 This is a randomized iteration of a possible 1-18 Seattle Fault earthquake and represents just one possible scenario As expected the synthetics generated using the 3D velocity model that accounted for amplification within the Seattle basin resulted in higher peak ground accelerations and more spatial variability within the basin north of the Seattle fault than the 1D velocity model particularly along the northern edge of the basin 5 Incorporating Site Amplification The broadband seismograms we generated by the methods described above represent shaking at the surface with a base shear wave velocity of 600 m s but most of the city is underlain by shallow layers of soil with much lower shear wave velocities that can amplify ground motion Pratt and Brocher 2006 Frankel et al 2002 Pratt et al 2003 Snelson et al 2007 Hartzell et al 2000 In order to simulate realistic ground motions we needed to account for site amplification relative to the 600 m s base layer No effective simple methods yet exist for adjusting a full seismogram in the time domain for site effects on a regional scale Most methods depend on the average shear wave velocity in the top 30 meters Vs30 which some argue is a poor predictor of site amplification e g Castellaro et al 2008 They are also developed to adjust response spectra Choi and Stewart 2005 Borcherdt 1994 and are thus not appropriate for adjusting Fourier spectra which is required to adjust time series seismograms As an intermediate approach we developed 67 representative shear wave velocity Vs profiles that represent the range of typical surficial geologic profiles in Seattle The complete profiles are reported in Appendix 1 We then used ProShake a software package that uses equivalent linear methods to approximate soil non-linearities to develop 1D site amplification transfer functions for each Vs profile using the base synthetic seismograms as the input ground motion level This method does not correctly handle the surface waves or P-waves in the waveforms but at the 1-19 frequencies being amplified and for horizontal components S-waves are dominant so it should be a good approximation We built the representative Vs profiles based on the geologic map of Seattle crosssections and typical thicknesses for each unit Troost et al 2005 and typical engineering properties shear wave velocity ranges and measured shear wave profiles for these units Savage et al 2000 Williams et al 1999 Wong et al 2010 Palmer et al 2004 The geologic units and the range of engineering properties we used to construct these representative profiles are shown in Table 1-1 For simplicity all unconsolidated deposits older than the last glaciation the Vashon stade of Fraser glaciation were lumped together as Qpf These units are nearly all classified as very dense and hard because they have been overconsolidated by one or more glaciations so we considered them to be equivalent to the base layer of 600 m s We assumed linear behavior of these units because soils of this site class NEHRP class C do not generally show much non-linear behavior Choi and Stewart 2005 The few soft rock sites all located in the southern part of the city were treated similarly We concentrated our efforts in the development of these representative shear wave profiles on areas that could generate landslides Consequently profiles for flat-lying areas such as the Duwamish valley Harbor Island and Interbay are highly oversimplified and should be improved if used for any other purpose Figure 1-5 shows the average shear wave velocity in the top 30 meters Vs30 calculated from these representative profiles 1-20 Table 1-1 Description of geologic units used in the development of the representative Vs profiles and the range of thicknesses and engineering properties they were assigned Wet density range Typical Thickness range m Vs range m s Qvt 8 400-600 2160-2400 Vashon Till Qva 10-50 300-600 1920-2160 Advance Outwash Deposits Description Age kg m3 Fraser Glaciation Vashon Stade pleistocene Unit 5 250-350 1680-1800 Recessional Outwash Deposits 5 250-350 1560-1800 Recessional Lacustrine Deposits Qvlc 15-30 200-500 1560-1920 Lawton Clay Qpf NA 450-600 2160-2400 Pre-fraser Deposits pleistocene Tertiary Tb NA 350-600 2300-2400 Blakely Formation weakly lithified sandstone soil 1 100 1440 Soil Qp 10 60 1260 Peat Qal 6-30 120-180 1440-1620 Alluvium Qt 6 120-130 1440 Terrace deposits Qls 3-10 120-140 1440-1500 Landslide deposits Fill 2-10 120-140 1440-1500 Artificial Fill Qb 8 120-140 1440-1500 Beach Ql 3 130-150 1560-1680 Lake Deposits postglacial holocene Qvr Qvrl Once we applied the corresponding transfer functions that we developed to each 5-meter grid cell the spatial variability of the ground motions increased significantly Figure 1-6 The ground motions in some of the low-lying areas with low shear wave velocities were deamplified due to soil non-linearity particularly areas of fill and alluvium where liquefaction is more likely than landsliding Areas that were significantly amplified relative to the base seismograms include 1 old landslide deposits along many of the steep coastal bluffs that overlie higher velocity undisturbed deposits 2 areas where thin lower velocity deposits such as recessional outwash or soil overlie pre-Vashon deposits and 3 soft rock sites that behave linearly The soft rock sites have a higher Vs30 than much of the city yet they also have some of the highest amplifications because they behave linearly and high impedance contrasts between the rock and overlying shallow soil and weathered layers can cause amplification at higher frequencies where 1-21 there is more seismic energy Accelerations reach 2g in a few of these localized areas on the hanging wall of the fault Figure 1-5 Average shear-wave velocity down to 30 m Vs30 computed from the representative Vs profiles compiled for this study 1-22 Figure 1-6 Maximum horizontal peak ground acceleration for a the base synthetic seismograms generated using the 3D basin velocity model with a surface layer velocity of 600 m s and b the same seismograms adjusted for 1D site amplification due to the shallow surficial soil layers at right Seattle fault zone is indicated by dotted lines 6 Model Outputs Next the critical acceleration for both dry and saturated soil conditions and ground motions for the scenario earthquake assigned to each cell were used to calculate the Newmark displacement for each cell using the methods described above We used the final Newmark displacement as an index for the relative likelihood of landsliding as in Jibson and Michael 2009 We designated seismically induced landslide hazard zones based on an empirical relation between Newmark displacement and probability of failure developed by Jibson et al 2000 This relation was derived from the landsliding catalog from the Northridge earthquake While the 1-23 soils and rocks that failed in the 1994 Northridge earthquake are different than the soils of Seattle using the probability curve developed for Northridge is currently the best option available due to the dearth of complete post-earthquake landslide surveys This is something that needs to be improved upon in future work We divided hazard into four zones: Low Moderate High and Very High Cells with more than 0 cm of displacement up to 3 5 cm of displacement corresponding to a less than 10% chance of failure were designated as Low seismically induced hazard The Moderate seismically induced landslide hazard zone corresponds to areas with Newmark displacements between 3 5 and 7 cm or 10-20% probability of failure High corresponds to 7 to 12 cm or 20-30% probability of failure and Very High corresponds to anything with more than 12 cm of displacement or a probability of failure above 30% The reason the highest landslide hazard zone cutoff is at a mere 30% probability of failure is because Jibson et al 2000 found that the probability of failure levels off at 34% beyond about 18 cm of displacement due to natural variability We generated relative seismically induced landslide hazard maps using these designated landslide hazard zones but also went one step further towards the scenario approach and designated predicted slope failures to assess the extent of landsliding one might expect To do this a random number generator chose a number between 0 and 1 for each cell If the chosen number was lower than the probability of failure assigned to that cell the slope represented by that cell fails Failure is defined as a detachment of the slope The failure of each cell is independent of all the others Once the distribution of failed cells throughout the city was determined adjacent failed cells were clustered together into landslide source areas Each cluster of adjacent failed cells was counted as one source Landslide damage can occur both in the source area and in downslope cells Deterministic models of runout are not practical on the scale required for this study and 1-24 empirical runout estimation methods that currently exist often based on the travel distance angle e g Hunter and Fell 2003 are derived from datasets of landslides primarily triggered by water not ground motion and are not appropriate for this scenario study where the water content of failed materials could be significantly lower Therefore we were not able to estimate runout from each failed cell in the scenario However Harp et al 2006 recommended a runout buffer zone of 60 meters below steep slopes based on the mean runout length of a set of landslides in Seattle We used this runout distance of 60 meters or until the slope reached 2 whichever came first to quantify the extent of infrastructure and buildings that are potentially at risk 7 Validation of Ground Motions In order to validate the methods we used to generate synthetic seismograms we calculated spectral accelerations for 5% critical damping of the synthetic seismograms and compared them to the spectral accelerations predicted for an Mw 7 0 thrust fault earthquake on the Seattle Fault by three of the Next Generation Attenuation NGA relations that account for basin depth: Campbell and Borzognia 2008 Chiou and Youngs 2008 and Abrahamson and Silva 2008 There is a directivity pulse in the broadband synthetics because of the updip rupture that appears primarily on the fault-normal North component so we also included a modification to the NGA relations developed by Shahi and Baker 2011 that accounts for a directivity pulse We calculated response spectra for the base synthetic seismogram NEHRP Class C site condition corresponding to each grid point on the 210-m grid and binned them in 2km wide bins based on the closest distance to the fault The mean spectral accelerations 1 standard deviation of the synthetics at a range of horizontal distances to the fault are shown in Figure 1-7 Spectral accelerations are shown for synthetics computed using both the 1D and 3D velocity models left and right respectively These are compared with the spectra for three NGA 1-25 Figure 1-7 Response spectra 5% critical damping of the broadband synthetics generated with the a 1D basin velocity model and the b 3D basin model compared with the mean values for three Next Generation Attenuation relations that are modified to include a directivity pulse using methods developed by Shahi and Baker 2011 Black is the mean of the synthetics at the distance bin noted 1km with one standard deviation indicated by the error bars The thick gray line is the mean of the three attenuation relations CB08 dash-dot is the response spectra for Campbell and Borzorgnia 2008 CY08 dotted is Chiou and Youngs 2008 and AS dashed is Abrahamson and Silva 2008 The bump at about T 3 seconds is due to the directivity pulse 1-26 relations and the mean of all three combined assuming the same distance for all types of distances to the fault required for each equation The fit is quite good particularly taking into account the large variability between the NGA attenuation relations themselves and their respective uncertainties the spatial variability within the synthetics as shown by the error bars and the fact that the y-axis is linear rather than logarithmic The synthetics made using the 3D model show much higher spectral accelerations at long periods because of basin amplification particularly around 17 km from the fault where there is strong amplification at the northwestern edge of the Seattle basin The directivity pulse at a period of 3 seconds in the synthetic seismograms matches the period predicted by Shahi and Baker 2011 for this event Their predicted pulse also matches the amplitude quite well for the 1D model but is exceeded by the 3D synthetics suggesting that amplification within the 3D structure also occurs at these frequencies To validate the transfer functions that we computed for representative Vs profiles throughout Seattle using ProShake we generated transfer functions for them using recordings of the 2001 Nisqually earthquake as the input ground motions We then compared the resulting transfer functions to the spectral ratios of the recorded Nisqually ground motions at several accelerometers located throughout the city using a soft rock site in Seward Park SEW as the reference site Comparisons between our modeled transfer functions for representative profiles and the spectral ratios of the real data are shown in Figure 1-8 We did not expect to fit the exact peaks and troughs of amplification shown in the spectral ratios because representative profiles cannot replicate site-specific peculiarities Instead we aimed to roughly match the frequencies and amplitudes of amplification for most sites The transfer functions match well for many stations e g WEK THO BRI MAR SEU particularly at less than 10 Hz but they diverge at 1-27 higher frequencies where shallow layers dominate the site response e g TKCO ALO BHD CRO HOLY Amplifications on this fine scale are beyond our ability to reproduce using representative profiles but most of the energy in the seismograms is below 10 Hz so this is not detrimental A few transfer functions do not match the spectral ratios as well e g NOWS QAW SEA These differences could be due to finer scale geological variability than is reflected in the geologic map of Seattle or issues with station or site response They illustrate the limitations of simplifying shear wave profiles into representative units for such a large region but the differences are not severe and only occur at a fraction of the sites Figure 1-8 The spectral ratio of the recorded ground motions of the Nisqually earthquake at 24 accelerometers using the soft-rock reference station SEW shown on the station map at right thin lines North is dashed East is solid compared to the transfer functions computed in ProShake for the corresponding representative Vs profiles computed using the Nisqually earthquake ground motions as the input ground motions thick black line 1-28 8 Validation of Landslide Simulation The 2001 Mw 6 8 Nisqually earthquake located at 52 km depth with a hypocenter 57 km SSW of Seattle location from the Pacific Northwest Seismic Network is the only one of the three large historic Puget Sound earthquakes for which dense ground acceleration records exist The earthquake triggered about 100 landslides throughout Puget Sound Stewart 2005 fewer than expected since the earthquake occurred during a rare winter dry period Highland 2003 Only landslides that caused damage and losses were included in a post-quake report on landsliding by Highland 2003 Most of these occurred closer to the epicenter south of Seattle Only two of the reported landslides in this report were within city limits: landsliding in one location of West Seattle damaged some houses and lateral spreading caused some damage to a viaduct downtown No comprehensive landslide survey was done due to the scarcity of significant landsliding within city limits As the best validation available we ran the Nisqually ground motions through the seismically induced landslide simulation model using the factor of safety map for dry conditions to see if it reproduced the observed scarcity of landsliding To do this we used 33 strong ground motion records the locations of these stations are shown on the map in Figure 1-8 In order to infer ground motion throughout the city from this sparse and irregular sampling we removed site amplification using spectral ratios relative to a reference site on a soft rock site in Seward Park SEW Then each 210-m grid point was assigned the closest actual recording with the recording station s site effects removed and corrected for geometrical spreading We then readjusted the ground motions for site effects using transfer functions developed in ProShake using actual recordings of the Nisqually earthquake as the ground motion input and the representative Vs profiles we developed Ground motions during the Nisqually earthquake were much lower than those for the Seattle fault simulation so 1-29 the site amplifications in the simulation for most representative profiles are actually higher for the Nisqually earthquake than for the Seattle fault event because they are not moderated as much by non-linear effects The landslide simulation for dry conditions - representative of the conditions during the Nisqually earthquake - predicted 26 landslide sources with a total area of about 1 000 m2 Tables 1-2 and 1-3 They are located in ten localities Figure 1-9 almost exclusively on extremely steep median slope of 40 undeveloped coastal bluffs and ravines - nearly half in city parks The simulation predicted that only 0 001% of the land area of Seattle had high landsliding potential nmdisp 7cm 20% probability of failure We consider this dearth of predicted landsliding and their locations in extremely steep undeveloped areas where they would be unlikely to affect structures or infrastructure or even be noticed to be a validation that our earthquake-induced landslide simulation generates realistic results We also ran the same landslide simulation of the Nisqually earthquake but for saturated soil conditions instead to see what might have happened if the earthquake had occurred after an extended period of heavy rainfall The results are drastically different: nearly 7 500 landslide sources were triggered 9 of those greater than 500 m2 in area These sources cover 0 3 km2 of the city and 0 4% of the land area of the city had high potential for landsliding nmdisp 7cm Tables 1-2 and 1-3 1-30 Figure 1-9 Percentage of cells in each area where failures were triggered as defined in the text for the a dry and b saturated soil conditions using ground motions from the 2001 Mw6 8 Nisqually earthquake For visibility individual failures are indicated for dry soil simulation because there were so few landslides triggered In reality so few shallow disturbed landslides were triggered by this quake that no post-quake landslide survey was done the location of just one damaging landsliding was documented by Highland 2003 which is indicated by an asterisk at left For the saturated soil simulation the shading corresponds to the percentage of 5-meter cells in each area that failed in the simulation smoothed with a 20x20 cell Gaussian kernel 9 Results of Landslide Simulation for Mw 7 0 Seattle Fault Earthquake The results of our seismically induced landslide simulation of the scenario Mw 7 0 Seattle fault earthquake for the best- and worst-case scenarios dry and saturated soil conditions respectively are summarized on Tables 1-2 and 1-3 Individual failures of 5-meter cells are too small to see on a citywide map so Figure 1-10 instead shows the percentage of cells that failed 1-31 in each area of the city smoothed with a 20x20 cell kernel 100 m x 100 m In addition high resolution maps of relative seismically induced landslide hazard for a Mw 7 0 Seattle fault earthquake are provided in Appendix 2 Figures A1 and A2 Zoom-ins on a few areas of interest of this map are shown in Figure 1-11 Hazard zone levels are based on Newmark displacement and the corresponding probability of failure as described above Table 1-2 Summary of landslide sources triggered by seismically induced landslide simulations Mw 6 8 Nisqually Earthquake Simulation Mw 7 0 Seattle Fault Earthquake Simulation Dry Conditions Saturated Conditions Dry Conditions Saturated Conditions Number of failed 5x5m cells 40 13 720 9 698 77 765 Number of sources 26 7494 4 977 30 699 Median slope of source cells degrees 40 35 29 26 Results using nearest original ground motion recording of the 2001 Nisqually earthquake for each cell with site effects removed and then adjusted for site amplification using the corresponding transfer functions developed for this study Results using broadband synthetic seismograms generated using a 3D velocity model and including site amplification Sources are clustered - adjacent failed cells are counted together as one source Table 1-3 Total land area potentially affected by seismically induced landsliding Mw 6 8 Nisqually Earthquake Simulation Dry Conditions Sources Saturated Conditions Mw 7 0 Seattle Fault Earthquake Simulation Dry Conditions Saturated Conditions Area km2 % Land area Area km2 % Land area Area km2 % Land area Area km2 % Land area 0 001 0 0004% 0 3 0 1% 0 2 0 1% 1 9 0 8% nmdisp 0cm 0 025 0 01% 3 2 1 4% 2 6 1 2% 10 1 4 4% nmdisp 3 5cm 0 006 0 001% 1 2 0 5% 0 9 0 4% 6 5 2 8% nmdisp 7cm 0 003 0 001% 0 9 0 4% 0 6 0 2% 5 6 2 4% nmdisp 12cm 0 002 0 001% 0 8 0 3% 0 4 0 2% 4 7 2 1% Results using nearest original ground motion recording of the 2001 Nisqually earthquake for each cell with site effects removed and then adjusted for site amplification using the corresponding transfer functions developed for this study Results using broadband synthetic seismograms generated using a 3D velocity model and including site amplification Percent of total land area of Seattle Seattle has a land area of 229 km2 nmdisp Newmark Displacement In our simulation for dry soil conditions 4 977 landslide sources are triggered by the earthquake covering 0 2 km2 - 0 1% of the total land area of the city In addition 0 2% of the city is in a high landslide hazard zone for this event nmdisp 7 cm probability of failure 20% 1-32 Landsliding is concentrated in the southern half of the city along the coastal bluffs of West Seattle the western side of Beacon Hill and scattered throughout Delridge The coastal bluffs of Magnolia and Queen Anne show some less concentrated landsliding and North Seattle escapes relatively unharmed with the exception of localized landsliding along coastal bluffs in North Ballard near Carkeek Park and in Lake City Figure 1-10 left locations of places mentioned are shown on Figure 1-1 Figure 1-10 Percentage of cells in each area where failures were triggered as defined in the text for the a dry and b saturated soil conditions for the Mw 7 0 Seattle Fault earthquake simulation For the same exact scenario but using the factor of safety map for saturated soil conditions instead the results are more drastic More than 30 000 landslide sources are triggered covering 1 9 km2 equal to 0 8% of the land area of the city In this case 2 4% of the city is in a 1-33 high landslide hazard zone nmdisp 7 cm Fortunately this simulation represents an unlikely scenario where the water table is effectively at the surface everywhere due to higher than normal seasonal rainfall followed by an intense precipitation event followed in turn by a lowprobability earthquake The distribution of landslide sources for saturated conditions contrasts with the dry scenario Figure 1-10 place names on Figure 1-1 In this simulation the southern half of Seattle experiences dense landsliding concentrated not only on the coastal bluffs and the slopes bordering the Duwamish river valley but also scattered inland throughout West Seattle Delridge Beacon Hill Seward Park and Rainier Valley Landsliding rims both Magnolia and Queen Anne hills and extends north all the way to Portage bay along Interstate-5 I-5 The northern half of Seattle though less hard-hit than the rest of the city is more severely affected in this case than in the dry scenario The coastal bluffs along Puget Sound experience dense landsliding in incised valleys up to 1 km from the coast particularly in the northwest corner of the city because of the strong amplification of low frequencies at the edge of the basin In both cases areas of steep topography on the hanging wall of the Seattle fault are most severely affected by seismically induced landsliding consistent with observations of landsliding triggered by other earthquakes worldwide e g Tang et al 2011 Overall patterns of predicted landsliding correspond to areas that are generally known to be landslide prone In fact 66% of known historical landslides in Seattle from the City of Seattle dataset lie within landslide hazard zones predicted by the Seattle fault earthquake simulation for dry conditions 80% for the saturated soil conditions However if we look at existing landslide hazard maps for static no ground shaking conditions a significant percentage of the landslides predicted by the simulation are in areas of low and medium relative hazard 1-34 Figure 1-11 Zoom-ins of the relative seismically induced landslide hazard map for a dry and b saturated soil conditions superimposed on infrastructure and building outlines Full high resolution versions are included in the electronic supplement Figures S1 and S2 Locations of each zoom-in are shown on the map of Seattle at right A Coastal bluffs in the northern part of Seattle are most affected when soils are saturated Many single family homes are located within landslide hazard zones as well as downslope from potential source areas where they could be 1-35 affected by runout B There are several areas along the I-5 corridor that are highly susceptible to landsliding for all soil saturation levels such as the area shown here near the access point to the West Seattle bridge C The hillsides in West Seattle along the Duwamish valley are at risk of seismically induced landsliding such as the area shown here There are industrial as well as residential buildings that could be affected by runout from landsliding in these areas D The coastal bluffs along Puget Sound in West Seattle on the hanging wall of the fault such as the area shown here are the most highly susceptible areas to landsliding in the city numerous residential structures are at risk from both potential landslide source areas and runout North is up on all maps based on static slope stability as delineated by Harp et al 2006 : 28% of the total landslides triggered by our dry soil conditions simulation occur in medium and low static landslide hazard areas for dry conditions and 40% for the saturated soil simulation Similarly a comparison between the cells that failed in the seismically induced landslide simulation and areas designated as potential sliding areas in the City of Seattle corporate GIS database also shows that a significant percentage of the predicted landsides lie outside the designated areas: for dry conditions 36% of failed cells are outside potential sliding areas 38% for saturated conditions The City of Seattle potential sliding areas were designated based on the contact between a permeable and an impermeable geologic unit Esperance sand and Lawton clay respectively where seepage occurs and many historical landslides have been triggered by water Clearly these maps are not adequate to delineate areas likely to produce landslides during earthquakes We cannot assume that seismically induced landslides will only be triggered in areas already designated as hazardous by studies focusing on static slope stability highlighting the importance of studies dedicated to seismically induced landslide hazard such as this one 10 Infrastructure Impacts Our results show that it is not only the relatively undeveloped coastal bluffs that are hit but landsliding also affects inland slopes that could threaten key transit routes and buildings 1-36 particularly in the saturated soil scenario To further investigate the infrastructure and buildings that may be at risk from seismically induced landsliding in such a scenario we calculated the number of buildings and total length of linear infrastructure such as roads and water lines that fall within the four different seismically induced landslide hazard zones as well as within a 60meter buffer or until the slope reaches 2 downslope from these hazard zones to determine susceptibility to potential runout from the triggered landslides as well Note that the numbers presented here do not mean that every single building and piece of infrastructure within these zones will be negatively affected when a Seattle fault earthquake eventually occurs The highest probability of failure for any hazard zone is 34% and most are much lower and the runout buffer zone is probably overestimated in most cases The numbers are simply a measure of the extent of infrastructure and buildings that are potentially at risk There are a significant number of buildings that are located directly within the seismically induced landslide hazard zones Figure 1-12 For dry soil conditions there are over 1 000 buildings that are within all hazard zones 400 of those in the two highest hazard designation zones 20% probability of failure Twice as many buildings are in the potential runout zones from these landslides For saturated soil conditions it is nearly an order of magnitude worse with 8 000 buildings within all hazard zones 5 000 of those within the two highest hazard zones 8 500 more buildings are within the potential runout from all hazard zones Additionally hundreds of total kilometers of linear infrastructure roads rail electric water and sewer lines also sit within these hazard zones The total length in kilometers of each type of infrastructure that is located within the two highest hazard zones 20% probability of failure and within the potential runout zone from these hazard zones is shown in Figure 1-13 We found that the majority of the length of linear infrastructure that is at risk is within the potential runout 1-37 areas rather than within the potential source areas For dry soil conditions with the exception of railroad tracks on the order of 1 km of each type is at risk from landslide sources while on the order of 10 km of each are in potential runout areas For saturated soil conditions the numbers are bumped up by an order of magnitude on the order of 10 km of each are within potential source areas and 100 km are within potential runout areas In any case the impacts to infrastructure from landsliding will be extensive when a large Seattle fault earthquake occurs for any soil saturation level and this could significantly slow down recovery Figure 1-12 The total number of buildings in each landslide hazard zone and also within a 60-meter runout buffer downslope from each hazard zone for both dry and saturated conditions Each building can only be designated in one hazard zone or potential runout zone so totals are mutually exclusive 11 Discussion The ground motions we developed include a much higher level of detail than is typically used to model seismically induced landsliding To determine which efforts and effects are most important and which could potentially be neglected without significantly altering the results we compared the total citywide Newmark displacement for various levels of ground motion complexity for dry conditions Summary on Figure 1-14 1-38 Figure 1-13 Total length of critical linear infrastructure that is located within the high or extremely high landslide zones and within the potential runout areas from these zones for saturated top and dry bottom soil conditions We first ran the simulation with and without site and basin amplification and found that both need to be rigorously accounted for in simulations like this Ignoring them could result in an under-prediction of seismically induced landsliding hazard For example the inclusion of 1D site amplification site effects quadruples the number of failed cells for dry soil conditions On top of that the inclusion of basin amplification using a 3D velocity model instead of 1D velocity model bumps up the number of slope failures by about 35% because the basin amplification is so strong in Seattle For an area that does not sit on a significant sedimentary basin the 1D velocity model may be sufficient but for Seattle using a 3D basin model to account for basin amplification is critical 1-39 Figure 1-14 Results of seismically induced landslide simulation for dry soil conditions for various levels of complexity Gray bars indicate the total number of failed cells as defined in text from the landslide simulation using both broadband seismograms and just the high frequency portion of the synthetic seismograms 1Hz using the 1D dark gray and 3D light gray velocity models for simulations that include and exclude 1D site amplification These results are compared with simpler methods black where ground motion prediction equations GMPE s are used to estimate ground motion parameters for a Mw 7 0 Seattle fault earthquake instead of synthetic seismograms and the Newmark displacement is calculated using a regression equation developed by Jibson 2007 Four Next Generation Attenuation relations were used to estimate PGA and Travasarou et al 2003 was used to estimate Arias Intensity Error bars indicate one standard deviation accumulated from both the GMPE s and the regression equations Next we compared the results of this study with what would be predicted by simpler methods Most previous regional assessments of seismically induced landsliding used empirical regression equations that estimate Newmark displacement as a function of simplified ground motion parameters that are obtained using ground motion prediction equations GMPE s We estimated landsliding for our scenario using these methods in order to compare the result with our more detailed simulation To do this we used four Next Generation Attenuation NGA relations Boore and Atkinson 2008 Abrahamson and Silva 2008 Chiou and Youngs 2008 Campbell and 1-40 Borzognia 2008 to estimate peak ground acceleration for each cell throughout the city for the same scenario earthquake All the NGA relations account for site effects by NEHRP site class that is based on the Vs30 of each site which we take from the Vs30 of the representative shear wave profile assigned to each cell The latter three NGA relations also require the depth to a defined shear wave velocity contour to account for basin depth We extracted those values from Delorey and Vidale s 2011 3D velocity model for each cell Once we obtained PGA we used the regression equation developed by Jibson 2007 that relates earthquake magnitude and PGA to Newmark displacement The mean number of failures triggered by each of the four NGA equations used is shown on Figure 1-14 along with error bars that span plus or minus one standard deviation for both the NGA predicted PGA values and the Newmark displacement predicted from it combined The four relations predict a similar number of ground failures between them but Boore and Atkinson 2008 predict the lowest values possibly because their methods do not account for basin amplification at all Arias intensity which depends on both shaking intensity and duration is considered a superior ground motion parameter for predicting landslide triggering Miles and Keefer 2000 Jibson 2007 so we computed it for each cell using the attenuation relationship developed by Travasarou et al 2003 and then used the regression equation developed by Jibson 2007 that relates Arias intensity to Newmark displacement The downside to this approach is that the uncertainties are much higher for Arias intensity than for PGA which explains why the positive error bar is literally off the charts The most obvious conclusion from Figure 1-14 is that the methods based on simplified ground motion parameters that are commonly used for seismically induced landslide hazard analyses predict far fewer failed cells than the full time series approach used in this study if just the mean values are used One possible explanation is that the ground motion prediction 1-41 equations are not able to account for 1D site amplification basin amplification and directivity as completely as we can with our synthetic seismograms that are specifically tailored to the city of Seattle But the error bars compounded from uncertainties in the attenuation relations used to predict the ground motion parameters and in the regression equations used to predict Newmark displacement exceed the number of failures calculated for the final results of our most detailed seismically induced landslide simulation This shows that approximating landsliding hazard using ground motion prediction equations and regression equations can be useful and is certainly simpler and less time consuming but the uncertainties are huge and must be taken into account Using just the mean values can severely underestimate the extent of landsliding Finally to test whether the most time consuming part of generating the synthetic seismograms - the long period deterministic portion of the synthetic seismograms - was important or could be neglected we ran the landslide simulation using only the stochastic portion of the synthetic seismograms 1 Hz This removes any directivity pulses basin surface waves and other coherent long period pulses For the synthetics calculated using the 3D velocity model removing the long periods cut the number of failed cells nearly in half For the 1D velocity model that does not account for basin amplification it cut the number of failed cells by about a quarter While theoretically the Newmark method depends on the absolute slope-parallel acceleration irrespective of the frequency of ground motion this finding illustrates that it does have some inherent frequency dependence Though the long period energy is too low in amplitude to cause much Newmark displacement on its own when combined with higher frequency energy final Newmark displacements are significantly increased because the long period motion boosts the higher frequency motion higher above the critical acceleration 1-42 This finding raises questions about the frequency dependence of seismically induced landslide triggering because if shallow landslide triggering is not sensitive to longer period ground motion then this simulation could be significantly overpredicting the seismically induced landslide hazard For example Jibson et al 2004 suggested that landslides triggered by earthquakes might be most sensitive to frequencies between 1 and 10 Hz based on field observations On the other hand laboratory studies have shown that the Newmark sliding block approximation is most valid when the resonant frequency of the landslide is much higher than the ground motion Wartman et al 2003 which would be the case in this study because these landslides are only a few meters thick and would have resonant frequencies between 20 Hz and 60 Hz much higher than most of the energy in the seismograms Clearly this is a topic that demands more research If shallow seismically induced landslides are solely triggered by inertial forces as modeled by the Newmark method then this study demonstrates that the ground motions used to simulate landsliding must have broadband frequency content in order to capture the full displacement particularly in areas with potentially strong long-period ground motion like the sedimentary basin underlying Seattle However if shallow landslide triggering is dependent on the frequency content of the ground motion whether due to site-specific amplifications in pre-weakened slopes e g Allstadt 2009 Moore et al 2011 or another mechanism such as the wavelength and coherence of ground motion then seismically induced landslide studies should only use band-limited ground motions This could simplify the calculation of synthetic seismograms significantly but introduces the issue of what frequency cutoff to use and whether the frequency cutoff varies depending on the size or shear wave profile of the potential failure mass This is not an insignificant decision In this study for example: if we highpass filter the seismograms at 1 Hz the total citywide Newmark 1-43 displacement is decreased by 50% However if we increase the frequency cutoff to just 2 Hz it is instead decreased by 80% hence the selection of a frequency cutoff cannot be chosen arbitrarily because it controls the results At this point in time the research on the matter is too feeble to justify using a band-limited version of the synthetic seismograms for this study so our final results are those generated using the full broadband synthetic seismograms 12 Conclusions This study shows that seismically induced landsliding will significantly impact Seattle s residents and its infrastructure when the next large earthquake occurs on the Seattle Fault The southern half of the city which is on the hanging wall of the fault will be particularly hard hit while North Seattle is less exposed with the exception of localized areas primarily along coastal bluffs Several hundred to thousands of buildings could be affected citywide many kilometers of roads could be obstructed including some key transit routes such as Interstate-5 and access roads to West Seattle If the groundwater table is low and shallow soils dry when the earthquake hits as simulated by the dry scenario the total area of landslide sources will be about an order of magnitude smaller than if soils are completely saturated We found that the geology of Seattle particularly on the hanging wall of the fault and over the Seattle basin as well as site amplification in the shallow unconsolidated subsurface played a dominant role in determining the final pattern of landsliding predicted The high impact of landsliding predicted by this simulation for a Seattle Fault earthquake shows that this secondary effect of earthquakes can be a significant contributor to overall earthquake hazard and should be studied on an equal level to other earthquake effects in landslide-prone areas In this paper we present the results of just one scenario event for Seattle to develop and demonstrate the methodology but now that the methods are compiled it would be 1-44 relatively easy to develop a library of plausible earthquake scenarios and the predicted extent of landsliding triggered by each to better quantify the seismically induced landslide hazard in the Seattle area and to assist emergency managers An ultimate goal could be to run hundreds of possible scenarios on various faults and for a range of ground saturation levels and use them to develop a probabilistic seismically induced landslide hazard map Another potential application is to set up the landslide triggering simulation to run automatically after an earthquake occurs to obtain a rapid estimate of affected areas similar to what was done in Godt et al 2008 using real ground motions from our ever-densifying urban strong ground motion networks such as the dense NetQuakes network recently installed in Seattle There are other cities nationwide and worldwide threatened by seismically induced landsliding that could also benefit from such an approach However in order to make such results more accurate and refined we have identified some areas that require further research First in order to better quantify uncertainties we need to develop a more robust relation between Newmark displacement and the probability that the slope will fail and the extent of that failure e g cracking vs complete detachment The relation we use in this study Jibson et al 2000 the only of its kind thus far is based on just one seismically induced landslide inventory However more complete post-earthquake landslide inventories are now available from more recent earthquakes and this relation should be improved for wider application Second there are currently no scientifically justifiable methods to estimate runout from seismically induced landslides Existing empirical runout estimation methods are based on datasets from water-induced landsliding whereas landslides triggered by earthquakes can be significantly drier and thus may have shorter runout lengths Since runout is often what causes the most damage because it covers more area and can reach less steep areas downslope 1-45 that are more likely to be developed we need to develop methods to estimate runout and its uncertainties for seismically induced landslides beyond the simple potential runout buffer-zone approach we used in this study Finally we found that the combination of high- and lowfrequency ground motions together results in much higher Newmark displacements and thus more slope failures than using the higher frequency ground motions alone However there has been little research on the frequency dependence of shallow seismically triggered landslides and it is not well understood Some suggest that these shallow landslides are not sensitive to longerperiod motions which would have important implications in the accuracy of assessing seismically induced landslide hazard in areas like Seattle where high long-period ground motions are expected The frequency dependence of seismically induced landslide triggering requires further investigation In conclusion in-depth scenario studies using broadband synthetic seismograms such as this one are becoming more practical with ever faster computing power the increasing availability of detailed geologic and geotechnical GIS databases evolving understanding of earthquake and landslide hazard and improving methods This type of study that integrates methods and data across disciplines to obtain a tangible final result serves as a good complement to the more thorough but less intuitive probabilistic hazard maps and can help us more effectively prepare for future earthquakes 13 Data and Resources Ed Harp and John Michael of the U S Geological Survey provided GIS files for the factor of safety maps developed for the Harp et al 2006 study that we used Andy Delorey provided us with the 3D velocity model of Seattle from Delorey and Vidale 2011 Ground motion recordings from the 2001 Nisqually earthquake were provided by the Pacific Northwest 1-46 Seismic Network and the USGS Seattle urban seismic array Strong motion records from PNSN stations are available via the Nisqually Earthquake Information Clearinghouse at http: www ce washington edu nisqually seis observations html last accessed May 2013 and data from the USGS array are available from ftp: ftpext usgs gov pub cr co golden hazards Carver Seattle last accessed May 2013 The City of Seattle GIS files used to calculate intersections between landslides and infrastructure were accessed from the Washington State Geospatial Data Archive available through the University of Washington library and from the publicly available Data Seattle Gov website last accessed October 2012 Public domain LIDAR GIS files were obtained through the Puget Sound LIDAR consortium Software packages used for this study include MATLAB from MathWorks ProShake from EduPro Civil Systems Inc ArcGIS from ESRI We also used MATLAB codes developed by the Baker Research Group at Stanford to compute the ground motions required using Next Generation Attenuation NGA relations these codes were accessed at http: www stanford edu bakerjw attenuation html in July 2012 14 Acknowledgements Research supported by the U S Geological Survey USGS under USGS award number G11AP20012 Randy Jibson and Ed Harp reviewed the manuscript We thank the associate editor of the Bulletin of the Seismological Society of America and anonymous reviewers for their helpful comments In addition many thanks to Randy Jibson Steve Kramer Ed Harp Andy Delorey Kathy Troost John Michael Tim Walsh Isabelle Sarikhan and the City of Seattle for sharing data ideas and advice 1-47 15 References Allstadt K and J E Vidale 2012 Seismically Induced Landsliding in Seattle: A Magnitude 7 Seattle Fault Earthquake Scenario Final Technical Report USGS under the National Earthquake Hazards Reduction program - grant G11AP20012 46p earthquake usgs gov research external reports G11AP20012 pdf last accessed May 2013 Allstadt K 2009 Study of Site Effects in Landslides using Weak Ground Motion Avignonet and S chilienne Landslides French Alps M S Thesis Universit Joseph Fourier and ROSE School 87p Abrahamson N and W Silva 2008 Summary of the Abrahamson & Silva 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Seismogenic landslides a new way to study landslide dynamics: Part a: Extracting Source Characteristics and Dynamics of the August 2010 Mount Meager Landslide from Broadband Seismograms Part b: The Seismic Story of the Nile Valley Landslide 2a- 1 Chapter 2a: Extracting Source Characteristics and Dynamics of the August 2010 Mount Meager Landslide from Broadband Seismograms The content of this chapter was published in: Allstadt K 2013 Extracting Source Characteristics and Dynamics of the August 2010 Mount Meager Landslide from Broadband Seismograms J Geophys Res 118 p 1-19 doi: 10 1002 jgrf 20110 2a- 2 Table of Contents Summary 2a-4 1 Introduction 2a-5 2 Data 2a-10 2 1 Seismic data 2a-12 3 Methods 2a-17 3 1 Validation 2a-21 4 Results 2a-23 4 1 Rockslide initiation 2a-26 4 2 Debris flow 2a-30 4 3 Aftershock 2a-35 5 Discussion 2a-38 5 1 Improvements to landslide characterization 2a-38 5 2 Limitations 2a-44 6 Conclusions 2a-45 7 Acknowledgements 2a-47 8 References 2a-48 2a- 3 Summary Seismic methods can substantially improve the characterization of the dynamics of large and rapid landslides Such landslides often generate strong long period seismic waves due to the large-scale acceleration of the entire landslide mass which according to theory can be approximated as a single-force mechanism at long wavelengths I apply this theory and invert the long period seismic waves generated by the 48 5 Mm3 August 2010 Mount Meager rockslidedebris flow in British Columbia Using data from five broadband seismic stations 70 to 276 km from the source I obtain a time-series of forces the landslide exerted on the earth with peak forces of 1 0 x 1011 N The direction and amplitude of the forces can be used to determine the timing and occurrence of events and subevents Using this result in combination with other field and geospatial evidence I calculate an average horizontal acceleration of the rockslide of 0 39 m s2 and an average apparent coefficient of basal friction of 0 38 0 02 which suggests elevated basal fluid pressures The direction and timing of the strongest forces are consistent with the centripetal acceleration of the debris flow around corners in its path I use this correlation to estimate speeds which peak at 92 m s This study demonstrates that the time-series recording of forces exerted by a large and rapid landslide derived remotely from seismic records can be used to tie post-slide evidence to what actually occurred during the event and can serve to validate numerical models and theoretical methods 2a- 4 1 Introduction Direct time-dependent observations of natural landslides are critical to improving our understanding of landslide dynamics and hazard However such observations can be hard to come by due to the destructive nature of landsliding events uncertainty about when and where they will occur and their sometimes-remote locations Seismology is a potential tool to span this observational gap Assuming the landslide under investigation radiates enough seismic energy to be recorded at existing seismic stations and the seismograms can be correctly interpreted seismic data can provide a time series recording of landsliding events that can be used to extract information about landslide dynamics and source characteristics This approach is comparable to how seismologists have been using seismograms to study earthquakes for over a century - but landslide seismology has the added benefits of being able to access the source area and of knowing the driving stress gravity When combined with field investigation theoretical methods and numerical landslide modeling a much clearer interpretation of the event being investigated can emerge e g Favreau et al 2010 Moretti et al 2012 Guthrie et al 2012 In order to correctly interpret seismic signals of landslides one must first understand how landslides radiate seismic energy Energy is radiated on two scales: coherent long-period waves at periods of tens to hundreds of seconds generated by the acceleration and deceleration of the failure mass as a whole Kanamori and Given 1982 Eissler and Kanamori 1987 and a more stochastic higher frequency signal at periods from a few seconds to frequencies of tens of Hz generated by momentum exchanges on smaller scales such as flow over smaller scale topographic features frictional processes e g Schneider et al 2010 and impacts of individual blocks e g Huang et al 2007 2a- 5 Large and rapid landslides in particular are effective at generating strong long period seismic waves particularly surface waves which attenuate slowly and can be detected at seismic stations for hundreds to thousands of kilometers These long period seismic waves are not sensitive to heterogeneities in the crust on much shorter scales than their wavelengths so they can be studied using simplified earth velocity models and are thus easier to work with than higher frequency seismic energy The long period seismograms generated by such large landslides are often recorded at great distances and have been used for decades to study landslides Some authors have directly interpreted the timing of pulses and variations in amplitude in long-period landslide seismograms to determine the occurrence duration speed and timing of events Berrocal et al 1978 Weichert et al 1994 McSaveney and Downes 2002 Guthrie et al 2012 Others have taken analysis further and used the long period seismic waves to study the source process directly In contrast to the double-couple mechanism of earthquakes the equivalent force mechanism of a landslide is a single force applied to the surface of the earth proportional to the acceleration and mass of the moving material This is what generates the long period seismic waves Kanamori and Given 1982 Eissler and Kanamori 1987 Hasegawa and Kanamori 1987 Kawakatsu 1989 Fukao 1995 Julian et al 1998 Many authors have used forward modeling to determine the amplitude and duration of the forces exerted on the earth that could generate the observed seismic waves and used the result to estimate the mass or the acceleration of the landslide and to interpret the sequence of events e g Kanamori and Given 1982 LaRocca et al 2004 These methods have even been used to argue that what was thought to be an earthquake was actually a landslide e g Eissler and Kanamori 1987 Hasegawa and 2a- 6 Kanamori 1987 Others have used this approach to constrain rheological characteristics For example Brodsky et al 2003 estimated the coefficient of friction beneath three large volcanic landslides based on the forces they exerted on the earth Favreau et al 2010 used long period seismic observations of the 2004 Thurweiser landslide in Italy to determine the rheological parameters to use in a numerical landslide model Moretti et al 2012 used the long period seismic signals generated by the 2005 Mount Steller landslide in Alaska to invert for the forces it exerted on the earth and used both to constrain details about the flow dynamics in a numerical model Most recently Ekstr m and Stark 2013 inverted seismic waves generated by 29 large and rapid landslides recorded by the Global Seismographic Network They used their catalog of landslide force inversions combined with field data to build empirical relations between maximum forces and mass momentum potential energy loss and surface wave magnitude These relations allow for rapid order of magnitude estimates of landslide size without having to wait for other evidence However the long period seismic signals generated by the acceleration of the landslide as a whole that can be approximated as a single-force mechanism are not always observed If the mass is too small and or the average acceleration of the landslide too slow the forces the landslide exerts on the earth will be smaller Kanamori and Given 1982 and less likely to generate a long period signal above the noise level on nearby seismometers Furthermore the period of the waves generated depends on the duration of the forcing Kanamori and Given 1982 so a slow landslide with an extended duration may not emit waves at seismic frequencies The higher frequency signal generated by smaller scale processes on the other hand has been often observed for a wide range of landslide sizes and many authors have used this type of signal to study landslides as well Often referred to as emergent cigar-shaped or spindle-shaped the 2a- 7 higher frequency seismic energy typically builds up gradually emerging from the noise without a clear onset or obvious phase arrivals and then tapers back into the noise afterwards e g Norris 1994 Dammeier et al 2011 Deparis et al 2008 La Rocca et al 2004 Schneider et al 2010 Suri ach et al 2005 Such signals are useful for determining the occurrence duration and timing of landslides e g Norris 1994 Helmstetter and Garambois 2010 It is more challenging to use these signals to obtain quantitative landslide characteristics such as failure volume fall height or runout distance because only a small percentage of the energy is transmitted seismically for all landslides Berrocal et al 1978 Deparis et al 2008 Hibert et al 2011 and higher frequency waves attenuate rapidly and are much more affected by smaller scale heterogeneities in the crust Despite this several authors have been successful in estimating landslide characteristics such as volume and runout length within an order of magnitude or better particularly in the presence of dense nearby seismic networks Norris 1994 Deparis et al 2008 Hibert et al 2011 Helmstetter and Garambois 2010 Dammeier et al 2011 Schneider et al 2010 investigated the physical basis for variations in amplitude in the higher frequency seismic signal and found that increases in the relative amplitude could be attributed to increases in the loss of power due to frictional processes the frictional work rate The frictional work rate can be elevated for example after a sudden increase in speed after passing a step in the path or when the sliding material hits a flatter area at high speeds and begins to decelerate as frictional resistance increases Schneider et al 2010 Thus the relative amplitude of the high frequency seismic signature can be used to tie the timing of the seismic signal to the passage of material over particular sections of the sliding path 2a- 8 In this study I inverted the long period seismic signals generated by the August 2010 Mount Meager rockslide and debris flow in British Columbia to solve for the source process that generated them - the forces the landslide exerted on the earth over time I built on the initial characterization of the landslide by Guthrie et al 2012 and show that the characterization of the dynamics and source process of the landslide can be substantially improved by these methods The time-series recording of forces exerted on the earth during the landslide can be used to significantly reduce the level of interpretation required to tie post-slide observations to what actually happened during the event Though this study is based on the same seismic records Guthrie et al 2012 used as part of their characterization they used just the raw seismograms of this event to qualitatively interpret the timing of events from peaks in amplitude of the signal By inverting the seismic signals I take a much more direct and quantitative approach to obtain information about the source process by determining what forces actually generated the observed seismic waves at the source location This is comparable to the inversion of seismic signals generated by earthquakes to obtain information about the source history of an earthquake Just as this type of analysis has advanced our understanding of earthquake physics such an analysis of the seismic signals generated by landslides can contribute to a greater understanding of the landslide physics In the following sections I first detail the known characteristics of the Mount Meager landslide and the seismic data available Then I describe the inversion methods used test these methods with synthetic data and invert the long period T 30 to 150 s seismic signals to determine the forces exerted on the earth by the landslide with time I compare this result to the envelope of the higher frequency portion of the signal and piece together the sequence and timing of events I also calculate the speed of the landslide with higher certainty than was 2a- 9 possible using just the raw seismic data This provides a validation for other less-direct landslide speed estimation methods I use this result to discern the direction of failure of subevents extract the coefficient of dynamic friction during the rockslide and observe changes in the behavior of the debris flow over time - characteristics that are otherwise difficult to determine in the absence of seismic analysis This case study illustrates the benefits of including a seismic source analysis in landslide investigations and its potential to improve numerical models an option that is becoming more readily available as seismic networks become denser and high quality digital data more accessible 2 Data On 6 August 2010 at about 10:27 UTC 3:27 a m local time the secondary peak gendarme and southern flank of Mount Meager part of the Mount Meager Volcanic Complex in British Columbia collapsed in a massive rockslide that quickly mobilized into a debris flow Guthrie et al 2012 A rockslide is a failure of bedrock where sliding occurs dominantly on a single failure surface Cruden and Varnes 1996 while a debris flow is a poorly sorted internally disrupted and saturated flowing mass controlled by both solid and fluid forces Iverson et al 1997 According to the interpretation of the event by Guthrie et al 2012 once the rockslide converted to a debris flow it traveled down Capricorn Creek valley turning two corners sloshing up the sides of the valley and plowing down swathes of trees When it reached the end of the 7 8 km long valley the debris flow burst out into the adjacent Meager Creek valley and ran 270 vertical meters up the opposing valley wall It then split and flowed up and downstream 3 7 and 4 9 km respectively where it finally stopped leaving vast fields of deposits and temporarily blocking the Lilloet River and its tributary Meager Creek This sequence of events is illustrated on Figure 2a-1 Field evidence showed that some deposition began almost 2a- 10 immediately below the initiation zone though most material was deposited after the convergence with Meager Creek Very little material was entrained along the path though later activity incised into the primary deposits Guthrie et al 2012 Figure 2a-1 Overview of the sliding path overlain on a post-landslide satellite image with approximate boundaries outlined Refer to inset map on Figure 2a-3 for regional location of Mount Meager The source material was an estimated 48 5 million cubic meters of highly fractured and hydrothermally altered rhyodacite breccias tuffs and flows with a porphrytic dacite plug in the steeper areas Guthrie et al 2012 Additionally the source mass was highly saturated evidenced by the rapid mobilization of the rockslide to a debris flow requiring the availability of a lot of water as well as surface seepage and large springs observed along the failure surface Guthrie et al 2012 Assuming a density range of 2000-2500 kg m3 representative of typical values for these types of rocks the total mass was 1 0-1 2 x 1011 kg 2a- 11 2 1 Seismic data This highly energetic event generated strong seismic signals that were visible above the noise level at over 25 three-component broadband seismometers throughout Canada Washington State and Alaska A record section of the seismograms of this event recorded across British Columbia and Washington State by the Canadian National Seismograph Network CNSN and the Pacific Northwest Seismic Network PNSN Figure 2a-2 shows that the entire seismic signal lasted about 5 minutes before fading into the noise The onset of the seismic signal is dominated by long period pulses which are then overtaken by a more chaotic short-period signal The two distinct frequency bands corresponding to the two types of signals radiated by landslides described earlier are apparent in the spectrum of the signal and their distinct characters are made more apparent by high- and low-pass filtering the same signal around 0 2 Hz Figure 2a-3 Note that it is impossible to pick out the P and S wave arrivals separately because the amplitudes of the body waves in the higher frequency signal are below the noise at the start of the event Figure 2a-3b 2a- 12 Figure 2a-2 Record section of vertical component broadband velocity seismograms generated by the Mount Meager rockslide and debris flow Seismograms are corrected for station response and are all plotted on the same vertical scale which is shown under the inset map The inset map shows station locations relative to Mount Meager ring-shaped symbols indicate stations used in the inversion of long period seismograms The consistency in the signal between distant stations Figure 2a-2 demonstrates that both the low and high frequency portions of the signal largely reflect source effects and not path effects or site effects at individual stations However one interesting difference is that the amplitudes of the higher frequency ground motion are significantly stronger at station LLLB than station SHB though it is only 3 km further from the source area This could be due to lower attenuation rates east of the source area site amplification at the location of LLLB or both Another contributing factor could be that the landslide moved towards station LLLB and away from SHB This change in location would affect the amplitudes of the shorter period waves more 2a- 13 than the longer periods because anelastic attenuation is strongly frequency dependent Therefore the movement of the source 10% closer to LLLB could result in a noticeable reduction in the attenuation of higher frequency waves over the course of the event Suri ach et al 2005 observed a similar effect for smaller landslides In this study landslide speeds are almost two orders of magnitude slower than the seismic wave velocities so this is probably not true directivity as observed during earthquakes which is related to the Doppler effect Douglas et al 1988 Figure 2a-3 The vertical component velocity seismogram recorded at WSLR a lowpass filtered below 0 2 Hz to isolate the long period pulses that start first at point 1 and b highpass filtered above 0 2 Hz to isolate the shorter period signal that emerges from the noise about 20 seconds later at point 2 c The two distinct frequency bands are apparent as two separate broad peaks on the velocity spectrum of the entire signal By point 3 the long period signal shifts to shorter periods By point 4 the seismic signal is largely over but does not fade completely back into the noise until point 5 nearly 5 minutes after the start of the signal 2a- 14 From the seismic data available I selected those that had the best signal quality in the frequency band of interest by visual inspection Five of the seismic stations had significantly better signal quality than the rest Rather than using more data with questionable signal quality I used just the data from these five stations because test inversions detailed in section 3 showed that high quality seismic signals from just a few seismic stations should be more than sufficient to recover the force-time function The seismic stations used for the inversion are shown in relation to the location of the landslide on the map on Figure 2a-2 and are detailed on Table 2a-1 At least one component of each station had a signal to noise ratio SNR above 8 in the frequency band used in the inversion T 30-150s The highest SNR was 57 The noise characteristics of each component of each station used are displayed on Table 2a-1 Table 2a-1 Broadband seismic stations used in the inversion WSLR LLLB SHB PASS MRBL Latitude 50 1265 50 6090 49 5930 48 9983 48 5183 Longitude -122 9212 -121 8815 -123 8805 -122 0852 -121 4845 Distance km 70 115 118 208 276 Source to station azimuth clockwise from N 142 90 192 150 149 I prepared the seismic data by deconvolving the instrument response integrating the seismograms from ground velocity to ground displacement and rotating the horizontal components to the radial and transverse direction for each station The radial component refers to motion directly towards or away from the source and transverse is perpendicular to radial I then bandpass filtered the data between periods of 30 and 150 seconds using a second order minimum-phase causal Butterworth bandpass filter Using shorter period waves in the inversion would require a detailed velocity model of the region because shorter period seismic waves are more sensitive to smaller scale heterogeneities and topography Periods longer than 2a- 15 150 seconds couldn t be used because such long periods are beyond the fall-off in the response curves of all of the seismic stations and including them amplified the noise at these longer periods and overwhelmed the signal The data were weighted for the inversion by the inverse of the root mean squared rms value of the noise before the signal at the periods used These weights are reported on Table 2a-2 Table 2a-2 Noise characteristics and solution misfit at each station station name WSLR LLLB SHB PASS MRBL Component Signal to noise ratio amplitude % noise weight 1 rms noise x 100 rms noise nm rms misfit solution nm Z 23 2% 2 5 40 124 R 4 11% 0 2 530 1002 T 4 9% 0 3 316 434 Z 8 4% 2 0 51 131 R 7 5% 1 2 86 168 T 57 2% 4 7 21 66 Z 8 8% 0 6 157 170 R 8 18% 0 4 282 657 T 3 12% 0 5 206 416 Z 31 6% 1 1 89 105 R 4 10% 0 9 110 266 T 7 16% 0 4 239 232 Z 23 3% 3 2 32 88 R 8 26% 0 5 220 306 T 7 7% 1 1 93 191 Z R T refers to vertical radial and transverse components respectively 2a- 16 3 Methods For a landslide simplified as a block of constant mass m sliding down a slope the magnitude of the slope parallel force F comes from the driving force of gravity opposed by the frictional force Ff : F mg sin - Ff 1 where g is the magnitude of the acceleration due to gravity is the slope angle and bold font indicates a vector quantity The magnitude of the frictional force on the block is equal to: Ff Fn 2 where is the apparent dynamic coefficient of friction which accounts for both friction and the basal pore fluid pressures and Fn is the magnitude of the normal force The sum of forces in the direction perpendicular to the slope is zero because the landslide does not accelerate into or out of the slope so the magnitude of the normal force is equal to: Fn mg cos 3 This also means that the magnitude of the net force Fnet is equal to the magnitude of the slope parallel force F and equation 1 can be rewritten as: Fnet mg sin cos 4 If the frictional force and gravitational driving force are unbalanced as they are in the case of a mobilizing landslide the block will begin to accelerate According to Newton s second law the net force acting on an object is equal to its mass times its acceleration a so equation 4 becomes: Fnet ma mg sin cos 5 According to Newton s third law the forces of two bodies on each other are equal and opposite Therefore at the long wavelength limit as the sliding block feels a force due to its gravitational 2a- 17 acceleration the earth feels an equal point force Fe in the opposite direction Fe is a 3component vector that can be written more explicitly as a time dependent phenomenon: Fe t ma t 6 where bolding indicates a vector This is the equivalent force system that is responsible for generating the observed long period energy generated by large rapid landslides Kanamori and Given 1982 Eissler and Kanamori 1987 Hasegawa and Kanamori 1987 Kawakatsu 1989 Fukao 1995 Julian et al 1998 Fe t is comparable to the source-time function of an earthquake so I refer to it as the force-time function in this study Friction and slope angle control the acceleration of the sliding mass equation 5 which in turn determines the forces exerted on the earth equation 6 Equation 6 dictates that the force felt by the earth will be in the opposite direction to the landslide acceleration So as the source mass accelerates downslope the earth feels a single force applied in the upslope direction Then as the mass decelerates accelerates upslope the earth feels a single force in the same direction as the sliding mass i e downslope When the landslide banks a curve the acceleration is towards the center of the curve centripetal acceleration and thus the equivalent force points away from the center of the curve Julian et al 1998 also describes the torque due to lateral displacement of the landslide mass as a potential source of seismic radiation However Brodsky et al 2003 did not find it to be a significant contributor of seismic waves in their analysis of similarly large and rapid landslides For this study the inclusion of torque as a seismic source was not required to fit the data and was not incorporated into the analysis In this study I inverted the seismic data to determine Fe t Once obtained the force-time function can be used with equations 5 and 6 combined with the field evidence imagery and geospatial calculations compiled by Guthrie et al 2012 to extract information about the source 2a- 18 characteristics and dynamics of the landslide However there are a few caveats to using equations 5 and 6 directly for interpretation: the rigid block model of a landslide is of course a simplification of reality and these equations do not account for all spatio-temporal dependencies First the area of application of the force will migrate with the landslide mass and will change in total area over time In spite of this the landslide can still be treated as a stationary single force point source for long period and thus long wavelength seismic waves even though in this case the sliding mass moved more than 12 km This is because the shift in arrival times between waves generated at the start and the end of the sliding path would be less than 2 seconds at all stations for the slowest waves in the frequency band used: Rayleigh waves of a 30 second period Two seconds is a negligible fraction of the wavelength The difference in arrival times would be even smaller for the faster longer period waves Secondly the mass may vary with time Mass may be added due to erosion and entrainment and removed due to deposition Significant changes in mass over time are important for inferring acceleration from force equation 6 and must be taken into account in the interpretation Further the failure mass spreads out in space and becomes internally disturbed and agitated when it transforms from a rockslide to a debris flow To be a pure single force the dislocation of the sliding mass needs to be spatially uniform otherwise higher order force components can contribute seismic radiation Fukao 1995 The complexities of debris flow motion and its elongation over its sliding path can hinder the straightforward interpretation of the force-time function This is particularly true in the case of Mount Meager where there are several sharp bends in the sliding path and segments of the debris flow may be accelerating in different directions simultaneously resulting in opposing forces 2a- 19 In order to invert the seismograms to obtain Fe t I first set up the forward problem relating how the source process translates to the observed seismograms The seismogram recorded at each station after the station response has been removed represents the effects of the source itself as well as its path through the earth To a good approximation at long periods the earth is a linear system that can be characterized by the seismogram that would be recorded at the seismometer location from an impulse force applied at the source location The set of impulse responses between each source and station pair are known as the Green s functions and they account for all types of seismic waves as well as attenuation along the wave path The seismograms for a realistic source can then be obtained by convolving the Green s functions with a source-time function that describes the evolution of the source process over time e g Stein and Wysession 2003 In the case of a landslide this is the force-time function Fe t Green s functions can be calculated if the velocity structure of the material the seismic waves are passing through is known The periods used in this study T 30 150 s have wavelengths on the order of hundreds of kilometers and a low sensitivity to smaller scale heterogeneities in the regional velocity structure or topography For this reason a generalized earth model was sufficient to use in the calculation of the Green s functions In this study I used the 1D ak135Q earth velocity and anelastic attenuation model Kennett et al 1995 I calculated the Green s functions between each station and the landslide location using the wavenumber integration method Bouchon 1981 as implemented in Computer Programs in Seismology CPS Hermann 2002 Only the source to station distance and the velocity and anelastic attenuation model were required for this step of the calculation The radiation patterns of the seismic waves were accounted for in the inversion equations based on the source to station azimuth as explained in the Appendix The source to station distance did not change over time in 2a- 20 the inversion because the location of the single force applied to the earth by the landslide is assumed to be a stationary point source for reasons explained earlier in this section Once the forward problem was set up I inverted for the force-time function using damped least squares e g Aster et al 2005 Complete details of the inversion process are located in the Appendix 3 1 Validation To validate the robustness of this inversion method I first tested it with synthetic data to see if it was capable of recovering an input force-time function and to test the noise tolerance I started by using the forward model equation A1 to generate three-component synthetic seismograms for an arbitrary force-time function I then progressively increased the noise in the synthetic seismograms by adding Gaussian noise with a standard deviation equal to a percentage of the maximum absolute peak of the noise-free synthetic data Figure 2a-4 I then used these data to invert for the force-time function using the process described in the Appendix to see how well it returned the original signal after the addition of noise The results of this inversion for a range of noise levels first using a single three-component station WSLR and then three threecomponent stations WSLR LLLB SHB are shown on Figure 2a-5 and 2a-6 respectively The success of the inversion in retrieving the input test signal confirms that a force-time function very close to the original can be retrieved using data from just a few high quality threecomponent stations if the noise levels are low and random Even with just one three-component station and a significant amount of noise this inversion method recovered a force-time function close to the actual input model The ability of the inversion to recover the signal starts to break down when noise levels reach 30 - 40% but the noise levels for the real seismic signals of the landslide in the time immediately before the earthquake were mostly below 10% Table 2a-2 2a- 21 Figure 2a-4 The vertical component of one station WSLR of the synthetic seismograms generated for an arbitrary force-time function with 0 to 40% Gaussian noise added to illustrate the range in signal quality used in the test inversions Figure 2a-5 The three-component force-time function recovered by the test inversion of synthetic seismograms for a single three-component station WSLR with 0 to 40% noise added The original force-time function that was used to generate the synthetic seismograms bottom line is shown for comparison All force-time functions are scaled identically The relative root mean squared errors in arbitrary units between the force-time functions obtained by the inversions and the original are indicated at the right of each signal 2a- 22 Figure 2a-6 Same as Figure 2a-5 but for the inversion of synthetic data for three threecomponent seismic stations WSLR LLLB SHB with varying amounts of noise added to the signal 4 Results Using the methods described above and in the Appendix I inverted the seismic data to solve for the force-time function of the Mount Meager landslide The result is shown in Figure 2a-7 A-C This is compared to the raw seismogram from the closest station Figure 2a-7D and the azimuth of the force vector at each point in time Figure 2a-7E To quantify the fit of the resulting forcetime function I generated synthetic seismograms from the inversion solution by plugging the force-time function back into the forward model The synthetic seismograms fit the real data remarkably well Figure 2a-8 with a variance reduction of 80% The model can even closely reproduce data that was not used in the inversion EDB bottom of Figure 2a-8 The worst misfits were for the stations and components that had strong long period noise in the signal so it was encouraging that the solution did not fit that noise when it was present before and after the landslide signal The root mean squared rms errors between the original and synthetic 2a- 23 seismograms are comparable to the rms of the noise prior to the signal Table 2a-2 though the rms errors are nearly all higher than the rms of the noise This is because the forward model is approximate I am fitting 15 channels of noisy data simultaneously and the noise may not be entirely random as it was in the test inversions Figure 2a-7 A-C The three-component force time function for both the broadband five-station inversion and the solely long period inversion The vertical force is positive up and the zero of the time scale corresponds to the start of the landslide D the vertical component of the original unfiltered broadband seismic signal at the closest station WSLR and the envelope of the energy above 0 2 Hz in the signal shifted to line up in time with the force-time function Intervals 1-5 correspond with events described in text Points a-e indicate the peak in the force-time function within each interval that was used to tie the arrival of the center of mass of the landslide with arrival at points of peak forcing along the path The location and horizontal direction of the force at each of these points is plotted on Figure 2a-10 E The azimuth of the force vector over time 2a- 24 Figure 2a-8 Comparison of observed displacement seismograms dashed line with the synthetic seismograms generated by the force-time function obtained in the broadband inversion T 30150 s when plugged back into the forward model solid line The number in the right corner of each box indicates the relative weighting of the original data used in the inversion Data from EDB shaded 270 km from the source is shown to demonstrate how well the model reproduces data from a station not used to develop the model Vertical units are centimeters The force-time function of the Mount Meager landslide starts at 10:26:55 UTC has a duration of about 215 seconds and peak force amplitudes on the order of 1011 N This is of the same order of magnitude as the forces generated by the similarly sized Mount Steller landslide Moretti et al 2012 but one to two orders of magnitude smaller than some much larger landslides in other volcanic areas Kanamori and Given 1982 Brodsky et al 2003 and four orders of magnitude smaller than some huge submarine landslides Hasegawa and Kanamori 2a- 25 1987 Eissler and Kanamori 1987 This is to be expected because force scales linearly with mass equation 6 The forces are primarily horizontal consistent with the findings of other studies of landslide single-forces e g Kanamori and Given 1982 Brodsky et al 2003 The amplitudes of the vertical forces are much lower and more prone to noise in the solution In particular the dip in the amplitudes prior to the start of the landslide an artifact that only occurs on the vertical component suggests the overall amplitudes may be reduced by an unknown amount As a result I focused on the horizontal components in the quantitative interpretation requiring absolute amplitudes I use the vertical component of force only for the relative direction up or down of the horizontal forces and timing of events along the path With knowledge about the sliding path the timing and changes in direction of the force vector can be attributed to events along the path The initiating rockslide is well approximated as a sliding block allowing us to make first order calculations about landslide dynamics using equations 5 and 6 directly The subsequent debris flow is not well approximated by a sliding block but we can also make some inferences about the debris flow behavior and estimates speeds based on the timing of changes in direction of the forces relative to the debris flow path Numerical landslide modeling might be necessary to fully interpret the features of the force-time function but that is beyond the scope of this study 4 1 Rockslide initiation The Mount Meager rockslide failed toward the south and according to theory the direction of the initiating single force should be in the opposite direction: northward and upslope That is in fact what occurs first in the force-time function but instead of one wide pulse there are two pulses superimposed on each other with about 20 seconds between their peaks Interval 1 2a- 26 Figure 2a-7 The acceleration direction of the first pulse had an azimuth of 191 3 followed by another pulse of failure in a more southwesterly direction 217 3 The errors in azimuth are estimated as the standard deviation of the slope angle in interval 1 on Figure 2a-7E This sequence suggests a progressive mobilization of the flank of the mountain Based on the shape of the source volume Figures 2a-1 the landslide may have started with the release of material lower down on the flank of the slope toward the south generating the first pulse As this started to mobilize it may have destabilized the material above the bulk of which is to the northeast of the lower flank and may have failed in a more southwesterly direction as the azimuth of the second pulse suggests This two-part failure is consistent with the report of two loud cracks heard at the start of the landslide by campers nearby Guthrie et al 2012 Though this indicates the flank mobilized in two pulses they occur close enough in time to act as one bulk movement in the generation of the longest period seismic waves which are not sensitive to shorter-timescale subevents This is apparent in the force-time function obtained by inverting only the longer period waves T 75-150 s Figure 2a-7 A-C In this result the overall mobilization of the rockslide now appears as a longer period single pulse with an overall acceleration towards 213 5 Figure 2a-7 After these initiating pulses at t 40 seconds the force vector starts to point downwards and towards the south possibly due to the rockslide starting to decelerate but this is interrupted by a sharp upward and then downward force suggesting a rapid vertical collapse and impact start of interval 2 Figure 2a-7 This could signify the collapse of part of the secondary peak gendarme of Mount Meager or other steep material from the headwall that was left unsupported as the flank below mobilized It is probably not the entire secondary peak however because its total volume was estimated as 8 to 10 Mm3 N Roberts pers comm 2013 which would 2a- 27 generate a vertical force of about 2 x 1011 N if it collapsed vertically using equation 6 and assuming a density of 2300 kg m3 much higher than that observed The vertical force observed has an amplitude of 4-6 x 1010 N depending on what point is taken as its starting point so it s volume would be more on the order of 1 Mm3 if the collapse was nearly vertical According to Varnes 1978 classification the sliding surface of a rockslide is along one or a few shear surfaces within a narrow zone and though the source material is disintegrating it is moving en masse and is not yet elongated in space and flowing This type of behavior can be approximated as a sliding block which allows for a few simple calculations First equation 6 can be used to determine the acceleration of the block and determine the trajectory of the mobilizing flank as a whole assuming the mass is relatively constant Using the longer-period version of the force-time function T 75-150 s to represent the whole-scale mobilization of the rockslide I calculated the horizontal acceleration of the mass at each second in time Unfortunately it is not possible to calculate the acceleration of the subevents separately because their respective masses are unknown I integrated the acceleration twice to obtain the displacement of the center of mass of the landslide at each moment in time and fit the displacement curve with the equation of motion: d t do vot 0 5at2 to obtain a best estimate of the average horizontal acceleration of the rockslide a where d t is the horizontal displacement with time t The initial horizontal displacement do and initial velocity vo were set to zero The best fit was an average horizontal acceleration of 0 39 m s2 Figure 2a-9 The median slope angle of the source area from the postslide digital elevation model 15 m resolution resolved in the azimuth of slope failure 231 5 was 23 1 so the vertical acceleration corresponding to the horizontal acceleration calculated above should have been 0 17 m s2 and the total slope-parallel acceleration 0 43 m s2 By this 2a- 28 calculation the rockslide as a whole mobilized slowly taking 36 seconds to accelerate to a speed of 15 m s traveling about 250 meters horizontally and dropping about 110 meters in that time Figure 2a-9 The horizontal trajectory of the rockslide calculated from the long period T 75150 s force-time function assuming a mass of 48 5 million m3 The solid line shows a quadratic fit to the trajectory to the form of the equation of motion relating displacement acceleration and time The best fitting average acceleration was 0 39 m s2 Using a rigid sliding block approach it is also possible to estimate the areally averaged apparent dynamic friction at the base of the rockslide given the angle of the sliding plane Using a rearrangement of equation 5 sin a g cos 1 7 yields a best estimate of the apparent friction coefficient of 0 38 0 02 assuming a slopeparallel acceleration of 0 43 m s2 and a slope angle of 23 1 The apparent friction coefficient accounts for the effects of both friction and basal fluid pressure and this value suggests high basal fluid pressures To quantify this the apparent coefficient of friction can be related to the true coefficient of friction that would be felt in the absence of pore fluids by: n n P 8 2a- 29 where P is the mean basal pore pressure and n is the mean normal stress at the base of the sliding mass When rearranged equation 8 relates the difference between the apparent and true coefficient of friction to the ratio of basal pore pressure over basal normal stress: P n 9 While we don t know what the actual dynamic coefficient of friction in the absence of basal fluids was for the rocks composing Mount Meager we know from lab experiments that is nearly always greater than 0 6 for dry rocks of a wide variety of lithologies Byerlee 1978 so equation 9 indicates that basal fluid pressures were at least 22% of the basal normal stress during the rockslide for 0 38 This is corroborated by the large springs and surface seepages found throughout the source area after the landslide Guthrie et al 2012 suggesting that groundwater was instrumental in triggering this slide and its rapid mobilization to a debris flow The value obtained here is within the bounds on the coefficients of friction of 0 2 to 0 6 that Brodsky et al 2003 found for three large landslides also in volcanic environments but significantly higher than the value used by Guthrie et al 2012 to numerically model this part of the event 0 06 The reason for this discrepancy is addressed in the discussion section 4 2 Debris flow After the initiating pulses two longer period horizontal oscillations dominate the forcetime function Figure 2a-7 A-C intervals 2 and 3 Based on the direction of these vectors Figure 2a-7E they are most likely the manifestation of centripetal accelerations of the debris flow material turning the two major corners in its sliding path Unfortunately it is not possible to take the same approach as above and use equation 6 to estimate the trajectory of the debris flow directly because a debris flow is poorly approximated as a sliding block The flow becomes 2a- 30 elongated in space which could result in differing flow directions amongst segments of the failure volume and the material is flowing and agitated and can have complicated flow patterns Iverson et al 1997 Zanuttigh and Lamberti 2007 However under the assumption that the timing of peaks in the force-time function correspond to the times when the center of mass reached points of maximum forcing the timing of peaks can be tied to points along the sliding path to estimate the debris flow speeds I defined the starting point as the center of mass of the landslide calculated from the depleted thickness map from Guthrie et al 2012 marked with an x on Figure 2a-7 and placed the location of the first peak point a 75 meters downslope from there corresponding with the distance traveled by the rockslide by the time it reached its peak at t 21 s Figure 2a-9 For intervals 2 and 3 on Figure 2a-7 I assumed that the peak in the force-time function corresponded to the time that the center of mass of the debris flow passed the portion of the path with the highest curvature i e highest centripetal acceleration To find these points quantitatively I fit a polynomial to the horizontal sliding path that was delineated by Guthrie et al 2012 and calculated the curvature of this polynomial analytically I then placed the peak force vectors for each curve at these peak points of curvature Figure 2a-10 points b and c If the assumption that the peak force corresponds to the center of mass arriving at the location of peak forcing is valid the direction of the acceleration should point towards the center of a circle tangent to the point of maximum curvature To test this I placed circles with radii equal to the radius of curvature tangent to the point of maximum curvature and the peak acceleration vectors do point to within a few degrees of the center of these circles as expected for a centripetal acceleration Figure 2a-10 2a- 31 Figure 2a-10 Outline of sliding path with the azimuth of the major peaks in the force-time function from Figure 2a-8 placed at locations of maximum forcing black arrows The acceleration is in the opposite direction gray arrows The path trace dashed line is from Guthrie et al 2012 except from segment d to e which was estimated from satellite imagery The x marks the approximate location of the start of the center of mass Peaks in the force-time function correspond to the arrival of the center of mass of the landslide at the designated locations and were used to estimate the average speed of the landslide between these intervals as summarized on Table 2a-3 and labeled along the path The next interval interval 4 is characterized by an eastward and upward force that I interpreted as the debris flow decelerating rapidly upon reaching the confluence with Meager creek and running into the opposing valley wall point d At this point the debris flow split and flowed both up and downstream and also left significant deposits at the confluence of the two valleys This complicated the interpretation of the force-time function in interval 5 because there were opposing accelerations and a significant decrease in moving mass However the distinct pulse of force toward the northwest point e is consistent with another centripetal acceleration of some of the debris as it sloshed up the side of a steep hill before making its final turn to the 2a- 32 northern depositional area point e Figure 2a-7 and 2a-10 I placed the location of this peak force vector at the estimated point of maximum curvature of this turn and used it to estimate the speed for this last segment To conservatively account for uncertainties in the determination of distances between points I assumed a possible distance interval range of 400 meters I assumed a timing error range of 2 seconds The location assigned to each major peak labeled on Figure 2a-7 is shown on Figure 2a-10 The direction of the force vector at each of these peak times is also plotted along with the corresponding acceleration vector pointing in the opposite direction I estimated the errors in the azimuth of the peak force as the standard deviation of the angle within the interval containing the peak force Figure 2a-7E All error ranges are within a few degrees except for point d probably due to the opposing flow directions of the material at this confluence Table 2a-3 Table 2a-3 Distances and speeds between points along path and corresponding azimuth of the force at each point Point Distance from previous point m Time from previous point s Average speed best estimate m s Possible range m s Azimuth of Force 75 21 2 4 3- 4 33 5 b 1850 400 48 2 39 32- 45 205 5 c 3360 400 44 2 76 64- 90 7 4 d 2400 400 26 2 92 71- 117 114 29 e 700 350 52 2 13 6- 22 290 3 Refer to Figure 2a-7 for the timing and Figure 2a-10 for the location of points a-e a The average speed of the center of mass of the landslide between each of these points calculated by simply dividing the distance over the time is reported on Table 2a-3 and plotted as the solid black line on Figure 2a-11 By this analysis the average speed from the starting point to the first curve was 39 m s increasing to 76 m s going into the second curve and to 92 m s as the 2a- 33 debris flow traversed the third segment and burst into the adjacent valley After reaching the opposing valley wall at point d the average speed decreased significantly and the portion of debris that continued downstream slowed to an estimated 13 m s before turning the final curve to main depositional area Figure 2a-11 The average speed of the center of mass along path distance from this study black dots with error bars The average speed estimates are plotted halfway between the distance markers defining each interval The solid line shows a linear interpolation to these points shading shows the error range The zero point corresponds to the location of the center of mass of the source area and the average speed estimates were plotted halfway between the distance markers used This result is compared to speed estimates by the three methods used by Guthrie et al 2012 Schneider et al 2010 showed that the relative amplitude of the envelope of the high frequency seismic signal correlates well with the total frictional work rate Frictional forces will be higher than the gravitational forces when the landslide reaches a slope shallower than the arc tangent of the coefficient of friction Schneider et al 2010 For the apparent coefficient of friction determined in this study 0 38 that angle would be 21 The slope of the sliding path is consistently less than 21 just past the toe of the source area so there should have been an increase in the amplitude of the higher frequency signal almost immediately after the rockslide 2a- 34 left the source area This is in fact what occurred: the envelope of the higher frequency 0 2 Hz energy started to build up about 20 seconds after the start of the landslide Figure 2a-7D As the mass started to disintegrate flow and reach high speeds the random kinetic energy should have increased as well This in turn should have increased the frictional resistance due to higher shearing rates and thus higher seismic amplitudes This is observed: the envelope of the higher frequency energy rose and reached a plateau after turning the first curve in the path interval 2-3 This is the part of the sliding path where the debris flow reached high speeds 76 m s over a relatively straight interval and random kinetic energy should have been high After passing the second curve point c Figure 2a-7 the amplitude of the envelope reached an even higher plateau this is where the estimated speeds reached their highest point but were followed by a rapid deceleration as the debris hit the wall was deflected and slowed down as it spread over the depositional area This section interval 4 has the highest amplitudes of high frequency shaking most likely due to high frictional resistance forces as the mass rapidly decelerated 4 3 Aftershock About 2 minutes after the end of the main landslide event there was an aftershock a smaller landslide that occurred after the main event This landslide also generated a long period seismic pulse I inverted the long period seismograms of this event to obtain its force-time function Figure 2a-12 I had to use shorter period seismic waves T 20 50 seconds in the inversion to capture this smaller event The shortest period waves used are too short to be accurately represented by the Green s functions so this is a more approximate inversion than the main event I also only used the closest three stations in the inversion because their mean signal to noise ratio SNR was 4 while the two more distant stations had a mean SNR of 2 with the lowest component having an SNR less than 1 The force-time function for this event indicates a 2a- 35 primarily vertical collapse towards the south-southeast probably off the now over-steepened headscarp The collapse quickly took on a more horizontal trajectory in the southeast direction The absence of a strong subsequent downward force suggests that there was no impulsive vertical impact so the material may have disintegrated along the slope as it fell The force of the vertical collapse is an order of magnitude smaller than the main event peaking around 6 x 109 N The second vertical pulse occurring about 30 seconds after the first could have been a second collapse or could be forces generated along the sliding path of the first collapse Since there is no way of estimating the volume of this secondary landslide from satellite data because it occurred just minutes after the main event I used the result of this inversion to estimate the volume solely from the seismic data To do this I assumed the same frictional value found for the main event 0 38 and took the arc tangent of the vertical over the horizontal forces at the peak of the vertical collapse to estimate a slope of 72 This results in an acceleration of 8 2 m s2 by equation 7 Since the magnitude of the forces at this point was 5 8 x 109 N using equation 6 this yielded an estimated mass of 7 x 108 kg or a volume of 0 3 million m3 assuming a density of 2300 kg m3 This volume of material is two orders of magnitude smaller than the main event yet the forces are only one order of magnitude smaller probably because accelerations were higher due to the near-vertical failure direction 2a- 36 Figure 2a-12 a A second smaller landslide an aftershock occurred a few minutes after the end of the main landslide as shown in the seismic data b-d Three components of force of the aftershock obtained by inverting seismic data at periods of 20 to 50 seconds from the three closest three-component stations WSLR LLLB SHB The time scale is consistent between all four plots 2a- 37 5 Discussion 5 1 Improvements to landslide characterization The time series recording of the forces exerted by the landslide allowed for significant improvements in the characterization of the dynamics of this event particularly when combined with the extensive field evidence and geospatial data compiled by Guthrie et al 2012 In particular the availability of the force-time function reduces the qualitative interpretation typically required to tie post-slide evidence to what happened during the event It also eliminates guesswork required to interpret the source of pulses in the raw seismograms directly by using the seismograms to find what the source was quantitatively As mentioned the force-time function showed that the rockslide initiation occurred in two pulses which I interpreted as a progressive failure of the flank of the mountain These events were followed soon after by a nearly vertical collapse that was smaller in volume This sequence of events is in contrast with the interpretation of Guthrie et al 2012 They proposed that the near-vertical collapse of the steep gendarme occurred first and its impact onto the shallower slopes below caused the flank to mobilize due to undrained loading and rapidly turn into a debris flow This is a reasonable interpretation from the evidence that was available at the time but with the additional information provided by the force-time function it is clear that the failure of the flank of the mountain started first and was likely the cause of the vertical collapse - though the collapse of this material onto the already-mobilizing flank still could have been responsible for its rapid disintegration and mobilization to a debris flow This is a reasonable argument given that the higher frequency portion of the signal attributable mainly to the debris flow rises quickly after the vertical collapse 2a- 38 The results of this study also improve on the interpretation of Ekstr m and Stark 2013 who included the 2010 Mount Meager landslide in their inversion of long period seismograms from 29 catastrophic landslides worldwide recorded on the Global Seismographic Network Though they do not include the entire force-time function in their results they reported peak forces of 1 48 x 1011 N for this event comparable but higher than the peak magnitude of the force found in this study of 1 0 x 1011 N However the start time they reported for the start of the event was two minutes later than the start time found in this study and reported by Guthrie et al 2012 Their start time corresponds instead to the time of the peak at point d Figure 2a-7 and 2a-10 This suggests they interpreted what this study found to be a centripetal acceleration of the debris flow around the second curve in the path as the initiation of the rockslide This discrepancy may explain why their estimated runout of 4 6 km was much shorter than the actual runout 12 km and highlights the care that must be taken when interpreting the force-time functions of landsliding events Though the methods used to estimate the speed of the landslide from the force-time function in this study still required some interpretation they are the closest to a direct measurement of the options available Guthrie et al 2012 used two common methods of estimating landslide speeds: a theoretical method called superelevation Chow 1959 and a numerical landslide model DAN-W Hungr 1995 Hungr and McDougall 2009 I validated these methods against the more physically based measurement available from the results of this study since the opportunity is not often available for natural landslides As mentioned Guthrie et al 2012 also used features of the raw seismograms to estimate speeds and I include that result in the comparison as well The four methods are plotted for comparison on Figure 2a-11 and were all adjusted to the same path starting point used in this study 2a- 39 The speeds predicted by the numerical model presented by Guthrie et al 2012 are much higher at the start of the debris flow than that determined in this study The initial acceleration in the first 20 seconds was about 4 5 m s2 which should have generated a force an order of magnitude higher than that observed in the force-time function so the speeds cannot have been that high at the onset The exceptionally low coefficient of friction they used in this simulation 0 06 compared to 0 38 determined in this study may partially explain the difference Guthrie et al 2012 chose this value to best fit the runout distance and velocities of the landslide interpreted from the raw seismograms and did not fit the superelevation estimates well This low value for is probably because they were trying to match initial speed estimates that were too high This mismatch highlights the potential of using the force-time functions and other information derived from seismic waves to validate and calibrate numerical models and tie them to the physical world as Moretti et al 2012 did in their study The limitation is that for complicated events - such as this one with subevents of unknown relative masses and a complex path causing opposing forces at times - numerical models may be needed to fully interpret the force-time function So in reality the comparison between numerical models and landslides may be more of an iterative process that may not necessarily have a unique solution The landslide speeds estimated roughly from the raw seismograms in Guthrie et al 2012 also had a much higher estimate of the initial speed Figure 2a-11 This is due to the aforementioned difference in their interpretation of mobilization sequence They assumed that the majority of the landslide mass - the flank of the mountain - did not mobilize until the secondary peak collapsed on it about 45 seconds after the start of the landslide With this interpretation there is very little time between the mobilization of the flank of the mountain and its arrival at the first corner thus resulting in the extremely high initial speeds they report As 2a- 40 explained above the force-time function shows the reverse sequence of events: the flanks of the mountain mobilized first followed by a vertical collapse If they had this information in the initial interpretation of the seismograms the initial speed estimate would have been much closer to the speeds obtained by this study Though the uncertainties are higher the best estimates of the speeds from the raw seismograms are close to those estimated in this study: between 10 and 30% lower but with error bars that overlap The main benefit of using the results of the seismic inversion to estimate speeds is the elimination of most of the guesswork involved in correlating pulses in the seismic record to exact locations of events along the path The speeds determined in this study compare most favorably with the values determined using the superelevation method Chow 1959 a theoretical method of determining speed by how much higher the debris flow reaches on the outside corners of turns than the inside corners The three superelevation measurement points are between 5 and 11% different from the projection of the speeds calculated in this study and are well within the error bars Figure 2a-11 providing a validation of this theoretical method with real data The main discrepancy is the average speed for the path segment between points c and d coming out of the last corner in the valley where the average speed from this study exceeds the projection line between superelevation estimates by 35% However it is not possible to conclude whether this discrepancy is real or not because the superelevation measurements are effectively point measurements at the points before and there is no information in between There is a possibility that the continuous increase in the debris flow speed until point d found in this study could be erroneous However the uncertainties incorporated in the calculation of the error bars of the speeds for this study were conservatively wide The main source of error would have to be a misinterpretation of the force-time function in this study due 2a- 41 to the complexity of flow at this junction This is possible but it is difficult to conceive where the pulse of eastward forces observed in interval 4 would come from if not from the material running up against the adjacent primarily west-facing valley wall point d so I consider this unlikely Assuming this late peak in speeds is real and the other methods are either erroneous or cannot resolve this peak there are a few potential explanations According to field evidence there was very little entrainment of material along the path in fact deposition started immediately below the initiation zone but most material was deposited beyond the Capricorn creek valley Guthrie et al 2012 so the mass was relatively constant during the fastest intervals along the landslide path A landslide of constant mass will continually increase in velocity if the angle of friction tan-1 is shallower than the slope angle Iverson 2012 The apparent coefficient of friction at the base of the rockslide estimated in this study to be 0 38 which translates to an angle of friction of about 21 The slope of the debris flow path is shallower than this averaging around 10 which means the coefficient of friction must have dropped below 0 18 tan 10 during the debris flow in order to still be accelerating along this path A drop in the coefficient of friction of a debris flow can occur due to undrained loading of wet bedded sediments by the overriding debris flow that causes an increase in the pore pressures at the bed Iverson et al 2011 This often also results in an increase in entrainment Iverson et al 2011 but entrainment was not observed in this case possibly because of the exceptionally high speeds which actually make entrainment less likely to occur Iverson 2012 Another contributing factor to the late high peak in speeds estimated in this study could be due to a common behavior of debris flows: the development of surging also referred to as roll waves As explained by Zanuttigh and Lamberti 2007 debris flow surges develop when 2a- 42 smaller flow instabilities grow and form surface waves that overtake each other with growing wavelengths and amplitudes As these instabilities progress downstream and continue to overtake each other they can coalesce into bigger surges often eventually forming one dominant first surge characterized by a concentration of boulders at the front sometimes followed by subsequent smaller surges Debris flow depths are often significantly higher in surge waves and the waves can travel up to three times faster and exert forces more than an order of magnitude higher than the rest of the regularly flowing mass The development of one or more large coalesced surges along the flow path of the Mount Meager debris flow could have moved the speed of the center of mass of the debris flow forward faster than the average flow but the forces exerted by the surges themselves were likely too short period and too low-amplitude to be resolved in the force-time function The timing of the speedup is consistent with the observation that larger coalesced surges tend to preferentially appear further down the flow path because it takes time for the instabilities to grow large enough and overtake each other Zanuttigh and Lamberti 2007 If the surge started to develop prior to reaching point c the speed estimate between b and c could also be higher than the regular nonsurging flow There is even a hint of what could be interpreted as two separate surges visible in the vertical component of the force-time function The vertical component of the force at point d has a shorter duration than the eastward component and is followed by a second smaller upward pulse Figure 2a-7A This could indicate that the bulk of the debris flow material did not run up vertically but was primarily deflected horizontally and it could have been the arrival of these two or three subsequent surges that were faster deeper and higher energy than the rest of the flow that was responsible for the high runup observed in the field The surges do not appear as discrete events on the east component of the force-time function however though this could be 2a- 43 because their masses are not large enough to contrast with the rest of the regular flow being deflected primarily horizontally 5 2 Limitations One major limitation to the application of the methods used in this study to other events is that there is a whole spectrum of landslide types and behaviors Varnes 1978 but these methods can only be used to study the small percentage that generate the required long period waves: exceptionally large and rapid landslides Scaling these methods down to more common shorter duration smaller rapid landslides would require a detailed characterization of the velocity and attenuation structure of the study area and better seismic coverage because they would generate lower amplitude and shorter period seismic waves Even if this can be done it doesn t address the problem of potential overlap in the frequency domain between the coherent pulses from the bulk mobilization of the landslide mass and the signal generated by stochastic smaller scale processes For larger landslides the two sources of seismic radiation are manifested in distinct frequency bands e g Figure 2a-3c but this may not be the case in a scaled down scenario and if they overlap the two can no longer be isolated with simple filtering On the other side of the spectrum slower events that may have large masses but slow accelerations and long durations such as large slumping events may be too slow to generate waves of short enough period to be observed by seismic methods though subevents or smaller scale forcing may be resolvable Another limitation is that the force-time function alone cannot be used directly to estimate useful information about the dynamics of the landslides Other information is required For example even if the landslide under investigation can be approximated as a coherent sliding block equation 6 dictates that the trajectory of the sliding block can only be calculated from the 2a- 44 force-time function if the mass is known Likewise the mass can only be calculated if the trajectory is known However even if neither is known order of magnitude estimates of mass can still be obtained due to physical limitations on acceleration I showed that the methods used in this study can be used to determine the sequence of events and the occurrence of subevents However this can also be a limitation because subevents can complicate the force-time function and thus make straightforward interpretation and calculations from it challenging In this study I was able to get around the fact that the rockslide initiation occurred in two subsequent failures because the two subevents were close enough in time and space that they acted as a single failure mass at the long period limit Care must be taken to correctly assess when and where the rigid sliding block approximation is valid and when it breaks down For example the approximation breaks down if subevents are too far apart in time or space to be considered one failure mass at long periods or when the failure mass is not moving coherently enough such as during the debris flow of this event where the material became elongated in space and internal agitation and complex flow patterns dominated 6 Conclusions In this study I inverted the long period seismic signals generated by the Mount Meager landslide to solve for the forces it exerted on the earth as the failure mass accelerated turned curves along its path and decelerated I used this result the force-time function to track landslide behavior over time This analysis is useful not only for unraveling the sequence of events and facilitating a more direct interpretation than is typically possible between post-slide evidence and what actually happened during the event but can also be used to make first order calculations about landslide dynamics 2a- 45 Using the three component force-time function I was able to identify the directions of the slope collapse and discern that the slope failure was progressive with the massive flank of the mountain starting to mobilize first in two discrete but closely timed subfailures followed by a much smaller nearly vertical collapse that might have been the collapse of part of the gendarme of the secondary peak of Mount Meager left unsupported as the flank mobilized The addition of this new information clarified the sequence of events suggesting that the initial interpretation made by Guthrie et al 2012 where they proposed that the vertical collapse occurred first and caused the flank to mobilize was actually reversed Using the mass of the failure determined from satellite imagery by Guthrie et al 2012 I was able to use the force-time function directly to estimate the trajectory of the center of mass of the rockslide showing that it had an average horizontal acceleration of 0 39 m s2 and estimated the apparent coefficient of friction at the base of the rockslide to be 0 38 a low value that suggests basal fluid pressures were high at least 22% of the normal stresses at the base of the slide assuming a minimum coefficient of friction of 0 6 for dry rocks Following the sequence of forces generated by the rockslide initiation the direction and timing of the primarily horizontal forces were consistent with the debris flow turning two corners in its path and then running up the wall of an adjacent river valley The horizontal forces from these centripetal accelerations were actually the highest forces overall A debris flow is poorly approximated as a sliding block so I could not make calculations or estimate the trajectory directly from the force-time function but instead tied the timing and direction of peak forces to points of peak forcing along the path to estimate the speed of the center of mass of the debris flow I found that speeds increased continuously as the debris flow progressed down the first valley peaking at 92 m s before rapidly decelerating upon reaching the adjacent Meager Creek 2a- 46 valley The speeds I found by this method were very close to the speeds predicted by superelevation providing a physically based validation to that theoretical method The forcetime function also provided a test of other speed estimation methods applied by Guthrie et al 2012 The initial speeds they estimated by numerical modeling were much higher than those estimated in this study and would have required forces an order of magnitude higher than those observed in the force-time function Their estimates of speed from the raw seismograms were close to those estimated in this study though with higher uncertainties but their speed estimates were also too high at the onset of the landslide because of their reverse interpretation of the sequence of initiating events The differences show that the addition of the information provided by the force-time function can significantly clarify landslide characterization Though the calculations I presented in this study are rough and large scale due to the long period nature of the seismic waves used and direct interpretation is difficult due to the complexities of debris flow behavior it is remarkable that using data from five broadband stations 70 to 276 km from the source it was possible to reconstruct details of this event that are unobtainable by other methods but nonetheless important for understanding landslide physics and improving numerical models As there are currently networks of broadband seismometers worldwide for which data are freely available the techniques I described could be applied to study other large landslides that occurred both in the past and to come 7 Acknowledgements Many thanks to Ken Creager who provided indispensable guidance on what started as a project for his Inverse Theory course and to my advisor John Vidale Also to Emily Brodsky Dick Iverson Rick Guthrie John Clague Anne Mangeney and Hiroo Kanamori for helpful 2a- 47 feedback reviews and discussions Nicholas Roberts for helping with some geospatial calculations the Pacific Northwest Seismic Network and Canadian National Seismograph Network for providing the seismic data and Sharon Watson for tolerating frigid fast flowing river crossings and quicksand to accompany me on a field visit of the landslide Additionally reviews by Jackie Caplan- Auerbach Agnes Helmstetter and two anonymous reviewers helped improve the manuscript significantly 8 References Aster R C B Borchers and C H Thurber 2005 Parameter estimation and inverse problems Elsevier Amsterdam Berrocal J A F Espinosa and J Galdos 1978 Seismological and geological aspects of the Mantaro landslide in Peru Nature 275 5680 532-536 Bouchon M 1981 A simple method to calculate Green s functions for elastic layered media Bull Seism Soc Am 71 959-971 Brodsky E E E Gordeev and H Kanamori 2003 Landslide basal friction as measured by seismic waves Geophys Res Lett 30 24 2236 doi:10 1029 2003GL018485 Byerlee J 1978 Friction of rocks Pure and Appl Geophys 116 4-5 615-626 Chow V T 1959 Open-channel hydraulics McGraw-Hill New York Cruden D M 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of Synthetic Seismogram Computation Version 3 30 Dept of Earth and Atmospheric Sciences Saint Louis University Accessed at: http: www eas slu edu eqc eqc_cps CPS CPS330 html Hibert C A Mangeney G Grandjean and N M Shapiro 2011 Slope instabilities in Dolomieu crater Reunion Island: From seismic signals to rockfall characteristics J Geophys Res 116 F4 F04032 doi: 10 1029 2011JF002038 Huang C J H Y Yin C Y Chen C H Yeh and C L Wang 2007 Ground vibrations produced by rock motions and debris flows J Geophys Res 112 F02014 doi: 10 1029 2005JF000437 Hungr O 1995 A model for the runout analysis of rapid flow slides debris flows and avalanches Can Geotech J 32 610-623 Hungr O and S McDougall 2009 Two numerical models for landslide dynamic analysis Comp Geosci 35 978-992 Iverson R M M E Reid and R G LaHusen 1997 Debris-flow mobilization from landslides Annu Rev Earth Planet Sci 25 1 85-138 2a- 49 Iverson R M M E Reid M Logan R G LaHusen J W Godt and J P Griswold 2011 Positive feedback and momentum growth during debris-flow entrainment of wet bed sediment Nat Geosci 4 2 116-121 doi: 10 1038 ngeo1040 Iverson R M 2012 Elementary theory of bed-sediment entrainment by debris flows and avalanches J Geophys Res 117 F03006 doi: 10 1029 2011JF002189 Julian B R A D Miller and G R Foulger 1998 Non-double couple earthquakes Rev Geophys 36 4 525-549 Kanamori H and J W Given 1982 Analysis of long-period seismic waves excited by the May 18 1980 eruption of mount St Helens a terrestrial monopole J Geophys Res 87 B7 54225432 Kawakatsu H 1989 Centroid single force inversion of seismic waves generated by landslides J Geophys Res 94 B9 12 363-12 374 Kennett B L N E R Engdahl and R Buland 1995 Constraints on seismic velocities in the earth from travel times Geophys J Int 122 1 108-124 La Rocca M D Galluzzo G Saccorotti S Tinti G B Cimini and E Del Pezzo 2004 Seismic signals associated with landslides and with a tsunami at Stromboli Volcano Italy Bull Seismol Soc Am 94 5 1850-1867 McSaveney M J and G Downes 2002 Application of landslide seismology to some New Zealand rock avalanches in Landslides J Rybar J Stemberk and P Wagner Eds pp 649-654 Balkema Lisse Netherlands Moretti L A Mangeney Y Capdeville E Stutzmann C Huggel D Schneider and F Bouchut 2012 Numerical modeling of the Mount Steller landslide flow history and of the generated long period seismic waves Geophys Res Lett 39 16 L16402 doi: 10 5167 uzh- 68355 Norris R D 1994 Seismicity of rockfalls and avalanches at three Cascade Range volcanoes: Implications for seismic detection of hazardous mass movements Bull Seismol Soc Am 84 6 1925-1939 Schneider D P Bartlet J Caplan-Auerbach M Christen C Huggel and B W McArdell 2010 Insights into rock-ice avalanche dynamics by combined analysis of seismic recordings and a numerical avalanche model: J Geophys Res 115 4 F04026 doi: 10 1029 2010JF001734 Stein S and M Wysession 2003 An Introduction to Seismology Earthquakes and Earth Structure Blackwell Malden MA 2a- 50 Suri ach E I Vilajosana G Khazaradze B Biescas G Furdada and J M Vilaplana 2005 Seismic detection and characterization of landslides and other mass movements: Nat Haz And Earth Syst Sci 5 791-798 Varnes D J 1978 Slope movement types and processes in: Landslides analysis and control Transportation Research Board Special Report 176 R L Schuster R J Krizek Eds pp 11-33 National Research Council Washington DC Weichert D R B Horner and S G Evans 1994 Seismic signatures of landslides: the 1990 Brenda Mine Collapse and the 1965 Hope Rockslides Bull Seismol Soc Am 84 5 15231532 Zanuttigh B and A Lamberti 2007 Instability and surge development in debris flows Rev Geophys 45 3 RG3006 doi: 10 1029 2005RG000175 2a- 51 Chapter 2b: The Seismic Story of the Nile Valley Landslide Most of the content of this chapter was presented at: Allstadt K Vidale J Thelen W and Bodin P 2010 The Seismic Story of the Nile Valley Landslide Poster Session presented at: Seismological Society of America Annual meeting 2010 2010 Apr 21-23 Portland OR 2b- 1 Table of Contents Summary 2b-3 1 Introduction 2b-4 2 Background 2b-5 3 Seismic Data 2b-10 4 Discussion 2b-13 5 Conclusion 2b-15 6 Acknowledgements 2b-16 7 References 2b-16 2b- 2 Summary The Nile Valley landslide of October 11th 2009 was one of the largest in recent Washington state history This translational slide involved a volume on the order of 107 cubic meters and destroyed 2 houses a portion of highway and flooded several houses when it partially dammed a stream Residents in the area reported noises and deformation starting 2 days beforehand and evacuated safely The main sliding sequence occurred over about 6 hours and two regional seismic stations 12 and 29 km away captured some of the signals generated by it Distinct seismic pops began to appear about 3 hours before a partial slope failure generated a continuous 2-minute signal with an emergent onset After this the pops became more frequent and evolved into the largest sliding event This appeared as a 13-minute broadband rumble centered on 4 5Hz with an emergent onset and spindle shaped signal Diminishing rumbling followed for another hour After the landslide occurred we installed 12 vertical geophones and 4 three-component seismic stations around the perimeter More than 60 small events were recorded at these stations in the days after the slide and are likely due to settling and continued deformation One particularly large movement 9 days after the main event generated a signal that also appeared on the more distant permanent stations This event had a similar shape to the main event but lasted only 15 seconds with about 25% of the amplitude Smaller events recorded on the seismic stations at the site showed a buildup in amplitude hours before this event This case adds to the body of knowledge on the seismic manifestation of landslides and gives more clues as to what happens before during and after a landslide of this type In addition our observations indicate that landslides may show precursory patterns that seismic monitoring can detect if they can be reliably identified 2b- 3 1 Introduction The Nile Valley landslide of October 11th 2009 Figure 2b-1 located on the east side of the Cascades along Highway 410 was one of the largest in recent Washington State history This translational slide involved a volume on the order of 107 cubic meters of material It destroyed a portion of state highway damaged several houses and diverted a river causing flooding Fortunately no one was injured because the landslide gave warning signals in the days and hours beforehand Figure 2b-1 Location of Nile Valley Landslide in Washington State on Google earth basemap The slopes failed over the course of about 24 hours in a complex series of events of various sizes and velocities Some of the more energetic events generated seismic signals that were captured by the Pacific Northwest Seismic Network PNSN regional stations 12 and 29 km away NAC and ELL Figure 2b-2 This highly precise seismic timeline in combination with detailed eyewitness reports provided to the Washington State Department of Transportation WSDOT and studies of the geology of the landslide conducted by the Washington State 2b- 4 Department of Natural Resources DNR resulted in a detailed account of the unfolding of a landslide unlike any other This study focuses mainly on the seismic manifestation of movements on the slide and how this case study can contribute to the sparse existing body of knowledge on landslide seismology Complementary details from eyewitness accounts and landslide geology are included Figure 2b-2 Location of nearby PNSN stations in relation to Nile Valley Landslide Google Earth basemap 2 Background The Nile Landslide may be related to or occur in deposits of the much larger ancient Sanford Pasture Landslide Figure 2b-3 which covers an area of over 50 square kilometers The Sanford Pasture Landslide is on a southern face of an oversteepened anticline The Nile Thrust fault approaches the surface inside this ridge Weak Ellensburg Formation interbeds siltstone volcaniclastics and sandstone created a perfect failure plane for the landslide The Sanford Pasture landslide is at most 2 million years old but the actual age is not well known The 2b- 5 present-day scar from this slide is apparent on Figure 2b-3 After failure erosion split the Sanford Pasture landslide and formed a river valley between the deposit area and the main body of the landslide now known as the Nile Valley Smaller blocks continued to move at least two major movements flow into the valley area and to the location of the Nile slide Hammond 2009a b Figure 2b-3 The size of the scar of the ancient Sanford Pasture Landslide dwarfs the Nile Valley Landslide circled in red basemap from Google maps A cross-section of the Nile Valley landslide of October 2009 is shown on Figure 2b-4 and a map view showing the different failures adapted based on interpretation by the WSDOT is shown on Figure 2b-5 the timing of the different failures depicted on this map will be discussed in the next section The headscarp of the Nile Valley Landslide formed along the contact with a separate landslide block of basalt beds Movement occurred on two failure planes located on interbeds between basaltic flows The upper failure plane is composed of sandstone and siltstone at an approximate depth of 20 meters Movement along this plane was translational with localized rotational blocks and flows and resulted in the main surface movement that covered 2b- 6 Highway 410 and diverted the Naches River The deeper failure plane was at a depth of around 60 meters and borehole drilling afterwards revealed high confining water pressures in this failure plane most likely confined by a clay-rich sedimentary layer overlying the basalt Badger 2010 pers comm This failure block moved into the valley creating deformation and folding and movement of the soft sediments at the toe of the landslide including shifting an entire intact block with a house on top of it eastern hill of uplifted areas labeled on Figure 2b-5 Figure 2b-4 Simplified cross section through the Nile Valley landslide showing two translational failure planes with rotational surface components Based on borehole data and LiDAR DEM collected by WSDOT and interpretation by WA DNR Location of Cross Section shown on Figure 2b-5 The following account of the sequence of events was compiled by the WSDOT Nile 2010 Signs that slopes were reawakening began up to one month before the main event: A fisherman observed clouds of dust coming from high on the slopes that would later fail Two days before the slide a local couple reported that their driveway was narrowing and occasional 2b- 7 rocks were tumbling down the slope The day before the main event nearby PNSN stations Figure 2b-2 picked up a faint low frequency rumble coming from the direction of the slide area coinciding with eyewitness reports of increased rockfall and thunder-like sounds coming from the ground Later that afternoon a small lobe of talus 10 to 15 meters wide marked initial slide on Figure 2b-5 mobilized This foreshock stopped short of the nearby houses by the late afternoon After this all was quiet and the slide seemed to be over Figure 2b-5 Overview of Nile Valley landslide cross-section A-A shown on Figure 2b-4 Then in the middle of the night: rockfall and rumbling recommenced Rumbling at 46Hz began to appear on the PNSN stations and started to increase in amplitude and the main sliding sequence began The rest of the sequence is illustrated on the timeline Figure 2b-6 2b- 8 2b- 9 Figure 2b- 6 This timeline in UTC shows the spectrograms from 1 to 10 Hz and the corresponding seismograms filtered from 1 to 7 Hz for the nearby vertical component short period PNSN stations NAC Naches WA and ELL Ellensburg WA Their locations relative to the landslide are indicated on Figure 2b-2 The seismic timeline is narrated along the top of this and the corresponding eyewitness timeline paraphrased from the WSDOT compilation Nile 2010 is explained along the bottom 3 Seismic Data Due to attenuation of higher frequencies only signals below 7 Hz appeared at NAC and ELL the two nearby short period vertical component PNSN stations Several early pops and rumbles highlighted in green on Figure 2b-6 coming from the direction of the landslide could not be tied to specific movements of the slide observed by eyewitnesses because it was dark at the time Two clear signals highlighted in red on the timeline on Figure 2b-6 can be tied directly with eyewitness reports of the two separate rapid slope failures The first signal at 14:38 UTC coincides with the rapid failure of the western portion of the slope refer to Figure 2b-5 for location The signal builds slowly up from the background rumbling at 4-6Hz and ends 100 seconds later more abruptly The spectrogram of this part of the signal shows two separate frequency centers and within each of these are discrete peaks of energy indicating multiple small sources within a complex failure sequence The signal at 16:43 UTC corresponds to the rapid failure of the larger eastern slope Figure 2b-5 This builds up from an increasing frequency of pops and rumbles apparent on NAC This signal has a clear center between 4-5Hz on NAC perhaps due to a site amplification effect at that station Eyewitnesses observed 10 to 20 seconds of rapid failure of this eastern portion of the slope Nile 2010 however the signal lasts for 15 minutes This and the fact that uplift began with this signal suggests that much of this signal may be due to the deeper movements on the sliding plane at 60 m depth Due to the shallow nature of the source and their 2b- 10 slower attenuation the seismometers probably recorded mainly surface waves but they are just vertical component instruments so we cannot confirm by looking at particle motions Figure 2b-7 Amplitudes in counts of post-slide landslide-related seismic events as recorded on the three stations closest to the activity Amplitudes are in counts and have not been corrected for station corrections The diurnal pattern is because construction noise drowned out any seismic signals during the day One week after the main sliding event we installed 12 vertical geophones and 4 threecomponent seismic stations around the perimeter to capture the near-source seismic records of any further movements of the slide Station locations are shown on a post-slide DEM of the area on Figure 2b-8 No further widespread movements occurred during the monitoring period but more than 60 small events were recorded at these stations in the days after the slide Figure 2b7 likely due to settling and continued deformation of the slide mass One movement 9 days after the main event generated a strong signal that also appeared on the more distant regional stations Smaller events recorded on the seismic stations at the site showed a buildup in 2b- 11 amplitude hours before this event The locations of these signals and other strong signals located by zero-lag cross correlation Almendros et al 1999 are shown on Figure 2b-8 Figure 2b-8 Location of stations installed after the landslide triangles and best-fit post-slide event locations circles Dashed line outlines approximate slide area The locations are all clustered in the same area located above the headscarp perhaps due to failure of slopes above the newly formed headscarp WTF2 was telemetered in real-time and 3-component stations were left out for two months to assist the WSDOT in monitoring and to ensure that the much larger Sanford Pasture landslide wasn t reawakening Two shallow earthquakes Md 0 7 with all other events in the family Any ungrouped events within each day were discarded This means that in order to be detected a repeating earthquake must repeat at least once within the same day - a condition easily met for the repeating earthquakes we are searching for Next we computed a median stack line all waveforms up in time and take the median at each time interval for each family of events detected in each day to suppress noise and condense the family into a single representative waveform Then we compared the stacks from each day to every other day within that month and grouped them again into larger families Families with more than 5 repeats in a month were saved All event families were visually examined and any false families like calibration pulses data spikes and repeating waveforms from events originating from nearby Mount St Helens were deleted The remaining families were then restacked and compared with all the families detected in the adjacent 3 months on either side and regrouped again At this step because we were comparing stacks and noise is suppressed we used a higher correlation coefficient of 0 8 to combine families These larger families were then restacked again and then each stacked waveform was scanned through the data as a template pulling out any missed detections within one month on either side of the first and last event detection of that family We used a lower cross correlation threshold of 0 6 in order to pull out even noisy events This template search resulted in some 3- 14 individual events being grouped into more than one family if two families were similar enough for that event to have a correlation above 0 6 with both of them so we found any events that were grouped into more than one family and deleted all instances of that event except for the one with the highest correlation Finally once this catalog was completed for both RCS and RCM we compared the two catalogs and families for which at least 10% of the total events overlapped between the two stations were considered to be the same family All these steps except for the visual inspection of waveforms were automated using MATLAB coding The entire search took about a week to run the biggest time limitation was downloading the archived seismic data 3 1 2 Results The results of this search are shown in Figure 3-3 events detected by at least one station are shown in red those detected on both RCS and RCM are shown in blue We only show events with a dominant frequency of less than 8 Hz on this figure We consider 8 Hz a cut-off for a low-frequency repeating earthquake We choose this cutoff because there is a clear clustering of the dominant frequency of repeating earthquakes families below 8 Hz Figure 3-2D and families with a higher dominant frequency typically do not appear on more than the closest station do not repeat at regular intervals and occur just as often or even more often in the summer as in the winter Allstadt et al 2012 suggesting they are related to a different source probably localized crevassing e g Neave and Savage 1970 We do not address these events in this study 3- 15 Figure 3-3 Repeating low-frequency earthquakes detected per hour by stations RCS and RCM Blue indicates detections that occurred on both stations gray shading indicates when at least one station had an abnormal signal RMS i e wasn t functioning properly Black lines indicate the span of select families the thick line delineates the span of 90% of the events in that given family RCS had less downtime and seems to record more repeating earthquakes than RCM probably because it is immediately adjacent to two major glaciers so its catalog is more complete We detected 299 558 repeating earthquakes grouped in 840 families at RCS Of these 3- 16 families 559 families containing 150 271 events had a dominant frequency of less than 8 Hz At RCM we detected 61 772 repeating earthquakes in 372 families 369 of these families had a dominant frequency below 8Hz containing 61 398 events Far fewer higher-frequency crevassing events were detected at RCM probably because it is not as close to major glaciers as RCS 87 families were shared between RCS and RCM The rest of the families that were not shared either were too low energy to appear above the noise on the other station or one of the stations was either not working or saturated with noise for example signals at RCM are often drowned out by high wind noise and RCM was not functioning for significant portions of the study period An initial glance at Figure 3-3 reveals that low-frequency repeating earthquakes have in fact been happening all along we just didn t know to look for them so we didn t find them Individual events often only show up at the three highest stations so the seismic network does not detect them automatically and visual detection is difficult because these high mountain stations are extremely noisy For this reason only the most obvious sequences were noticed in the past Secondly Figure 3-3 shows that though there is always a background level of low-frequency earthquake activity that hovers around 5 events per hour the big swarms of activity like the ones that originally attracted attention to this phenomenon e g Thelen et al 2013 only occur from late Fall to early Spring - essentially the accumulation season Most swarms reach at least 20 events per hour but the repeating earthquake activity sometimes exceeds 50 events per hour meaning there is an event nearly every minute A third conclusion one can make from Figure 3-3 is that there is a secular increase in lowfrequency repeating earthquake activity starting in the autumn of 2009 This cannot be attributed 3- 17 to changes in the seismic stations The changes that have occurred at RCM include a change in the type of sensor from a Kinemetrics Ranger SS-1 to a Mark Products L-4 on 6 Aug 2006 and a replacement of the L-4 on 13 Aug 2010 The gain was halved on 1 April 2008 and then increased by half on 13 Aug 2008 and has stayed stable since RCS has been a Mark L4 sensor since 2003 the only change was that it was replaced with a new one on 7 July 2005 and moved to a quieter location a few meters away on 26 July 2006 The only gain change since 2003 was when the gain was halved on 1 April 2008 None of these changes correspond to obvious changes in the number of repeating earthquakes detected except for a reduction in the outage time staring mid2006 To clarify the complex behavior of these swarms we focus on a time period containing a few consecutive swarms and plot a timeline of repeating earthquake activity Figure 3-4 The swarms are typically composed of more than one dominant family that all start around the same time typically coinciding with an increase in the snow depth recorded at PVC Each family tends to start out with large variability in the correlation between individual events and the stack of all events in the family but after a few hours or days the waveforms become more consistent i e highly correlated Then the correlation and event rate gradually drifts and the family ends When another storm passes through and drops more snow old families tend to shut off though there are some important exceptions like family 681 on Figure 3-4 which will be discussed later and new families appear and follow a similar pattern There are exceptions to these general observations Some event families such as families 704 and 721 on Figure 3-4 do not follow these trends but the families that contribute most to the swarm-like character of the repeating earthquake activity do 3- 18 Figure 3-4 Timeline showing the evolution of repeating earthquake families with at least 100 repeats during two snowstorms Each individual earthquake is a circle plotted on a line corresponding to its event family The family name is labeled at left The number of earthquake occurrences contained in each event family is labeled at right The color of each circle corresponds to the cross correlation between that individual event and the stack of all the events in that family The snow depth measured at Paradise is shown in the background 3 2 Correlation with Weather In order to look more explicitly at the apparent correlation between weather and repeating earthquake swarms we compared temperature and precipitation to low-frequency repeating earthquake activity over several years in Figure 3-5 This figure clearly shows that the start of each swarm of earthquake activity coincides with a period of intense precipitation in almost every case This is particularly apparent in the stormy winter of 2011-2012 each clear step up in the snow level coincides with a clear peak in earthquake activity 3- 19 Figure 3-5 Daily temperatures recorded near seismic station RCM and snow height and precipitation rain & melted snow recorded at Paradise compared with repeating earthquake activity Dotted lines show that peaks in repeating earthquake activity correspond to peaks in precipitation in most cases Figure 3-6 A Normalized cross correlation between daily red and hourly black repeating earthquake activity and precipitation The boxed area is shown on B showing the clear peak that occurs around 1-2 days lag Dashed lines indicate the maximum correlation obtained when the precipitation data was randomized and correlated against earthquake occurrence 10 000 times 3- 20 To quantify this relationship we performed a normalized cross correlation between precipitation liquid equivalent recorded at PVC and repeating low-frequency earthquake activity Figure 3-6 We did this for both hourly and daily time series discretizing the two time series in time exactly the same way To understand the significance of a correlation between these two distinct processes we adopted methods similar to those used by Martini et al 2009 by generating randomized precipitation data and performing the cross correlation between this random data and the vector of repeating earthquakes per day or hour 10 000 times to determine the maximum correlation value that could be obtained if the data were completely random These maxima are shown as dashed horizontal lines on Figure 3-6 We generated the random data by creating a vector of random numbers with the same mean and standard deviation using the lognormal distribution of the actual precipitation data The resulting correlation oscillates with a period of about one year Figure 3-6A because both processes are seasonal though there is a lag in the oscillation of about a month probably because the repeating earthquake activity does not start to appear until a few weeks into the accumulation season as is apparent in Figure 3-5 The most significant correlation is obtained when the repeating earthquake activity lags 1-2 days behind the precipitation indicating a delay time between when precipitation falls and when the repeating earthquake activity appears The peak which far exceeds the correlation value that could be obtained randomly has a broad base particularly on its right side indicating that there is variability in the lag time skewed towards longer times by a few days The correlation is higher for the daily time series comparison than the hourly time series most likely because there is more variability in precipitation on an hourly time scale than in repeating earthquake activity but both are smoother on daily timescales 3- 21 3 3 Locations Knowing the location of these events is crucial to understanding their source Yet locating individual events is nearly impossible because the signals only appear on at most the three edifice stations not enough to determine the location Also precise timing of the first P-wave arrivals required for traditional earthquake location methods is impossible because the signal doesn t emerge from the noise until some time after the first P-wave arrival These limitations are apparent in Figure 3-7 where a record section of the vertical components of an individual event is plotted in the left column Fortunately these earthquakes repeat up to several thousand times so we can line the seismograms up in time and stack the signals to suppress noise and augment the signal We obtained the time lags to apply to data from all seismic stations using the station with the clearest waveforms typically RCS If there were sufficient repeats of an event a clear signal emerges on the three highest stations with essentially no noise and a less clear but still usable signal emerges on the more distant stations where before there was no observable signal whatsoever Figure 3-7 middle column In this study we use the median stack rather than the mean stack to avoid the influence of outliers like spikes in the data The clarification of the signal is such that clear P- and S-wave arrival times are sufficient in number to use traditional location methods for families that have hundreds to thousands of repeats and we were also able to determine the direction of the first motion on the three closest stations The are significantly smaller than the subsequent waves and are not even visible on Figure 3-7 even in the virtual absence of noise unless we zoom in explaining why individual events appear to emerge from the noise Almost all families have mixed first motions on the vertical components though for some families some of the first motions are too small and 3- 22 uncertain to say for sure Unfortunately we cannot go further and estimate the focal mechanisms from these first motions because we only have three stations on which we can reliably recognize first motions if that and cannot estimate take-off angles well-enough in this complex terrain to provide good control of focal mechanisms 3- 23 Figure 3-7 Record section demonstrating that a single occurrence of one of these earthquakes in this case from family 796 only appears above the noise level at the three summit stations left column but when data from hundreds of events are lined up in time and stacked the noise is suppressed and the signal emerges at stations as far as 20 km from the summit This processing allows events to be located and the first motions to be determined on the closest stations First motions are indicated with gray arrows middle column The spectrum of these stacks shows that there is very little energy above 6Hz there aren t clear shared spectral peaks between stations and higher frequencies are more attenuated further from the volcano right column We only attempted to locate families that had enough repeats to clarify the signal sufficiently upon stacking to be locatable We focused on families that had more than 700 repeats and a dominant frequency of 30 at Mount Rainier where at least some of the repeating events are originating When a load of snow falls on the glacier during a storm there are a few immediate effects Figure 3-13B The driving shear stress and the effective normal stress normal stress minus basal fluid pressure are both increased at a ratio depending on the slope angle: 3-4 3-5 where the apostrophe indicates the new value is the density of the new snow g is the acceleration due to gravity hs is the thickness of new snow is the slope angle and k is the fraction of the increase in load that will be offset by an increase in basal water pressure which will be spatially variable because the subglacial water system is poorly connected The increased effective normal stress also results in increased frictional forces that resist the increased driving stresses by an amount proportional to the friction coefficient 3- 47 Figure 3-13 Conceptual model of proposed mechanism for velocity increase triggered by snow loading A Typical winter basal configuration in map view: poorly connected distributed basal cavities filled with water with spatial variability Arrows indicate direction of ice motion B Cross section of steep upper part of alpine glacier after snow added to surface C Change in basal configuration several days after the snow loading begins when stick-slip sliding ensues See text for more detailed explanation In any case the immediate increase in any of these stresses would be just 0 05 - 0 2% assuming slopes of 30 - 45 for the amount of snow that occurred prior to any of the select families This is such a small increase that it could trigger stick-slip sliding only if a particular part of a particular glacier bed was extremely close to a critical state and just a tiny increase in velocity or a tiny increase in effective normal stresses could kick it into an unstable sliding regime In this case the 1-2 day lag between peaks in precipitation rate and peaks in repeating event rates Figure 3-6 could be interpreted as the time it takes for enough snow to build up to push it over the threshold However the sharp peak at a 1-2 day lag time between snow loading and the appearance of repeating earthquakes more strongly suggests that a time-dependent process related to changes in subglacial hydrology is responsible When the additional normal load from the snow is added to the top of the glaciers it also squeezes the fluid filled cavities This increases the fluid pressures 3- 48 pw in each of the isolated basal cavities by the same amount temporarily because they are poorly drained and poorly connected: 3-6 So although the overall shear and effective normal stresses may increase by a fraction of a percent the initial basal fluid pressures in the isolated cavities may be much lower than the effective normal stresses Therefore the fluid pressure could be increased by a larger percentage relative to the initial state and this would occur over a widespread area since snow falls on the entire glacier This has the effect of essentially squeezing the water out of the cavities into adjacent areas resulting in the lubrication of a larger area of bed of the glacier i e reducing the areally averaged effective stresses This could then increase sliding velocities This change in sliding velocities would take time to occur because the movement of water in response to the pressure increase is limited by the hydraulic properties of the system providing a potential explanation for the 1-2 day lag Then as explained earlier a sudden increase in sliding velocities in turn could trigger stick-slip sliding Scholz 1998 at patches of the bed where conditions are favorable to stick-slip sliding i e colder dirtier better drained Zoet et al 2013 This could be for example a patch of fractured bedrock and is most likely a different area than those responsible for the increased velocities because it must be poorly lubricated initially Figure 313C We cannot compute magnitudes because the waveforms are so highly altered and we do not know the scaling laws to apply in this case to estimate the fault size and amount of slip anyway Thelen et al 2013 estimated the size of the seismogenic patch could range from 0 4 to 104 m3 in any case much smaller than the area under any of the glaciers involved meaning just 3- 49 part of the glacier bed is seismogenic the rest may be sliding aseismically The change in event location over time Figure 3-12 could be explained by a particularly dirty ice patch moving over an area that favors stick-slip behavior The family disappearance could occur either when the dirty ice patch moves beyond this area or excess fluid pressures have had sufficient time to drain away and sliding velocities drop back down to previous levels In most cases event families die off in about a week or two which provides a timescale for these processes Basal conditions are highly variable Fountain and Walder 1998 and there are likely to be places that meet conditions favorable to stick-slip sliding at the base of any glacier Zoet et al 2013 If more than one place under a single accelerating portion of a glacier meets the requirements or if more than one glacier responds in this way we can get multiple simultaneous event families as we observed Figure 3-4 The idea that certain parts of certain glaciers are more prone to the observed behavior is supported by the fact that event families with highly similar waveforms reappear years apart Figure 3-14 Of course these are not really the same families but instead stick-slip sliding occurring again in a very similar location to where it occurred before This suggests that some areas of some glaciers are much more prone to this behavior than others over long timescales Hanging glaciers and icefalls in particular may be prone to transient stick-slip sliding because they are less stable to begin with which may make them more prone to increases in sliding velocity from minor changes in the system They also are less likely to have thick layers of deformable basal till beneath them like lower parts of the glaciers might Deformable till may favor aseismic sliding These factors may explain why the locations of at least the select event families occur at hanging glaciers and icefalls as opposed to other areas 3- 50 Figure 3-14 Event families that share similar waveforms to the select families brown text The month in which each family occurred is labeled Waveforms shown are the stack of all events recorded at RCS One may ask why this behavior doesn t also occur in the late spring and summer when there can be rapid and high volume inputs of water from melt water and rain that can cause sliding velocity increases e g Harper et al 2007 Fudge et al 2009 The absence of swarms of repeating low-frequency earthquakes from basal slip in the summer is probably at least in part due to the difference in the configuration of the subglacial drainage system between summer and winter The summer configuration is efficient and well connected and thus less favorable for the buildup of high fluid pressures Fountain and Walder 1998 The absence of repeating earthquake swarms during the spring melts when the basal configuration may still be distributed 3- 51 and there can be rapid influxes of rain and melt water could be in part due to the observation by Zoet et al 2013a that if the bed of a glacier is already well lubricated a minor increase in lubrication from a velocity increase is relatively small and is less likely to result in stick-slip sliding There may just be too much water coming too fast When there is a lot of basal fluid in the system widespread bed separation occurs removing areas of higher drag Mair et al 2001 Stick-slip sliding may be triggered for a short time with the initial influx of water but could quickly be shut off as more and more water enters the system providing more and more lubrication that can t be drained away fast enough to allow stick-slip sliding to continue This is consistent with the observations There are low-frequency repeating earthquakes occurring year round at a background level of about 5 per hour Figure 3-3 Furthermore the larger glacial earthquakes observed at Mount Rainier and other Cascade volcanoes by Weaver and Malone 1979 and also at Mount Baker by Moran et al 2009 were classified as stick-slip events Those events occurred more often in the summer indicating that stick-slip sliding probably occurs at some locations of some glaciers year round just not in the prolonged swarms of repeating earthquakes that seem to rely on winter-like subglacial drainage conditions Another reason these larger stick-slip events in the summer are not as repeatable as the smaller winter earthquakes of this study could be because the fault area and total slip are larger so it may require fewer stickslip cycles for a given patch of entrained debris to move past an area of the bed favorable to stick-slip sliding Precipitation does not tend to trigger swarms of repeating earthquakes early in the accumulation season Figure 3-5 It takes a few weeks of winter conditions for them to start to appear which may be the amount of time required for the subglacial conduits to collapse viscously and for the drainage system to transition from summer to winter conditions 3- 52 There is also the secular trend to explain: the apparent increase in low-frequency repeating earthquake activity over the past ten years Figure 3-3 This may simply be a function of storminess for example the most repeating earthquake activity was detected in the winter of 2011-2012 which also was characterized by fewer storms dropping larger amounts of snow Figure 3-5 Stormier behavior i e large amounts of snow falling in short amounts of time would be more likely to trigger sudden velocity increases by the mechanisms we propose than many small storms depositing snow incrementally 4 3 Broader Implications Beyond proposing a solution to the puzzle of a peculiar seismic source on one mountain the findings of this study and our proposed mechanisms have wider implications both in glaciology and beyond This case adds to the body of knowledge on alpine glacier behavior We show that some parts of some glaciers can be extremely sensitive to minor changes in external loading Our observations suggest that if conditions are right surges in basal sliding velocity can be triggered by surface loading that is a fraction of a percent of the total overburden load at least in the winter months when the subglacial drainage system is composed of isolated and poorly connected cavities Furthermore though stick-slip behavior has been confirmed geodetically for large shallowly sloping ice streams in Antarctica e g Wiens et al 2008 this is the strongest evidence of seismicity resulting from stick-slip glacial sliding at steep temperate alpine glaciers that we know of The long-term year round record of repeating earthquake activity provides a window into seasonal differences in the behavior of alpine glaciers particularly the behavior of the high reaches of alpine glaciers in wintertime an essentially inaccessible environment that is thus difficult to study with other methods The behavior documented here adds to the spectrum of known glacier behavior This may also have ramifications for subglacial morphology as some 3- 53 studies suggest stick-slip sliding may have a connection to erosional processes e g Zoet et al 2012 Our hypothesis that these events are initiated by a surge in the sliding velocity of hanging glaciers and icefalls also may have implications for ice avalanching hazards If a velocity increase were to cause sliding to accelerate critically something we could observe from telemetered seismic data like the accelerating stick-slip seismicity Caplan-Auerbach and Huggel 2007 observe prior to ice avalanches at Iliamna volcano in Alaska the end result could be an ice avalanche The long-term year-round record of repeating earthquake activity also allowed us to show with more confidence that the majority if not all of the observed repeating low-frequency seismicity is not related to volcanic activity This type of behavior is common and occurs every year The catalog we compiled also allows us to characterize what is normal behavior so that when Rainier reawakens we are better equipped to discriminate harmless glacier-quakes from seismicity related to the volcano A near real-time method for monitoring repeating earthquake activity that sends alerts when activity is beyond pre-determined bounds on normal behavior is already under development and testing Allstadt et al 2012 These methods could be customized and applied to other glacier-covered volcanoes that present similar monitoring challenges These repeating earthquakes at Mount Rainier can provide insight into repeating earthquakes and earthquake behavior in other environments provided we understand the limitations of the analogy e g ice melts at a much lower temperature than rocks It is rare to have such an extensive catalog of earthquakes that occur so frequently: nearly 300 000 repeating earthquakes with more occurring every day This allows us to identify certain seismicity patterns that we do 3- 54 not typically have enough data to observe for regular earthquakes For example we showed that these events show slip-predictable behavior on short timescales but even minor changes in external loading such as a tiny increase in the normal load or a gradually decreasing slip rate throw off this relation but in systematic ways Shelley 2010 and Shelly and Johnson 2011 observed similarly abrupt changes in the recurrence intervals of small stick-slip earthquakes and non-volcanic tremor on the San Andreas fault near Parkfield that were brought on by stress changes from nearby earthquakes This is a comparable environment because the repeating earthquakes at this section of the San Andreas are proposed to be sticky spots on a larger plane that is slipping mostly aseismically similar to the sticky patches at the base of a glacier surrounded by areas that continue to slide aseismically proposed for this study Ocean and earth tides and even dynamic loading from seismic waves of distant earthquakes also change the normal and shear stresses in the earth by amounts that are a fraction of the total stresses but have all caused observable changes in the behavior of tectonic events e g Rubenstein et al 2008 Nakata et al 2008 Peng et al 2009 Apparently even minor changes in the stress field can alter fault behavior on a range of scales even for glaciers The mechanism we invoked as a trigger for the swarms of glacier quakes at Mount Rainier fluid redistribution and increased aseismic slip around a sticky patch has been invoked as a trigger for swarms in tectonic environments e g Vidale and Shearer 2005 Vidale et al 2006 Though Vidale and Shearer 2005 suggest tectonic swarms are triggered either by the redistribution of fluids or by accelerated aseismic slip but the mechanism we propose for this study requires both perhaps both mechanisms are involved in such cases in tectonic environments as well 3- 55 5 Conclusions In this study we compiled a complete catalog of repeating earthquake activity that occurred over the past decade at Mount Rainier We found nearly 300 000 repeating earthquakes About half have dominant frequencies below 8 Hz low-frequency and many of these repeat at regular intervals the type of event that motivated this study We found that this type of seismicity has occurred every year for at least the past decade but previously went undetected Though low frequency repeating earthquakes occur year round at a background level of about 5 per hour big swarms of activity occur only in late autumn to early spring We used this catalog to fully characterize this type of earthquake to understand the source and to confirm that the source is glacial and not related to volcanic activity We found that the swarms often are composed of several distinct families occurring at different areas of the mountain simultaneously Swarms correlate strongly with precipitation with a normalized cross correlation coefficient of nearly 0 5 peaking sharply around a 1-2 day lag Within each family we showed that recurrence intervals inter-event correlations and event energy all vary over time often gradually but sometimes suddenly and these sudden changes often correlate with minor changes in loading 30% Transit Highways Arterials Railways A2-3 Figure A2-1 N Landslide Hazard Zones Newmark displacement probability of failure Low 1-3 5cm 0-10% Moderate 3 5-7cm 10-20% High 7-12cm 20-30% Very High 0 1 2 4 km 12cm 30% Transit Highways Arterials Railways A2-2 Appendix 3 Details of Inversion Methods This section details the inversion process used to obtain the force-time function in Chapter 2a The forward problem to obtain the displacement seismograms generated by a single force applied at the source location is: di t Gij t mj t A1 where the seismogram di t at each component of each station i is equal to the Green s functions Gij t for station component i for an impulse force applied at the source location in direction j convolved with the force-time function of the source mj t where j is the directional component of the force Up North East Note that mj t is equivalent to Fe t - the change in notation is for consistency with inverse theory conventions where m refers to model Equation A1 assumes a stationary force vector applied to a single point on the surface of the earth Though the landslide is moving it can be approximated as a stationary point force for the long period wavelengths used in the inversion as explained in the methods section Green s functions are the response of the earth to an impulse source In this study I calculated the Green s functions relating an impulse force at the source location to the response at the distance and azimuth corresponding to each seismic station I computed these using the wavenumber integration method Bouchon 1981 as implemented in Computer Programs in Seismology CPS Hermann 2002 The velocity model used for these calculations was ak135Q Kennett et al 1995 This is a one-dimensional radially stratified global earth velocity model and does not account for regional or smaller scale variations However it was sufficient for this study because the long period waves T 30 150 s used in the inversion are not sensitive to smaller scale variability A3- 1 Using CPS I computed the Green s functions corresponding to each seismic station used in the inversion for a Dirac delta function impulse force applied to the surface of the earth at the location of the landslide Five Green s functions are required for each station used in order to calculate three-component synthetic time histories for a single force mechanism applied in any direction at the source Hermann 2002 The radial component of the seismogram is positive in the direction pointing directly away from the source The transverse component is perpendicular to the radial direction positive in the direction clockwise from north Vertical is positive upwards The five Green s functions are abbreviated as follows: ZVF Vertical component of the seismogram for a downward vertical force RVF Radial component for a downward vertical force ZHF Vertical component for a horizontal force in radial direction RHF Radial component for a horizontal force in radial direction THF Transverse component for a horizontal force in transverse direction The first four Green s functions correspond to the P-SV system while THF corresponds to the SH system The Green s functions calculated for station SHB 118 km from the source are shown on Figure 2a-A1 These illustrate the role of the earth s structure in the waveforms observed at station SHB due an impulse force of 1 N at the source The Rayleigh wave dwarfs the P and S arrivals on the top four Green s functions but has not moved out and dispersed much yet because of SHB s proximity to the source Note that due to the nature of causal filters the relatively compact unfiltered Green s function becomes distorted when filtered the energy is smeared out later in time This is not a problem in the inversion because identical filters are applied to the data so it is distorted in the same way This is confirmed in that a nearly identical force-time function is obtained when a zero-phase acausal filter is used Also note that the A3- 2 duration of the source force-time function is much longer than the Green s functions unlike for most regular earthquakes which is why such a detailed force-time function can be derived from the seismograms These Green s functions can be used to calculate synthetic ground displacement seismograms for any single force vector impulse or time series by: uz f1cos f2sin ZHF f3ZVF A2 ur f1cos f2sin RHF f3RVF A3 ut f1sin -f2cos THF A4 Hermann 2002 where is the source to station azimuth measured clockwise from north The single force f f1 f2 f3 is in a north N east E vertical Z respectively Cartesian coordinate system where Z is positive down note however that Z was switched to positive up in the force-time function plots in this paper to be more intuitive The ground displacement seismograms are in spherical coordinates local to each source-station pair where vertical is positive up uz radial ur is positive in the direction away from the source and tangential ut is positive at a right angle clockwise from ur A3- 3 Figure 2a-A1 Green s functions calculated for this study for station SHB located 118 km from the source for a impulse force of 1 N The functions are shown unfiltered 0 5 Hz sample rate and bandpass filtered between periods of 30 to 150 seconds using the same causal minimum phase butterworth filter applied to the data and Green s functions prior to inversion The amplitude of the filtered Green s functions is amplified by a factor of ten relative to the unfiltered version See text for discussion In order to do the inversion the forward problem equation A1 was rewritten as matrix multiplication rather than a convolution A convolution is equivalent to reversing one of the two signals being convolved in time and passing them by each other multiplying all points and summing them up at each time interval To convolve a Green s function with a force vector via matrix multiplication the Green s functions were reversed in time and staggered by shifting the Green s function by one sample in each successive row to produce a convolution matrix To illustrate this setup Equation A5 shows the convolution via matrix multiplication between a 4sample Green s function g and a 3-sample force-time function m to obtain the seismogram d that is 6 samples long: d1 % g1 d2 g2 d3 g3 d4 g4 d5 0 d6 & 0 0 g1 g2 g3 g4 0 0% 0 m % g1 1 m g2 2 m3 & g3 g4 & A5 Equation A5 illustrates the convolution with just one Green s function for one station and one component of the force-time function The actual Green s function convolution matrix must be set up to include all the Green s functions corresponding to each component of each seismic station used and to incorporate the equations that relate the source to station azimuth to account A3- 4 for the radiation patterns of each type of wave equations A2-A4 This setup can be illustrated for two three-component stations by: d1z % ZVF 1 1 1 d r RVF d1t 0 2 2 d z ZVF d 2r RVF 2 2 d t & 0 ZHF 1 cos RHF 1 cos THF 1 sin ZHF 2 cos RHF 2 cos THF 2 sin ZHF 1 sin % RHF 1 sin m Z % THF 1 cos mN ZHF 2 sin m E & RHF 2 sin THF 2 cos & A6 Each dic in Equation A6 is a column vector that contains the seismogram for the station i and component c z vertical r radial and t transverse The left side of Equation A6 is a column vector consisting of all the data displacement seismograms concatenated end to end Each entry in the G matrix is a Green s function convolution matrix indicated by superscript for the Green s function specified by its abbreviation for each station indicated by the superscript Each mj is a column vector containing the force-time function for each component j of force The sines and cosines come from equation A2-A4 For this study as described in the text I downweighted the noisy data based on the inverse of the root mean squared value of the noise before the signal at each component of each station To include this in the inversion I constructed a weighting matrix W W was built by filling the weights in along the diagonal of W organized so that the correct scalar weight value multiplied the entire seismic signal of the corresponding component of each station when W is multiplied with the data vector For example the weight for the vertical component of the first station d1z fills in the diagonal of W from W11 to Wii where i is the length of d1z W weights both the data vector d and the Green s functions matrix G which when weighted are denoted as dw and Gw respectively because the same processing must be done to both sides of the equation For the same reason the individual Green s functions and the seismograms were bandpass A3- 5 filtered identically as well prior to building the matrix G In this study I used a minimum phase causal Butterworth filter but a nearly identical result is obtained when using a zero phase acausal filter because the same filtering is applied to both sides of the equation The next step was to solve the damped least squares problem to invert for m: m GwTGw 2I 1GwTdw A7 where superscript T indicates the transpose I is the identity matrix and is the regularization parameter chosen as the trade-off between keeping the model small while still fitting the data well The matrix setup of the forward problem using data from five seismic stations with three components of motion each becomes very large but the inversion was still manageable: it took less than a minute to run in MATLAB on a desktop computer An additional step I took in this study was to constrain that all components of the single force must add to zero in the end because the total momentum of the earth must remain stable Fukao 1995 This did not significantly change the solution but is more physically correct To constrain this in the solution I added equations to the forward problem by concatenating matrix A a 3x3N matrix where N is the length of the data from one component of one station to the bottom of the Green s function matrix G A was constructed so that the first third of the first row was ones and the rest was zeros so that it multiplied and added up just the z component of m a corresponding zero is added to the bottom of the data vector d to constrain that these forces add to zero The same was done for the next two rows to multiply and add up the north and east components of m to equal zero The A matrix was scaled up to the same magnitude as the weighted Green s functions so that it influenced the final solution A3- 6
    • Dilmen, Derya - Ph.D. Dissertation
      The Role of Coral Reefs on Tsunami Dynamics in an Island Setting: A Case Study of Tutuila Island 2016, Dilmen,Derya,Derya Dilmen Copyright 2016 Derya Itir Dilmen The Role of Corals on Tsunami Dynamics in an Island Setting: A Case Study of Tutuila Island Derya Itir Dilmen A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2016 Reading Committee: Vasily V Titov Chair Gerard H Roe Joanne Bourgeois Program Authorized to Offer Degree: Earth and Space Sciences University of Washington Abstract The Role of Coral Reefs on Tsunami Dynamics in an Island Setting: A Case Study of Tutuila Island Derya Itir Dilmen Chair of the Supervisory Committee: Affiliate Professor Vasily V Titov Earth and Space Sciences On September 29 2009 at 17:48 UTC an Mw 8 1 earthquake in the Tonga Trench generated a tsunami that caused heavy damage across Samoa American Samoa and Tonga One of the worst localities hit was the volcanic island of Tutuila in American Samoa Tutuila Island located 250 km from earthquake epicenter experienced tsunami inundation and strong currents on the north and east coasts causing 34 fatalities and widespread structural and ecological damage The surrounding coral reefs of the island also suffered heavy damage This damage was formally evaluated based on detailed surveys before and immediately after the tsunami which provides a unique opportunity to evaluate the role of coral reefs on tsunami dynamics In the first part of this research estimates of tsunami dynamics are obtained with the MOST numerical tsunami model Titov and Synolakis 1997 which is currently the operational tsunami forecast tool used by the US National Oceanic and Atmospheric Administration NOAA The earthquake source function was constrained using real-time deep-ocean tsunami data from three DART Deep-ocean Assessment and Reporting for Tsunamis systems in the far field and by tide-gauge observations in the near field We compare the numerically estimated run-up with observations to evaluate the simulation skill of MOST We present an overall synthesis of tidegage data survey results of the run up inundation measurements and the datasets of coral damage around the island in order to evaluate the overall accuracy of MOST run-up prediction for Tutuila and the model s performance of simulating in the locations covered with corals during the tsunami event Our primary findings are 1 there is a tendency for MOST to underestimate run-up on Tutuila and 2 the locations where the model underestimates run-up tend to have experienced heavy or very heavy coral damage whereas well-estimated run-up locations characteristically experienced low or very low damage This brought us to the conclusion regarding how coral reefs affect tsunami dynamics through their influence on bathymetry and dissipation Second we focus on numerical simulations of this event to evaluate: 1 how roughness variations affect tsunami run-up and if different values of Manning s roughness n improve the simulated run-up compared to observations and 2 how depth variations in coral reef bathymetry control run-up and inundation on the coastlines they shield We find as a result of the simulations that no single value of n provides the best match to observations and we find large bay-to-bay variations in the impact of varying n The results suggest that there are aspects of tsunami wave dissipation that are not captured by the drag formulation in the MOST model The primary impact of removing coral bathymetry is to reduce run-up from which we conclude that at least in this setting the bathymetric impact of coral reefs is to increase run-up and inundation We conclude that future studies should focus on two key issues for further research: 1 the representation of the turbulent dissipation in terms of the governing equations and their coefficients and 2 detailed numerical experiments on all aspects of reef settings such as reef widths reef types and coastal geometry on the scale of individual bays TABLE OF CONTENTS List of Figures iii List of Tables iv Chapter 1 Introduction 1 1 1 The phenomenon of tsunamis 1 1 2 The generation of tsunamis 2 1 2 1 The three stages of the tsunami 2 1 3 The history of tsunamis 5 1 4 Tools to prevent decrease the damage and loss of lives due to tsunamis 9 1 5 What are the challenges of tsunami modeling 11 1 6 Island settings coral reefs and an outline of the thesis 16 Chapter 2 Evaluation of the relationship between coral damage and tsunami dynamics 19 2 1 Introduction 19 2 2 Tutuila Island 22 2 3 The Samoa event 24 2 4 Observations of the event 25 2 5 Modeling the event 28 2 5 1 The model set-up 28 2 5 2 Choice of the source function 29 2 5 3 Evaluation of the model results with DART and tide gauges 30 i 2 6 Analysis 31 2 7 Summary and discussion 41 Chapter 3 The Role of coral reef roughness and bathymetry on tsunami dynamics case study: 2009 Samoa tsunami 44 3 1 Introduction 44 3 2 Analysis 45 3 2 1 The impact of changing Manning s roughness n 45 3 2 2 Changes in reef bathymetry 52 3 1 Discussion 56 Chapter 4 Concluding remarks 57 Appendix A 65 Appendix B 66 ii LIST OF FIGURES Figure 2 1 Tutuila Island 24 Figure 2 2 Photographs of the coral survey methods and typical observations 26 Figure 2 3 The boundaries of the nested A B and C grids used 29 Figure 2 4 Observed and simulated water surface elevations at the tide gauge 32 Figure 2 5 Observed and simulated water surface elevations at three DART buoys 33 Figure 2 6 Coral damage versus observational run-up 35 Figure 2 7 Two examples comparing observed run- up with MOST run-up 36 Figure 2 8 Maximum wave amplitudes peak currents peak fluxes a nd max stresses 37 Figure 2 9 Scatter plot of simulated versus observed run-up m 39 Figure 2 10 A summary of the comparison between model run-up and coral damage 40 Figure 3 1 A comparison of model and field run- up for the simulations with varying n 47 Figure 3 2 Simulated maximum wave amplitudes near Seetaga and Amaneve 48 Figure 3 3 Comparison of water surface elevations at selected virtual tide gauges 51 Figure 3 4 C grids of synthetic bathymetry 53 Figure 3 5 Simulated max wave amplitudes for Seetaga and Amaneve for different bathymetry 54 Figure 3 6 Comparison of water surface elevations at selected virtual tide gauges in Seetaga and Amaneve 55 Figure A-1 Scatter plots of coral damage 83 iii LIST OF TABLES Table 2 1 Sources compiled by NGDC to create the three nested grids 28 Table 2 2 Parameters of the two tsunami unit source functions S 1 and S2 31 Table 2 3 Simulated and field run-up differences and coral damage at selected villages 33 Table B1 Simulated run-up for different Manning s roughness values at selected villages 84 Table B2 Simulated run-up for different Manning s roughness values at selected villages 85 iv ACKNOWLEDGEMENTS I would like to take this opportunity to extend my thanks to several people without whom this would not have been possible I am grateful to my advisor Vasily Titov He gave me a wonderful opportunity to study in UW Prof Gerard Roe graciously committed his time and energy that helped to complete my research I am very grateful: For his support and his enthusiasm of teaching mentoring and doing science Thank you to my committee members Joanne Bourgeois Randall LeVeque Frank Gonzales and Ahmet Cevdet Yalciner They were always there whenever I looked for mentorship I would like to acknowledge JISAO for providing the funding that supported this research Thanks to NOAA s tsunami research group NOAA Center for Tsunami Research-NCTR: Yong Wei Liujuan Tang Edison Gica Christopher Moore Marie C Eble and Hongqiang Zhou Thanks to my wonderful friends especially to Daria Valchonak and Gulsah Dagkiran Lastly thank you to my family for their patience It has been privilege to study learn and teach science at University of Washington v DEDICATION to my mom vi Chapter 1 INTRODUCTION 1 1 THE PHENOMENON OF TSUNAMIS Tsunamis are among the deadliest natural hazards on Earth They have caused over 400 000 fatalities in the last century ranking them fourth after earthquakes floods and volcanic eruptions NGDC NOAA 2015 The threats we face from tsunamis are 1 direct deaths and injuries 2 structural and ecological damage and 3 the subsequent spread of diseases and harmful chemical substances A tsunami is a long series of low-crested gravity waves often generated by the energy transferred from a seafloor displacement to the ocean The global historical tsunami database of the National Geophysical Data Center1 World Data Source NGDC WDS provides information on over 2 400 tsunamis from 2100 BC to the present in the Pacific Atlantic and Indian oceans and the Mediterranean and Caribbean seas NGDC WDS 2015 of which 75% of those recorded tsunamis occurred due to earthquakes Most large tsunamis are caused by the seafloor displacement due to large shallow earthquakes along subduction zones Less commonly nonsubduction-zone earthquakes landslides volcanic eruptions nuclear explosions meteorite impacts and meteorological events also generate tsunamis Gusiakov 2007 Etymologically the term tsunami comes from Japanese tsu - breaking upon a harbour name -waves These phenomena were called harbor waves because of strong water currents unexpected wave oscillations and damage to harbors were the first signs of an approaching tsunami for far-field events 1 NOAA s National Geophysical Data Center NGDC was recently renamed the National Centers for Environmental Information NCEI the website remains https: www ngdc noaa gov as of August 2016 In this dissertation I refer to the tsunami database source by its more familiar name NGDC 1 An early appearance of the word tsunami in western literature was an article by Eliza Schidmore in National Geographic about the 1896 Sanriku tsunami which killed more than 22 000 people Cartwright & Nakamura 2008 Schidmore 1896 Although always in the minds of shore-dwelling populations in high-risk areas tsunami hazards received a renewed public focus on tsunami hazards came after the devastating Indian Ocean Tsunami of 26 December 2004 which took close to 230 000 lives and injured countless more USGS 2005 Further sobering evidence of the power of tsunamis to wreak destruction was the Great Japan earthquake and tsunami of 11 March 2011 which - even in this tsunami-aware and prepared society claimed nearly 16 000 lives Subsequently tsunami generated flooding caused a nuclear meltdown and radiation leaks at Fukushima which led to the permanent dislocation of a 230 000 people Oskin 2015 1 2 THE GENERATION OF TSUNAMIS A typical tsunami begins with a rupture on a submarine plate-boundary fault which displaces the ocean floor and transmits a dynamic impulse to the water column Gravity acts to restore mean sea level by converting the potential energy of the water displacement into gravity waves These waves radiate the resulting potential energy away from the source of the tsunami and propagate through the ocean till they reach shorelines The size of the tsunami depends on the main parameters that govern the earthquake: the energy release magnitude the source mechanism and depth of the hypocenter the fault rupture velocity and water depth over the source region Earthquakes with large magnitudes greater than 8 in Moment Magnitude Scale and shallow hypocenters 30 km depth in Earth produce the largest tsunamis 2 1 2 1 The Three Stages of the Tsunami There are three major stages associated with a tsunami: generation propagation and runup inundation: During a typical tsunamigenic submarine earthquake a segment of ocean floor is rapidly uplifted and displaces a volume of water some other part of the seafloor may also subside This creates a hump or trough on the ocean surface which is unstable due to the force of gravity The pressure gradient formed due to gravity causes waves to flow sideways generating a train of waves a tsunami Okada 1985 derived the equation for the initial displacement of the ocean surface by computing the static field of vertical deformation on the ocean floor assuming the water is incompressible and the deformation occurs in seconds The model has been widely used in numerical tsunami models to estimate initial tsunami wave amplitudes Once generated tsunami waves can reach coastal areas after traveling hours to days with negligible frictional dissipation in the open ocean Titov 1997 However the wave structure evolves substantially as waves spread out over the bathymetry When an individual tsunami wave approaches a shoreline it transfers some of its kinetic energy into potential energy The waves increase in height The amplified tsunami wave then overruns and inundates the coastline A broad spectrum of wavelengths formed during tsunami generation leads to dispersion of the wave packet during their travel from the source to the coast consequently there can be a prolonged period of repeated shoreline inundation upon the tsunami s arrival at a coastline A typical tsunami wave length 10 km to 200 km is much larger than typical water depths 2-4km in the deep ocean Therefore the propagation of a tsunami can be described accurately by the equations for waves in inviscid shallow-water until the waves approach the shore These equations are derived from depth-integrated Navier-Stokes equations for conservation of mass 3 and linear momentum in a fluid The assumptions of shallow water equations are: the fluid is incompressible constant density the horizontal length scale is much greater than the vertical length scale and the flow is homogeneous Bricker et al 2015 The shallow-water equations describe a thin layer of fluid where water depth h to wave length L ratio is in the order of 10-2 They are subjected to a constant gravitational force bounded by the bottom topography below and by a free surface above In the case of tsunami for shallow-water approximation the waves are assumed to be non-dispersive and to travel with a linear wave speed c of: 1 1 where g is gravity and h is the water depth For deep-ocean conditions where the ocean depth is several kilometers a tsunami wave velocity of around 200 m s is typical Even communities that receive warning may have only minutes or up to a few hours to prepare for trans-oceanic tsunamis to prepare Within a few minutes after generation the tsunami develops into a sequence of long wavelength 10 km to 200 km typical depending on source parameters waves that grow rapidly in height as the tsunami approaches the shore As the waves approach the depth of water decreases causing the tsunami to slow down at a rate proportional to the square root of the water depth Eqn 1 1 Wave shoaling then forces the wave amplitude A to increase at an inverse rate with local undisturbed water depth h governed by Green s law Green 1837 Eqn 1 2 : 1 1 4 1 2 For energetic events the wave height above sea level at the maximum point of inundation or run-up can reach upwards of 40 m as seen in 2011 Great Tohoku Japan Tsunami run-up observations Mori et al 2011 4 When a tsunami finally reaches the shore it may appear as a rising or falling wave a series of breaking waves or a bore The waves return at intervals of several minutes for up to days before finally dissipating The geomorphology of the littoral setting strongly affects the tsunami Submerged features such as reefs bays entrances to rivers and the slope of the beach all act to modify the dynamics of the tsunami as it approaches the shore and these numerous influences make it harder to comprehend and model tsunami wave dynamics on the coast Therefore understanding the inundation run-up stage of tsunami is the main objective of tsunami hazard mitigation 1 3 THE HISTORY OF TSUNAMIS The present version of the National Geophysical Data Center catalog on tsunamis and tsunamilike events covers the period from 2000 BC till present NGDC WDS 2015 The catalog provides insights into tsunami processes of generation propagation and inundation run-up It also helps determine the source of each tsunami with probabilistic and deterministic approaches identify locations that are particularly prone to tsunamis and forecast probable inundation limits by combining the data of tsunami source of the NGDC data with probabilistic analyses or computational models The forecasting results are also crucial to determine wave amplitude thresholds of operational tsunami warnings and thus whether a tsunami warning will be issued According to the NGDC 2008 catalog more than 600 000 people have died due to 2130 individual tsunamigenic events since 2000 BC Whitmore 2009 Ten trans-oceanic tsunamis during the last 250 years are responsible for 49% of those deaths Gusiakov 2007 Of the total 2130 events 1206 occurred in the Pacific Ocean Every tsunami is unique but here I note a few 5 that have had groundbreaking impact on progress in tsunami research based primarily on more extensive review by Okal 2011 : The 1755 Lisbon tsunami remains the deadliest trans-oceanic tsunami in historical times with a death toll approaching 100 000 in Europe NGDC WDS 2015 The effect of this earthquake and tsunami was not only scientific but also was social and political Since all the churches in Lisbon were destroyed on All Saints Day it has been seen as a manifestation of divine judgment Paice 2008 Numerical model case studies of this event have been used to demonstrate that even a minor change in fault source location could significantly affect directionality and focusing resulting in a distinctly different distribution of tsunami wave amplitudes Zahibo et al 2011 The 1896 Meiji Tsunami the first identified tsunami earthquake earthquake whose magnitude is smaller than the magnitude of tsunami created Kanamori 1972 remains the deadliest tsunami in Japan s recorded history The tsunami was much larger than expected from the amplitude of its seismic waves with run-up reaching more than 30 m in the near field up to 5 m in Hawaii and damage reported in California Okal et al 2009 After the 1933 Great Sanriku tsunami buildings were relocated to higher grounds as a first countermeasure against a tsunami Murao 2014 The 1923 Kamchatka tsunami is considered as the first tsunami for which a far-field warning was given even though local authorities of Hawaii did not take it seriously It is an early instance of an insufficient interaction between scientists and decision makers Okal 2011 The 1946 Aleutian Islands tsunami is the first tsunami disaster in US history causing fatalities The tsunami warning center at Honolulu Geomagnetic Observatory was established after this event in 1949 Igarashi et al 2011 6 The 1960 Chile tsunami was generated by the largest earthquake in the historical record Mw 9 5 an estimated moment magnitude of 2-5 x 1030 dyn cm An important lesson learned from this disaster was that the maximum wave during a distant tsunami is rarely the first one The long periods of tsunami waves can give a sense of feeling secure to residents and to authorities even though the worst is yet to come Okal 2011 The 1964 Alaska tsunami led the creation of the Alaska West Coast Tsunami Warning Center in 1967 Sokolowski 1990 It was incidentally recorded on a pressure sensor deployed on the ocean floor about 1000 km far from the earthquake epicenter and which had been installed for an unrelated seafloor magneto-telluric experiment Filloux 1982 This observation led to the development of specifically engineered tsunami pressure detectors coupled with realtime communications creating the Deep Ocean Assessment and Reporting of Tsunami DART Network in 2003 by NOAA for the purpose of forecasting coastal tsunami impacts Bernard & Milburn 1985 The 1992 Nicaragua tsunami: was the first to be systematically surveyed by international teams Synolakis and Okal 2005 Such comprehensive and consistent databases of inundation and run-up continue to be used to test tsunami computational model results This tsunami survey documented substantial values of run-up 4-10 m along a 290 km stretch of coastline Satake et al 1993 which was underestimated by then-standard simulation algorithms that stopped the wave height and current estimations at an imaginary reflective boundary wall at a shallow-water depth of typically 10 m Imamura et al 1993 In the models tsunami waves were as much as one order of magnitude smaller than the surveyed values This led to the introduction of new numerical algorithms for computing run-up and inundation that were able to successfully reproduce the surveyed values of waves penetrating over initially dry land Titov and Synolakis 7 1998 The MOST tsunami code used in this thesis is one of the models developed after this event and this new suite of models have been tested by laboratory and field survey data for different events and scenarios since then For the first time in 1995 during the Colima-Jalisco tsunami in Mexico the withdrawal of the sea in was documented with photographs along the southern end of Tenacatita Beach Borerro et al 1995 The 1998 Papua New Guinea tsunami: The event has been the subject numerous discussions and controversies due to its unexpected tsunami magnitude and unresolved mechanism of the earthquake A moderate magnitude of earthquake triggered a submarine landslide which was the source of a locally catastrophic tsunami raising awareness of this mode of tsunami generation Tappin et al 2008 Education on tsunami risk lessened the loss of lives was the lesson taken from this tsunami 1999 the Vanuatu tsunami Okal 2011 A few months previously the 1998 Papua New Guinea tsunami at Vanuatu had occurred and subsequently villagers at Vanuatu were educated to immediately self-evacuate low-lying areas upon feeling strong earthquake tremors especially if followed by a retreating of sea In 1999 an earthquake struck the Vanuatu Island and the earthquake-triggered tsunami completely destroyed the village However only three residents lost their lives Caminade et al 2000 The 2003 Aleutian islands tsunami: This was the first successful operational use of DART buoys in real time Lautenbacher 2005 The Sumatra-Andaman 2004 tsunami: The deadliest tsunami in recorded history with a death toll close to 275 950 was recorded by USGS 2005 Among its many aspects the following changed the attitude of researchers planners and policy makers on both the technical and 8 operational ways of tsunami risk mitigation Okal 2011 1 communication during the disaster was a failure 2 tsunamis have come to be regarded as a global threat 3 caused an acceleration of a global effort to establish tsunami warning centers 4 funding and research investments from national governments increased to enhance tsunami programs 2011 Great Tohoku Japan tsunami: Lessons from this event: 1 Safer more flood resilient buildings - particularly power plants and evacuation structures - are needed 2 Developing a robust tsunami numerical model for prediction of tsunami impacts is urgent 1 4 TSUNAMI MODELING AS A TOOL TO PREVENT DECREASE THE DAMAGE AND LOSS OF LIVES DUE TO TSUNAMIS After the Great Tohoku Japan tsunami event in 2011 the urgency of developing a robust tsunami numerical model for prediction of tsunami impacts has become obvious and globally accepted As noted in 2003 by Titov et al 2003a A robust tsunami numerical model should provide siteand event-specific maximum wave amplitude information well before the first wave arrives at a threatened community and accurate enough to mitigate tsunami hazard in real time Tools such as direct tsunami measurements as well as post tsunami surveys and geological records of tsunami deposits are used to constrain tsunami sources and dynamics in numerical models Direct tsunami measurements in the aftermath of a tsunami taken with tide gauges and DART - type gauges can assist in validating and analyzing earthquake source characteristics and can be incorporated into numerical tsunami simulations Starting from 1908 analog tide gauges were used to estimate tsunami wave heights in Japan Mofjeld 2009 In the 1960s tide gauges reported wave height information to warning centers and were used to determine whether to issue a tsunami warning or just a tsunami watch Nowadays they work as calibration and comparison tools for the numerical tsunami models However it has been established in 9 numerous studies eg Miller 1972 Rabinovich 1997 that the effects of local resonance within the bays or harbors where tide gauges are located have an observable impact on wave characteristics at the tide gauge limiting their value for predicting run-up Titov 2009 Furthermore the wave period recorded by the tide gauge mostly depends its location rather than on the tsunami source characteristics On the other hand bottom-pressure stations DARTs installed in the open ocean obtain more direct tsunami wave data before tsunamis develop complex dynamics on the continental shelf and the coastal region as well as resonance effects inside bays and harbors Measuring fluctuations in bottom pressure by transferring the data via satellite to shore the latest development DART systems provide open-ocean accurate time series of tsunami water levels for tsunami source analysis Titov 2009 The first wave in an observed tsunami time series is particularly important in any analysis related to the tsunami source This is because it is the least affected by the reflections scattering and wave interference that complicate later waves The timing amplitude period and sign trough or crest wave of this first wave indicate the pattern of vertical ground displacement of the earthquake source Numerical models use the first tsunami waves observed at DART Stations to refine the preliminary tsunami sources by inverting the data back to the source using pre-computed model simulations Post tsunami surveys including the information of the extent of the tsunami inundation maximum wave heights on the coast number of damaging waves transport of debris sediment rock and corals provide a ground truth for remotely sensed data and test cases for numerical models of tsunami inundation Later post tsunami surveys such as damages in corals help fill the gaps in the measurements The refined numerical model results by direct tsunami measurements and post tsunami surveys are shared with tsunami warning centers and their related systems to 10 reduce loss of lives by providing warnings to coastal residents Whitmore 2013 Geological records of tsunami deposits also provide test cases for the inundation modules of the tsunami models Bourgeois 2009 1 5 WHAT ARE THE CHALLENGES TO TSUNAMI MODELING In general the run-up of a tsunami on land will be influenced by a very large number of factors including the earthquake source seismic moment and geometry and its physical environment earthquake depth bathymetry of the source area and the properties of the receiving shoreline above and below sea level topography of the beach presence of bays harbors estuaries etc Other factors can play a role too All large earthquakes can trigger landslide failures which in turn can generate tsunamis with run-up values locally much larger than those of the main earthquake as in Plafker 1997 While the basic equations for numerical analysis of tsunamis have been known for decades development of numerical models for real-time forecasting has taken over 20 years beginning with the 1993 tsunami modeling efforts of Japan Models advanced with benchmarks and validation tools such as the large-scale laboratory experiments analytical methods and DART gauge recordings The models have evolved through a meticulous process Synolakis & Kanoglu 2009 of validation and verification In a series of workshops on long-wave run-up models in the 1990s a number of benchmark tests were suggested comparing numerical solutions to analytical predictions and to certain laboratory measurements Liu Woo & Cho 1998 The detailed history and background of the benchmarks and tests are summarized in Synolakis et al 2008 and in Synolakis and Kanoglu 2009 Tsunami models have been developed with a variety of different numerical methods and of spatial and temporal discretization techniques The vast majority of current tsunami models are 11 based either on the Boussinesq or the non-dispersive shallow water long wave equations derived from depth-integrated Navier-Stokes equations In these models the Navier-Stokes equations are averaged from the seafloor to the free surface and viscous stresses are either neglected or presumed to follow bottom friction laws Depth-averaged Navier-Stokes equations are known as the nonlinear shallow water equations linearizing the nonlinear terms then gives the linear shallow water equations Depth-averaged models that study propagation of tsunami waves in one direction are referred to as 1 1 and similarly 2 1 models refer to two-directional propagation On the coast wetting-drying algorithms of the models predict tsunami run-up and inundation limits When the first advances in numerical tsunami models began in the 1970s in Japan they were concentrated on solving either non-linear 1 1 Boussinesq equations reviewed in Shuto and Fujima 2009 or 2 1 shallow water equations Synolakis and Kanoglu 2009 In 1974 Houston and Garcia 1974 solved a linear form of the spherical long-wave equations in 2 1 form up to the edge of the continental shelf using a finite difference method The same year Hibberd and Peregrine 1974 calculated the evolution of bores over a sloping beach with a shoreline algorithm of non-linear shallow water equations Advances in modeling in the 1990s were stimulated through two landmark scientific meetings: the first one was in Russia in 1989 the other was in California in 1990 Synolakis and Kanoglu 2009 In 1997 Goto and Ogawa proposed a finite-difference method with upwind scheme in Eulerian form of the non-linear shallow water equations During the same time interval at a meeting in Russia Titov and Synolakis 1995 presented the finite difference 2 1 algorithm of VTCS now called MOST which computes far-field tsunami propagation and inundation in a variable spatial grid for weakly dispersive tsunamis MOST has been used 12 operationally by NOAA and also is the model used in this thesis for tsunami run-up and inundation calculations in Tutuila At the 1990 meeting in California the pervasive need for laboratory data to enable further progress in computational models particularly for 2 1 run-up computations found voice The following is a review of tsunami models developed by different research groups: In the early 1990s Prof Imamura of the Disaster Center of Japan has developed the TUNAMI Tohoku University s numerical analysis model for inundation model which estimates tsunami propagation in deep water and inundation on land Imamura 1996 Currently TUNAMI has been accepted by 43 organizations in 22 countries as the numerical code to predict damage of tsunami on coasts It is an open source fully tested model evaluated for most of the historical tsunamis such as 1883 Krakatau Tsunami 1935 North Sumatera Tsunami 1992 Flores Tsunami 1994 East Java Tsunami 1996 Toli-Toli Tsunami 1996 Biak Tsunami 2000 Bangai Tsunami 2004 Aceh Tsunami and 2006 South Java Tsunami and 2011 Great East Japan Tsunami and benchmark problems Yalciner et al 2014 Another numerical model extensively used for tsunami modeling is COMCOT Cornell Multi-grid Coupled Tsunami model Liu Woo & Cho 1998 which is composed of a nested grid system The system dynamically couples up to 12 levels with different grid resolutions to fulfill the need for tsunami simulations at different scales In both TUNAMI and COMCOT models shallow-water equations are used and a flux-conserving algorithm preserves the water mass throughout the computations COMCOT adopts an explicit staggered leap-frog finite difference scheme to solve shallow-water equations in both Spherical and Cartesian coordinates In 2001 the Environmental Assessment and Monitoring Department in France developed CEA DASE The model is certified and fully tested with benchmark tools The code has been 13 also applied for the probable tsunami scenarios in French Polynesia Pacific and Indian oceans and Mediterranean Sea eg Hebert et al 2001 A similar model to CEA DASE UBO-TSUFD was developed by Bologna University Italy in 2003 The non-linear shallow water equations were solved using finite-element and two-step time integration methods The grid type is either triangular elements or a Cartesian coordinate system on a fixed boundary The Coriolis force can be included in this model The model is being applied for the several tsunami scenarios and past tsunami events in Mediterranean Sea and in the Indian Ocean 2004 Sumatra 2006 Java and several scenarios Tinti & Tonini 2013 Titov Tsunami Forecasting 2009 In 2002 the Norwegian Geotechnical Institute ICG Norway developed SKREDP The model is certified and tested with analytical benchmarks The coordinate system is Cartesian Any initial sea-surface deformations prescribed source functions for landslides and earthquakes are inputs of the tsunami source for this model The model has been applied to northeast Atlantic to the Arctic and Indian oceans to Norwegian fjords and the Mediterranean and South China seas as well as to hydropower reservoirs in Norway and the Philippines Harbitz et al 2007 GeoClaw is a recently validated tsunami model developed by R LeVeque s Applied Math group at the University of Washington Gonzales et al 2011 It uses a dynamic mesh refinement for an arbitrary number of nested levels The model uses finite volume Riemann solvers as numerical schemes and 2D 1 rectangular mesh with adaptive refinement as mesh grid type During the calculations individual grid cells are tagged for refinement using a criterion such as wave height thus disturbed water parcels are gradually better resolved The flagged cells at each level are clustered into rectangular boundaries for refinement to the next level The 14 model is also robust in calculating wave dynamics in the presence of bores and steep gradients George & LeVeque 2006 The MOST model is used as an operational real-time tsunami forecasting tool at NOAA for the Pacific Ocean Wei et al 2008 and is the model used in this dissertation Examples of the model s forecasting capability are given and explained well in Wei et al 2008 and Tang et al 2012 MOST has ability to track the shoreline by adding new grid points as a function of time A pre-computed generation propagation database and selection of a linear combination of scenarios that most closely matches the observational data can be used as initial conditions for a site-specific inundation algorithm The database contains 246 model scenarios that cover most active subduction zones around the Pacific It stores all simulations for each solutions of numerical analysis including amplitudes and velocities for each offshore location Titov 2009 From all of these examples it is clear that the validation of numerically computed tsunami run-up against observations gathered in real settings is the key Estimation of tsunami behavior on land is essential for tsunami mitigation and also for designing an optimal community evacuation system along the coast in the event of such a catastrophe Furthermore Synolaks et al 2008 further argues that no testing of a tsunami run-up algorithm in idealized laboratory experiments can ensure robust model performance nor can such testing substitute for field data benchmarking Even though there are significant improvements in terms of the accuracy and speed of forecasting tsunamis it is still a challenge to model them and improvements are desirable One way forward is through careful numerical case studies of well observed events field studies in order to better understand tsunami dynamics and numerical model performance One such casestudy example and the focus of my thesis is the 2009 Samoa earthquake and tsunami 15 1 6 ISLAND SETTINGS CORAL REEFS AND AN OUTLINE OF THE THESIS On 29 September 2009 at 17:48 UTC an Mw 8 1 earthquake occurred along the TongaKermadec Trench A complicated fault rupture outer-rise earthquake produced bottom deformations and resulted in tsunami waves that generated localized run-ups exceeding 17 m on the island of Tutuila Fritz et al 2011 These waves claimed 34 lives on Tutuila out of a total 192 deaths for the event and caused extensive damage around the island The impact of the tsunami on Tutuila was well documented in surveys on tide gauges and on far-field deep water pressure gauges The event has been widely discussed in the literature Annunziato 2012 Beaven et al 2010 Clark et al 2011 Fritz et al 2011 Irish et al 2012 Lay et al 2010 Lynett & Lui 2011 Okal et al 2010 Roeber et al 2010 Thompson et al 2011 Zhou et al 2012 The tsunami was detected by coastal tide gauges and offshore sea-level sensors located in the Pacific Ocean The tectonic setting of the Tonga Trench has produced several tsunamis during the past hundred years Okal 2011 A similar tsunami occurred for example on 26 June 1917 after an earthquake with a magnitude of Mw 8 3 located approximately 100 km south of Samoa Gutenberg & Richter 1936 The 2009 tsunami on Tutuila and environs has become a canonical but challenging case study for numerical tsunami models The island setting the presence of both barrier and fringing reefs and the complicated bathymetry and shoreline geometry are all complicating factors of great interest By studying such an event in great detail we can learn general lessons about island tsunamis and in this tropical case about the role of their surrounding coral structures in the resulting run-up and inundation Chapter 2 of this thesis summarizes the existing literature on the role of corals on tsunami dynamics and describes the often contradictory conclusion these studies have reached Chapter 2 16 also describes my numerical modeling of the earthquake source and the subsequent tsunami using the MOST model already introduced above I describe the Tutuila Island event and the earthquake that created it A feature of particular note for this event was pre- and post-tsunami surveys of the damage to the coral structures surrounding Tutuila The run-up and inundation from this event were also documented in detail at several dozen villages around the perimeter of the island Chapter 2 also describes my numerical modeling of the earthquake source and the subsequent tsunami using the MOST model already introduced above The model results show some skill for simulated run-up variations around the island compared to observations but overall the MOST model underestimates run-up by an average of 40% We find no relationship between modeled dynamical fields and coral damage implying either that there are additional complicating factors that preclude an association or that the coral-damage survey although more detailed than any previous study was nonetheless not comprehensive enough to identify the linkages Chapter 3 of this thesis builds on the numerical simulations presented in Chapter 2 Two key factors in modeling tsunami dynamics are studied in more detail: the magnitude of the surface roughness and the near-shore bathymetry surrounding the island Reducing the roughness coefficient used in the model can improve the overall simulation of run-up for this event but the effect is far from uniform for all villages and for a significant fraction of villages the simulation is actually degraded In analyses of virtual tide gauges from the model output I show interesting resonance effects within individual bays For simulations in which the bathymetry is changed we find the basic results reflect Green s Law - overall reefs create shallower bathymetry and model simulations show a corresponding increase in wave amplitude Varying the bathymetry has a strong effect on wave resonance within the bays I studied 17 Our results point to several research directions that will be necessary for improved simulations of tsunami run-up and inundation In the highly heterogeneous littoral and coastal environments spatial variations in basal roughness will have to be considered and perhaps a mathematical reformulation of the dissipation terms used in tsunami modeling The bulk drag formulae used in MOST and many other tsunami models although possessing the advantages of convenience and simplicity are a crude representation of the highly sheared turbulent flow at these scales and their continued use will necessarily limit the predictive capabilities of such models 18 Chapter 2 EVALUATION OF THE RELATIONSHIP BETWEEN CORAL DAMAGE AND TSUNAMI DYNAMICS 2 1 INTRODUCTION Large tsunamis can wreak devastation upon the near-shore environment There is abundant documentation of the impacts on the subaerial portion of that environment but much less on the impacts on the submarine portion In many tropical settings coral reefs form an important component of the submarine environment being the cornerstone of the local ecosystems as well as shaping the near-shore bathymetry There is thus the potential for two-way interactions between reefs and tsunamis The reef bathymetry influences the tsunami dynamics and tsunami events may cause significant damage to fragile coral structures In this thesis we report on a unique opportunity to document tsunami-related damage and to evaluate whether the damage can be straightforwardly related to particular aspects of the tsunami dynamics On 29 September 2009 at 17:48 UTC an Mw 8 1 earthquake occurred along TongaKermadec Trench A complicated fault rupture produced bottom deformations and resulted in tsunami waves that generated localized run-ups exceeding 17m on the island of Tutuila These waves claimed 34 lives out of total 192 deaths for the event and caused extensive damage around the island The tsunami was detected by coastal tide gauges and offshore sea-level sensors located in Pacific Ocean The tectonic setting of the Tonga Trench has produced several tsunamis during past hundred years Okal et al 2010 Following the September 29 2009 tsunami field surveys were conducted Fritz et al 2011 to document the relationship between the physical near-shore environment and the tsunami impact According to survey results the tsunami produced a maximum run up of 17m at Poloa on the western coast of Tutuila 12m at Fagasa on the northern coast and 10m at Tula on the 19 eastern coast The survey team recorded large variations in the impacts of the tsunami along the coastal bays: a wide range of tsunami run-up wave directions and inundation The high degree of spatial variability in these various tsunami fields was somewhat of a surprise to scientists studying the event Fritz et al 2011 Okal et al 2010 Beaven et al 2010 Roeber et al 2010 but was clearly established in the field surveys and confirmed by residents The impact of this tsunami on Tutuila has proven unusually hard to simulate in numerical models Beaven et al 2010 Okal et al 2010 Roeber et al 2010 Fritz et al 2011 The discrepancies between observations and models have been variously attributed to many factors including the low-resolution bathymetry and topography the possibility of resonance over the coral reefs but most importantly the unusual complexity of the tsunami source mechanism that may have included multiple ruptures of several fault systems at the same time Beaven et al 2010 In this study we also perform a simulation of this event and aim to build upon the experience of these earlier studies: we try to eliminate any bathymetric and topographic discrepancies by using a very high-resolution 10 m dataset Lim et al 2009 further we optimize the tsunami source function by calibrating it with direct tsunami observations Both farfield pressure sensors DARTs and near-field coastal sea-level stations tide gauges were used to calibrate the tsunami source for this event We establish good agreement with the near-field tide gauges Section 3 meaning that it is unlikely that additional details in the source function would impact the simulation One challenge of modeling tsunamis in tropical settings such as this are the pervasive barrier and fringing coral reefs which create tremendous complexity in bathymetry and topography Figure 2 1 The impact of reefs in tsunami dynamics has been a topic of discussion in the literature Such analyses point to a complex picture and conclusions can occasionally appear 20 contradictory Baba et al 2008 performed numerical simulations of the 2007 Solomon Islands Tsunami to explore the effect of Great Barrier Reef GBR on tsunami wave height using the low-resolution bathymetry and ignoring sea-bottom friction and wave dispersion The results indicate reefs decrease the tsunami wave height due to the refraction and reflection Kunkel 2006 performs 1D and 2D numerical modeling of tsunami run-up for an idealized island with barrier reefs around the island and shows that coral reefs reduce tsunami run up by order of 50% However the Kunkel 2006 simulations also suggest the possibility that gaps between adjacent reefs can result in flow amplification and actually increase local wave heights Fernando et al 2005 and Fernando et al 2008 lend support to these numerical results: coral reefs protect coastline behind them but local absences of reefs cause local flow amplification due to gaps Their results are based on field observations laboratory measurements Fernando et al 2008 and interviews done by local people in Sri Lanka after the 2004 Indian Ocean tsunami However their laboratory simulations treated corals as a submerged porous barrier made of a uniform array of rods which likely oversimplifies the complex structural distribution of coral reefs Other studies find no effect or even suggest the opposite conclusions Kunkel et al 2006 Based on quantitative field observations of coral assemblages at less than 2m depth in Aceh after the 2004 Sumatra-Andaman tsunami Baird et al 2008 conclude that the limit of inundation at any particular location is determined by a combination of wave height and coastal topography and is independent of the reef quality or development prior to the tsunami Further Chatenoux et al 2006 perform statistical and observational analysis of 56 sites located in Indonesia Thailand India Sri Lanka and Maldives with a coarse resolution bathymetry and qualitative coral damage data They find that the higher the percentage of the corals the larger the 21 inundation distances behind coral reef on the coast Lastly Roeber et al 2010 identify strong correlations between the high variability of run-up and inundation along bays at Tutuila during the 2009 Samoa tsunami with the geomorphology of the island and suggest a role for high concentrations of resonance energy within particular bays All of these locations of high-energy concentration have fringing reefs extending 100 m to 200 m from the shores Based on their tsunami simulations they hypothesize that fringing reefs might amplify near-shore tsunami energy and worsen the impact of short-period dispersive waves In this chapter wave heights inundation at the coast and tsunami wave dynamics are simulated for the island of Tutuila for the 2009 tsunami The simulations are compared with field observations at the coast and wave pressure gauges DARTs located around Tutuila to find a relationship between coral damage and coastal metrics of tsunami dynamics The results contribute to an ongoing discussion about how tsunami dynamics impact corals and how in turn that damage might potentially be used to constrain tsunami simulations The remainder of the chapter is organized as follows Section 2 describes the study area the earthquake and tsunami event and the observational data sets Section 3 describes the numerical modeling of the earthquake source and the subsequent tsunami Section 4 presents an analysis of the relationships among the observational data sets and simulated tsunami fields We conclude with a Summary and Discussion that suggests an outline for future research directions 2 2 TUTUILA ISLAND The study area of my research is Tutuila Island in American Samoa the United States southernmost territory The Samoa island chain in the central South Pacific Ocean includes five islands of which Tutuila is the largest and also its center of the government It is located at roughly 14 south of the equator between longitudes 169 and 173 west Figure 2 1 The 22 following will summarize some aspects of the geometry of Tutuila Island that created unique challenges in modeling of the tsunami The island formed in the late Quaternary period from oceanic crust as the Pacific tectonic plate moved over a hotspot Terry et al 2005 Due to its volcanic formation it has rocky steep topography and bathymetry with narrow valleys that rise from ocean floor McDougall 1985 The island sits on a shallow submarine platform which then drops off to a depth of over 3000 m to meet the abyssal plain Tutuila is approximately 32 km long with a width that ranges from less than 2 km to a maximum of 9 km An insular shelf 100 m depth with an average width of 4 km extends along the entire north coast and the southwest region of the island Figure 2 1 The island is surrounded by fringing and barrier coral reefs which contain a diversity of coral reef habitats and coral species The island has possibly subsided faster than coral reefs could grow upward leaving former barrier reefs as submerged offshore banks along the seaward edges of the insular shelf Birkeland et al 2007 Fringing reefs have a width ranging from 0 to 600 m but 90% of them are less than 217 m Gelfenbaum et al 2011 The barrier reefs are located 2-3 km from the coastline The total area of coral reefs in the territory of Tutuila is approximately 300 km2 23 800 10km N 30 29 Tide Gauge 31 1 28 27 16 23 22 25 24 26 17 18 19 21 15 20 600 400 200 0 2 3 4 -200 5 6 8 9 11 7 10 12 13 -400 -600 14 -800 -1000 Figure 2 1 Tutuila Island The black lines around the island on main map indicate the fringing coral damage survey track lines The beige and light purple colors show the location of the fringing and barrier reefs The location of Tutuila Island is given as red star on the lower right map The yellow dot on the same map shows the epicenter of the 2009 Samoa Earthquake In the inset panel the location of the DART buoys used in optimizing the earthquake fault source used in the MOST simulations are shown In the main panel the location of the PagoPago Tide gauge in Tutuila is shown as red star 2 3 THE SAMOA EVENT The tsunami from the September 29 2009 earthquake was generated at the most active region of deep seismicity of Tonga Trench and reached the Samoan Island chain approximately 20 minutes later The tsunami caused devastating property damage and loss of life on Tutuila Island because of its close proximity to the epicenter and the high population density on its coasts The cause of the earthquake was the rupture of a normal fault with a moment magnitude of Mw 8 1 in the outer trench-slope at the north end of the trench near the sharp bend to the west 24 followed by two inter-plate ruptures on the nearby subduction zone with moment magnitudes of Mw 7 8 Lay et al 2010 Fault displacements measured by seismic signal Global Positioning System GPS Stations and ocean-bottom pressure sensors Beaven et al 2010 for these three separate faulting events support this picture These fault displacements led to vertical movement of the seafloor and created a complex tsunami source mechanism 2 4 OBSERVATIONS OF THE EVENT This particular tsunami afforded a unique opportunity to systematically evaluate the relationship between tsunami dynamics and coral-reef damage Six months prior to the tsunami NOAA Coral Reef Ecosystem Division CRED -certified divers performed comprehensive surveys of the reefs around Tutuila The survey lines totaled 110 km in length Observers measured the number of live dead and stressed corals sea cucumbers micro-algae crown of thorns and urchins along track lines at the depths of 10-20 m In the immediate aftermath of the tsunami the divers retraced most of the original survey lines They documented clear evidence of fresh damage at depths between 10 and 20 m This depth range was selected because of the location of the fore-reef at these depths which is where the coral population is a maximum Damage at depths shallower than 10 m was not recorded during the survey Brainard et al 2008 The divers operated a tow board of instruments as it was tugged behind a boat at a depth of about 15 m Data taken included direct observations from the diver a downward facing camera and electronic instrumentation including GPS Figure 2 2 The downward-pointed camera recorded the sea bottom habitat It also captured images at 15 s intervals NOAA-PIFSC-CRED unpublished data Selected images of broken and overturned table corals and broken branching corals are presented in Figure 2 2 The survey covered a total of 83 km linear distance within a 5 25 m horizontal zone either side of the track line Divers were careful to try to differentiate between damage directly due to the tsunami itself and land-originating debris entrained into the water Figure 2 2 Photographs of the coral survey methods and typical observations Upper left image shows the NOAA-certified diver surveying a track line with a tow board tugged behind a boat Lower left image shows the instrument suite on tow boards among which are observer data sheet gauges and timers a camera and strobes Upper right shows the table and branching corals that have been overturned lower right shows a table coral that has been broken due to the tsunami Images are taken from NOAA-Marine Debris Division The damage survey report synthesized the direct observations aggregating track-line data into groupings based on 31 nearby villages and reported the total number of damage observations Examples of such summaries are: at Onenoa Village coral damage was low with only one damaged tabulate Acropora sighting was recorded between both divers and at 26 Amaluia Village it consisted of isolated sightings of broken branching species of Pocillopora and Acropora corals Even though the survey is not an absolute measure of coral damage and involves a degree of subjectivity it is nonetheless a useful window onto the impact of tsunami dynamics in the immediate aftermath of the event Since the full coral density of the island is not available variation in coral density might influence the results NOAA-PIFSC-CRED unpublished data The datasets of the damage collected by the divers are discontinuous and unevenly distributed and this precludes classifying the data in terms of damage with conventional methods such as standard deviation or equal intervals Instead we used Jenks Natural Breaks classification method a univariate version of k-means clustering Jenks 1967 by sorting it from lowest value to highest and looking for large gaps or natural breaks This is done by seeking to minimize each class s average deviation from the class mean while maximizing each class s deviation from the means of the other classes In other words the method iteratively seeks to reduce the variance within the same classes and maximize the variance between classes The final classification in terms of coral damage is 0 no damage 1-27 low 38-63 medium 83-159 high 310 very high damage While we felt the Jenks method is most appropriate for this data our overall conclusions are not sensitive to this choice An international tsunami survey team observed and recorded tsunami run-up and inundation on the islands of the Samoan archipelago including Tutuila a week after the tsunami Fritz et al 2011 The surveys followed the tsunami survey protocols reviewed by Synolakis & Okal 2005 The team marked the values of run-up at 59 different field locations at Tutuila 27 2 5 MODELING THE EVENT 2 5 1 The Model Set-up We simulate the 2009 Samoa Event using the MOST Model Titov & Gonzales 1997 The primary metrics for comparison with observations are wave run-up and inundation MOST solves the shallow water equations with a leapfrog finite difference scheme Titov & Synolakis 1998 We define three nested bathymetric and topographic grids The earthquake dislocation is input as the tsunami source several predetermined tsunami sources were tried Zhou Wei & Titov 2012 in order to optimize the agreement with tide-gauge observations Regional bathymetry and topography datasets Table 2 1 were compiled and provided by National Geophysical Data Center NGDC and used to create the three nested grids resolutions of 360 m 60 m and 10 m respectively see Figure 2 3 Table 2 1 Sources compiled by NGDC to create the three nested grids Lim et al 2010 Source of Data Production Date NGDC 1962 to 1998 NGDC NGDC 2009 1996-2005 Gaia GeoAnalytical NAVEOCEANO 2008 SCSC USGS 2002 1996-2006 2006 Data Type Single beam echosounder Digitized coastline Multi-beam Swath Sonar Estimated depths from satellite imagery Bathymetrictopographic data Vector Data NED Digital Elevation Model Horizontal and Vertical Datum Spatial Resolution m 100 30 30-90 WGS-1984 and MHW 5 5 10 30 28 Figure 2 3 The boundaries of the nested A B and C grids used in the MOST simulations 2 5 2 Choice of the Source Function We simulated the 2009 Samoa Tsunami with a tsunami source function f calibrated to direct observations For this event several combinations of source functions f have been developed for use in previous works Zhou et al 2012 Uslu Eble & Wright 2013 and Liujuan Tang personal communication 2009 Earthquakes are modeled as a combination of unit sources S1 S2 S3 and so on Eq 1 1 Each unit source is a reverse thrust of a given strike dip and depth and each has a moment magnitude of 7 5 Gica et al 2008 The parameters for these unit sources were chosen according to the inversion results of the method described in Gica et al 2008 The tsunami source function f is converted into an initial wave height using the elastic model of Okada 1985 Okal et al 2010 This assumes the rupture of rectangular fault planes cause vertical displacements of the sea floor and that the initial water level movement is equal 29 and instantaneous with the corresponding vertical sea-bottom displacement The inversion finds the linear combination of unit sources that best matches the DART buoy data Percival et al 2011 We tested four previously optimized source function f Our choice of source function f was based on optimizing the agreement to the PagoPago tide gauge data Of the source functions we considered that of Uslu Eble & Wright 2013 performed the worst underestimating wave heights by a factor of four The other three sources all performed comparably and performed well: for the first four waves they all matched the tide-gauge wave amplitudes to within about 10% and the timing of crests and troughs to within 20 minutes We confirmed our results were robust to the choice of f by simulating time series of wave-height i e virtual tide gauges Appendix A at a model grid-point west of the island for each of the fs The outlier f for PagoPago remained an outlier and there was close agreement among the other three fs Although our results would be similar for any of these three fs we picked the source function with the best agreement to PagoPago for which 6 45 1 6 21 2 2 3 where the specific parameters of S1 and S2 are given in Table 2 2 2 5 3 Evaluation of the Model Results with DART and Tide Gauges We first compare the tsunami wave amplitudes simulated with MOST to the tide-gauge observations in PagoPago in the near field and three DART Buoys 51425 51426 and 54410 in the far field regions For their locations see Figure 2 1 The simulated amplitudes match fairly well with the recorded values particularly for PagoPago Figure 2 4 and particularly the first half-dozen fluctuations The DART buoys record high-frequency crustal Rayleigh waves in the 30 hour or so ahead of the arrival of the lower frequency tsunami waves Figure 2 5 Because the DART buoys lie farther from the source than Tutuila phase discrepancies are expected to appear which is particularly evident for DART Buoy 52425 Figure 2 5a The discrepancies between the computed and recorded values at the DART buoys are likely also due to a secondary rupture occurred during the earthquake which has been characterized in the model as one instantaneous rupture of the source function f However because of the excellent agreement with the PagoPago tide-gauge observations we are confident these discrepancies are negligible for the purpose of run-up and inundation computations around Tutuila Table 2 2 Parameters of the two tsunami unit source functions S 1 and S2 Eq 2 1 used to simulate the 2009 Samoa tsunami Unit Source 1 Longitude E Latitude S Dip 187 2330 16 2754 9 68 Rake Strike Depth m 182 1 5 00 342 4 6 57 90 2 2 6 187 8776 15 6325 57 06 Mw L km W km Slip m 8 1 100 50 1 Scaling parameter 6 45 6 21 ANALYSIS A comprehensive summary of data and analyses are presented in Table 2 3 We first evaluate whether there is any clear relationship between the two main observational datasets for this event the coral damage and tsunami run up for the 31 village sites From Figure 2 6 it is visually obvious that no such relationship exists r 0 12 Even excluding outliers 13 m run up 100 damage numbers at Vaitogi 5 m run up and 310 damage numbers at Fagatele the data still do not yield a clean story r 0 18 Across a range of run ups between 2 and 8 m coral damage is as likely to be low or very low as it is to be high or very high 31 Figure 2 4 Comparison of observed black and simulated red water surface elevations at the PagoPago tide gauge see Fig 1 in the four hours after the rupture at t 0 17:48:10 UTC on Sep 29th 2009 The MOST model estimated a maximum surface elevation of 2 3m at the tide gauge which agrees well with the recorded value We are obviously constrained by the limitations of the data that is available to analyze but on this basis no clear relationship between observed run-up and coral damage can be inferred It is not known whether this is because of limitations in the coral dataset being only a subsampling of the reef environment whether run-up is not the most relevant metric of tsunami dynamics or whether the occurrence of coral damage is actually driven by many other unknown factors and antecedent conditions 32 Figure 2 5 A comparison of the observed black and simulated red water surface elevations at three DART buoys in the four hours after the rupture at t 0 17:48:10 UTC on Sep 29th 2009 : a Buoy 51425 b Buoy 51426 and c Buoy 54401 High frequency crustal Rayleigh waves are seen ahead of the arrival of the lower-frequency tsunami waves The MOST model estimated maximum surface elevation of 0 05m at selected DART locations Table 2 3 Model simulated and field run-up differences and coral damage at selected 31 villages around Tutuila Longitude Latitude Village Model Run-up m Field Run-up m Run-up difference m Difference % -170 653 -14 259 3 52 4 31 -0 79 -18 33 -170 651 -14 26 3 6 4 08 -0 48 -11 76 -170 653 -14 26 3 9 4 41 -0 51 -11 56 -170 654 -14 259 3 4 3 75 -0 35 -9 33 -170 652 -14 26 3 69 3 59 0 1 2 79 -170 654 -14 258 3 05 2 59 0 46 17 76 3 2 25 0 75 33 33 -170 654 -14 257 AFONO1 AFONO2 Average by Village % Coral Damage Coral Dam numbers -3 05 medium 41 38 43 medium 41 33 Longitude Latitude Village Model Run-up m Field Run-up m Run-up difference m Difference % 3 1 2 16 0 94 43 52 4 2 5 89 -1 69 -28 69 -170 654 -14 258 -170 8 -14 332 -170 82 -14 331 AGUGULU 2 5 6 12 -3 62 -59 15 -170 659 -14 253 AMALAU 2 12 2 93 -0 81 -27 65 -170 658 -14 253 2 13 2 4 -0 27 -11 25 -170 83 -170 796 -14 325 -14 33 AMANAVE ASILII 5 25 6 7 74 6 81 -2 49 -0 81 -14 333 AMALUIA -170 792 AFAO AMAUA -170 623 -14 272 -170 584 -170 583 -14 273 -14 273 -170 585 -14 26 -170 571 -14 271 AUASI AUNU U -170 56 -14 286 -170 636 -14 28 -170 632 -14 281 -170 826 -170 827 -14 307 -14 307 -170 725 -14 288 -170 81 -14 299 AMOULI AOA Average by Village % Coral Damage Coral Dam numbers -59 15 lowmedium high 86 -19 45 no data no data -32 17 -11 89 -32 17 -11 89 high medium 151 -3 53 high no damage 116 low 13 5 2 5 39 -0 19 -3 53 3 2 2 91 0 29 9 97 3 36 3 1 3 38 3 -0 02 0 1 -0 59 3 33 2 2 2 23 -0 03 -1 35 3 08 3 79 -0 71 -18 73 -28 69 9 97 1 37 1 42 0 -18 73 no damage medium 38 -0 47 high 121 -3 36 low 14 -1 35 0 2 14 2 15 -0 01 -0 47 3 3 3 92 -0 62 -15 82 3 2 75 0 25 9 09 FAGAILII 5 15 4 61 5 82 6 24 -0 67 -1 63 -11 51 -26 12 -18 82 no data no data FAGASA 4 2 4 13 0 07 1 69 1 69 no data no data 3 6 39 -3 39 -53 05 3 5 6 79 -3 29 -48 45 -48 71 no damage 0 3 2 5 78 -2 58 -44 64 3 3 4 92 -1 62 -32 93 -32 93 very high 310 AVAIO FAGAMALO -170 81 -14 298 -170 81 -14 299 -170 76 -14 365 -170 611 -170 615 -14 27 -14 267 FAGAIT UA 4 75 5 3 5 2 72 1 25 2 28 35 71 83 82 59 77 no data no data -170 826 -14 329 FAILOLO 2 7 6 54 -3 84 -58 72 -58 72 high 159 -170 787 -14 335 2 65 2 75 -0 1 -3 64 -170 783 -14 336 3 2 0 97 2 23 229 9 67 86 high 83-116 -170 789 -14 336 3 75 4 85 -1 1 -22 68 -170 631 -170 63 -14 253 -14 258 MASEFAU 4 4 4 2 96 4 84 1 04 -0 44 35 14 -9 09 13 02 no data no data -170 606 -14 259 MASAUSI 3 15 2 79 0 36 12 9 12 9 no data -170 806 -14 329 4 2 4 09 0 11 2 69 no data no damage -170 582 -14 252 2 6 2 74 -0 14 -5 11 -170 581 -14 251 2 4 2 51 -0 11 -4 38 -170 834 -14 316 7 6 17 59 -9 99 -56 79 -170 834 -14 315 4 93 10 04 -5 11 -50 9 -170 834 -170 834 -14 316 -14 317 8 8 5 12 99 12 31 -4 99 -3 81 -38 41 -30 95 -170 598 -14 257 SAILELE 2 25 2 95 -0 7 -170 812 -14 325 SEET AGA -170 564 -14 256 -170 564 -14 256 FAGAT ELE LEONE NUA ONENOA POLOA T ULA 2 69 0 -4 75 no damage 0 -44 26 low 24 00 -23 73 -23 73 low 1 -2 11 low 5 -40 87 medium 63 00 5 57 5 69 -0 12 -2 11 3 8 9 52 -5 72 -60 08 3 8 7 62 -3 82 -50 13 34 Longitude Latitude Village Model Run-up m Field Run-up m Run-up difference m Difference % -53 25 -170 564 -14 256 3 24 6 93 -3 69 -170 566 -14 253 3 79 3 79 0 0 -170 815 -170 663 -14 329 -14 288 4 1 8 4 51 3 36 -0 51 -1 56 -11 31 -46 43 UT UMEA VAIT OGI Average by Village % Coral Damage -11 31 low -46 43 high Coral Dam numbers 13 96 Figure 2 6 Coral damage versus observational run-up The y-axis shows coral damage numbers reported by the survey team and the x axis is the average of the run up observations after aggregating the data into 31 separate village locations see Table 2 3 and Figure 2 1 There is no clear relationship between these two datasets We begin by presenting a comparison of the MOST simulations with observations for two representative locations For the first Figure 2 7a in the vicinity of the villages of Amaneve 35 Figure 2 7 Two examples comparing observed run-up with MOST run up and maximum wave height Coastal run up is shown as black bars observed and red bars simulated Colors show contours of maximum wave height simulated by MOST a the villages of Amaneve Failolo and Agugulu locations 4 5 & 6 in Figure 2 1 and Table 2 3 b the village of Utumea West Seetaga and Nua locations 7 8 & 9 in Figure 2 1 and Table 2 3 The survey tracks nearest these villages are also shown color-coded according to the damage scale in Figure 2 10 Failolo and Agugulu 4 5 and 6 in Figure 2 1 observed run up averaged 8 m The MOST model does poorly underestimating the run up by an average of 45% This was a region where high coral damage was documented For the second Figure 2 7 b near the villages of Utumea West Nua and Seetaga 7 8 and 9 in Figure 2 1 average run up was 4 m Here the MOST model does well simulating run up to within 2 4% The documented coral damage was very low Even though these two locations are only 3 km apart these very different run ups coral damage and simulation performance illustrate the complexities of the setting Figure 2 8 shows some of the dynamical fields simulated by MOST for this event: maximum wave amplitude panel a maximum current panel b maximum momentum flux 36 panel c and peak stress panel d respectively together with the coral damage along the survey tracks From a visual analysis there are not obvious strong relationships between coral damage and tsunami dynamical fields Take just two examples Leone and Fagatele 13 and 14 in Figure 2 1 : at Fagatele the maximum flux current and maximum amplitudes are low but coral damage is very high In contrast at Leone the maximum flux is high with low maximum amplitudes and currents and high coral damage Figure 2 8 Maximum wave amplitudes peak currents peak momentum fluxes and maximum stresses calculated from the MOST simulation of the 2009 Tutuila tsunami Also shown are the post-tsunami survey tracks with coral damage according to the color scale in Figure 2 10 The absence of a statistically significant relationship between the modeled tsunami fields and the observed damage is confirmed by averaging MOST output along each survey track and creating scatter plots of observed damage vs track-averaged model output for several relevant model fields see Appendix A 37 The clearest basis that we identify for comparing the observations and the model is the observed coral damage and run-up and the simulated run up at each of the 31 sites where observations were made Table 2 3 compiles the complete results from all the available observations We have aggregated the observed and computed run-up values into reports at 31 villages by taking the mean of the total data points at every village The complete data set for the whole island is presented graphically in Figure 2 9 and in Figure 2 10 A scatterplot of simulated vs observed run up correlates at r 0 78 demonstrating significant overall skill for the MOST model Figure 2 9 Despite this success it is also clear MOST underestimates in many places Of the 31 total villages there are 15 for which MOST underestimates run up by more than 10 percent Figure 10 shows the bulk of these are on the west side of the island although not exclusively so At only 5 villages was the run-up overestimated by more than 10% Therefore at the remaining 11 villages the model simulated the observed run up to within 10% Thus while the nearby tide-gauge observations are well simulated by MOST Figure 2 9 there is an overall tendency for MOST to underestimate run-up for this event Turning to the coral damage reports for these villages the data is suggestive of a general relationship with the accuracy of the run-up simulations Table 2 3 Of the 15 villages where the model under-estimated the run up the breakdown in terms of coral damage is 8 very high high 4 medium 3 low very low 1 no damage 1 no data For 11 villages where the model estimates run up well the coral-damage is 2 very high high 1 medium 3 low very low 4 no damage 1 no data 38 Figure 2 9 Scatter plot of simulated versus observed run-up m The blue line shows the 1to-1 line The simulated vs observed run up is correlated at r 0 78 Pearson product-moment calculation coefficient but MOST underestimates run up at many places For the 5 villages where run-up is overestimated limited coral-damage data precludes strong interpretation 1 high 1 medium 3 no data We expected to see a relationship between coral damage and tsunami dynamics since damage is directly relevant with tsunami energy and this with the dynamics of waves 39 Figure 2 10 A summary of the comparison between model run-up skill and coral damage where Rectangles indicate the difference between modeled and observed run ups The filled dots indicate the coral damage reports using the qualitative classification described in the text Lines are the color-coded survey track-lines followed to estimate the damage on corals See also Table 2 3 40 2 7 SUMMARY AND DISCUSSION Focusing on the impact of the 2009 Samoa tsunami on Tutuila Island we conducted numerical model simulations of tsunami run-up and inundation at the coastal zones We performed an integrated analysis to evaluate the relationship between the tsunami hydrodynamics and the coral damage by using numerical modeling and post-tsunami surveys The results for 31 villages on Tutuila island suggest that while the numerical model simulates run-up with a high correlation to the observations there is also a tendency to underestimate run-up in regions of high or very high coral damage and that run-up tends to be better estimated in locations where coral damage is low The dataset synthesized in Table 2 3 is a preliminary assessment of the damage to the fringing reef coral Although the 2009 Tutuila tsunami was a one-of-a-kind opportunity to investigate coral damage and tsunami dynamics the data has some limitations In particular the damage assessments inevitably involve a degree of subjectivity and the damage reports have not been normalized to the background coral density Moreover the data covers only the east and west side of Tutuila due to the bad weather conditions that existed on the south and north side of the island during the surveys In the present setting of Tutuila island the variable simulated run-up differences in our highresolution tsunami model might be due to sharp changes in bottom roughness values caused by coral reefs One expects that in reality there are strong spatial variations in roughness values Nunes et al 2008 However a constant roughness value was defined in the MOST simulations To our knowledge this is a limitation shared by most current tsunami models A model sensitivity analysis simulating the effect of varying the depths where coral reefs exist may better elucidate their role in controlling run-up on the coastlines they shield 41 While we have found some intriguing relationships between tsunami dynamics and coral damage at least in the spatial variations in the skill of the numerical simulations it is clear these are only tentative gleanings amid a great deal of variability We did not find any clear relationships between coral damage and other simulated dynamical tsunami fields Such relationships might be drawn out in more targeted and more detailed simulations but the real situation is obviously very complicated at small scales and many factors operate The failure to establish a stronger connection between the simulated dynamical tsunami fields and coral damage may be because the coral-damage dataset was not comprehensive enough or because the MOST model does not represent the correct spatial scales in roughness or bathymetry or the MOST model does not represent the processes that actually cause damage for instance damage may be inflicted on corals by retreating waves carrying debris and sand or because coral damage is inherently stochastic and unpredictable and depends unknowably on antecedent conditions Since so little is known about the damage to coral reefs by tsunamis more studies are needed to examine the influence of water depth three-dimensional effects wave-wave interactions and coral strengths In some ways it is discouraging to find no correlation between the run-up and coral datasets On the other hand it is important to establish that result and it also points to new questions The documentation of the submarine ecological impacts of a tsunami is an important goal in its own right but the tentative inference from our study the first of its kind is that the relationship of coral damage to a variety of tsunami metrics i e observed run-up and inundation modeled maximum currents fluxes and stress is not a simple one at least in our setting Tutuila represented a target of opportunity since the all-important pre-tsunami survey existed Therefore understanding in more detail the impact of two important controls: magnitude of the 42 roughness and the near-shore bathymetry is the research subject of the following chapter in understanding impact of reefs on tsunami run-up and inundation results 43 Chapter 3 THE ROLE OF CORAL REEF ROUGHNESS AND BATHYMETRY ON TSUNAMI DYNAMICS CASE STUDY: 2009 SAMOA TSUNAMI 3 1 INTRODUCTION It has proven difficult for numerical simulations of 29 September 2009 Samoa tsunami event to successfully reproduce the large variations in tsunami run-up and inundation among the many coastal villages where observations were made One challenge for numerical tsunami models in tropical settings such as this is to properly simulate the impact of the pervasive barrier and fringing coral reefs Figure 2 1 In many respects the 2009 Samoa tsunami serves as a benchmark event for tsunami numerical modeling experts to test their models in a complex submarine environment and to better understand tsunami risks for island communities like Tutuila around the world In Chapter 2 of this dissertation we showed that numerical simulations had some predictive skill but overall the model tended to underestimate run-up by about 40% we also showed that there was a high degree of variability in simulated run-up even among adjacent bays The work further suggested that understanding in more detail the impact of two important controls roughness and bathymetry would be a useful next step in understanding the impact of reefs on tsunami dynamics In this chapter we investigate the effects of reef roughness and reef bathymetry on Tutuila Island We focus on two main goals: firstly we want to understand how roughness variations affect run-up and inundation secondly we perform a model sensitivity analysis varying the bathymetry where fringing coral reefs exist to elucidate their role in controlling run-up on the coastlines they shield 44 The remainder of the chapter is organized as follows: Section 2 presents the analyses of this chapter Section 3 is the summary and discussion 3 2 ANALYSIS 3 2 1 The Impact of Changing Manning s Roughness n In the MOST numerical model the effects of bottom friction are implemented by incorporating a basal shear stress with components into the shallow water equation and parameterized by a drag formula: 2 2 3 1 where U V are the components of the velocities D is the fluid depth is density Titov et al 2003 CB is a dimensionless friction coefficient which can in turn be related to Manning s roughness parameter n as: 2 1 3 3 2 The concept of Manning s roughness was originally developed for open channel flow Manning s n values have been measured empirically for a wide variety of different materials in laboratory experiments Chow 1959 and by large-scale field studies of river flow for fully turbulent conditions Bricker et al 2015 From Eq 3 1 is depth-dependent with increasing depth implying decreased friction For example for n 0 025 s m-1 3 CB 0 006 for D 1 m but CB 0 0025 for D 15 m Bottom friction typically has the greatest impact at depths of 0 10 m and is negligible for tsunami propagation in the deep ocean Levin & Mikhail 2016 The simple form of n and its relatively straightforward implementation within shallow-water equations has led to its 45 widespread adoption in tsunami modeling Imamura et al 2008 for the representation of frictional dissipation of tsunami energy in coastal zones for both the submerged and subaerial portions of the domain In many studies a value of n 0 025 s m-1 3 has been adopted as appropriate for a smooth sea bottom or land A range of other values has also been suggested from n 0 01 to 0 1 s m-1 3 depending on the setting and basal conditions Kunkel et al 2006 Tang et al 2009 Jaffe et al 2010 Gelfenbaum G et al 2011 and Bricker et al 2015 In Chapter 2 of this thesis we selected n 0 03 s m-1 3 Both far-field pressure sensors DARTs and near-field coastal sea-level stations tide gauges were used to calibrate the tsunami source for this event Simulated wave amplitudes matched well with tide-gauge observations However the comparison of simulated and observed run-up for 31 villages in Tutuila revealed that MOST underestimates the run-up at 15 village sites for this event In this part of the research we first evaluate whether a different value of n can decrease the discrepancy between simulated and observed run-up at selected 31 villages For some villages several separate run-up observations were made For such villages we took the average of all run-up observations In the MOST model we took the highest value of computed run-up within a 3x3 grid box 30 m x 30 m around the locations of each of the observations and averaged them We also tried taking the highest value of computed run-up around the locations of all observations and compared this value with the highest value of the run-up observations at that village Finally we tried taking the value of computed run-up at the exact locations where we have run-up observations without averaging them and concluded that our results are not sensitive to which of these various methods we use for selection of simulated run-up We performed MOST simulations varying n from 0 01 to 0 1 s m-1 3 where the lowest n value represents an essentially smooth reef For n 0 01 s m-1 3 although the simulations could be 46 completed the MOST model exhibited clear signs of numerical instability in the simulations gridpoint noise and unphysical wave heights and therefore we do not present those results In Figure 3 1 we present the remaining simulations for varying n as a scatterplot of observed vs simulated run up at 31 villages around Tutuila Locations of the villages are shown in Figure 2 1 A comprehensive summary of data and analyses is presented at Table A1 Figure 3 1 A comparison of model and field run-up for the simulations with varying n at 31 villages in Tutuila Island The blue line shows the 1:1 line Points falling on or close to the blue line show where there is good agreement between simulations and observations Overall for most of the villages the variation of run up with n is straightforward with higher values of n having less run-up For some villages however the relationship is not monotonic and the highest simulated run-up does not always occur for the lowest value of n Thus at individual locations the complex patterns of refraction and reflection and nonlinear interactions can complicate the relationship between dissipation and run-up This is also clear 47 from the different spread among the simulated run-ups for different values of n at individual villages At some villages there is very little spread in simulated run-up values as n varies e g Fagatele village observed run-up 4 92 m the spread is 4% of the mean simulated value whereas at others the spread is large e g Poloa village observed run-up 13 5 m the spread is 76% of the mean simulated value 1km 1km Figure 3 2 Simulated maximum wave amplitudes are shown for the bays near the villages of Seetaga top panels and Amaneve lower panels for n 0 08 0 04 0 02 and 0 015 s m-1 3 The pre-tsunami shoreline is shown as a thin black line Colors inland of that line therefore show the degree of inundation Village locations are shown as red stars Black arrows indicate tsunami direction from its source 48 The results are mixed with regard to whether different values of n improve the simulated run up compared to observations The model estimation of run-up is improved by changing n for some villages and doesn t change significantly at others Of the total 31 villages at 10 villages the difference between observed and estimated run-up is smallest when n 0 02 s m-1 3 At 9 villages the closest match occurs for n 0 03 s m1 3 At 5 villages the closest match occurs for n 0 015 s m-1 3 For the remaining 6 villages two villages each achieve the closest match to observations when n 0 04 s m-1 3 n 0 06 s m-1 3 and n 0 08 s m-1 3 In our simulations n is uniform throughout the model domain which obviously does not capture the real situation of a heterogeneous littoral and coastal environment Equations 3 1 and 3 2 represent dissipation in these environments An obvious next step in tsunami modeling is to evaluate whether variations in basal conditions might be represented by spatial variability in n Introducing spatial variations in n would add tunable degrees of freedom in the model and in practical applications it would be important not to over-constrain a model Nonetheless evaluating whether spatial variations in n might be optimized to provide agreement with detailed measurements in case studies such as ours would represent a best-case for the ability of equations to simulate run-up in these events Next we evaluate the spatial patterns of the maximum tsunami amplitudes for two representative villages Seetaga and Amaneve as a function of n In Chapter 2 we showed that for standard parameters n 0 03 s m-1 3 MOST successfully simulated the run-up observations at Seetaga agreeing to within 2 4% On the other hand just 3 km southeast from Seetaga MOST did a relatively poor job for the village of Amaneve MOST underestimated observed run-up by 45% This very different simulation performance illustrates the complexities of the setting and thus 49 makes Seetaga and Amaneve suitable to use for the comparison of case studies for change in n and reef bathymetry The simulated maximum wave amplitude fields are shown in Figure 3 2a-d for Seetaga and in Figure 3 2e-f for Amaneve For Seetaga n 0 03 s m-1 3 provides the best agreement in run-up 5 69 m observed 5 57 m MOST whereas for Amaneve n 0 02 s m-1 3 gives closest agreement 7 74 m observed 6 32 m MOST For higher values of n the wave amplitude fields vary smoothly on scales of a few hundred meters with the highest values of run-up are found in the center of both bays suggesting a refraction or focusing of wave energy there As n is reduced from 0 04 to 0 02 s m-1 3 some significant localized increases in wave amplitude and inundation appear particularly in Amaneve bay where wave amplitude approaches double that of the n 0 08 s m-1 3 simulations For n 0 015 s m-1 3 wave amplitudes have increase throughout each bay and the increases are clearly co-located with the clusters of near-surface reef structures that are dotted around the perimeter of each bay and which can be seen in detail in Figure 3 3a and Figure 3 3c Figure 3 2 also shows evidence that lower values of n have some impact offshore with a more complex wave pattern and more small-scale structure perhaps indicating more scattering of wave energy and a cascade to smaller scales We next turn to a comparison of water surface elevations estimated for shallow-water virtual tide gauges near the coasts of Seetaga and Amaneve for varying n Figure 3 3b-d At these villages the wave amplitude maximizes during the first surge For the Seetaga tide gauge the maximum water elevations are 3 1 3 2 and 3 3 m for n 0 08 0 04 and 0 02 m s-1 3 respectively Figure 3 3b At Amaneve the maximum water elevations are 3 1 3 4 and 3 9 m for n 0 08 0 04 and 0 02 m s-1 3 respectively Figure 3 3d The various values of n do not affect the timing of the waves and have most impact on the amplitude of the first wave 50 Both Seetaga and Amaneve tide gauges show some evidence of resonance or constructive interference between approaching and receding waves Figure 3 3 We generally expect successive wave heights to decrease in amplitude after several waves but at both sites wave elevations increase between the fourth and sixth waves then decrease again after the seventh wave At the tide gauge close to Seetaga after the third wave approaching and reflecting waves from the reefs interfere and form constructive superposed waves Another intriguing thing to see at the Amaneve virtual tide gauge is that the tsunami waves drop off in amplitude more quickly than at Seetaga and have a less sinusoidal form By 1 5 hr after the first waves the tsunami has become a distorted noisy wave-train This behavior indicates more nonlinearity and more overall dissipation compared to Seetaga perhaps because of the more complicated reef structures within the bay that cause the waves to be dispersed in the reef areas Figure 3 3a compared with Figure 3 3c Figure 3 3 Comparison of water surface elevations at selected virtual tide gauges in the near-shore regions of villages of Seetaga Fig a-b and Amaneve Fig c-d Maps show the location of the 51 villages as red stars and the locations of the virtual tide gauges are shown as blue square In b and d water surface elevations are given for varying n during the 4 h after the fault rupture at t 0 3 2 2 Changes in Reef Bathymetry In this section we evaluate how variations in coral reef bathymetry affect the tsunami run-up and inundation limits inside the bays at the 31 villages around Tutuila We generate synthetic bathymetries for the B and C grids by first removing all bathymetry with less than 90 m depth i e bathymetry in the range 0 to 90 m is set equal to 90 m Let be the real bathymetry and let be the extreme flattened bathymetry We performed several experiments varying the bathymetry smoothly between these limits using the parameter r in the following equation: 1 3 3 Thus r 1 corresponds to the real bathymetry and r 0 to the flattened bathymetry We varied r from 0 to 1 in increments of 0 2 The resulting bathymetries are shown in Figure 3 4 In all simulations a value of Manning s roughness of n 0 03 m s-1 3 has been implemented We first focus on maximum wave amplitudes in the MOST simulations with these varying bathymetries implemented The wave-amplitude fields near Seetaga and Amaneve are shown in Figure 3 5 and the results for simulated run-up for villages around Tutuila are given in Table A2 In general we find that wave amplitudes and run-up are smaller when the reef bathymetry is removed contrary to the common belief that reefs protect reef-surrounded coasts from tsunamis Baba et al 2008 Kunkel et al 2006 When there is no reef r 0 the tsunami run-up achieves its lowest value at 22 out of the 31 villages For the remaining 9 villages 4 villages achieve the smallest run- 52 up when r 0 2 2 villages achieve the smallest run-up when r 0 4 and 3 villages achieve the smallest run-up when r 0 6 Table A2 Figure 3 4 C grids of synthetic bathymetry generated from Eqn 3 shown for the west side of Tutuila Island r 1 original bathymetry r 0 no reefs from 0 m to 90 m depths The same basic behavior is observed in the maximum wave amplitude fields near Seetaga and Amaneve Figure 3 5 Wave amplitudes are larger for the real reef bathymetry than for the flattened bathymetry The MOST model estimates the maximum water surface elevations at Seetaga village as 3 2 2 2 and 2 1 m for r 1 0 0 8 and r 0 0 respectively At Amaneve the maximum water surface elevations at the tide gauge are 3 4 2 8 2 1 m for r 1 0 0 8 and 0 0 respectively These simulations are most simply explained as a manifestation of Green s Law wave amplitudes increase when reefs are present because of the shoreward-shoaling bathymetry and the extra dissipation occurring over the shallower depths is not enough to offset this basic tendency When the reefs are removed the impinging tsunami waves encounter more of a wall and are 53 predominantly reflected rather than dissipated The inundation limits can be seen in Figure 3 5 from the color shading that lies inland of the pre-tsunami shoreline It is interesting to note that the inundation limits are not a strong function of the offshore bathymetry despite the very large variations we ve implemented It suggests that inundation is determined more by the coastal geometry than the tsunami wave dynamics in these bays 1km 1km Figure 3 5 Simulated maximum wave amplitudes are shown for the bays near the villages of Seetaga top panels and Amaneve bottom panel for different bathymetry r 0 0 0 4 0 8 and 1 0 The pre-tsunami shoreline is shown as a thin black line Colors inland of that line therefore show the degree of inundation Village locations are shown as red stars Black arrows indicate tsunami direction We also present simulated wave heights calculated at the same virtual tide gauges near Seetaga and Amaneve villages Figure 3 6 In contrast to the results for varying n changing the 54 bathymetry has a big impact on the wave dynamics recorded at the tide gauges As the bathymetry is progressively removed 0 the first waves arrive 5 to 10 minutes earlier and the period of successive waves gets shorter consistent with faster velocities in deeper water Figure 3 6 Comparison of water surface elevations at selected virtual tide gauges in the near-shore regions of villages of Seetaga and Amaneve Refer to Figure 3 3 for location of gauges Water surface elevations are given for varying r in the 4 h after the fault rupture at t 0 17:48:10 UTC on Sep 29th 2009 A notable feature of the simulations is that varying the bathymetry has a big impact on the wave resonance that was observed to be particularly prominent in Seetaga bay Figure 3 5a As the bathymetry is progressively removed 0 the increase in amplitude of waves 4 to 7 seen in Seetaga Bay diminishes and eventually disappears Obviously then the bathymetry is playing an 55 important role in the constructive interference of reflected and incident waves As the bathymetry is progressively removed the first waves arrive earlier and the period of successive waves gets longer consistent with faster velocities in deeper water The dataset synthesized in Table A1 and A2 are summaries of the model results In a related study Roeber et al 2010 showed the shortening of wave period by comparing their model results with the reef distribution around the island In locations of observed higher runup i e Poloa Fagasa Tula and Pago Pago the reefs extend from 0 m to at least 100 m from the shore The reefs capture the tsunami waves and their energy and form wave resonances around the Tutuila Island Wave resonances formed inside the bay cause increase in wave run-up on the coast The reefs trap the tsunami energy and worsen the impact of short period waves Roeber et al 2010 3 1 DISCUSSION The impact of the 2009 Samoa tsunami dynamics on the coral reefs of Tutuila island has been the main focus of this study We conducted numerical model simulations of tsunami run-up and inundation at the coastal zones for varying Manning roughness n and reef bathymetry For 31 villages on Tutuila island there is an overall tendency that when n decreases in the model the estimated run-up values increase However the results are mixed with regard to whether different values of n improve the simulated run up compared to observations: the model estimation of run-up is improved by changing n in the model at some villages and doesn t change significantly at others 56 Manning roughness n was spatially uniform in the simulations Although this is standard practice in most current tsunami models arguably such an approximation is only valid at large scales and cannot capture the real situation of a heterogeneous reef environment An important frontier in tsunami modeling research is whether in pursuit of more accurate predictions models should incorporate spatially varying n or whether the mathematical representation of the dissipation Eqns 1 and 2 must be reformulated When we remove reefs the modelled run-up values on the coast decrease consistent with Green s law A notable feature of the simulations is that varying the bathymetry has a big impact on the wave resonance that was observed The bathymetry is playing a significant role in the constructive interference of reflected and incident waves Inundation was not strongly impacted by varying the bathymetry which suggests it is determined more by the coastal geometry than the tsunami wave dynamics Rather than focusing on individual structures we focused on reef bathymetry broadly around the island and to some degree our results must depend on the proximity of the reefs to the shore Broader reefs further from shore for instance might dissipate wave energy enough to reduce onshore run up Given the degree of complexity we found in simulations it would for instance be hazardous to conclude that reefs provide universal protection for their inshore coastlines Chapter 4 CONCLUDING REMARKS This study is the first attempt to quantify the relation between corals tsunami run-up and tsunami dynamics The role of reefs in tsunami dynamics remains enigmatic Our results add to a body of literature exploring the important question: What is the role of reefs on tsunami dynamics for an island setting The second chapter concludes that non-linear shallow water models have a 57 tendency to underestimate run-up in regions of high or very high coral damage and that run-up tends to be better estimated in locations where coral damage is low No clear relationship has been observed between coral damage and tsunami dynamics with the existing coral damage data of 2009 Samoa Tsunami In Chapter 3 at the first set of our experiments for 31 villages on Tutuila island there is an overall tendency that when n decreases in the model the estimated run-up values increase However the model estimation of run-up is improved by changing n in the model at some villages and doesn t change significantly at others Variation of Manning s n does not change the accuracy of run-up In the second set of experiments we removed reef bathymetry and found that run-up decreases with removing the reef bathymetry Rather than focusing on individual structures we focused on reef bathymetry broadly around the island and to some degree our results must depend on the proximity of the reefs to the shore Broader reefs further from shore for instance might dissipate wave energy enough to reduce onshore run up Given the degree of complexity we found in simulations it would for instance be hazardous to conclude that reefs provide universal protection for their inshore coastlines We also found that the geometry of the bays is a more important factor than the bathymetry on determining the limits on inundation To conclude while the impact of coral reefs on the dynamics of tsunamis impinging on tropical islands is obviously complicated and depends on many factors our results reinforce a focus on two key issues that call for further 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2-12 Liu P L Woo F & Cho Y S 1998 Computer Programs for Tsunami Propagation and Inundation Cornell University New York: Cornell University Lynett P & Lui P 2011 Numerical Simulation of Complex Tsunami Behavior Comput Sci Eng 13 50 50-57 McDougall I 1985 Age and Evolution of the Volcanoes of Tutuila American Samoa Pacific Science 39 4 311-320 Miller G R 1972 Relative Spectra of Tsunamis Hawaii Inst of Geophys 72 8 7-10 Mofjeld H 2009 Tsunami Measurements In E Bernard & A R Robinson Eds The Sea Tsunamis Vol 15 pp 201-235 Cambridge USA: Harvard University Press Mori N Takahashi T Yasuda T & Yanagisawa H 2011 Survey of 2011 Tohoku Earthquake Tsunami Inundation and Run-up Geophysical Research letters 38 1-10 Murao O 2014 Recovery After Sanriku Tsunamis in 1896 and 1933 and Transition of Housing Location Before the 2011 Great East Japan Earthquake and Tsunami In O Murao R Shaw & T Izumi Eds Tohoku Recovery pp 93-105 Tohoku Japan: Springer NGDC NOAA 2015 May 1 NGDC NOAA Natural Hazards NOAA Producer Retrieved from https: www ngdc noaa gov hazard NGDC WDS N G 2015 June 1 National Geophysical Data Center World Data Service NGDC WDS Retrieved from http: www ngdc noaa gov docucomp page xml NOAA NESDIS NGDC MGG Hazards iso xml G02151 xml&view getDataView&header none NTHMP N T n d Proceedings and Results of the 2011 NTHMP Model Benchmarking Workshop Proceedings and Results of the 2011 NTHMP Model Benchmarking Workshop 436 Boulder: US Department of Commerce NOAA NTHMP Nunes V & Pawlak G 2008 Observations of Bed Roughness of a Coral Reef Journal of Coastal Research 24 2B 39-50 Okada Y 1985 Surface Deformation Due to Shear and Tensile Faults in a Half-Space Bull Seism Soc Am 75 1135-1154 Okal E 2011 Tsunamigenic Earthquakes: Past and Present Milestones Pure and Applied Geophysics 168 969-995 Okal E Fritz H Synolakis C E Borrero J C Weiss R Patrick L J Chan I 2010 Field Survey of the Samoa Tsunami of 29 September 2009 Seismological Reserch Letters 81 4 577-591 Okal E Synolakis C E Uslu B Kalligeris N & Voukouvalas E 2009 The 1956 Earthquake and Tsunami in Amorgos Greece Geophysical Journal international 178 3 1533-1554 Oskin B 2015 May 7 Livescience Retrieved 7 1 2016 from http: www livescience com 39110-japan-2011-earthquake-tsunami- facts html Paice E 2008 Wrath of God: The Great Lisbon Earthquake of 1755 London: Quercus 62 Percival D B Denbo D W Eble M Edison G Motfjeld H & Spillane M C 2011 Extraction of Tsunami Source Coefficients Via Inversion of DART Buoy Data Natural Hazards 58 1 567-590 Plafker G 1997 Catastrophic Tsunami Generated by Submarine Slides and Backarc Thrusting During the 1992 Earthquake on Eastern Flores 1 Indonesia Geol Soc Am Cordill Sect 29 57-67 Rabinovich A B 1997 Spectral Analysis of Tsunami Waves: Seperation of Source and Topography Effects Journal of Geophysical Research 102 C6 12663-12676 Roeber V Yamazaki Y & Cheung K F 2010 Resonance and impact of the 2009 Samoa Tsunami Around Tutuila American Samoa Geophysical Research Letters 37 21 21604 Satake K 1994 Mechanism of the 1992 Nicaragua Tsunami Earthquake Geophysical Research Letters 21 4 2519-2522 Schidmore E 1896 9 1 National Geographic Magazine Retrieved from http: ngm nationalgeographic com 1896 09 japan-tsunami scidmore-text Shuto N & Fujima K 2009 A Short History of Tsunami Research and Countermeasures in Japan Proceedings of the Japan Academy Series B 85 5 267-275 Sokolowski 1990 The Alaska Warning Center NOAA Technical Memorandum NWS AR-38 Alaska: National Weather Service Stokes G G 1845 On the Theories of the Internal Friction of Fluids in Motion and of the Equilibrium and Motion of Elastic Solids Cambridge Philosophical Transactions 8 3 287-305 Sutherland J & O Donoghue T 1998a Wave Phase Shift at Coastal Structures Journal of Waterway Port Coastal and Ocean Engineering 124 90-98 Synolakis C E & Okal E A 2005 1992-2002 Perspective on a Decade of Post Tsunami Surveys Advances in Natural and Technological Hazards Research 23 1-29 Synolakis C E Bernard E N Titov V V Kanoglu U & Gonzales F I 2008 Validation and Verification of Tsunami Numerical Models Pure and Applied Geophysics 165 11 2197-2228 Synolakis C & Kanoglu U 2009 Tsunami Modeling: Development of Benchmarked Models In P Lynette Ed Nonlinear Wave Dynamics 1 pp 127-145 Novosibirsik: World Scientific Singapore Tang L Titov V V & Chamberline C D 2009 Development Testing and Applications of Site-specific Tsunami Inundation Models for Real-time Forecasting Journal of Geophysical Research 114 C12 114-124 Tang L Titov V V Bernard E Wei Y Chamberline C Newman J C Spillane M 2012 Direct Energy Estimation of the 2011 Japan Tsunami Using Deep-Ocean Pressure Measurements Journal of Geophysics Research Letters 117 C8 1-28 Tappin D R Watts P & Grilli S T 2008 The Papua New Guinea Tsunami of 17 July 1998: Anatomy of a Catastrophic Event Natural Hazards Earth Syst Sci 8 2 243-266 Terry J P Kostaschuk R A & Garimella S 2005 Sediment Deposition Rate in the Falefa River Basin Upolu Island Samoa Journal of Environmental Radioactivity 86 1 45-63 Thompson R Fine I Rabinovich A Muhaly S Davis E Heesemann M & Krassovski M 2011 Observation of the 2009 Samoa Tsunami by the NEPTUNE-Canada Cabled Observatory: Test Data for an Operational Regional Tsunami Forecast Model Geophysical Research Letters 38 11 L11701-L11708 63 Tinti S & Tonini R 2013 Thr UBO-TSUFD Tsunami Inundation Model: Validation and Application to a Tsunami Case Study Focused on the City of Catania Italy Natural Hazard and Earth System Sciences 13 7 1795-1816 Titov V V 1997 Numerical Modeling of Long Wave Run-up University of Southern California 58 05 2613-2628 Titov V V 2009 Tsunami Forecasting In A N Bernard A R Robinson A N Bernard & A R Robinson Eds The Sea Volume 15: Tsunamis Vol 15 pp 371-400 Cambridge MA USA: Harvard University Press Titov V V & Gonzales F I 1997 Implementation and Testing of the Method of Splitting Tsunami MOST Model NOAA Technical Memorandum ERL PMEL 11 30 Titov V V & Synolakis C E 1998 Numerical Modeling of Tidal Wave Run-up Journal of Waterway Port Coastal and Ocean Engineering 124 157-171 Titov V V Gonzales F I Bernard E N Eble M C Motfjeld H O Newman J C & Venturato A J 2003 Real-time Tsunami Forecasting: Challenges and Solutions Natural Hazards 35 35-41 Titov V V Gonzales F I Motfjeld H O & Venturato A J 2003 NOAA TIME Seattle Tsunami Mapping Project: Procedures Data sources and Products Seattle: NOAA USGS 2005 1 1 USGS Retrieved from http: earthquake usgs gov: http: earthquake usgs gov earthquakes eqinthenews 2004 us2004slav us2004slav php Uslu B Eble M & Wright L 2013 A Tsunami Forecast Model for PagoPago Harbor American Samoa NOAA Technical Memorandum 19 1 Wei Y Bernard E Tang E Weiss L Titov V Weiss R Kanoglu U 2008 RealTime Experimental Forecast of the Peruvian Tsunami of August 2007 for U S Coastlines Geophysical Research Letters 35 4 1-7 Whitmore P 2009 Tsunami Warning Systems In E Bernard A R Robinson & E B Robinson Ed The Sea Vol 15 pp 14-28 Cambridge USA: Harvard University Press Yalciner A C Zaytsev A Aytore B Insel I Heidarzadeh M Kian R & Imamura F 2014 A Possible Submarine Landslide and Associated Tsunami at the Northwest Nile Delta Mediterranean Sea Oceanography 27 2 68-75 Zahibo N Pelinovsky E Yalciner A C Kurkin A Koselkov A & Zaitsev A 2003 The 1867 Virgin Island Tsunami Natural Hazards and Earth System Sciences 3 367-376 Zahibo N Pelinovsky E Yalciner A Zaytsev A Talipova T Nikolkina I & Chernov A 2011 Trans-Atlantic propagation of 1755 tsunami and its effects on the French West Indies Open Oceanography Journal 8 5 30-41 Zhou H Wei Y & Titov V V 2012 Dispersive Modeling of the 2009 Samoa Tsunami Geophysical Research Letters 39 16 603-610 64 APPENDIX A We construct scatterplots by averaging the MOST output for maximum amplitude current flux and stress along each survey track associated with a village Figure 2 1 and plotting against the corresponding observed coral-damage numbers The correlations for each scatter plot are given in the caption of Figure A1 None are statistically significant Figure A-1 Scatter plots of coral damage on the x-axis vs a maximum amplitude b maximum current c maximum flux and d maximum stress along coral damage track-lines The dynamical fields are averaged over each track-lines associated with each village Figure 2 1 to evaluate any relationship between coral damage and dynamica l fields 65 APPENDIX B These tables present MOST model output for maximum amplitude along selected villages Figure 2 1 for locations of the villages There is a tendency that run-up increases with decreasing Manning and the model better estimates run-up Table B1 There is also a tendency that run-up decreases with removing reefs Table B2 66 Table B1 Model simulated run-up for different Manning s roughness n values at 31 villages around Tutuila Villages LAUILI AMALAU AFONO1 AFONO2 AVAIO MASEFAU AMAUA FAGAITUA MASAUSI SAILELE AOA AMOULI ONENOA AUASI TULA AUNUU POLOA AMANAVE FAGAILII FAILOLO AGUGULU UTUMEA SEETAGA FAGAMALO NUA AFAO ASILII AMALUIA LEONE FAGATELE Field Run-up Run-up Run-up Run-up Run-up Run-up Run-up m n 0 08 n 0 06 n 0 04 n 0 03 n 0 02 n 0 015 3 36 1 35 1 58 1 78 1 80 2 12 2 35 2 5 1 46 1 49 1 52 2 12 1 55 1 72 2 18 1 92 1 98 2 06 3 00 2 20 2 45 3 8 2 04 2 11 2 21 3 50 2 41 2 68 3 7 2 81 2 95 3 12 3 15 3 59 3 98 4 3 32 3 30 3 27 4 20 3 37 3 74 2 91 3 05 3 23 3 43 3 20 3 81 4 23 3 5 3 60 4 26 5 02 4 75 5 31 5 90 2 79 2 46 2 48 2 50 3 15 2 56 2 84 2 95 1 99 2 01 2 01 2 25 2 00 2 23 2 23 1 36 1 60 1 82 2 20 2 05 2 28 3 15 2 76 3 18 3 53 3 20 4 18 4 64 3 6 2 20 2 21 2 23 2 50 2 24 2 48 3 79 2 57 3 06 3 47 3 08 3 73 4 14 7 3 11 3 44 3 66 3 80 3 89 4 32 2 15 1 54 1 71 1 85 2 14 2 03 2 25 13 23 6 10 6 49 7 03 7 30 7 62 10 74 7 74 4 69 4 85 4 93 5 25 6 32 5 79 6 4 77 4 78 4 84 4 90 5 33 7 90 6 54 2 87 2 79 2 69 2 70 3 29 3 14 6 12 1 93 2 11 2 35 2 50 2 23 2 43 4 51 3 05 3 15 3 76 4 00 4 52 5 68 5 69 4 98 5 09 5 50 5 57 6 29 5 19 6 39 2 88 3 22 3 37 3 30 3 30 15 00 4 09 3 61 3 86 4 15 4 20 3 85 3 86 5 89 3 46 3 83 4 10 4 20 3 98 4 74 6 81 5 05 5 30 5 66 6 00 6 94 5 74 5 39 5 14 5 26 5 26 5 20 5 60 6 21 2 8 1 26 1 89 2 58 3 00 2 66 2 01 4 92 3 12 3 21 3 28 3 30 3 33 3 33 67 Table B2 Model simulated run-up for different r values representing varying bathymetry at 31 villages around Tutuila Villages Field Run-up m Run-up r 1 LAUILI AMALAU AFONO2 AFONO1 AVAIO MASEFAU AMAUA FAGAITUA MASAUSI SAILELE AOA AMOULI ONENOA AUASI TULA AUNUU POLOA AMANAVE FAGAILII FAILOLO AGUGULU UTUMEA SEETAGA FAGAMALO NUA AFAO ASILII AMALUIA LEONE FAGATELE 3 36 2 5 2 18 3 8 3 7 4 2 91 3 5 2 79 2 95 2 23 3 15 3 6 3 79 7 2 15 13 23 7 74 6 6 54 6 12 4 51 5 69 6 39 4 09 5 89 6 81 5 39 2 8 4 92 1 8 2 12 3 3 5 3 15 4 2 3 2 4 75 3 15 2 25 2 2 3 2 2 5 3 08 3 8 2 14 7 3 5 25 4 9 2 7 2 5 4 5 57 3 3 4 2 4 2 6 5 2 3 3 3 Run-up Run-up Run-up Run-up Run-up r 0 8 r 0 6 r 0 4 r 0 2 r 0 0 1 13 2 05 2 34 2 70 2 46 2 80 1 93 3 14 2 15 1 55 1 90 3 67 1 69 2 24 2 38 2 07 5 32 3 29 4 75 2 11 1 93 3 12 3 71 1 99 2 78 2 87 4 14 4 50 3 44 2 23 1 05 1 89 2 30 2 79 2 25 2 49 1 86 2 78 2 10 1 63 1 76 2 87 1 41 2 16 2 22 1 90 5 12 3 06 4 36 2 07 1 99 2 86 3 30 1 92 2 46 2 80 4 34 4 15 2 69 1 85 0 98 1 76 2 33 2 75 2 25 2 58 1 79 2 86 1 99 1 47 1 72 2 93 1 42 2 02 2 07 1 78 4 79 2 85 4 08 2 10 1 96 2 86 3 43 1 84 2 53 2 65 3 91 4 06 2 75 1 88 0 94 1 65 2 24 2 77 2 27 2 61 1 75 2 88 1 95 1 49 1 69 2 87 1 40 2 02 2 07 1 78 4 46 2 73 3 82 2 02 1 98 2 88 3 46 1 81 2 54 2 60 3 96 4 01 2 69 1 85 0 89 1 54 2 17 2 72 2 30 2 70 1 67 2 95 1 98 1 43 1 63 2 80 1 33 1 88 1 98 1 67 4 14 2 59 3 56 1 95 1 94 2 92 3 59 1 72 2 17 2 64 3 83 3 86 2 62 1 75 68 VITA Author of this research is born and raised in Turkey She came to US to study her PhD At University of Washington with the privilege of getting fellowship from Joint Institute for the Study of Atmosphere and Ocean University of Washington She gained interest into tsunami science starting from her senior level in Middle East Technical University Ankara Turkey She published two peer-reviewed papers and coauthored three papers during her education She takes motivation of working on tsunami science by thinking that she can save a person s life from tsunamis She can speak English Turkish and German fluently She likes to ski swim and travel Education: PhD: Department of Earth and Space Sciences 2009-2016 University of Washington Seattle WA USA B Sc & M S : Civil Engineering Hydromechanics & Ocean 2002-2009 Middle East Technical University-METU Ankara Turkey Publications: 1 Dilmen D I 2009 GIS Based Tsunami Inundation Maps Case Studies From Mediterranean Masters Thesis Middle East Technical University Civil Engineering Ankara Turkey 2 Dilmen D I Kemec S Yalciner A C Duzgun S Zaytsev A 2014 Development of Tsunami Inundation Map in Detecting Tsunami Risk in Gulf of Fethiye Turkey Pure Appl Geophys 2014 Springer Basel 3 Dilmen D I Titov V V Roe G H 2015 Evaluation of the Relationship Between Coral Damage and Tsunami Dynamics Case Study: 2009 Samoa Tsunami Pure Appl Geophys 2015 Springer Basel 4 Kemec S Duzgun S Zlatanova S Dilmen D I Yalciner A C 2010 Selecting 3D Urban Visualisation Models for Disaster Management: Fethiye Tsunami Inundation Case Proceedings of TIEMS 2009 Annual Conference Istanbul 5 Pelinovsky E Zahibo N Yalciner A Zaitsev A Talipova T Chernov A Insel I Dilmen D Ozer C Nikokina I 2009 1755 Tsunami Propagation in Atlantics and its Effects on the French West Indies Geophysical Research Abstracts Vol 11 EGU2009502 2009 EGU General Assembly 6 Yalciner A Y Gulkan P Dilmen D I Aytore B Ayca A Insel I Zaytsev A 2014 Evaluation of Tsunami Scenarious for Western Peoponnese Greece Bollettino do Geofisica Teorica ed Applicata Related Work Experience: 1 Research GSRA and Teaching Assistant TA at University of Washington Seattle 2 Project Engineer at European Union Funded Research Projects SEEHELLARC and TRANSFER METU Turkey 70
    • Welch, Mark - M.S. Thesis
      Separating Volcanic Deformation and Atmospheric Signals at Mount St. Helens Using 2016, Welch, Mark, Mark Welch Separating Volcanic Deformation and Atmospheric Signals at Mount St Helens Using Persistent Scatterer InSAR Corresponding Author a Mark D Welch - mdw12 uw edu a David A Schmidt - dasc uw edu a University of Washington Department of Earth and Space Sciences Postal Address: University of Washington Johnson Hall Rm- 070 Box 351310 4000 15th Avenue NE Seattle WA 98195- 1310 1 of 35 Abstract Over the past two decades GPS and leveling surveys have recorded cycles of inflation and deflation associated with dome building eruptions at Mount St Helens Due to spatial and temporal limitations of the data it remains unknown whether any deformation occurred prior to the eruption of 2004 Interferometric Synthetic Aperture Radar InSAR with its fine spatial resolution has the potential to resolve pre- eruptive deformation that may have occurred but eluded detection by campaign GPS surveys because it was localized to the edifice or crater Traditional InSAR methods are challenging to apply in the Cascades volcanic arc because of a combination of environmental factors Past attempts to observe deformation at Mount St Helens were unable to make reliable observations in the crater or on much of the edifice In this study Persistent Scatterer InSAR known to mitigate issues of decorrelation caused by environmental factors is applied to four SAR data sets in an attempt to resolve localized sources of deformation on the mountain from 1995- 2010 Many interferograms are strongly influenced by phase delay from atmospheric water vapor and must be corrected To assess the bias imposed by the atmosphere we perform sensitivity tests on a suite of atmospheric correction techniques including several that rely on the correlation of phase delay to topography We also explore approaches that directly estimate phase delay using the ERA- Interim climate reanalysis data set We find that phase- based corrections and the ERA- Interim atmospheric correction produce velocities on the edifice of Mount St Helens that differ by up to 1 cm yr due to variability in how atmospheric artifacts are treated in individual interferograms Additionally simple phase- based techniques run the risk of minimizing any surface deformation signals The PS InSAR results for overlapping tracks are inconsistent with one another and do not provide conclusive evidence for any pre- eruptive deformation at a broad scale or localized to the crater or edifice leading up to the 2004 eruption However we cannot rule out the possibility of deformation less than 5 mm yr or discern whether deformation rates increased in the preceding months The results do however significantly improve the spatial density of 2 of 35 observations and also our ability to resolve or rule out models for a potential deformation source for the pre- eruptive period 1 Introduction and Motivation Since its explosive eruption in 1980 Mount St Helens has undergone cyclic inflation and deflation associated with dome building eruptions and the re- pressurization of its magmatic system at depth Palano et al 2012 The record of surface deformation at Mount St Helens over that time period is incomplete and what is known was measured primarily by ground based geodetic techniques including GPS and trilateration surveys Lisowski et al 2008 Dzurisin et al 2008 Prior to the dome building eruption 2004 that began on October 1 surveys of deformation were both temporally and spatially coarse Campaign GPS and trilateration surveys were conducted with repeat intervals of one to three years and the closest continuous GPS station was located 9km from the crater at the Johnston Ridge Observatory Dzurisin 2003 The results of these surveys revealed that following the eruption of 1980 a broad region surrounding the edifice underwent surface dilatation indicating expansion and presumably the recharge of a deep magma reservoir Lisowski et al 2008 Interestingly this expansion ceased some time before 1991 and deformation on that scale was not detected again until two weeks before the 2004 eruption coincident with the onset of seismic unrest Dzurisin et al 2008 Because none of these surveys were capable of making accurate measurements on the edifice itself it is possible that pre- eruptive deformation did occur but was localized to the edifice or crater The eruption in 2004 spurred the installation of additional continuous GPS stations in the proximity of Mount St Helens Dzurisin et al 2008 This updated network was able to record the co- eruptive deflation and the transition back to a phase of inflation which continues through 2016 Palano et al 2012 As in the past the subtle surface deformation signal at St Helens continues to be monitored primarily by ground based geodetic techniques 3 of 35 The remote sensing tool Interferometric Synthetic Aperture Radar InSAR has the potential to substantially augment these techniques by providing spatially dense precise measurements of surface displacements and may also reveal other volcanic or surficial processes too localized to be detected by ground based methods InSAR methods are capable of producing time- series of deformation with millimeter precision at a resolution of meters to tens- of- meters over study areas ranging from kilometers to hundreds- of- kilometers in extent Zebker et al 2000 Simons and Rosen 2007 Traditional SAR interferometry is challenging to apply to the stratovolcanoes of the Cascades but has been implemented successfully in the past observing deformation at Medicine Lake and Three Sisters Volcanoes Wicks et al 2002 Poland et al 2006 Poland and Lu 2008 Dzurisin et al 2009 Riddick and Schmidt 2011 Widespread phase decorrelation caused by persistent snow cover and dense vegetation combined with large orographic elevation dependent atmospheric phase delays mask or make deformation signals difficult to detect The combination of these factors impeded previous attempts to image pre- eruptive deformation at Mount St Helens using standard interferometry and stacking Poland and Lu 2008 These authors were able to image the co- eruptive deflation signal that was also observed by the newly installed GPS instruments but the results from InSAR for the time period preceding the 2004 eruption were inconclusive with respect to volcanic deformation By applying the StaMPS Stanford Method for Persistent Scatterers Persistent Scatterers PS technique phase decorrelation in challenging study areas like Mount St Helens can be mitigated by utilizing only the pixels with the highest statistically derived signal- to- noise ratio in a time- series composed of many interferograms Hooper et al 2012 The persistent scatterer technique has been shown to vastly improve the coherence and number of reliable observations in natural terrains around the world exemplified by a study of Volcan Alcedo in the Galapagos and a study of slow- slip in Guerrero Mexico Hooper et al 2007 Hooper et al 2012 4 of 35 Even if a coherent signal can be obtained on the edifice of Mount St Helens using the PS technique additional work must be done to separate potential deformation from atmospheric phase delay the largest remaining source of error for current InSAR studies Hannsen 1998 Atmospheric phase delay arises primarily in interferometry when the distribution of water vapor present in the troposphere differs between the two SAR scenes Changes in water vapor content alter the refractivity of the atmosphere which leads to a phase delay in the interferograms Zebker et al 1997 Atmospheric phase delay is often correlated with surface topography and under certain circumstances appears as a radially symmetric surface deformation signal centered over a volcano Beauducel et al 2000 The phase signal associated with changes in atmospheric refractivity is often broken down into a stratified and a turbulent component Hanssen 2001 The stratified component is elevation dependent and spatially correlated over large distances while the turbulent component is related to small scale or stochastic atmospheric variations and cannot be modeled simply There are a variety of techniques available for estimating and removing the stratified component of atmospheric delay which fall into two major groups The first group of methods relies on the relationship between phase delay and the elevation of a given point Beauducel et al 2000 Remy et al 2003 Ding et al 2008 A linear or power- law function can be fit to the phase and elevation data to estimate and remove the atmospheric signal However because volcanic deformation is also often strongly correlated with elevation it is extremely difficult to distinguish between the two with a single or small number of interferograms and attempts to model the atmospheric noise at volcanoes with this technique run the risk of removing the desired deformation signal along with the atmospheric noise The second category of atmospheric removal techniques uses an independent data set to estimate or model the atmospheric phase delay Foster et al 2013 Jolivet et al 2014 Bekaert et al 2015b These data sets typically provide measurements of pressure temperature and water vapor as a function of altitude The vertical profiles are derived either 5 of 35 from measurements made by satellite borne instruments including NASA s MODIS and MERIS or from climate reanalysis models such as ERA- Interim WRF and NARR Measurements made by instruments like MODIS and MERIS are not always ideal as the data typically have low spatial resolution especially at night and are only usable in the absence of clouds The MERIS instrument which was mounted on the European Space Agency s Environmental Satellite ENVISAT is particularly useful for correcting phase delay in interferograms generated with SAR data from that mission as the atmospheric and radar data are collected concurrently Corrections made with climate reanalysis models benefit from the fact that they incorporate multiple data sources and techniques used for weather prediction to improve temporal resolution to 4- 8 time- steps per day However this may still be insufficient to capture some transient atmospheric events Maps of predicted phase delay are generated by spatially interpolating measured vertical profiles of pressure temperature and water vapor to cover the SAR scene at the desired resolution These profiles can be transformed into profiles of refractivity equation 1 which are then used to calculate the integrated phase delay along the line of sight path for a given pixel in an interferogram using equation 2 Hanssen 2001 Bekaert et al 2015a Refractivity N is a combination of total atmospheric pressure P temperature T partial pressure of water vapor e and empirical constants k1 k 2 and k3 Tropospheric phase delay tropo is the integral of refractivity from the elevation of the ground surface h1 to the top of the troposphere htop multiplied by geometric factors dependent on the radar incidence angle and the radar wavelength Equation 1 N k1 P T hydr k2 e T k3 e T 2 wet Equation 2 tropo - 4 10- 6 cos 6 of 35 & & & & In this study we attempt to resolve the near- field deformation on Mount St Helens using PS InSAR SAR data from the ERS- 2 and ENVISAT missions spanning more than fifteen years 1995- 2010 are processed with the StaMPS package to image the surface deformation associated with a complete eruptive cycle of Mount St Helens The low signal- to- noise ratio prompts us to carefully consider potential biases particularly from atmospheric water vapor delay In order to confidently interpret anomalies in the signal as volcanic deformation the effect of atmospheric phase delay must be minimized and the biases associated with the analysis and correction techniques well understood A series of sensitivity tests are conducted to assess the bias imposed by both the atmospheric phase delay and the choice of method used to correct it The removal techniques tested in this study include a variety of approaches for fitting trends in phase and elevation and also models of phase derived from ERA- Interim climate reanalysis data Each atmospheric correction is applied to the data within the StaMPS framework to deduce its effect on PS velocities and the time series of deformation 2 SAR and Atmospheric Data Description Four separate SAR data sets were processed using the persistent scatterer processing package StaMPS in order to image any pre- eruptive or post- eruptive deformation associated with the 2004 eruption of Mount St Helens Two tracks from the European Space Agency s ERS- 2 satellite cover the pre- eruptive period while two from their ENVISAT mission cover the post- eruptive period The number and size of available and appropriate data sets listed in Table 1 are limited by the 35- day repeat interval and prioritization of targets to be imaged by the satellite and also by a variety of factors relating to the coherence or quality of interferograms For much of the year the edifice of Mount St Helens is covered in deep snow To minimize the effect of snow and maximize the area of coherent phase only SAR acquisitions from the 7 of 35 summer and fall months June- October were considered Figure 1 Timeline of SAR scenes for four data sets covering the pre- and post- eruptive periods The vertical red bar st indicates the onset of the 2004 eruption on October 1 Satellite ERS-2 ERS-2 ENVISAT ENVISAT Scenes 8 11 11 9 Track 385 156 156 20 Frame 2673 2673 2673 909 Master 8 28 98 8 9 98 6 6 08 7 18 07 Start 9 24 95 6 14 96 8 17 05 9 30 05 End 9 2 01 6 28 02 8 26 09 9 24 10 Table 1 A summary of SAR data used in this study Under the standard StaMPS processing routine all interferograms share a common master scene The master scene for each data set Table 1 is chosen by minimizing the sum decorrelation from the temporal and perpendicular baselines of the SAR scenes using the technique outlined by Hooper et al 2007 holding the Doppler centroid and thermal noise terms constant When either the temporal or perpendicular baseline between the chosen master and a given scene is too large the resulting interferogram will be incoherent and so the scene is excluded from the data set To maximize the signal- to- noise for surface velocities only data sets with more than eight scenes were processed in this study The ground surface in the area surrounding Mount St Helens especially within the crater was modified during the 2004 eruption repositioning the scattering elements on the ground This leads to significant decorrelation Thus interferograms spanning the eruption were not made or utilized in the time series analysis 8 of 35 NASA s SRTM digital elevation model DEM was used to remove the topographic phase from interferograms with dates prior to 2004 Farr and Kobrick 2000 Interferograms for the post- eruptive period were corrected using a hybrid of SRTM and LiDAR Mosbrucker 2014 DEM s in order to accurately represent the major changes to topography by spine emplacement and dome building within the crater of Mount St Helens Scott et al 2008 The hybrid elevation model was constructed by creating a mosaic of the two data sets in ArcMAP giving priority to the LiDAR data set A weighted average of the SRTM and LiDAR data was then conducted for pixels near the edges of the smaller LiDAR data set to reduce jumps at the boundaries The atmospheric phase delay corrections were made using the ERA- Interim global atmospheric reanalysis data set produced by the European Centre for Medium- Range Weather Forecasts ECWMF Estimates of past atmospheric conditions are made by integrating a range of observations into coupled models of the climate system Dee et al 2011 The model produces vertical profiles of pressure humidity and temperature with data- points at 60 pressure levels from the earth s surface to an altitude corresponding to 0 1 hPa The vertical profiles are generated at six- hour spacing and a horizontal resolution of 80 km Because the time steps of the ERA- Interim model differ from the timing of radar acquisitions the atmospheric data must be interpolated temporally which can potentially introduce significant error especially in cases of rapidly changing weather conditions 3 Methods 3 1 InSAR data processing Four SAR data sets spanning the time period from September 1995- 2010 were processed with the Persistent Scatterer software package StaMPS MTI developed by Hooper and others 2012 The StaMPS methodology requires that a single scene be chosen as the 9 of 35 master image for all of the interferograms in a data set In each case the perpendicular and temporal baselines were calculated for all possible interferogram pairs and a master was selected by minimizing the combined expected effect of the spatial and temporal baselines Multiple master scene candidates with low expected decorrelation were tested for each data set and the master which produced the most visually coherent interferograms was selected After a master was chosen interferograms were generated using the basic routine outlined in the StaMPS MTI software package To reduce the required computing power and processing time the SAR scenes were cropped to an area centered over Mount St Helens with dimensions on the order of 20km- by- 40km Interferograms were visually inspected for quality and those with no distinguishable visible coherence were discarded The remaining set of geo- coded interferograms were imported into the MATLAB based StaMPS framework where stable PS pixels are selected and average velocities and time- series calculated Figure 2 Location and coverage of cropped SAR scenes for the four data sets ERS- 2 tracks 385 and 156 are in blue and red respectively while ENVISAT tracks 156 and 20 are in purple and yellow respectively Location relative to the state of Washington is shown in the inset map 10 of 35 3 2 StaMPS methodology The StaMPS method can significantly reduce the effects of decorrelation and improve signal- to- noise in interferometric results by statistically identifying pixels with the least stochastic noise and using only those pixels in the final products To estimate the random noise of a pixel the contribution to the interferometric phase from deformation atmosphere orbit error and DEM error is estimated and removed The phase contribution from each of these sources is estimated using a combination of spatial and temporal filters and also correlative relationships between phase and perpendicular baseline By removing these deterministic contributors to phase from the time- series of each pixel an estimate for the stochastic component of the noise through time is obtained Pixels whose resulting time- series of stochastic noise have the least variance or in other words are the least noisy and most stable through time are selected as PS pixels Hooper et al 2007 2012 Using the more reliable PS pixel candidates the models of the deterministic contributors to phase can be refined This process is repeated until it converges on a statistically robust set of pixels with high signal- to- noise such that less than five percent of the pixels are false positive stable scatterers While we expect the selected PS pixels to have a very low amount of random noise it can still be extremely difficult to distinguish between and separately quantify the phase contributions of the deterministic factors The phase delay introduced by the atmosphere can be especially difficult to differentiate from the desired deformation signal because of its large amplitude and nearly identical spatial characteristics Often both the atmospheric and volcanic deformation signals have spatial wavelengths on the order of several kilometers and are centered over the edifice This issue can be overcome to a degree by increasing the number of scenes in the SAR data set leveraging the fact that atmospheric delay is uncorrelated over timescales longer than one day Emardson et al 2003 Parker and others 2015 demonstrated that in the Cascade volcanic arc between 4 and 11 consecutive interferograms are required to average out the atmospheric variability enough to 11 of 35 detect a volcanic deformation signal with an average velocity of 1 cm yr The authors predict that a minimum of 6- 8 interferograms would be needed in the case Mount St Helens which indicates that the size of the data sets in this study should be sufficient for detecting a 1 cm yr signal but that they may be near the limit In order to increase precision and the chances of detecting a subtle signal techniques for correcting atmospheric phase delay must be applied 3 3 Atmospheric Testing Many approaches for modeling and removing atmospheric phase delay from interferograms exist and can be simply implemented within the framework of the StaMPS software A sensitivity test was conducted to assess the impact of the choice of atmospheric removal technique on the surface velocities obtained with PS methods This was accomplished by applying a suite of different correction techniques to the larger of the two ERS- 2 data sets A variety of approaches towards modeling phase delay using the phase- elevation correlation were tested along with the ERA- Interim climate reanalysis derived model The models that utilize the correlation between tropospheric phase delay tropo and elevation h assumed three basic forms either a linear power- law or windowed moving average relationship between the two variables In the case of the power- law fit the form of the equation is as follows from Bekaert et al 2015a : Equation 1 tropo K h0 h a In this form K is the coefficient which relates phase to elevation h0 assumed to be 7000m is the reference height above which the atmosphere is considered stable and a is the power- law exponent often determined from balloon sounding data assumed to have a value of 1 6 in this study The window size used for the moving average was 300m of elevation Modified versions of the linear and power- law fit models were also tested In the modified models the free parameters relating phase and elevation data were calculated using only specific spatial 12 of 35 subsets of the PS pixels The advantage of spatial subsampling is that some data points are likely more representative of the physical correlation between phase delay and elevation specifically over the edifice of Mount St Helens The subsets tested were defined as: all points within 4km of the crater center all points above an elevation of 1300 meters all points excluding suspected pumice plain deformation and a set of points down- sampled 10x with an even distribution over the range of elevations One additional modification of the trend fitting process that was tested was to weight each pixel in the inversion by a metric of its phase stability determined by StaMPS so that noisier pixels have less effect on the fit This weighting scheme was applied to all other phase- elevation fitting corrections to compare weighted and un- weighted results Models of atmospheric phase delay that incorporate data from the ERA- Interim climate reanalysis were generated using the freely available Toolbox for Reducing Atmospheric InSAR Noise TRAIN developed by David Bekaert et al 2015b and are seamlessly integrated into the StaMPS framework The estimates of phase delay produced by TRAIN are derived from spatially and temporally interpolated vertical profiles of measured and modeled meteorological parameters Phase delay for each PS pixel is calculated as the integral of refractivity along the line of sight from the satellite to the ground Hannsen 2001 Bekaert et al 2015 3 4 Statistical Analysis and Synthetic Modeling Each atmospheric correction method produces a map of phase delay for all interferograms in the data set which are then integrated into StaMPS to produce 23 line of sight velocity and time series products The standard deviation of velocities for each pixel was calculated to demonstrate the possible magnitude of bias inherent in the choice of an atmosphere correction method Next a jack- knife analysis i e Agram and Simons 2015 was applied to the 23 average velocity data sets by individually removing each set and recalculating 13 of 35 the mean and standard deviation of velocities This test determines which corrections had the largest effect on the variance or differed the most from the mean To assess whether phase- elevation based modeling techniques might potentially remove any desired volcanic deformation signal at Mount St Helens a synthetic test was carried out First a set of common- master synthetic interferograms containing deformation signal from a spheroidal magma chamber expanding at a constant rate were generated using the dMODELS written by Battaglia et al 2013 The depth to the chamber and pressure increase were set to be 2000 meters and 1250 MPa respectively to create a substantial velocity signal of 15mm yr Next the ERA- Interim derived correction was added into each interferogram to simulate atmospheric noise and then modeled and removed using a linear fit to phase and elevation within the StaMPS framework The resulting maximum velocities over the edifice were compared to the expectations based on the spheroidal model to quantify the error or bias introduced by using the linear phase based technique 4 Results 4 1 Individual Interferograms The individual interferograms processed in this work all have significant areas of decorrelation caused by the factors discussed earlier With the exception of two interferograms created with slave scenes acquired within two months of the master coherence was limited to areas lacking both dense vegetation and persistent snow cover namely recent lava flows the pumice plain and lower edifice The map in Figure 3 shows the distribution of dense forest surface water and ice where low coherence is expected The effect of atmospheric phase delay is clearly visible in the coherent regions of many interferograms with one or in some cases two phase cycles correlated with elevation on the edifice corresponding to 2 8 to 5 6 cm of apparent surface deformation Also visible in several interferograms is a signal of subsidence occurring on the pumice plain to the northwest of Mount St Helens 14 of 35 Figure 3 Environmental factors known to negatively affect interferometric coherence are shown in color overlaid on a hill- shaded digital elevation model Green indicates areas with greater than 50% canopy cover while blue indicates either surface water or ice NLCD Coherence in interferograms correlates very well with the absence of the environmental factors see Figure 4 Figure 4 Example geocoded interferogram from the descending ERS- 2 track 156 data set spanning 9 12 1997 8 28 1998 overlain on radar amplitude image One cycle fringe of color indicates 28mm of displacement Fringes indicating atmospheric phase delay correlated to topography on the edifice can be seen clearly summing to an apparent displacement of 30mm A subsidence signal on the pumice plain north of the crater is also visible 4 2 Persistent Scatterer Velocities The StaMPS algorithm identifies on the order of 10 000 persistent scatterer pixels in each SAR scene whose locations correlate very well with regions of high spatial coherence in interferograms and with mapped regions of low vegetation snow or ice cover PS pixels are 15 of 35 identified on all parts of the Mount St Helens edifice and within the crater but in far lower densities than on the pumice plain and lower slopes of the mountain Figure 5 PS average velocities for the four data sets lain over a shaded relief DEM Pre- eruptive data sets are on 2 the left and post- eruptive on the right Areas with less than 50 pixels km are masked out to highlight areas where phase- unwrapping errors are unlikely Open black circles indicate the locations of time series plotted in Figure 6 Arrows in upper right of each map indicate the radar line of sight LOS and satellite flight direction perpendicular PS InSAR results for the crater and edifice during the pre- and post- eruptive period reveal LOS Line of Sight velocities less than 1 cm yr Figure 5 suggesting that any signal is at or below the level of the noise In addition the apparent signal in those regions has opposite sign depending on the data set over the same time period In the pre- eruptive period ERS- 2 track 385 indicates uplift of the edifice at a rate of approximately 5 mm yr while track 156 shows subsidence at a similar rate For the post- eruptive period ENVISAT track 156 indicates uplift of the edifice at a rate of approximately 10 mm yr while track 20 shows subsidence at roughly 8 mm yr 16 of 35 The subsidence signal on the pumice plain first detected by Poland and Lu 2008 is seen clearly in all plots of average velocity for all data sets regardless of atmospheric correction technique The subsidence rate varies spatially and between data sets with a maximum detected rate of 10 mm yr By comparing pre- and post- eruptive velocity maps the subsidence signal appears to migrate to the northwest and become more localized through time 4 3 Time Series Ground displacement time- series show in greater detail the same findings as the average velocity plots Time series for locations on the edifice and in the crater from all four data sets show that average velocities are low and when comparing between data sets for the same time period the displacement trends have opposite sense of direction Figure 6 The time series for the two locations on the pumice plain show much more consistency between data sets and suggest that the subsiding region migrated spatially through time It can be seen that the time series for pixels on the edifice and crater have a good deal of scatter compared to their velocities Figure 6 The discrepancies in velocities and time series for the edifice and crater become worse when atmosphere is not modeled and removed indicating atmospheric modeling does improve the quality of the result The application of the ERA- Interim correction method leads to an average reduction in the variance of time series for all pixels of 21 4 mm or 74 percent 17 of 35 Figure 6 Time series of displacement and average velocities for three locations at Mount St Helens across all four data sets Each time- series shown is the average time- series for the set of all PS pixels within a circle of radius 200m where the error- bars for each point represent one standard deviation for the set of displacements Average velocity as the slope of the line of best fit is shown for each set Displacements in InSAR are relative not absolute and so the time- series are shifted along the Y- axis for visual clarity Map locations of the time- series are indicated as open black circles in Figure 5 The vertical red bar indicates the onset of the eruption Pumice plain velocities indicate subsidence across all data sets while the time- series for the crater and edifice do not show consistent deformation 4 4 Sensitivity Test of Atmospheric Correction Statistical and visual comparisons show that the vast majority of atmospheric correction techniques produce very similar LOS velocity results In particular results that utilize any modification of either a linear or power- law fit to the phase versus elevation data are virtually identical This is shown clearly by the results of the jack- knife analysis Table 2 When the velocities corrected by linear or power- law based models are removed from the set the jack- knife mean does not change significantly from the mean of the full set Furthermore when 18 of 35 comparing a typical pair of phase based corrections the average difference in velocity for a given pixel is only 0 13 mm yr or about 8 1% For example a linear fit restricted to points with elevations above 1300 meters compared to using all of the PS points results in a change in velocity of only 0 2 to 0 25 mm yr for pixels on the edifice and less than 0 15 mm yr for those in the majority of the surrounding region Correction Name ERA-Interim Moving Average Weighted Moving Average Power-law Deformation Mask Weighted Power-law Deformation Mask Linear Deformation Mask Weighted Linear Deformation Mask Weighted Linear Distance Crop Weighted Power-law Distance Crop Linear Distance Crop Power-law Distance Crop Weighted Power-law No Crop Weighted Linear No Crop Power-law No Crop Linear No Crop Weighted Power-law Height Crop Power-law Height Crop Weighted Linear Height Crop Linear Height Crop Linear Downsampled Power-law Downsampled Weighted Linear Downsampled Weighted Power-law Downsampled Average Change in Mean by Removal mm yr 0 036 0 014 0 012 0 009 0 009 0 009 0 009 0 007 0 007 0 006 0 006 0 005 0 004 0 004 0 004 0 003 0 003 0 002 0 002 0 002 0 002 0 002 0 002 Average Standard Deviation after Removal mm yr 0 16 0 23 0 23 0 24 0 24 0 24 0 24 0 24 0 24 0 24 0 24 0 24 0 24 0 24 0 24 0 24 0 24 0 24 0 24 0 24 0 24 0 24 0 24 Table 2 Jack- knife results show for the average pixel in the ERS- 2 Track 156 data set how different or similar the velocity produced by one particular atmospheric correction is to that of the full set of 23 different corrections If for the average pixel the mean velocity of the set changes greatly or the standard deviation of velocities is reduced by the removal of a correction then it is dissimilar to the set Apart from the ERA- Interim and moving average corrections the choice of correction technique has little impact on the velocity results Models that utilize a moving average with an elevation window of 300m to predict atmospheric delay from phase produce results that are appreciably different from the other phase based techniques When the moving average corrected velocities are removed from the 19 of 35 set the standard deviation of velocities for the average pixel decreases by 4 3% indicating its dissimilarity from other phase- based corrections To further illustrate this point the velocities predicted by the moving average correction are up to 2 mm yr higher on the edifice than those from a linear model The jack- knife results in Table 2 also show that the ERA- Interim correction produces velocities that differ the most from the mean of all atmospheric corrections tested Removal of the ERA- Interim correction reduces the standard deviation of velocities for the average pixel by 34% Applying the ERA- Interim correction leads to velocities on the edifice and within the crater that have opposite sign to those from linear and power- law models For pixels on the edifice the difference in velocity produced by the linear and ERA- Interim corrections is between 5 and 6 mm yr Comparing the linear and ERA- Interim corrections for individual interferograms in phase- elevation space it can be seen that the two models predict phase delays with opposite sense of direction for some interferograms especially at high elevations Figure 7 causing the large discrepancy in average LOS velocities on the edifice Figure 7 A comparison of the ERA- Interim red and basic linear blue atmospheric corrections for all 10 interferograms of ERS- 2 track 156 in phase- elevation space The date of the slave scene is in the upper right of each 20 of 35 frame A correlation between phase and elevation is seen in the unwrapped phase of many but not all interferograms The two corrections predict phase delays with opposite sense of direction for some interferograms especially at high elevations For clarity the number of points is reduced by a factor of 10 5 Discussion 5 1 Atmospheric Corrections Because the phase is correlated with topography in the vast majority of interferograms for Mount St Helens it is clear that an attempt should be made to model and remove atmospheric phase delay to improve the signal- to- noise Within the category of phase- elevation based corrections the choice between techniques does not significantly affect average velocities as seen in Table 2 A comparison of phase based corrections produced for a single interferogram Figure 8 shows that except for windowed moving average corrections the phase- based techniques are nearly indistinguishable Methods that rely on climate reanalysis models and those that rely on the phase- elevation correlation produce similar corrections for individual interferograms in some cases The similarities and differences between the two techniques are shown in Figure 7 which compares the linear phase- based and ERA- Interim corrections in phase- elevation space for all interferograms in a single data set The two techniques likely agree more closely when the atmospheric conditions change more slowly and avoid being aliased by ERA- Interim temporal sampling rates The two methods are more similar at low elevations below 1500 meters but tend to diverge at high elevations 21 of 35 Figure 8 A comparison of atmospheric correction models for a single interferogram ERS- 2 track 156 9 12 1997 8 28 1998 in phase- elevation space A clear correlation between phase and elevation is seen in the unwrapped phase Except for the windowed moving average trend fitting corrections are nearly indistinguishable The ERA- Interim model produces a similar correction to the phase based corrections but diverges especially at high elevations For some interferograms the ERA- Interim and phase- based corrections can differ greatly which can lead to markedly different average velocities and time- series results For example with regard to the pre- eruptive data set from ERS- 2 track 156 the two corrections produce velocities for the edifice which differ by 5- 6 mm yr on average Figure 9 The high difference in velocities produced by the two corrections for both this ERS- 2 data set and also for ENVISAT Track 20 is large enough to change the sense of direction uplift versus subsidence of displacements on the edifice This implies that the choice of atmospheric correction is extremely important and has an enormous impact on studies of volcanoes with large topographically correlated atmospheric signals and low signal- to- noise 22 of 35 Figure 9 Comparison of average velocities produced using the ERA- Interim and simple linear corrections for ERS- 2 track 156 Velocity differences on the edifice are 5- 6 mm yr on average but can exceed 10 mm yr at some points large enough to cause a change from apparent subsidence to uplift Fine scale turbulent structures in the atmosphere produce phase delay in interferograms that cannot be represented accurately by reanalysis style corrections because of the low temporal and spatial resolution of the climate models The residual atmospheric delay in individual interferograms that is not removed by correction techniques will affect the scatter in displacement time- series and correspondingly add uncertainty to estimates of average velocities However as described by Parker and others 2015 because the turbulent component of atmospheric delay does not correlate with time averaging across at least 8 interferograms in a StaMPS data set should minimize its effect which is manifested as a residual error in the corrected interferograms While phase based corrections are fast and easy to apply and do not require the acquisition of additional data they run the risk of removing or significantly reducing a deformation signal which is centered over a volcanic edifice This effect is evaluated by generating synthetic interferograms with a hypothetical inflation source at Mount St Helens that produces velocities on the edifice of 12- 15 mm yr Figure 10 Atmospheric phase delay from one of the ERS- 2 data sets modeled by the ERA- Interim technique is added to ten 23 of 35 interferograms and then the interferograms are corrected with a linear fit to phase and elevation The resulting velocities for the edifice and crater differ from the true deformation signal by up to 12 mm yr Figure 10 thereby minimizing the observed uplift Therefore we do not expect average velocities corrected by phase and elevation trends to accurately reflect volcanic deformation in applications where the signal- to- noise or deformation rates are low This problem is most relevant to volcanic studies because the deformation pattern tends to be radially symmetric around the volcanic edifice While the ERA- Interim correction cannot in theory fully remove the atmospheric signal it does not misidentify model and remove volcanic deformation as atmospheric phase delay Consequently the ERA- Interim climate reanalysis correction method was preferred in this work despite its drawbacks Figure 10 Left Synthetic average velocities produced by a spheroid model centered under the edifice with a depth of 2 km and a pressure change of 1250 MPa The synthetic data set includes 10 interferograms using an ERS- 2 viewing geometry Right Velocities produced after adding synthetic atmosphere from ERA- Interim and correcting with a linear fit to phase and elevation Velocities on the edifice differ greatly 5- 10 mm yr from the velocities expected from deformation indicating the shortcomings of the most simplistic phase trend fitting corrections 24 of 35 5 2 Volcanic Deformation 5 2 1 PS InSAR Interpretations Persistent Scatterer analyses of data sets covering both the pre- and post- eruptive periods of Mount St Helens 2004 eruption indicate that any volcanic deformation that may have occurred must have been very subtle After correcting for atmospheric phase delay using the ERA- Interim model maps of average velocities and time series from both of the pre- eruptive data sets show small LOS signals centered on the edifice that have inconsistent or opposite sense of direction with respect to one another Figures 5 and 6 This inconsistency of edifice velocities is repeated for the two data sets from the post- eruptive period In both cases one data set shows average movement of points on the edifice towards the satellite inflation while the other has movement away from the satellite subsidence We propose that this contradiction mainly reflects the propagation of bias from the atmospheric correction to velocities with other sources of error quite low as a result of PS processing It is possible that a pressure change at depth leading up to the eruption was accommodated inelastically leading to a lack of expression at the surface The pressure change and associated surface deformation may also have occurred primarily in the final year or months leading up to the eruption and is therefore not captured by the data used in this study One final alternative is that the surface displacements were localized to the crater where environmental factors lead to poor coherence and low density of pixels preventing accurate observations from being made While the StaMPS processing was able to identify a good density of scatterers on the lower to mid edifice not many statistically stable pixels were selected within the crater Figure 5 Furthermore the velocities of pixels within the crater are not as spatially coherent as those in regions of higher pixel density Considering the low density of pixels and great variety of physical processes capable of producing surface displacements within the crater i e glacial movement or erosive instability of the crater walls and lava domes no confident interpretation can be made for that region As was the case for the edifice average velocities for points in the 25 of 35 crater had opposite sense of direction depending on the data set considered It is likely however that if a larger signal was present it would be detectable 5 2 2 Spheroid Model Resolution Testing In order to better understand the capability of the PS InSAR and GPS data sets from the pre- eruptive period to detect a potential deformation source at Mount St Helens we tested their ability to resolve the depths and pressure changes of synthetic deformation sources over a range of parameter combinations Displacements for a spheroidal source were calculated at all pre- eruptive campaign and continuous GPS locations in a 12 km radius of the mountain and at all PS pixels using scripts from Battaglia et al 2013 which are based on equations from Yang et al 1988 and Newman et al 2006 Figure 11 Locations of the 25 campaign GPS stations Red Triangles used in synthetic testing of spheroidal deformation sources Stations used were within 12 km of the crater and occupied in multiple surveys prior to the 2004 eruption The magma chamber was assigned a long- axis radius of 500 meters and an aspect ratio of 0 5 Spatially correlated synthetic noise which mimics the final velocity observations of this work was added to the synthetic PS velocities The random spatially correlated noise was generated 26 of 35 by first applying a two- dimensional Fourier transform to the final velocity results corrected by the ERA- Interim technique to obtain a power spectrum The power spectrum was randomly permuted by small increments and then transformed back into the spatial domain resulting in noise with similar spatial characteristics to the input Noise was also generated for the campaign GPS sites using the velocity uncertainties reported in Lisowski et al 2008 which was then added to the forward modeled GPS velocities Surface velocities from a modeled spheroidal deformation source were calculated for 120 combinations of depth and pressure change The ranges of depths to the magma chamber and changes in pressure were from 500 to 7000 meters and 20 1000 MPa respectively For each parameter combination the pressure change and depth of the chamber were estimated using a Monte Carlo approach repeated for 1000 iterations of random spatially correlated noise The Monte Carlo approach was used because of the non- linear relationship between the parameters and surface velocities The 1000 best fitting depths and pressure changes and their associated residuals were recorded for each spheroidal deformation source and utilized to quantitatively assess the ability of the GPS and InSAR data to resolve the model parameters as a proxy for detection 27 of 35 Figure 12 Monte Carlo fits of a hypothetical inflation source Example clouds of best fitting parameter solutions for 1000 iterations of noise The true parameter value and mean best fitting value are indicated by the red and green dots respectively The true depth and pressure change for this example are 2860m and 575 MPa respectively It can be seen by comparing the widths of the clouds that PS InSAR outperforms radial campaign GPS for constraining pressure and to a lesser extent depth The results of the inverse modeling of synthetic velocities from a range of spheroidal deformation sources indicate that PS InSAR and the existing GPS are able to constrain both depth and pressure quite well for models with shallow depths and larger changes in pressure Figure 12 shows the best fitting depths and pressures for an example spheroidal source with a depth of 2860 and a pressure change of 575 MPa solved over 1000 iterations of noise The uncertainty in resolving depth or pressure for a given model considering expected levels of noise is represented by the standard deviation width of the cloud of the 1000 best fitting solutions Figure 13 shows contours of the standard deviation of the clouds of best fitting depths and pressures over the range of all tested source parameter combinations The standard deviations are normalized by the true value of the parameter to show the uncertainty as a percent error The depth and pressure of models residing in areas above and to the left of the contour lines shallow depths and high pressure change are well resolved and are unlikely to have occurred and remained unobserved Models laying in the model space below the contours are poorly resolved and may have occurred in the pre- eruptive period but remained obscured by atmospheric and other sources of noise The results in Figure 13 B show that the PS InSAR and horizontal campaign GPS perform similarly with regards to constraining the depth of magma chambers Interestingly Figure 13 A reveals that PS InSAR is more capable of constraining the pressure change of the modeled deformation source in almost all cases Additionally as one would expect given typical GPS uncertainties the horizontal component is far more valuable than the vertical component for resolving the model parameters 28 of 35 Figure 13 Model resolvability for InSAR and campaign GPS for the pre- eruptive period Shown are contours of percent error in constraining pressure change A and depth B over the space of parameter combinations The depth and pressure of models above and to the left of the contour lines are well resolved and are unlikely to have occurred and remained unobserved Models below the contours are poorly resolved and may have occurred in the pre- eruptive period but remained obscured by noise The 30% and 50% error contours for PS InSAR red vertical GPS blue and radial GPS green are represented by solid and hashed lines respectively Our results do not definitively rule out pre- eruptive deformation at Mount St Helens but they do provide improved constraints on the allowable ranges of depth and pressure change for a potential deformation source in the time period of 1996- 2004 Deformation sources with combinations of pressure and depth that lie above the 30% error contour are unlikely to have occurred and remain undetected by our measurements Models which lie outside of this contour are still within the realm of possibility of having occurred and would require some combination of larger higher quality SAR data sets improved interferogram coherence and or improvements to the atmospheric data sets and correction techniques It is assumed that deformation sources whose parameters are well resolved by the synthetic data sets are more likely to stand out from the noise and produce a confident detection in a given real data set Spheroidal deformation models for the co- eruptive deflation proposed by Lisowski et al 2008 and Palano et al 2012 derived from continuous GPS observations suggest a source 29 of 35 at a depth of 7 9- 8 0 km and a volume decrease of approximately 8 to 12 million cubic meters Based on assumptions made by Palano et al 2012 this volume change equates to a pressure change of roughly 1000 MPa The results of the resolution test shown in Figure 13 indicate that it is likely that the authors proposed co- eruptive deformation models would not be well resolved or detected by the SAR data used in this work 5 3 Pumice Plain All four data sets processed in this study consistently show definite subsidence LOS Increase of an area of the pumice plain 6 km north of the edifice The patch of subsidence covers several square kilometers and has a peak average velocity on the order of 10 mm yr When comparing LOS velocities between contemporaneous data sets there are only minor discrepancies in the pre- eruptive period Larger discrepancies on the order of 2- 3 mm yr exist between the average velocities of the two post- eruptive data sets in some locations but they merely reflect scatter in the time series and do not suggest that the apparent subsidence is actually noise The subsidence signal appears more localized through time with some locations experiencing increased rates of subsidence while rates at many other locations decreased One physical interpretation of the subsidence signal is that large amounts of ice were entrained and buried in flows during the 1980 eruption and having being well insulated by debris are still slowly melting as suggested by Poland and Lu 2008 Another possible cause suggested by Poland and Lu is the gradual settlement and compaction of unconsolidated eruptive deposits Finally the subsidence can possibly be attributed to some hydrologic change in the subsurface possibly tied to nearby Spirit Lake which was significantly impacted by the 1980 eruption Poland and Lu 2008 30 of 35 6 Conclusions InSAR studies of deformation at volcanoes with high vertical relief are highly affected by atmospheric phase delays caused by changes in the distribution of water vapor through time which must be removed in order to obtain accurate surface velocities A statistical test on a suite of atmospheric removal techniques reveals that within the category of phase- elevation trend fitting techniques velocity results do not vary significantly Contrastingly methods that use independent climate data can produce markedly different results from those corrected by a trend fitting technique In some cases especially when the signal- to- noise is low the results of the two types of correction techniques differ by so much that the sense of direction of apparent ground motion is reversed In the case of volcanic deformation centered on an edifice methods that model atmospheric phase delay using independent climate data are preferred because unlike the trend fitting techniques they do not remove or reduce any real topographically correlated deformation signal The PS InSAR results for the two data sets covering the period of 1995 to 2002 are inconsistent with one another and do not provide conclusive evidence for any pre- eruptive deformation at a broad scale or localized to the crater or edifice Furthermore the velocities for the edifice and crater are quite low on the order of 1 cm yr or less making any true signal difficult to distinguish from the noise It is possible that surface deformation occurred on the edifice during the pre- eruptive period but it was either below the level of the noise obscured by atmospheric artifacts or cannot be resolved with the temporal availability of data Although subtle co- eruptive deflation of up to 15 mm yr and a transition to post- eruptive inflation is known to have occurred through analyses of data provided by the dense GPS network installed in late 2004 the PS InSAR results again contradict one another and do not confirm the observed signal The existence of a patch of subsidence on the pumice plain north of the edifice discovered previously is confirmed across all data sets from 1995 to 2010 It also appears that the subsidence slowed and has become more localized through time 31 of 35 While pre- eruptive deformation is not imaged on either the edifice or in the crater we expect that PS InSAR should successfully resolve large signals on Mount St Helens Resolution tests performed on synthetic spheroidal deformation data with noise analogous to that of this study are able to constrain the range of allowable depths and pressure changes of a potential source While pre- eruptive deformation sources with low changes in pressure at greater depths are unlikely to be imaged by GPS or InSAR data available from that time period Persistent Scatterer analyses do significantly improve the spatial density of observations and also our ability to resolve or rule out combinations of depth and pressure for a potential source Acknowledgements SAR data were obtained from the WInSAR and the 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  • 2014
    • Globokar, Danika - M.S. Thesis
      Testing thermal viscous remanent magnetization (TVRM) as a tool to date geomorphic events 2014, Globokar, Danika , Danika Globokar TESTING THERMAL VISCOUS REMANENT MAGNETIZATION TVRM AS A TOOL TO DATE GEOMORPHIC EVENTS Danika Globokar A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science University of Washington 2014 Committee: Juliet Crider Russell Burmester Terry Swanson Program Authorized To Offer Degree: Department of Earth and Space Sciences Copyright 2014 Danika Globokar Page i University of Washington ABSTRACT Testing thermal viscous remanent magnetization tvrm as a tool to date geomorphic events Danika Globokar Chair of the Supervisory Committee: Assistant Professor Juliet Crider Earth and Space Sciences When a rock forms it acquires a thermal remanent magnetization TRM aligned with Earth s magnetic field If the rock becomes misaligned with the magnetic field by e g rockfall or glacial plucking and deposition it may acquire a thermal viscous remanent magnetization TVRM which partially overprints the TRM The strength of the TVRM is dependent on the exposure time and temperature Neel 1949 Given the temperature and duration of heating required to remove the TVRM along with estimates of the environmental temperature one can determine the exposure time required to produce it thereby dating displacement I evaluate the potential for TVRM dating using a suite of cosmogenically-dated granodiorite moraines in the Icicle Creek drainage of the North Cascades Washington with ages ranging 13-112 ka About 40% of boulders and 25% of samples contained both a TVRM and TRM component A subset of these were identified as qualifying samples whose TVRM components were in the direction of magnetic north This is a critical distinction to make as it indicates that the TVRM was more likely acquired since moraine emplacement The temperature at which a TVRM is removed from a sample is the unblocking temperature Tu or turning point temperature I used nomographs published by Pullaiah et al 1975 and Middleton and Schmidt 1982 to translate Tu to a displacement age and compared output ages from both methods The Middleton Page ii and Schmidt equation yielded moraine ages within about an order of magnitude of cosmogenic ages while the equation of Pullaiah et al yielded ages that differed by multiple orders of magnitude This difference suggests that pseudo-single-domain magnetite is the remanence carrier in the moraine boulders Error inherent in the dating method includes mis-identification of the turning point due to a diffuse TVRM TRM relationship correcting for oven temperature gradients and relying on assumptions for field acquisition conditions all of which have the potential to introduce large variation into an age At present TVRM is a useful relative dating method to confirm geomorphic interpretations and may provide approximate age constrains where no other methods are applicable Page iii ACKNOWLEDGEMENTS First and foremost I offer my sincerest gratitude to my advisor Professor Juliet Crider for her constant unwavering support throughout my entire tenure at the University of Washington Her patience and dedication to my research particularly when the going got tough helped guide me through developing and writing my thesis It s difficult to find words to express my gratitude for the countless hours of guidance and encouragement provided over the past three years so I leave it as a simple and heartfelt Thank you I could not have done it without you Juliet Russell Burmester Research Associate at Western Washington University was also instrumental in my paleomagnetism research I fondly call him the paleomag guru when I explain my thesis to friends and colleagues and I attribute much of my understanding of paleomagnetism to his teachings During my laboratory work Russ was right beside me studying the results His promptings and questions forced me to evaluate my samples more thoroughly and seek answers through more in-depth analysis My research spans two disciplines and he provided a strong support pillar for one of those My other committee member Terry Swanson furthered my understanding of the Icicle Creek basin s glacial history Not many professors would spend an entire day playing show and tell in the field for a single graduate student I also would like to thank the Geological Society of America and the University of Washington s Department of Earth and Space Sciences for the funding they were able to provide to me in order to make this thesis possible Additionally the Pacific Northwest Paleomagnetic Laboratory at Western Washington University provided the equipment needed to analyze my samples My peers Brandon Miller and Karl Lang provided much-needed hands in the field in freezing snow and scorching summer heat respectively Thanks guys Finally I thank my family To my sister thanks for teaching me how to edit my figures To my husband thanks for the steady supply of encouraging words and for pushing me to keep inching towards that light at the end of the tunnel I wouldn t have made it without you Page iv TABLE OF CONTENTS Page 1 0 INTRODUCTION 1 1 1 Geomorphic Events and Motivation 1 1 2 Other Dating Techniques 1 1 2 1 Relative Dating Methods 2 1 2 2 Absolute Dating Methods 2 1 3 Basic Paleomagnetism 4 1 4 TVRM 4 1 4 1 Jumping Magnetic Moments 6 1 4 2 Multi-Domain Magnetite 6 1 5 Testing the TVRM Technique in Granodiortie Moraines 7 2 0 GEOLOGIC SETTING 8 2 1 Moraine Sequence and Nomenclature 8 2 2 Moraine Ages 9 2 3 Moraine Recognitition and Testing Conventions for this Study 10 3 0 PALEOMAGNETISM STUDIES OF THE MOUNT STUART BATHOLITH 12 4 0 METHODS 15 4 1 Field Sampling 15 4 2 Laboratory Methods 16 5 0 RESULTS 20 5 1 Petrologic Characteristics 21 5 2 Characteristic Demagnetization Behaviors on Zijderveld Diagrams 23 5 3 Specimen Core Boulder Homogeneity 24 5 4 Choosing a Turning Point Temperature 24 5 5 Oven Temperature Gradient 26 5 5 1 Applying Turning Point Correction Factors 27 5 6 Turning Point Temperature Statistics 28 5 7 Hysteresis Loops 28 5 8 Day Plot Results 30 Page v TABLE OF CONTENTS CONTINUED Page 6 0 ANALYSIS 32 6 1 Day Plots Hysteresis and VSM 32 6 2 Stereonet Data Yields Qualifying Samples 33 6 3 Samples and Averages are in Chronological Order 34 6 4 Converting Turning Point Temperatures to Ages 35 6 4 1 Middleton & Schmidt vs Pullaiah Nomographs 35 6 4 2 Field Acquisition Temperature Assumptions 36 6 4 3 5oC Turning Point Identification Error 37 6 4 4 Age Variation Within Single Moraine 37 6 4 5 Moraine Age Prediction Using TVRM Method 38 6 5 Qualifying Samples: Boulders Cores Samples Needed 38 6 6 Turning Point Temperatures 39 7 0 CONCLUSIONS 41 8 0 REFERENCES CITED 42 LIST OF TABLES Table 1 Relative and pseudo-quantitative dating methods of boulders and moraines 46 Table 2 Evolution of Icicle Creek glacial nomenclature 46 Table 3 Moraine population mean and oldest cosmogenic ages 46 Table 4 Boulders cores and specimens collected for each moraine 46 Table 5 Weathering classification reproduced from Brown 1981 47 Table 6 Boulder petrologic and weathering characteristics 48 Table 7 Summary of demagnetization behaviors by moraine 49 Table 8 Turning point temperature statistics by moraine 49 Table 9 Qualifying Samples summary table 50 Table 10 Average moraine turning point temperatures for qualifying samples 50 Table 11 Predicted Ages from Acquisition Temperatures 50 Table 12 TVRM dating method age outputs and comparison with cosmogenics 51 Page vi TABLE OF CONTENTS CONTINUED Page LIST OF FIGURES Figure 1 Example TRM TVRM Zijderveld Plot 52 Figure 2 Different Domain States Of Magnetite 52 Figure 3 Icicle Creek Drainage Basin Study Area 53 Figure 4 Spatial Extent of Mount Stuart Batholith and Magnetic Mineralogies 54 Figure 5 Moraine Crests and Sample Locations 56 Figure 6 Boulder Petrologic Fabric Example 57 Figure 7 Characteristic Zijderveld Plots 58 Figure 8 Oven Temperature Gradients 59 Figure 9 Hysteresis Loops of Paramagnetic Material SD and PSD Magnetite 61 Figure 10 VSM Results Plotted on Day Plot 62 Figure 11 Stereonets of TVRM and TRM Directions for Qualifying Samples 63 Figure 12 Turning Point Temperatures for Qualifying Samples by Moraine 64 Figure 13 Pullaiah vs Middleton & Schmidt: Rat Creek and Mountain Home 65 Figure 14 M&S Nomographs: Field Acquisition Temperature Assumptions 66 Figure 15 M&S Nomographs: - 5oC Turning Point Identification Error 67 Figure 16 M&S Nomographs: Age Variation Within Single Moraine 68 Figure 17 M&S Nomographs: Age Predictions For All Moraines Using TVRM Method 69 Page vii 1 0 INTRODUCTION Can thermal viscous remanent magnetization TVRM be used to date geomorphic events such as rock fall and moraine deposition Unlike other dating methods commonly used by geomorphologists the TVRM dating method doesn t depend on surface exposure quartz content or organic matter It has the potential to cover a wide range of ages several decades to 100ka date various rock types and is relatively inexpensive Potential applications include dating rock fall moraine deposition and archeological masonry I first review common geomorphic dating tools and their shortcomings Then I will introduce the TVRM dating method and how it was used in the context of this study 1 1 Geomorphic Events and Motivation Geology tectonic geomorphology and archeology are only some of the numerous disciplines that require time controls on landscapes to answer a wide array of scientific questions Ages of rock fall moraine deposition fault propagation and anthropogenic displacement of rocks serve to increase hazard awareness elucidate historic climate shifts and give insight into human occupation in an area The variety in types of dateable events combined with differences in the question being asked precision needed material being dated and environmental and physical constraints has led to the development of a wide arsenal of dating techniques for geomorphology 1 2 Other Dating Techniques A fundamental division of dating techniques is the distinction between relative and absolute dating methods Relative dating yields only relational information moraine X is older than moraine Y whereas absolute dating allows us to assign a numerical age to a surface without reference to another surface Additionally geomorphologists classify some dating methods as pseudo-quantitative in that they are relative dating techniques but can be used to obtain absolute ages if calibrated to a locally known event or boulder age Page 1 1 2 1 Relative Dating Methods Some commonly used relative dating techniques their range of ages as well as materials needed to date the surface or event are summarized in Table 1 Clast seismic velocity is more commonly known as clink vs thud Geomorphologists have used this technique for years by hitting the boulder to be dated with a hammer Younger less weathered boulders produce a sharp clink sound whereas older boulders produce a dull thud Although this method was quantified by Crook 1986 it is still limited as the user is forced to calibrate the technique against locally-known surfaces of the same rock-type Gillespie 1982 The weathering rind dating method relies on the basic assumption that minerals near the surface of a boulder will experience chemical and mechanical weathering thereby creating a rind of altered minerals The thickness of the rind is related to length of time the boulder has been emplaced Though geomorphologists have sought to quantify this technique it remains at best a pseudo-quantitative method as different lithologies local climate and vegetation all introduce age uncertainty and calibration to a known local surface age is required Colman and Pierce 1986 In addition to the aforementioned relative dating tools we can also obtain relative ages for moraines by comparing where one moraine is in relation to another: the oldest moraine is the moraine furthest down-valley whereas the youngest moraine is the furthest up-valley Intermediate-aged moraines would fall between the two This dating method is valid as long as the moraines themselves are still present and not completely degraded 300 ka 1 2 2 Absolute Dating Methods Common absolute dating methods include among others radioisotopic dating for organic material such as wood shells and coral thermoluminescence dating quartz and feldspar sands paleomagnetic secular variations fine sediment tephrochronology volcanic ash Page 2 dendrochronology tree rings sclerochronology coral and cosmogenic nuclide surface exposure dating Cosmogenic nuclide dating used to date the length of time a rock surface has been exposed to the Sun s cosmic rays is currently one of the most commonly used dating techniques in geomorphology Heyman et al 2011 Putkonen and Swanson 2003 This method measures the amount of cosmogenic nuclides that have accumulated in a sample sitting at Earth s surface the amount of which can be equated to age because the nuclides are produced at a known rate Numerous isotopes can be used depending on the mineralogy of the rock to be dated 10Be 26Al He Ne 36Cl and the technique can be used to date surface exposures from 0 4 Ma Phillips et al 1986 Under certain conditions this method has very high precision but there are shortcomings to cosmogenic dating which can introduce significant uncertainty A rock can have more or fewer nuclides than expected if it was previously at the surface slowly exhumed over time covered with snow for part of the year eroded resting at an unexpected angle angle of incidence or shielded by a nearby cliff In an analysis of published cosmogenic exposure ages for moraine boulders Putkonen and Swanson 2003 calculated an average range of 38% between the oldest and youngest boulders from each moraine Though one of the more precise dating tools cosmogenic nuclide dating is also one of the most expensive costing up to 2 000 or more per sample Purdue Rare Isotope Measurement Laboratory 2014 Although there are many relative and absolute dating methods each with different strengths and weaknesses they are not always appropriate or applicable in all situations TVRM offers a complementary tool for dating geomorphic events TVRM directly dates the length of time a rock has been displaced rather than simply surface exposure TVRM acquisition occurs even if the sample is buried and it does not require quartz or organic matter This technique has the potential to date a variety of rock types a range of ages and is relatively inexpensive especially compared to some dating techniques currently being used Page 3 1 3 Basic Paleomagnetism Magnetite hematite and pyrrhotite are the most common minerals that retain a magnetization When these minerals grow large enough or cool in an igneous rock through their blocking temperature they can acquire a remanent magnetization in the direction of the ambient magnetic field Size and composition control when during growth or cooling a grain is magnetized or acquires its thermal remanent magnetization TRM This magnetization is in line with Earth s magnetic field at the time and location of cooling Mineral size and composition along with grain shape are the main controls of stability of the magnetization Stable magnetizations are used to obtain paleomagnetic directions paleopole locations and thereby reconstruct plate and continental movement Butler 1992 Tauxe 2010 Magnetizations that are less stable allow changes in a rock s magnetization with time which can be used for other purposes such as TVRM dating 1 4 TVRM If a rock topples or is displaced so that it is no longer in-situ such as in a rock fall or moraine plucking and deposition it will likely be deposited such that its TRM is no longer in alignment with Earth s magnetic field This misalignment causes some of the weak moments in the magnetic carriers to jump and align with the external magnetic field This introduces a second component of magnetization a thermal viscous remanent magnetization TVRM which partially overprints the TRM Tauxe 2010 The strength of the TVRM is dependent on exposure time and temperature Neel 1949 Thus assuming constant temperature the larger the TVRM component the longer a rock has been displaced from its original orientation in the magnetic field The sum of these two components is the natural remanent magnetization NRM An example TVRM TRM demagnetization plot is shown in Figure 1 In principle a rock s TVRM can be removed by thermally demagnetizing the sample at a timetemperature combination that is equivalent to that at which the TVRM was acquired Neel 1949 The temperature at which the TVRM component is completely erased is termed its unblocking temperature Tub For single-domain magnetite Neel 1949 describes the Page 4 theoretical relationship between TVRM acquisition conditions and unblocking conditions which Taxue 2010 simplifies to: where C is the characteristic frequency of thermal fluctuation 1010 Hz Neel 1949 Pullaiah 1975 Ms T is magnetic susceptibility as a function of Temperature T is temperature in either the lab or field and is the relaxation time a measure of the probability of a mineral to change or flip its remanence Relaxation time varies greatly depending on grain size grain shape and temperature As magnetite grain size increases relaxation time logarithmically increases from seconds unstable remanence to over one billion years Tauxe 2010 Furthermore increasing the temperature to which a mineral is exposed decreases relaxation times The TVRM dating method exploits the time-temperature relationship described by Neel 1949 We can directly measure unblocking time and temperature in the laboratory and make an educated estimate of the paleotemperature of the rock at Earth s surface With the values of Ms and C being constant and known the only undefined variable is field This the relaxation time in field conditions is the length of time the rock has been acquiring a TVRM in its new orientation to Earth s magnetic field Sets of nomographs of equivalent time-temperature combinations for single domain magnetite have been published by Pullaiah et al 1975 and Middleton and Schmidt 1982 though the two are quite different from one another Both sets of authors initially derive their nomographs from the single domain theory of Neel 1949 Pullaiah et al supplement their calculations with laboratory results using experiments on single-domain magnetite grains Middleton and Schmidt supplement their work with field observations and found their results to be more closely in accord with Walton s 1980 calculations which assume a log-normal grain-size distribution of magnetite in natural settings This deviates from the purely single-domain theory of Neel 1949 in that it accounts for a larger grain-size distribution of magnetite and applies to pseudo-single domain magnetite Walton 1980 modifies Neel s equation to: Page 5 which assumes a log-normal grain size distribution of magnetite grains in a sample Sets of nomographs following Walton s 1980 above equation been published by Middleton and Schmidt 1982 These nomographs and those of Pullaiah 1975 are two of the more commonly used nomographs in the paleomagnetism community 1 4 1 Jumping magnetic moments Ferromagnetic mineral grains seek to minimize their total energy by changing their magnetic configurations Tauxe 2010 Within a single magnetic crystal certain directions are at a lower energy than others and the magnetic moment can switch from one easy direction to another Doing so however requires overcoming the energy barriers that hold the direction of magnetic remanence in place When a mineral s moment is misaligned with an external magnetic field the moment has additional energy similar to the potential energy a mass has when placed in a gravitational field The forces keeping the magnetic moment in place are the magnetocrystalline and shape anisotropy energies Butler 1992 If the external magnetic energy overcomes the resistant anisotropy energies the moment will jump across the barrier and align itself in a new easy direction The likelihood of this happening is defined by a minerals relaxation time tau which is a measure of the probability that a grain will have sufficient thermal energy to overcome the anisotropy energies and switch its moment Two ways to overcome the anisotropy energies are by applying a sufficiently large external field or increasing the temperature of the mineral Tauxe 2010 Butler 1992 1 4 2 Multi-domain magnetite TVRM as described by Neel 1949 theory applies to single-domain SD magnetite Single domain particles have relatively low self-energies and are uniformly magnetized in one direction Page 6 As magnetite crystal size increases past 80nm the internal self-energy increases and a single direction of magnetization is no longer the lowest energy state To reduce self-energy large magnetite grains separate their magnetization into multiple magnetic domains in which several antiparallel moments are separated by domain walls Figure 2 It is common for magnetite in rock to vary in grain size from nanometers through 80nm pseudo-single domain PSD and greater than 200nm multi-domain MD Tauxe 2010 Due to multiple directions of magnetization in a crystal as well as domain walls which accommodate some of the crystal s self energy MD magnetite does not strictly behave within the confines of SD theory Unblocking temperatures obtained from thermal demagnetization of MD magnetite are higher than SD magnetite theory predicts making the TVRM acquisition period seem longer than it truly is Dunlop et al 1997 For this reason rocks with remanence carried by MD magnetite are not optimal candidates for the TVRM dating method 1 5 Testing the TVRM technique in granodiorite moraines The TVRM dating technique has been used successfully to date basalt landslides Smith and Verosub 1994 Crider et al 2010 emplacement of limestone blocks in archeological sites Borrodaile and Almqvist 2006 and regionally acquired TVRM in limestone Kent 1985 These studies obtained ages within an order of magnitude accuracy with increased accuracy when calibrated to another event of known age With the exception of Kent 1985 each study dated events younger than 20ka In my study I evaluate the application of TVRM dating to granodiorite boulders in events of ages 12ka -105ka with the eventual goal of expanding applications further Page 7 2 0 GEOLOGIC SETTING The study area is in the Icicle Creek drainage basin along the Eastern margin of the Cascade Mountain Range in central Washington State Figure 3 The basin has experienced multiple pulses of glaciation in the past 200 000 years Glaciation has left its mark upon the landscape in the form of the classic U-shaped valley as well as the deposition of till outwash and moraines The moraines are comprised almost solely of granodiorite boulders from the southeast region of the Mount Stuart Batholith MSB 2 1 Moraine Sequence and Nomenclature The glacial-geologic history of the basin has been studied since the early 1900 s with the first description of the moraines published by Page 1939 In his study Page identified three distinct moraines that provided evidence for three successive Pleistocene glaciations each of which was less extensive than the previous In order from most to least extensive he named the glacial deposits Peshastin Leavenworth and Mount Stuart He described the Peshastin deposit as notably decayed with till boulders representing less than 5% of the ground surface Though mostly composed of granodiorite boulders other rock types such as schist gneiss serpentine conglomerate sandstone and shale were present in small amounts He notes that some of the average-sized granodiorite boulders 3 or 4 feet in diameter are weathered to the core and that all boulders show weathering to a depth of 3-8 inches below the surface The Leavenworth deposit is identified as a well-preserved lateral moraine that runs several miles along Boundary Butte Ridge It is 400 to 600 feet high and Page describes the moraine as resembling a railroad embankment of gigantic proportions Boulders in this moraine usually cover 5-75% of the ground and are much less weathered than Peshastin boulders The youngest moraine Page identified was what he named the Stuart moraine Moraines from this glaciation exist solely in the higher parts of the region and one of the moraines at the mouth of Rat Creek is described as a perfect horseshoe Page reports that boulder composition and count are similar to Leavenworth deposits down valley Page 8 A subsequent study by Porter 1969 renamed the three deposits previously identified by Page and also recognized a fourth older moraine in the region that he designated as Peshastin Porter also subdivided the Leavenworth deposits into four separate substages with Page s Rat Creek Stuart glaciation representing the youngest Leavenworth advance Waitt 1977 proposed additional nomenclature changes of the two older moraines to Mountain Home and Boundary Butte and further subdivided the Leavenworth deposits into five stages See Table 2 for nomenclature history In Porter and Swanson s recent work 2008 eight distinct moraines were identified and nomenclature was revised The five Leavenworth stages proposed by Waitt were separated into two stages of Rat Creek moraines previously Page s Stuart deposits and two stages of Leavenworth moraines Porter and Swanson revert back to the Peshastin nomenclature Page used for the prominent yet highly weathered moraine and retain Waitt s designation of Boundary Butte for the oldest moraine that lies upslope from it They also identified two previously unrecognized lateral moraines between the Leavenworth and Peshastin deposits One deposit can be traced discontinuously for 5km and nearly parallels the local Mountain Home Road this has been designated the Mountain Home moraine The second moraine has limited exposure consisting of only two short lateral moraine segments that lie outside the Mountain Home moraine Porter and Swanson propose that it could potentially be Peshastin-aged but designate it as pre-Mountain Home 2 2 Moraine Ages Page 1939 and Porter 1969 compared Icicle Creek moraine deposition to global glaciations and both speculated that Leavenworth deposits were late-Wisconsin in age Porter further inferred that the Peshastin moraine was pre-Wisconsin and that the intermediate deposit was early Wisconsin in age Waitt 1977 estimated that the Leavenworth moraines are 11 500 to 18 000 years old the Mountain Home moraine Peshastin is 130 000 to 140 000 years old and the Boundary Butte moraine is 700 000 to 850 000 years old based on theoretical weathering rates of boulders Waitt et al 1982 trace the Galcier Peak tephra layer Porter 1978 to the outer edge of cirque glaciers above the Rat Creek moraines This implies that the Rat Creek Page 9 advance must be older than 11 000 to 11 300 14C years which is the age of the tephra Foit et al 1993 and Wait et al 1982 conclude the Rat Creek advance took place between 11 000 and 13 000 years ago Perhaps the greatest step forward in establishing numerical ages for the local pulses of glaciation was work by Porter and Swanson 2008 which utilized 36 Cl cosmogenic nuclide dating to calculate surface exposure ages for the moraines Chlorine-36 is produced in rocks in the top meter of the lithosphere through cosmic-ray-induced reactions with natural 35 Cl 39 K and 40 Ca present in the rocks These reactions and the subsequent accumulation occur at a known rate but vary based on latitude elevation angle of incidence to the sun and snow cover Zreda et al 1991 By calibrating Icicle Creek isotope production rates with samples from the Puget Sound region at the same latitude Swanson and Caffee 2001 Porter and Swanson 2008 were able to date the Icicle Creek moraines quantitatively using the cosmogenic dating method as applied to 36 Cl Though average surface exposure ages were calculated for each moraine Porter and Swanson concluded that the true age of an individual Icicle Creek moraine is more likely represented by the age of the oldest boulder that is not a statistical outlier Putkonen and Swanson 2003 As the moraine weathers boulders are gradually exhumed and start accumulating cosmogenic isotopes at different times Hence excluding statistical outliers the oldest cosmogenic age would belong to a boulder that did not have prior inheritance and was near the top of the moraine crest Both mean cosmogenic ages and oldest cosmogenic age from the Porter and Swanson study are summarized in Table 3 2 3 Moraine recognition and testing conventions for this study For this study I accept the oldest moraine ages provided by Porter and Swanson to be most accurate and adopt the nomenclature from their 2008 study I test the TVRM dating technique by comparing our age results to those published ages Because of the close ages of Rat Creek I to Rat Creek II as well as Leavenworth I to Leavenworth II I do not expect to distinguish between those pairs of ages I also did not sample pre-Mountain Home deposits because of their close Page 10 age-accordance with the Peshastin deposits Porter and Swanson had difficulty dating the Boundary Butte deposits because of extreme weathering and boulder degradation In the field I was unable to locate any boulders competent enough from which to obtain samples and therefore excluded the Boundary Butte age from this study By combining or not testing certain moraines I limit this study to test four distinct ages: Rat Creek II 13 5ka Leavenworth II 17ka Mountain Home 72 2ka and Peshastin 112 8ka Page 11 3 0 PALEOMAGNETISM STUDIES OF THE MOUNT STUART BATHOLITH The bedrock of this area from which the moraine boulders are derived is the Mount Stuart Batholith MSB A granodioritic pluton of Cretaceous age the origins of the batholith remain controversial Two primary competing hypotheses exist that attempt to explain its history over the last 90Ma Beck and Noson 1972 were among the first to study the paleomagnetic properties of the MSB and they reported highly discordant paleomagnetic directions from current magnetic North in batholith rocks and other Cretaceous rocks of the North American Cordillera These results gave rise the Baja British Columbia Baja-BC hypothesis Irving 1985 Umfoeher 1987 Cowan et al 1997 Housen and Beck 1999 which proposes that the Insular Superterrane including the MSB formed 90 to 95Ma at a location 3000km south of its present location Subsequent northward translation along the continental margin between 85 and 55Ma resulted in the terrane s present location and discordant paleomagnetic direction Some workers reject the possibility of thousands of kilometers of translation and instead prefer tectonic reconstructions that limit latitudinal displacement of these terranes Mahoney et al 1999 Recent sedimentary studies both support Krijgsman and Tauxe 2006 and disagree Kim and Kodama 2004 with the Baja-BC hypothesis Though the Baja-BC hypothesis has been subjected to logically crucial tests Cowan et al 1997 Mahoney et al 1999 Housen and Beck 1999 to evaluate geologic possibility the basis for the hypothesis relies largely on paleomagnetic evidence from the terranes Because of heavy reliance on the paleomagnetic data Housen et al 2003 compiled existing paleomagnetic data and collected additional data from new sites in order to review the part that the Mount Stuart batholith played in the Baja BC controversy Their reevaluation of the MSB confirms prior paleomagnetic findings in that paleomagnetic directions are highly discordant and also supports the Baja BC hypothesis Central to finding these paleomagnetic directions is understanding how magnetic remanence is carried and recorded in the host rock with different minerals showing different characteristics during demagnetization Initial paleomagnetism work in the MSB by Beck and Noson 1972 and Beck et al 1981 used alternating field AF demagnetization to show that magnetite is the Page 12 magnetic carrier of remanence in much of the batholith Conversely Paterson et al 1994 concluded that the remanence of the batholith was carried by pyrrhotite since 23 of their 27 sites showed low unblocking temperatures 0 4 T and did not reach its unblocking temperatures when thermally demagnetized Only one site distinctly shows low 270-320 unblocking temperatures which indicates the presence of pyrrhotite Other sites from the Housen et al 2003 study show poorly defined demagnetization behaviors with low unblocking temperatures again indicating pyrrhotite as the remanence carrier This carrier was found to be spatially restricted to dikes and areas within 1km of the edge of the batholith Housen et al 2003 conclude that the remanence of the majority of their MSB sites along with 10 of 11 of the MSB sites from Beck et al 1981 Page 13 are carried solely by magnetite From the results of their laboratory tests they further classify the magnetic carrier as single-domain magnetite Housen et al 2003 explain the discordance between their results and Paterson et al s 1994 as a result of several possible factors First Paterson et al define the presence of pyrrhotite based on laboratory unblocking temperatures of 330oC some samples started to crumble and show signs of internal fracturing To prevent granular disintegration select samples were immersed in a clear non-magnetic ceramic hardener for two to five minutes Oven temperature over the course of heating was monitored and logged to increase accuracy Although there is digital display of oven temperature accuracy of these monitors was confirmed by the use of non-reversible temperature labels These labels are a one-time usage indication that a specified temperature has been exceeded and are useful in a situation where an operator does not have access to the label during a test These labels retain the record of temperature reached even after heating is over The temperature labels were placed on samples in different zones of the oven far left center far right to measure the temperature gradient within the oven and to observe discrepancies between the temperature at the surface of the rock samples and oven sensor temperatures With the exception of the LTD treatment the above steps are standard paleomagnetism techniques in thermal demagnetization Neel 1949 Butler 1992 Housen 2003 In this study I additionally employed LTD to reduce the contributions of multi-domain MD magnetite grains to our results Intermediate to felsic plutons like the Mount Stuart Batholith are commonly coarse grained and thus likely contain large MD magnetite grains 200 nm Dunlop et al 1997 observed anomalously high unblocking temperatures distributed over a wide range 250oC in rocks containing MD magnetite Both the average and maximum unblocking temperatures in this range were much higher than expected when compared to single-domain Neel 1949 theory These high unblocking temperatures resulted in the TVRM acquisition event to appear older than it actually was Additionally the TVRM recorded by MD grains even if acquired at low temperatures can have laboratory unblocking temperatures of up to the Curie temperature of magnetite 580oC Dunlop and Xu 1994 Although Housen et al 2003 determined SD magnetite to be the primary carrier of remanence in the Southern end of the MSB I cannot assume that MD grains are absent from the samples Page 17 due to the nature of the bedrock being a coarse-grained felsic pluton Because the TVRM dating technique relies on identifying the precise unblocking temperature of the TVRM component the large range of unblocking temperatures resulting from the presence of MD magnetite could reduce precision and accuracy of ages obtained using this method Misidentification of the unblocking temperature by even 5oC results in a 20-40% error in age If MD magnetite is found to dominate the samples the Middleton and Schmidt 1982 nomographs should be used rather than nomographs generated by Pullaiah et al 1975 To reduce the contribution and overprint of MD magnetite to a sample s true remanence I employed low temperature demagnetization LTD so as to erase MD remanence and isolate SD remanence After I measured initial remanent magnetization at room temperature I immersed approximately 90% of the samples in liquid nitrogen T 77K in a non-magnetic container After 20 minutes of immersion the samples were extracted and allowed to rewarm to room temperature in a field-free room for 10-20 minutes Magnetization of each sample was measured again Samples that experienced a great change in magnetic moment after LTD treatment were treated in liquid nitrogen again until remanence changed by less than 5% between subsequent measurements The physical basis for the LTD treatment is described at length by Dunlop and Ozdemir 1997 and Housen et al 2003 At a temperature of 120K magnetite undergoes a phase transition from cubic structure to monoclinic structure The changes in magnetite s magnetic and electrical properties as it passes through this temperature are referred to as the Verwey transition Verwey 1939 Thermally cycling a rock between the Verwey temperature and room temperature in a field-free room has a different effect on the remanence carried by single- versus multi-domain magnetite While single domain grains retain a near perfect memory of their original room temperature remanence larger multi-domain grains lose a significant portion of their remanence The MD magnetite is thought to demagnetize by unpinning domain walls caused by internal crystal defects within an individual grain Dunlop and Ozdemir 1997 Tauxe 2010 For a sample containing both single- and multi-domain magnetite grains LTD cycling will preferentially erase the remanence carried by MD grains and leave SD grains remanence unaffected Dunlop et al 1997 Housen et al 2003 The LTD treatment has been used in past Page 18 studies Housen et al 2003 Warnock et al 2000 Borrodaile and Almqvist 2006 to isolate and erase the remanence carried by MD magnetite and leave the more stable SD remanent magnetization intact to be measured In particular Dunlop et al 1997 found that pretreating their MD-containing samples with the LTD treatment resulted in unblocking temperatures that matched the temperatures predicted by Pullaiah et al s model 1975 It is worth noting that remanence carried by MD magnetite could possibly be stabilized by unknown mechanisms unaffected by the LTD treatment The 2-G 755 DC-SQUID magnetometer measures and records a sample s magnetism at each temperature step The output of these measurements is a set of x y z coordinates that can be translated into polar coordinates of inclination and declination All of the temperature step measurements from a single sample were then plotted on the same Zijderveld diagram to observe changes in magnetic direction and intensity with progressive thermal demagnetization Figure 1 I utilized further tests to determine magnetic mineralogy of my samples I placed rocks chips from unheated subsamples in a Vibrating Sample Magnetometer VSM to obtain hysteresis curves isothermal remanent magnetization IRM curves and direct current demagnetization DCD measurements Some samples signals were overshadowed by the paramagnetic behavior of biotite To remove this signal from the samples I crushed four samples each displaying a different hysteresis behavior and separated the quartz and plagioclase from the biotite The crushed felsics particles internal crystal lattice energy the magnetization will be in the opposite direction upon removal of the magnetic field Loops are generated by subjecting a specimen first to a very strong positive field and then gradually decreasing th field until it is very strong in the opposite direction The process is then repeated changing the field from negative to positive Different minerals such as hematite biotite and magnetite SD MD react differently to the alternating external fields The differences are primarily caused by the mineral s ability to hold Page 28 remanent magnetization or their memory of the field that has been applied to them in the past Thus some minerals have characteristic unique hysteresis loop shapes By visually observing hysteresis loops from the Icicle Creek moraines as well as graphing the ratio of their resulting magnetic parameters I can gain insight into the magnetic carriers within my samples The characteristic hysteresis loops found in this study are shown in Figure 9 A straight diagonal line with a slope of 1 Figure 9A is indicative of a specimen dominated by paramagnetic behavior A paramagnetic mineral like biotite hold no remanence Thus it only holds a magnetization in the presence of an external field and when the field is removed the specimen loses its magnetization The strength of the remanence carried is proportional to the external field stronger field stronger apparent mineral magnetization Many samples hysteresis loops show this behavior which is not surprising given that biotite is visually abundant in the MSB granodiorite The slight jog in the hysteresis loop near the origin is evidence of another magnetic carrier one that actually holds remanence in the sample Biotite itself does not hold a true remanence: it merely overpowers the signal of the actual remanence carrier To gain insight into the true magnetic remanence carrier in the rocks I crushed the specimens and manually separated the felsic minerals plagioclase and quartz from the biotite It is assumed that the microscopic magnetite minerals are inclusions within the felsics Dunop and Ozdemir 1997 I then placed the powdered felsic minerals in a gel capsule and ran the specimen on the vibrating sample magnetometer to generate its hysteresis loop Adjustments were made in order to correct for grain vibration in the gel capsule as well as to account for the background magnetization of the capsule itself The hysteresis loops for a crushed Leavenworth sample and crushed Rat Creek sample are shown in Figure 9B and 9C respectively The Leavenworth loop is characteristic of a specimen whose remanence carrier is single-domain magnetite with uniaxial anisotropy indicating that SD magnetite could be the magnetic carrier within this particular specimen Although the Rat Creek hysteresis loop appears to have a similar shape to the Leavenworth sample the narrower curve the result of a lower M r Ms ratio Page 29 is indicative of lower magnetic stability This hysteresis behavior is indicative of pseudo-single domain magnetite Both Rat Creek specimens for which I ran hysteresis experiments showed this PSD behavior as did the two Peshastin specimen Leavenworth specimens on which I performed the most tests showed a mixture of PSD and SD behavior I did not perform hysteresis experiments on any Mountain Home specimens 5 8 Day Plot Results While hysteresis loops can shed light into the remanence carrier and or domain state they provide additional useful information by way of the parameters Mr Ms and Hcr These parameters combined with the parameter Hc obtained from additional magnetic tests allow us to plot the ratios of saturation remanence to saturation magnetization Mr Ms against the ratio of coercivity of remanence to coercivity Hcr Hc on Day Plots sometimes referred to as Day diagrams A graph of these ratios was proposed by Day et al 1977 and further developed by Parry 1982 as a method of identifying magnetite domain state single-domain SD pseudo-singledomain PSD multidomain MD and by implication grain size Theoretical calculations and actual results allowed Day to place quasi-theoretical boundaries on the Mr Ms vs Hcr Hc plot thereby allowing us to plot the ratio of these parameters for any specimen and at a glimpse determine the domain state of the magnetite within a specimen The Day plot is one of the principal ways paleomagnetists determine domain state and grain size Tauxe 2010 Butler 1992 The Day diagram is divided nominally into regions of SD PSD and MD magnetite It is generally accepted that any specimen with a Mr Ms value of 0 5 contains SD magnetite and 200oC demagnetization steps: Blue LW 212oC Red LW 197oC Green MH LW 204oC Purple Rat Creek 225oC Dashed Lines with corresponding colors indicate the temperature shown on the digital display for that particular boat B Low temperature
    • Harrold, Zoe - Ph.D. Dissertation
      Investigating the effects of Bacillus subtilis endospore surface reactivity on low-temperature aqueous geochemical systems 2014, Harrold, Zoe , Zoe Harrold Investigating the effects of Bacillus subtilis endospore surface reactivity on low-temperature aqueous geochemical systems Zo R Harrold A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2014 Reading Committee: Drew Gorman-Lewis Ph D Chair Ronald Sletten Ph D Bruce Nelson Ph D Program Authorized to Offer Degree: Earth and Space Science 1 Copyright 2014 Zo R Harrold 2 University of Washington ABSTRACT Investigating the effect of Bacillus subtilis endospore surface reactivity on low-temperature aqueous geochemical systems Zo R Harrold Chair of the Supervisory Committee: Drew Gorman-Lewis Ph D Earth and Space Sciences Microbes are a ubiquitous component in water-rock systems including ground and surface waters soils mid-ocean ridge hydrothermal systems and deep sedimentary basins Microbial envelopes provide complex organic surfaces that serve as a physical interface between cellular and geochemical processes and thus represent a confluence of the bio- hydro- and lithospheres As an intrinsic component in water-rock systems microbes have the capacity to influence geochemical cycling in their surroundings through surface mediated pathways This dissertation utilizes Bacillus subtilis endospores a metabolically dormant cell type to isolate and quantify the effects of bacterial endospore surfaces on low-temperature aqueous geochemical processes including ion adsorption and silicate weathering rates Chapter 2 outlines novel methods describing B subtilis endospore growth and harvesting as well as a quality control technique enabling quantification of endospore harvest purity using bright-field and fluorescence microscopy imaging in conjunction with automated cell counting software The resultant average endospore purity was 88 11% 1 error n 22 with a median value of 93% 3 Chapter 3 couples potentiometric titration and isothermal titration calorimetry ITC analyses to quantify B subtilis endospore-proton adsorption We modeled the potentiometric titration and ITC data using four- and five-site non-electrostatic surface complexation models NE-SCM Log Ks and site concentrations describing endospore surface protonation are statistically equivalent to B subtilis cell surface protonation constants while enthalpies are more exothermic The thermodynamic parameters defined in this study provide insight on molecular scale spore surface protonation reactions and provide a robust chemical framework for modeling and predicting endospore-metal adsorption behavior in systems not directly studied in the lab Chapter 4 investigates the B subtilis endospore adsorption capacity of two major elements: magnesium Mg and silica Si We measure Mg and Si adsorption as a function of solution pH adsorbate to adsorbent ratio and in systems containing both Mg and Si NE-SCMs described in Chapter 3 provide a framework for modeling endospore-Mg Mg adsorption to the endospore surface increases with increasing pH adsorbent to adsorbate ratio and high concentrations of total Si Si adsorption was negligible under all conditions studied These findings suggest direct endospore-Mg adsorption is more likely to influence geochemical processes than endospore- Si adsorption In Chapter 5 B subtilis endospores are used to isolate and quantify the effects of bacterial surface reactivity on the rate of forsterite Mg2SiO4 dissolution at circumneutral pH Assays utilizing homogeneous and dialysis bound mineral powder compare the influence of direct spore-mineral and indirect spore-ion interactions on forsterite dissolution rate We show that endospore surface reactivity enhances forsterite dissolution rates through both direct and indirect pathways and as a function of endospore concentration 4 To my grandmother Frances Rhodes and my mother and father Yvonne and James Harrold 5 ACKNOWLEDGEMENTS I would like to express my deepest gratitude to Dr Drew Gorman-Lewis for his guidance and support over the course of my Ph D Dr Gorman-Lewis expertise in surface reactivity and creative approach to experimentation is further complimented by his patient- humble- and positive-nature I am truly fortunate to have learned from and worked with such an adept scientist and could not have asked for a better mentor to lead me through the Ph D process I would also like to thank my committee members Dr Ronald Sletten and Dr Bruce Nelson for their support over the years The opportunity to serve as a field-assistant in Greenland under Dr Sletten provided me with a renewed interest in academia and inspired my ongoing curiosity for sub-glacial geomicrobiology and polar research Dr Nelson s encouragement and enthusiasm for my work have provided me with a sense of excitement for research and have been instrumental to my success at the University of Washington Feedback and suggestions from both Dr Sletten and Dr Nelson helped make this body of work a success I would also like to recognize Dr John Baross my Graduate School Representative for his thoughtful contributions and readiness to help Additional thanks to my brothers David and Andrew Harrold for helping me find humor and light in all things to my extended family for all their encouragement and to my grandmother Frances Rhodes whose adventurous life as a pioneer for women s progress has inspired me since childhood Finally I would like to thank my parents James and Yvonne Harrold for their unending support over the past 28 years It is with their guidance and encouragement that I have learned to seek out and find excitement in challenging endeavours 6 Table of Contents LIST OF FIGURES iii LIST OF TABLES v Chapter 1: Introduction 1 References 8 Chapter 2: Optimizing Bacillus subtilis spore isolation and quantifying spore harvest purity 14 2 1 Abstract 14 2 2 Introduction 14 2 3 Methods 17 2 3 1 Spore Separation 17 2 3 2 Contamination Quantification 18 2 4 Results and Discussion 20 2 5 Conclusions 27 2 6 References 28 Chapter 3: Thermodynamic analysis of Bacillus subtilis endospore protonation using isothermal titration calorimetry 30 3 1 Abstract 30 3 2 Introduction 31 3 3 Methods 33 3 3 1 Spore growth and isolation 33 3 3 2 Dipicolinic Acid DPA analysis 33 3 3 3 Isothermal titration calorimetry 34 3 3 4 Potentiometric titration reversibility 36 3 4 Results and Discussion 37 3 4 1 Spore harvest purity 37 3 4 2 DPA release 37 3 4 3 Potentiometric Data 39 3 4 4 Model Interpretations 49 3 4 5 Comparison to B subtilis cell protonation 53 3 5 Conclusions 56 3 6 References 57 Chapter 4: Magnesium and silica- Bacillus subtilis endospore adsorption: investigating the influence of endospores on silicate weathering products 62 4 1 Abstract 62 4 2 Introduction 63 4 3 Methods 65 4 3 1 B subtilis endospore growth and isolation 65 4 3 2 Adsorption Assays 66 4 3 3 Elemental Analyses 68 4 4 Results and Discussion 68 4 4 1 Dipicolinic acid 68 4 4 2 Mg endospore adsorption 70 4 4 3 Si endospore adsorption 77 4 4 4 Multi-element endospore adsorption 79 4 5 Conclusions 84 4 6 References 85 i Chapter 5: Microbially enhanced forsterite dissolution through non-metabolic surface reactivity 90 5 1 Abstract 90 5 2 Introduction 91 5 3 Experimental Procedures 93 5 3 1 B subtilis endospore growth and isolation 93 5 3 2 Forsterite characterization and preparation 93 5 3 3 Dialysis assays: indirect microbe-mineral interaction 94 5 3 4 Homogeneous assays: indirect and direct microbe-mineral interaction 98 5 3 5 Chemical analyses 99 5 3 6 Scanning Electron Microscopy SEM 101 5 4 Results 102 5 4 1 Forsterite characterization 102 5 4 2 Dipicolinic Acid 103 5 4 3 Dialysis assays 104 5 4 4 Homogeneous assays 111 5 5 Modeling 116 5 5 1 Abiotic rate and transition point determination 116 5 5 2 Isolating the indirect and direct biotic rate components 117 5 5 3 Chemical equilibrium modeling 125 5 6 Discussion 127 5 6 1 Abiotic dissolution 127 5 6 2 Biotic weathering 128 5 7 Conclusions 133 5 8 References 134 Chapter 6: Conclusions 139 References 143 ii LIST OF FIGURES Figure 2 1 Percent frequency of spore purity determined by CellC and manual counts of purified B subtilis spore harvests 22 Figure 2 2 Corresponding brightfield fluorescent microscopy images and the binarized CellC output for a purified spore harvest 24 Figure 2 3 Linear regression correlating manual versus CellC based % spore data 25 Figure 3 1 Heat flow from a B subtilis spore surface protonation assay measured by isothermal titration calorimetry 34 Figure 3 2 DPA release and pH change as a function of time for 20 and 35 g L-1 B subtilis spore suspensions 38 Figure 3 3 DPA release and pH change over time for 100 g L-1 B subtilis spore suspensions 38 Figure 3 4 mols of adsorbed protons per gram of B subtilis spores in 0 1 M electrolyte at 25 oC as a function of solution pH 40 Figure 3 5 Duplicate 35 g L B subtilis spore reversibility titrations showing the initial suspension titration and secondary titrations following suspension readjustment to pH 10 41 Figure 3 6 Triplicate Ca-Cb data in mol L-1 as a function of pH correspond to 20 30 and 35 g L-1 B subtilis spore suspensions in a 0 1 M electrolyte at 25 oC 43 Figure 3 7 Corrected heats of B subtilis spore surface protonation from triplicate ITC analyses of 20 30 and 35 g L-1 spore suspensions in a 0 1 M electrolyte at 25 oC 47 Figure 4 1 Mg-endospore adsorption as a function of solution pH for a 0 3 g L-1 endospore suspension in 25 mM NaClO4 72 Figure 4 2 Mg-B subtilis endospore adsorption as a function of Mg:endospore ratio at pH 7 3 0 3 2 76 Figure 4 3 Si-endospore adsorption as a function of solution pH for duplicate 1 2 g L-1 B subtilis endospore suspensions with 35 9 M Si total 77 Figure 4 4 Percent silica adsorbed as a function of Si:endospore ratio at pH 7 5 0 4 2 The Si total is increased relative to the initial endospore suspensions of 0 66 g L-l 78 Figure 4 5 Mg and Si adsorption as a function of increasing Mg total for an initial 0 66 g L-1 endospore suspension with 107 M Si total 81 Figure 4 6 A Si and Mg speciation for an assay with variable Si total and constant 123 M Mg at pH 7 1 and assuming SiO2 cr does not precipitate due to a kinetic barrier Si B and Mg C adsorption as a function of increasing Si total for an initial 0 66 g L-1 endospore suspension with 123 M Mg total 83 iii Figure 4 7 Mg adsorption black data points as a function of pH in assays with increasing Si total for an initial 0 66 g L-1 endospore suspension with 123 M Mg total 84 Figure 5 1 Panels A and B SEM image of unreacted forsterite powder reveals a wide range of grain sizes Fine particulates likely lead to large variation in BET surface area results Panels C and D Assay 9H exhibits a clear decrease in total fines relative to unreacted forsterite A and B Panels E and F Assay 4H with masses of endospores clumping on forsterite grains after filtration Potential etch pits features are visible in panel F 95 Figure 5 2 X-ray diffraction patterns for Fo89 5 powder use in dissolution assays and forsterite standard XRD pattern 96 Figure 5 3 Dissolution data for dialysis and homogeneous abiotic control assays as a function of time s 107 Figure 5 4 Dissolution data as a function of time for dialysis assays corresponding to 4 endospore concentrations 108 Figure 5 5 Mg aq for all biotic dialysis assays compared to abiotic assay concentrations 109 Figure 5 6 Mg:Si ratios as a function of time for biotic and abiotic dialysis assays 110 Figure 5 7 Forsterite dissolution in terms of Si aq as a function of time in homogeneous forsterite-endospore assays Abiotic homogeneous control data is provided for comparison 113 Figure 5 8 Mg aq for all biotic homogeneous assays compared to abiotic assay concentrations 114 Figure 5 9 Mg:Si ratios as a function of time for biotic and abiotic black diamonds homogeneous dissolution assays 115 Figure 5 10 Indirect endospore-ion affected dissolution rate as a function of endospore concentration Linear regression solves for the simplified rate law relating dissolution rate to endospore concentration 122 Figure 5 11 Forsterite dissolution rate ascribed to direct endospore-mineral adhesion based on the steady state abiotic dissolution rate and presented as a function of endospore concentration Linear regression line describes the dependence of rate on endospore concentration according to the simplified rate law 123 Figure 5 12 Forsterite dissolution rate ascribed to direct endospore-mineral adhesion based on the initial homogeneous abiotic dissolution rate and presented as a function of endospore concentration Linear regression line describes the dependence of rate on endospore concentration according to the simplified rate law 124 Figure 5 13 Saturation indices SI for a selection of mineral phases at or near oversaturation based on the Mg aq Si aq and predicted Fe total for homogeneous assay 3H panels A-C and dialysis assay 3D panels D-F 126 iv LIST OF TABLES Table 2 1 CellC parameters and the corresponding input values used for batch fluorescent image analysis 19 Table 2 2 Spore purity data for 8 smears made from the same purified spore suspension Cell and spore counts for each smear include 10 fluorescent and corresponding brightfield images 26 Table 3 1 F-test parameters and results comparing four and five site SCM fits 44 Table 3 2 Four-site adsorption model parameters for B subtilis spore surface protonation in a 0 1 M electrolyte at 25 degrees C from a five site SMC according to the reaction R-Li- H R-LiH 45 Table 3 3 Five-site adsorption model parameters for B subtilis spore surface protonation in a 0 1 M electrolyte at 25 degrees C from a five site SMC according to the reaction R-Li- H R-LiH 46 Table 3 5 p values based on a two-tailed T-test comparing B subtilis cell and spore protonation thermodynamic SCM parameters 55 Table 4 1 NE-SCM model input and output parameters 73 Table 5 1 Forsterite chemical composition 97 Table 5 2 Forsterite powder surface area 98 Table 5 3 Dialysis and Homogeneous experimental parameters 100 Table 5 4 Dialysis assays: linear regression model results 118 Table 5 5 Homogeneous assays: linear regression model results 119 v Chapter 1: Introduction Microbes are intrinsic to nearly all water-rock systems including soils Siala et al 1974 ground-water Alfreider et al 1997 deep-sea hydrothermal vents Sogin et al 2006 hot springs Phoenix et al 2003 subglacial lakes Skidmore 2011 and even the driest environments such as the Atacama Desert Barros et al 2008 Whitman et al 1998 estimate the global abundance of prokaryotes ranges from 4-6 x 1030 cells and is equivalent to 60 -100 % of total terrestrial plant biomass Unlike terrestrial plants and other multicellular organisms however the physiology of single celled microbes effectively maximizes their surface area to volume ratio This configuration evolved in part to facilitate the exchange of nutrients and waste products between the cell and surrounding medium The repercussions of microbial physiology go beyond cellular efficiency by providing a highly reactive complex organic surface in most environmental media Chemical reactions occurring at the cell wall have the capacity to promote or inhibit bacterial metabolism and thus viability as well as directly affect aqueous geochemical processes occurring within the hydro- and lithospheres Consequently the microbial surface serves as the physical interface between cellular and geochemical processes and represents a physical confluence of the bio- hydro- and lithospheres Understanding how and to what extent bacterial cell walls influence geochemical processes is integral to grasping the impact of microbes on regional and global geochemical cycles Extensive research over the past 30 years has expanded our understanding of vegetative cell-surface reactivity e g Alessi and Fein 2010 Beveridge and Murray 1980 Borrok et al 2004 Gorman-Lewis et al 2006 Studies of Bacillus subtilis a model gram-positive bacterial species have provided a detailed structural model of the primary polymer making up the grampositive cell wall peptidoglycan Other components of bacterial cell walls include lipopolysacharides proteins and techoic acids Each of these cell wall components hosts an array of proton active organic acid moieties also known as functional groups The capacity and 1 pH range of cell surface proton adsorption is typically determined via potentiometric titration e g Borrok et al 2004 Fein et al 2005 Data for a variety of bacterial species indicate cell surface protonation occurs over a range of environmentally relevant alkaline to acidic pH Complimentary calorimetric data which measures the heat of protonation provides a measure of protonation enthalpies Gorman-Lewis et al 2006 The development of surface complexation models based on balance chemical equations and their application to bacterial surface protonation has enabled the deconvolution of potentiometric titration and calorimetric data e g Gorman-Lewis et al 2006 Results of these studies provide valuable insight on the chemical identity of proton active organic acid moieties on the cell surface Commonalities between the surfaces of a variety of bacterial species include the presence of carboxyl and phosphate groups e g Beveridge and Murray 1980 Borrok et al 2005 Gorman-Lewis et al 2006 Kelly et al 2001 Findings also indicate the presence of proton active hydroxyl amine and sulfhydryl moieties Cox et al 1999 Fein et al 2005 Pokrovsky et al 2008 Some members within the Firmicute phylum including the Bacillus and Clostridium genera are capable of forming a metabolically dormant cell-type known as endospores Endospores function to preserve the bacterium DNA when cells are exposed to environmental stresses such as low nutrient supplies or desiccation Nicholson 2002 It is likely that endospores are a common and perhaps prolific component of natural microbial consortia due to temporal and spatial variations in a variety of environmental parameters such as periodic wetting and drying and irregular nutrient fluxes that make cellular growth unfavorable Indeed a study by Siala et al 1974 showed endospores constituted up to 50 % of the microbial population in an acidic soil sample Endospore formers and their endospores have been identified in a range of environments including soils Hong et al 2009 Siala et al 1974 regoliths rock varnishes and aqueous systems e g Nicholson 2002 Despite their prevalence and our detailed understanding of vegetative cell surface adsorption the surface reactivity of bacterial endospores is poorly constrained This dissertation provides a detailed investigation of 2 endospore surface reactivity by isolating B subtilis endospores and measuring and modeling their surface reactivity major element adsorption potential and influence on forsterite mineral dissolution rate Unlike the vegetative cell surface endospores are enveloped within a tough proteinaceous coat This coat is one of the many defense mechanisms enabling endospores to persist in unfavorable conditions Driks 1999 2002 Nicholson et al 2002 The number and composition of proteins within the coat varies across endospore species and as a function of growth medium Driks 2002 Endospore surface reactivity is likely associated with the proton active functional groups of amino acids making up coat proteins The most prevalent amino acids within the B subtilis endospore coat are glutamic acid aspartic acid cysteine lysine and tyrosine Bhattacharyya and Bose 1967 Pandey and Aronson 1979 Glutamic and aspartic acid both host carboxyl functional groups while cysteine lysine and tyrosine host thiol amine and phenol functional groups respectively The reactivity of organic acid moieties within a protein structure can be heavily influenced by the tertiary and quaternary structures of the protein Li et al 2005 Thurlkill et al 2006 Proton active amino acid functional groups embedded deep within a complex protein may even be rendered unreactive with respect to the bulk solution It is therefore necessary to study endospore surface reactivity to determine which organic acid functional groups interact with and adsorb aqueous species Our current understanding of endospore surface reactivity is limited to a few studies regarding surface protonation and metal adsorption Electrophoretic mobility studies for a variety of endospores report the development of a negatively charged surface electric field with increasing solution pH suggesting deprotonation of organic acid moieties like those found on vegetative cell surfaces Douglas 1954 1957 Potentiometric titration data for marine Bacillus sp SG-1 indicate surface protonation occurs over a pH range loosely corresponding to the pKa of carboxyl and phosphate groups He and Tebo 1998 He and Tebo 1998 show endospores of the marine Bacillus species SG-1 are capable of adsorbing Cu Revis et al 1997 measured Pb 3 Hg Cr As Cd Ba and Sr adsorption onto B megaterium endospores Soft lewis acids such as Hg and Pb exhibited a higher adsorption affinity with the B megaterium endospore surface Revis et al 1997 These findings may indicate the presence of adsorption sites characterized as soft lewis bases such as sulfhydryl groups in accordance with hard and soft Lewis acid and base HSAB theory where soft hard acids form stronger bonds with soft hard bases Most research investigating endospore-metal interactions however focuses on their ability to irreversibly oxidize Mn II and precipitate Mn IV -oxides e g Bargar et al 2000 Francis and Tebo 2002 The chemical identity of organic acid moieties responsible for endospore adsorption is largely unknown Endospore surfaces exhibit hydrophobic properties in addition to the presence of charged hydrophilic reactive sites Two-phase separatory solutions effectively isolate endospores from their vegetative cell counterpart by concentrating them in an organic top phase The partitioning of endospores into the organic phase indicates the endospore surface is more hydrophobic than vegetative cells Doyle et al 1984 Sacks and Alderton 1961 Endospores also adhere better to both hydrophobic and hydrophilic surfaces than their vegetative cell counterparts R nner et al 1990 Consequently it is possible that both hydrophobic and hydrophilic reactions drive endospore surface adsorption This chemical dichotomy makes endospore surfaces an intriguing and complex component in water-rock systems Investigating endospore surface reactivity requires milligrams of pure biomass free of cells and cell lysis products capable of adsorbing H and metals Challenges associated with endospore growth and isolation pose a barrier to focused endospore surface reactivity studies Bacterial endospores develop within a host cell when exposed to unfavorable conditions Gould and Hurst 1969 Growing cultures under such conditions can inhibit initial cellular growth and lead to small biomass yields Other approaches require multiple aseptic additions and the transfer of established cultures into sporulation medium Donnellan et al 1964 processes that 4 increases the risk of culture contamination Further complications arise after sporulated cells undergo lysis and release large quantities of potentially reactive cellular material into suspension Incomplete sporulation results in vegetative cell contamination Chapter 2 of this dissertation provides a method for B subtilis endospore growth and isolation with a semiautomated approach for determining the purity of an endospore harvest These methods enable research regarding endospore surface reactivity by providing a substantial endospore biomass with low cell contamination Ch 2 is published in the Journal of Microbiological Methods Harrold et al 2011 Methodology contributions and manuscript edits from Dr Drew GormanLewis as well as extensive lab assistance from Mikaela Hertel helped make this paper a success Chapter 3 addresses our lack of knowledge regarding endospore surface reactivity by coupling potentiometric titration and isothermal titration calorimetry data describing B subtilis endospore surface protonation Results from potentiometric titration data are processed based on the proton mass balance of the system and modeled according to non-electrostatic surface complexation modeling NE-SCM theory NE-SCMs are built on balanced chemical equations describing discrete adsorption sites on the adsorbate surface This modeling approach is ideal for describing the reactivity of complex surfaces such as the endospore coat where a range of organic acid moieties with varying pKa values are likely responsible for surface protonation behavior NE-SCM model outputs include best-fit reactive site concentrations and log K values corresponding to discrete reactive sites on the endospore surface Parallel calorimetric data are modeled based on the protonation NE-SCM and constrain the enthalpies and entropies of protonation for each discrete site Best-fit log K values enthalpies and entropies describing discrete protonation sites provide thermodynamic constraints on the chemical identity of adsorption sites on the endospore surface NE-SCMs are also applicable to macro-scale systems not directly studied in the laboratory unlike commonly used empirical models such as distribution coefficients KD Bethke and Brady 2000 Results from Ch 3 provide the most robust chemical description of the organic acid moieties responsible for B subtilis endospore 5 surface reactivity to date This work is published in Geochimica et Cosmochimica Acta Harrold and Gorman-Lewis 2013 Dr Drew Gorman-Lewis provided significant contributions and support regarding experimental design mathematical modeling approach and manuscript editing all of which contributed to the success of this publication The reactivity of microbial surfaces extends beyond protonation to include elemental and molecular adsorption reactions The nature of these reactions depends on the chemical identity of surface bound organic acid moieties and the adsorbing species Surface complexation reactions between aqueous components and the cell surface include both inner-sphere and outer-sphere complexes Surface complexes may also be characterized by ionic or covalent bond formation The presence of multiple aqueous elemental or molecular components can lead to complex speciation or ternary complexes that enhance or inhibit cell surface adsorption Alessi and Fein 2010 Gorman-Lewis et al 2005 Geochemical factors influencing cell wall adsorption include but are not limited to ionic strength pH of the aqueous medium and the presence of other chelators e g Borrok and Fein 2005 Fein and Delea 1999 Gorman-Lewis et al 2005 Such adsorption reactions have the capacity to concentrate and alter the aqueous activities of trace and major elements Many fundamental low-temperature aqueous geochemical processes are driven by the activities of major elements Aqueous silica Si and common metals such as iron Fe magnesium Mg and calcium Ca are among the most important major elements associated with both primary mineral dissolution and a wide range of secondary precipitates Major cations such as Mg2 and Ca2 readily adsorb to a range of microbial surfaces while direct silica adsorption onto the B subtilis cell wall is negligible Iron oxide coated microbial surfaces however support subsequent silica adsorption Fein et al 2002 Other researches have also indicated ternary metal-silica adsorption complexes as the main driver of microbial-silica adsorption Urrutia and Beveridge 1993 Urrutia and Beveridge 1994 These findings corroborate the silicic or clay-like coatings found on in situ microbes which develop in 6 association with iron oxides Konhauser et al 1993 Konhauser et al 1994 Urrutia and Beveridge 1994 Surface based mineral precipitation may contribute to microfossil formation and microbial preservation in the geologic record Chapter 4 investigates the affinity of B subtilis endospore Si and Mg adsorption to better evaluate the influence of endospores on low-temperature aqueous geochemical systems and compare their surface reactivity to vegetative cells This body of work assesses Mg and Si adsorption over a wide range of pH and adsorbent to adsorbate ratios as well as adsorption behavior in aqueous systems containing both Mg and Si Mg endospore adsorption data is modeled based on the NE-SCM described in Ch 3 The rate of primary mineral dissolution is a fundamental low-temperature aqueous geochemical process capable of both controlling and being controlled by the activity of aqueous major ions Organic acids such as those identified on the endospore surface have the capacity to enhance primary silicate dissolution rates e g Bennett et al 1988 Olsen and Rimstidt 2008 Dissolution rate enhancement occurs through direct organic acid- mineral surface adhesion by binding with the mineral and lowering the activation energy of dissolution e g Bennett 1991 Olsen and Rimstidt 2008 Indirect pathways increase dissolution kinetics when organic acids complex with and lower the activity of mineral dissolution products shifting the chemical system further from equilibrium Bennett et al 1988 Hutchens et al 2006 Traditionally viewed as an abiotic process mineral dissolution is now known to increase in the presence of microbes e g Rogers and Bennett 2004 Microbially enhanced dissolution is primarily associated with metabolic processes or the production and release of organic acids Studies investigating the effect of microbes on mineral dissolution rate however inherently include any effects associated with microbial surface reactivity The few studies aimed at isolating the effects of microbial surface reactivity on mineral dissolution rates encountered significant complications associated with cellular metabolism and cell lysis Lee and Fein 2000 7 Pokrovsky et al 2009 Wightman and Fein 2004 The affect of microbial cell surface reactivity on mineral dissolution rate remains enigmatic Endospores are an ideal candidate for isolating the effects of microbial surface reactivity on mineral dissolution rate due to their metabolic dormancy and structural integrity in the absence of nutrients Chapter 5 utilizes B subtilis endospores as a tool for quantifying both direct and indirect influences of microbial surface reactivity on the rate of forsterite Mg2SiO4 dissolution Similarities between endospore and cell surface reactivity determined in Ch 3 and 4 make B subtilis endospores a first order proxy for a wide range of vegetative cells Results from Chapter 5 have implications regarding microbe-mineral interactions in a wide range of microbe-water-rock systems Manuscript feedback in addition to experimental and analytical advice from Dr Drew Gorman-Lewis was instrumental to the formulation of Chapters 4 and 5 Chapters 4 and 5 are slated for submission to a peer-reviewed journal within the year References Alessi D S Fein J B 2010 Cadmium adsorption to mixtures of soil components: Testing the component additivity approach Chemical Geology 270 186-195 Alfreider A Krossbacher M Psenner R 1997 Groundwater samples do not reflect bacterial densities and activity in subsurface systems Water Research 31 832-840 Bargar J R Tebo B M Villinski J E 2000 In situ characterization of Mn II oxidation by spores of the marine Bacillus sp strain SG-1 Geochimica Et Cosmochimica Acta 64 2775-2778 Barros N Feij o S Salgado J Ramajo B Garc a J R Hansen L D 2008 The Dry Limit of Microbial Life in the Atacama Desert Revealed by Calorimetric Approaches Engineering in Life Sciences 8 477-486 8 Bennett P C 1991 Quartz dissolution in organic-rich aqueous systems Geochimica et Cosmochimica Acta 55 1781-1797 Bennett P C Melcer M E Siegel D I Hassett J P 1988 The dissolution of quartz in 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Soil with Special Reference to Bacillus subtilis J Gen Microbiol 81 183-190 Skidmore M 2011 Microbial communities in Antarctic subglacial aquatic environments Geophysical Monograph Series 192 61-81 Sogin M L Morrison H G Huber J A Welch D M Huse S M Neal P R Arrieta J M Herndl G J 2006 Microbial diversity in the deep sea and the underexplored rare biosphere Proceedings of the National Academy of Sciences 103 12115-12120 Thurlkill R L Grimsley G R Scholtz J M Pace C N 2006 pK values of the ionizable groups of proteins Protein Science 15 1214-1218 Urrutia M M Beveridge T J 1993 Mechanism of silicate binding to the bacterial cell wall in Bacillus subtilis Journal of Bacteriology 175 1936-1945 Urrutia M M Beveridge T J 1994 Formation of fine-grained metal and silicate precipitates on a bacterial surface Bacillus subtilis Chemical Geology 116 261-280 Whitman W B Coleman D C Wiebe W J 1998 Prokaryotes: The unseen majority Proceedings of the National Academy of Sciences 95 6578-6583 Wightman P G Fein J B 2004 The effect of bacterial cell wall adsorption on mineral solubilities Chemical Geology 212 247-254 13 Chapter 2: Optimizing Bacillus subtilis spore isolation and quantifying spore harvest purity 2 1 Abstract Investigating the biochemistry resilience and environmental interactions of bacterial endospores often requires a pure endospore biomass free of vegetative cells Numerous spore isolation methods however neglect to quantify the purity of the final endospore biomass To ensure low vegetative cell contamination we develop a quality control technique that enables rapid quantification of endospore harvest purity This method quantifies spore purity using brightfield and fluorescence microscopy imaging in conjunction with automated cell counting software We applied this method to Bacillus subtilis endospore harvests isolated using a two phase separation method that utilizes mild chemicals The average spore purity of twenty-two harvests was 88 11 % error is 1 with a median value of 93 % A spearman coefficient of 0 97 correlating automated and manual bacterial counts confirms the accuracy of software generated data 2 2 Introduction Bacterial endospores are ubiquitous in the environment play an integral role in the bacterial life cycle and may influence biogeochemical cycles De Vrind et al 1986 He and Tebo 1998 Nicholson 2002 Nicholson et al 2002 Investigating the biochemistry resilience and environmental interactions of endospores requires a pure endospore biomass free of vegetative cells Unlike culturing vegetative cells generating a pure bacterial endospore here after referred to as spore biomass that is free of vegetative cells deemed cells is more difficult Complications arise when not all cells sporulate the spore does not completely shed the 14 encasing cell material or residual cell debris remains in the culture Methods to produce a pure spore crop and quantify the amount of cell contamination in the final spore biomass are necessary for research including spore coat protein isolation survival rates spore germination triggers and surface reactions Numerous procedures have been used to address the issue of producing pure spore crops These methods utilize special mediums that promote sporulation in bacterial cultures Sporulation can be induced when endospore-forming bacteria become carbon nitrogen and sometimes phosphorous limited or when GTP concentrations are reduced Harwood and Cutting 1990 Nutrient limitation is achieved through natural exhaustion of the growth medium or by transferring cells to a nutrient limited sporulation broth Defined complex mediums requiring autoclaving filtration and sterile additions are used to achieve bacterial sporulation in most methods One exception is the commercially available Difco Sporulation Medium Harwood and Cutting 1990 Many of the accepted Multi-step sporulation medium preparations and cell transfer methods however can be time consuming and may increase the risk of culture contamination Many separation methods use chemicals such as lysozyme and EDTA to lyse cells and remove cellular material from the spore coat Goldman and Tipper 1978 He and Tebo 1998 Rosson and Nealson 1982 Recommendations for foam floatation include raising the suspension pH to 11 5 or an acetone treatment to facilitate B subtilis spore separation Boyles and Lincoln 1958 While these techniques may suffice for some research goals exposure to these chemicals and extreme pH may alter spore coat proteins or spore viability resulting in experimental errors A method devised by Sacks and Alderton 1961 utilizes mild chemicals to separate spores from cells based on the more hydrophobic behavior of spore surfaces A two phase solution is generated using polyethylene glycol 4000 PEG 4000 and a strong potassium phosphate buffer In the suspension spores are concentrated in the top organic PEG 4000 15 phase while cells and cell debris collect at the interface and in the bottom electrolyte This separation process is ideal for investigations that require isolating a significant mass of spores without damaging the spore surface and removal of the separation solution by dilution and repeated washing Sacks and Alderton 1961 recommend multiple additions and extractions of equilibrated PEG 4000 solution While effective the multiple extractions make this process very time and resource intensive This separation technique is known to be successful however to our knowledge no work has been done to quantify its effectiveness Regardless of the separation method used it is likely that some residual vegetative cells contaminate the spore extracts For many experiments it is prudent to determine the amount of cell contamination in each purified spore harvest determine spore versus cell partitioning One method utilizes colony counts to This technique involves heat treating a bacterial suspension to kill vegetative cells then incubating the suspension on agar plates to produce visible colonies which are then compared to colony counts from a non-heat treated suspension Colony counts resulting from the untreated bacterial suspension correspond to total cell and spore counts while heat treated plate counts are representative of viable spore concentrations Siala et al 1974 This technique is time consuming and dependent on cell and spore viability which may introduce errors in determining the degree of cell contamination in a purified spore biomass Additional errors may arise from incomplete extermination of cells within the heat treated biomass Despite the importance of spore purity for subsequent investigations many researchers neglect to conduct a thorough analysis quantifying the level of purity achieved in the final spore biomass and used in experiments Boyles and Lincoln 1958 He and Tebo 1998 Revis et al 1997 Rosson and Nealson 1982 Sacks and Alderton 1961 In this research we utilize Tripticase Soy Broth TSB a commercially available growth medium to generate a substantial Bacillus subtilis spore biomass Spore isolation is achieved using Sacks and Alderton s 1961 two-phase extraction system for B subtilis spore separation and streamlined by eliminating the need for additional organic phase extractions To determine 16 the percent of spores within the purified spore biomass we develop a method to quantify cell contamination using the common Schaffer-Fulton Schaeffer and Fulton 1933 differential staining technique for spores and cells in conjunction with microscopy imaging and image processing 2 3 Methods 2 3 1 Spore Separation Bacillus subtilis cultures maintained on 3 % trypticase soy broth TSB and 0 5 % yeast extract agar plates were inoculated into test tubes with 3 5 ml of 3 % TSB and 0 5 % yeast extract Following 24 h of incubation at 37 C the cultures were transferred to 1 or 2 L volumes of 0 3 % TSB in a 1 tube to 1 L ratio Large broth cultures were incubated at 37 C for 6 d On the sixth day the bacterial biomass was harvested via centrifugation at 6000 g for 15 m and transferred into 50 mL falcon tubes The biomass was washed three times by suspending it in 30 mL of 0 1 M NaCl and vortexing for 1 m Between each wash the biomass was pelleted by centrifugation at 10 000 g for 5 m and the supernatant discarded Following the third wash biomass from 1 L of growth was suspended in 5 ml of 18 M cm-1 water 15 ml of biomass suspension equivalent to 3 L of biomass growth was added to a two phase extraction system containing 11 18 % w v PEG 4000 34 % v v 3M potassium phosphate buffer 1 76 M K2HPO4 1 24 M KH2PO4 and 50 % v v 18 M cm-1 water Sacks and Alderton 1961 with a final volume of 200 mL Sacks and Alderton 1961 observed particulates from the combined solutions collecting at the interface of the two-phase extraction system Reagent filtration is recommended if the extraction requires a blank interface Sacks and Alderton 1961 Our procedure however avoids interface removal Consequently interfacial contamination was irrelevant and we did not filter the reagents 17 To homogenize the two phases we mixed the solution vigorously for approximately 15 m and subsequently induced phase separation via centrifugation at 100 g for 2 m A high concentration of B subtilis spores collect in the top phase near the interface Sacks and Alderton 1961 We carefully siphoned off approximately 60 mL or 80 % of the top organic phase with a vacuum bulb to achieve maximum biomass while minimizing uptake of the interface We diluted the extracted top phase with 500 ml of de-ionized DI water and pelleted the spore biomass by centrifugation at 6 000 g for 30 minutes The resulting pellet was washed five times as previously described to remove any residual PEG 4000 from the spores On the final wash we removed 50 l of spore suspension for use in quantifying the percent cell contamination A final wet weight was determined after two 30 m centrifugation cycles at 6100 g 2 3 2 Contamination Quantification The 50 L spore suspension aliquot was diluted 3 to 10 times with 0 1 M NaCl to yield bacterial counts between 20 and 400 cells per field of view at 1000 X magnification 10 L of the diluted spore suspension was used to make smears on ethanol cleaned glass slides Dried smears were heat fixed and stained with malachite green and safranin according to the Schaeffer-Fulton method Schaeffer and Fulton 1933 Spores were stained first by flooding the heat fixed slide with a 5 % w v malachite green stain and heated over a beaker of boiling water for 5 m We rinsed off excess malachite green stain after the slide cooled and flooded the smear in a 0 6 % w v safranin stain for 30 s A final 5 m rinse step removed residual malachite green and safranin stain from the smear This method stains spores a blue-green color while vegetative cells are dyed red Viewed under a light microscope it is easy to differentiate cells from spores based on color When observed with a mercury lamp light source and 546 nm excitation 590 nm emission filter both the spores and cells fluoresced red In most cases cells and spores fluoresced more brightly than 18 excess stain or debris on the slides We took both bright-field and fluorescent microscopy images of the same field of view at 1000 X magnification using a Zeiss Axiostar plus microscope equipped with a Neofluar 100 X oil immersion lens and a Zeiss AxioVison camera Ten randomly chosen fields of view were imaged from a single smear for each purified spore harvest The total number of spores and cells termed total counts were determined from the fluorescent images either manually or using CellC Selinummi et al 2005 CellC is image processing software designed to count cells in microscopy images based on the intensity of cells relative to the background Selinummi et al 2005 The CellC program can be downloaded for free at http: sites google com site cellcsoftware We optimized the CellC analysis by comparing manual total counts to those generated by CellC and adjusting the image analysis parameters to generate the smallest deviation between the hand and automated counts Table 2 1 All ten fluorescent images from a smear were batch analyzed based on an intensity threshold chosen to best enumerate the total count in the first image Table 2 1 CellC parameters and the corresponding input values used for batch fluorescent image analysis CellC Parameter Background correction Automatic intensity threshold figure 1 Automatic intensity threshold figure 2 Divide cell clusters into single cells Cluster division algorithm Use micrometers instead of pixelsa Fill holes of cells Auto removal of over undersized cells Type of Image a Specific to microscope objective Input On Off batch dependent 0 28 0 70 NA 0 95 Cell Shape 1pixel 0 064516 m Off Off Fluorescence Microscopy Cells were counted manually in the bright-field images and included spores with significant portions of safranin stained cell material adhered to their surface Percent spores %S in the final purified spore biomass was determined from the difference between the sum of 19 the cells counted in each of the ten brightfield images C and the sum of total spores and cells counts T in the ten fluorescence images divided by the sum of total counts Eq 2 1 Eq 2 1 % 100 We tested the repeatability of this method by quantifying the percent spore concentration for 8 separate smears made from the same purified spore suspension 2 4 Results and Discussion While many researchers use a specialized sporulation media or defined chemical medium to generate spores Berlin et al 1963 Boyles and Lincoln 1958 Harwood and Cutting 1990 Roth et al 2010 we use a dilute commercially available growth media With an incubation time of 6 days B subtilis cells in 0 3 % TSB undergo extensive sporulation and many shed their host cell material This growth process provides a simple method to induce sporulation and generate milligrams of spore biomass without the use of a specialized medium or more complex chemically defined mediums It also eliminates the need for sterile solution or cell transfers that can increase the risk of culture contamination The average yield following spore purification was 40 mg spores per L of B subtilis growth Spore yield is dependent on numerous factors including the concentration of spores produced in the growth culture the biomass to extraction solution ratio and the distribution of spores within the top phase of the extraction solution Stepwise removal and centrifugation of the top organic phase provided qualitative evidence suggesting spores are not evenly distributed in the top phase of the extraction solution and instead tend to concentration closer to the twophase interface This is in agreement with findings from Sacks and Alderton 1961 for B subtilis spore extraction Due to multiple factors influencing the final spore concentration and 20 uneven distribution of spores within the top extraction phase it is not possible to determine the percent of total spores isolated in the final purified biomass Our adjustments to the two phase extraction protocol originally outlined by Sacks and Alderton 1961 included a specified ratio of sporulated unprocessed B subtilis biomass to two phase extraction solution volume Changing this ratio will likely change the final purity of a single top phase extraction due to finite cell and spore carrying capacities within the organic electrolytic and interfacial solution phases We also reduced the recommended 1500 g centrifugation step used to separate the organic and electrolyte phase Sacks and Alderton 1961 to 100g This centrifugation step simply speeds up the separation of the two phases High speed centrifugation was unnecessary to achieve the observed results With these adaptations a single top phase extraction step is capable of producing a high purity B subtilis spore biomass We purified twenty-two spore crops and quantified their spore concentrations based on both manual and automated CellC total counts spores and cells Percent spores were calculated using manually determined cell counts that included safranin stained cells and spores with significant safranin stained material still attached This provides a conservative low-end value for the spore purity within each harvest Manually counting the cells within a set of ten brightfield images takes approximately 10 m when using a counting tool that records a number at each point clicked on an image e g Photoshop counting tool The low occurrence of cells within a purified spore harvest makes this portion of the spore quantification method rapid and on par with the time required to take 10 images of the slide The overall time saved by avoiding regrowth steps and manual colony counting is significant The medcouple MC a measure of data skewness that ranges from 1 to -1 with 0 describing a Gaussian distribution was calculated for both the CellC and manually derived percent spore data to determine the proper statistical tests for summarizing and relating the two data sets Brys et al 2004 Hubert and Van der Veeken 2008 For manually and CellC determined percent spore purity data n 22 we calculated MC values of -0 54 and -0 62 21 respectively These negative MC values indicate a highly left skewed data set Manual and CellC generated total counts from batch image analyses had MC values of 0 44 and 0 40 respectively indicating right skewed data The MC values describing our data warrant the use of nonparametric statistical analyses which do not assume Gaussian distributions The spore isolation processes described in Section 2 1 resulted in an average spore concentration and 1 standard deviation of 88 11 % based on manual cell and spore counts from 22 spore crops Nearly 60 % of the 22 analyzed spore crops however were 91-100 % spores according to manual counts Fig 2 1 This distribution resulted in the observed nonparametric data set and negative MC values Due to data skewness the median can provide a more accurate data summary and prediction of typical spore purity results The median of the manually derived spore purity data is 93 % % Frequency 100 90 CellC 80 Manual 70 60 50 40 30 20 10 0 51-60 61-70 71-80 81-90 91-100 % Spore Purity Figure 2 1 Percent frequency of spore purity determined by CellC and manual counts of purified B subtilis spore harvests n 22 Cell counts include spores with significant safranin stained material still attached and provide an upper estimate of cell contamination 22 We accelerated spore purity quantification by using CellC to generate a total count from the fluorescent images The average percent spore purity and 1 standard deviation based on total counts generated by CellC for the same 22 spore crops is 87 11 % with a median of 92 % Fig 2 1 displays the frequency of spore crops within a given range of spore purity for both manual and CellC generated values Variation in the percent spore purity can result from numerous sources including temperature variations Sacks and Alderton 1961 removal of interfacial solution inadequate homogenization of the two-phase solution and variations in the spore content of the growth medium Errors in cell and spore counts were estimated to be 5 % for manual counts and 10 % for CellC generated counts Errors in both manual and CellC counts may arise from bacterial aggregates and biotic debris in the smears Total counts from CellC however tend to yield lower values relative to manual counts Fig 2 2 CellC error sources include limitations in resolving cell and spore boundaries in an aggregate and an inability to discern fluorescing debris from actual cells and spores The latter of these complications seems to be less of an issue for CellC counts since the intensity threshold of the analyses appeared to filter out fluorescing debris and CellC counts rarely exceeded manual counts Bacterial aggregates were reduced by diluting the spore suspension prior to making smears Visual inspection and comparison of the binarized CellC image output with the original microscopy images indicated that individual bacteria within aggregates were not adequately isolated and often undercounted despite the use of cell division algorithms An example of this can be seen by comparing bacterial aggregate separation in the binarized CellC image Fig 2 2C with the original microscopy images Fig 2 2A and B and the total CellC and manual counts of 152 and 161 respectively These inaccuracies in bacterial aggregate separation make a large contribution to the final CellC count error Additional errors in CellC counts can arise from batch image binarization based on a single intensity threshold where inconsistencies in the background and cell fluorescence intensities within individual images and a batch of images can result in counting errors 23 A Figure 2 2 Corresponding brightfield A fluorescent microscopy images B and the binarized CellC output C for a purified spore harvest stained according to the Schaffer-Fulton method The manual total count is 161 and the CellC total count is 152 24 Lower total counts from CellC enumeration result in lower percent spore purity for the CellC derived data This can be observed in a linear regression plot of manually versus CellC determined percent spore data Fig 2 3 where the y-intercept is negative due to lower percent spore values in the CellC data The relationship between CellC bias and the calculated percent spore value is a function of Eq 2 1 This calculation assumes that the percent spores cannot exceed 100 % If we calculated percent spores using a manually derived spore count the manual spore count from an image with 100 % spores could exceed the CellC total count due to the low count bias This would result in a CellC derived percent spore value in excess of 100 % and a relationship between CellC and manually derived percent spore values inverse to that observed in our data We choose to use Eq 2 1 since manually counting the cells within a purified spore biomass image is much more rapid than manual spore enumeration Based on these considerations we recommend and utilize a 10 % error for CellC counts when determining the error in individual percent spore values Propagation of both CellC and manual count errors produced smaller individual errors than the standard deviation of the entire data set % spores CellC total count 100 0 90 0 80 0 70 0 60 0 50 0 50 0 60 0 70 0 80 0 90 0 100 0 % spores manual total count Figure 2 3 Linear regression correlating manual versus CellC based % spore data 1 0 3 2 R2 0 97 25 The accuracy of CellC generated total counts from fluorescent images can be assessed by determining the spearman coefficient which compares CellC and manual counts The Spearman coefficient is used to relate skewed data sets based on the rank of each data point and average of each data set The spearman coefficient correlating CellC and manual total count data from batch image analysis of 22 spore crops was 0 97 Based on this Spearman coefficient it is evident that CellC batch analyses generate reliable total cell and spore counts from our fluorescent images despite bacterial clumping and unavoidable variations in the background intensity of each image Table 2 2 Spore purity data for 8 smears made from the same purified spore suspension Cell and spore counts for each smear include 10 fluorescent and corresponding brightfield images Percent spore purity values provide a low end estimate by including spores with attached safranin stained material in the cell count value Replicate B1 B2 C1 C2 D1 D2 E1 E2 a Total Count CellC 1865 1394 1633 973 687 1034 1631 1159 Cell Count manual 100 112 76 47 45 49 40 62 Average a % Spore Purity 95 92 95 95 93 95 98 95 95 3 error is 2 Selinummi et al 2005 utilized the Pearson coefficient r a correlation coefficient for data sets with a Gaussian distribution based on the averaged total count standard deviations in the two data sets and the total number of data points in a data set to correlate their CellC and manual count data Their Pearson coefficient for DAPI stained bacteria was 0 98 Despite the non-Gaussian nature of our data we also calculated a Pearson coefficient to enable direct comparison of our CellC counting accuracy to Selinummi et al 2005 Our Pearson coefficient 26 correlating CellC generated and manual total counts within 22 batches of images was 0 98 which is in good agreement with the r value determined by Selinummi et al 2005 Our CellC based percent spore quantification method proved to be repeatable over 8 smears made from the same spore suspension Spore purity for each smear was determined using CellC total counts and yielded an average value of 95 3 % error is 2 Table 2 2 This level of repeatability indicates that the distribution of cells and spores within a smear is roughly homogeneous over ten randomly chosen fields of view at 1000 X magnification and representative of the parent solution 2 5 Conclusions In this study we refined and developed efficient methods for B subtilis spore growth separation and quantification that minimizes cell contamination errors in Bacillus subtilis spore research A 0 3 % TSB growth medium produced significant Bacillus subtilis cell growth and subsequent sporulation over a six day incubation period Based on the method of Sacks and Alderton 1961 we produced a highly purified spore biomass on the order of milligrams by extracting approximately 80 % of the spore laden organic phase from a two-phase extraction system To determine the purity of spore harvests we devised a semi-automated method to quantify spore harvest purity that combines the Shaffer-Fulton differential staining technique brightfield and fluorescence microscopy imaging and CellC image processing Spore purity quantification results indicate that the combination of a defined biomass to two-phase extraction solution ratio a reduction in the centrifugal force used for phase separation and a single top phase extraction step produces a high purity spore biomass This eliminates the need for additional extraction steps saving both time and resources The spore purity quantification method described here enables rapid analysis of individual spore crop 27 purity and allows for better quality control in repeat experiments requiring a cell-free spore biomass 2 6 References Berlin E Curran H R Pallansch M J 1963 Physical surface features and chemical density of dry bacterial spores J of Bacteriol 86 1030-1036 Boyles W A Lincoln R E 1958 Separation and concentration of bacterial spores and vegetative cells by foam flotation Appl Microbiol 6 327-334 Brys G Hubert M Struyf A 2004 A robust measure of skewness J of Comp and Graph Stat 13 996-1017 De Vrind J P M De Vrind-De Jong E W De Voogt J -W H Westbroek P Boogerd F C Rosson R A 1986 Manganese oxidation by spores and spore coats of a marine Bacillus species Appl Environ Microbiol 52 1096-1100 Goldman R C Tipper D J 1978 Bacillus subtilis spore coats: Complexity and purification of a unique polypeptide component J of Bacteriol 135 1091-1106 Harwood C R Cutting S M 1990 Molecular biological methods for Bacillus Wiley Chichester New York He L M Tebo B M 1998 Surface charge properties of and Cu ii adsorption by spores of the marine Bacillus sp Strain sg-1 Appl Environ Microbiol 64 1123-1129 Hubert M Van der Veeken S 2008 Outlier detection for skewed data J Chemomet Vol 22 pp 235 Nicholson W L 2002 Roles of bacillus endospores in the environment Cell Mol Life Sci 59 410-416 Nicholson W L Fajardo-Cavazos P Rebeil R Slieman T A Riesenman P J Law J F Xue Y M 2002 Bacterial endospores and their significance in stress resistance Antonie Van Leeuwenhoek Int J Gen Molec Microbiol 81 27-32 28 Revis N W Hadden C T Edenborn H 1997 Removal of dissolved heavy metals and radionuclides by microbial spores Technical Report DOE OR 21492--T9 US DOE Rosson R A Nealson K H 1982 Manganese binding and oxidation by spores of a marine bacillus J Bacteriol 151 1027-1034 Roth S Feichtinger J Hertel C 2010 Characterization of bacillus subtilis spore inactivation in low-pressure low-temperature gas plasma sterilization processes Vol 108 Blackwell Publishing Ltd pp 521-531 Sacks L E Alderton G 1961 Behavior of bacterial spores in aqueous polymer two-phase systems J Bacteriol 82 331-341 Schaeffer A B Fulton M D 1933 A simplified method of staining endospores Science New York N Y 77 Selinummi J Sepp l J Yli-Harja O Puhakka J A 2005 Software for quantification of labeled bacteria from digital microscope images by automated image analysis BioTechniq 39 859-863 Siala A Hill I R Gray T R G 1974 Populations of spore-forming bacteria in an acid forest soil with special reference to bacillus subtilis J Gen Microbiol 81 183-190 29 Chapter 3: Thermodynamic analysis of Bacillus subtilis endospore protonation using isothermal titration calorimetry 3 1 Abstract Bacterial proton and metal adsorption reactions have the capacity to affect metal speciation and transport in aqueous environments We coupled potentiometric titration and isothermal titration calorimetry ITC analyses to study Bacillus subtilis spore-proton adsorption We modeled the potentiometric data using a four and five-site non-electrostatic surface complexation model NE-SCM Heats of spore surface protonation from coupled ITC analyses were used to determine site specific enthalpies of protonation based on NE-SCMs The five-site model resulted in a substantially better model fit for the heats of protonation but did not significantly improve the potentiometric titration model fit The improvement observed in the five-site protonation heat model suggests the presence of a highly exothermic protonation reaction circa pH 7 that cannot be resolved in the less sensitive potentiometric data From the log Ks and enthalpies we calculated corresponding site specific entropies Log Ks and site concentrations describing spore surface protonation are statistically equivalent to B subtilis cell surface protonation constants Spore surface protonation enthalpies however are more exothermic relative to cell based adsorption suggesting a different bonding environment The thermodynamic parameters defined in this study provide insight on molecular scale sporesurface protonation reactions Coupled ITC and potentiometric titrations can reveal highly exothermic and possibly endothermic adsorption reactions that are overshadowed in potentiometric models alone Spore-proton adsorption NE-SCMs derived in this study provide a framework for future metal adsorption studies 30 3 2 Introduction Microbially hosted adsorption reactions have the potential to influence the distribution and fate of dissolved chemicals in aqueous systems Our knowledge of vegetative bacterial cell referred to here as cell surface reactivity has grown rapidly to include thermodynamic data for proton and metal adsorption Thermodynamic stability constants enthalpies and entropies derived from calorimetric data and surface complexation modeling give insight into the mechanisms underlying cell surface complexation and provide parameters for modeling cell surface adsorption in natural aqueous systems Comparatively little work however focuses on adsorption reactions hosted by bacterial endospores termed spores in this paper Bacterial spores are a metabolically dormant cell type produced by numerous bacterial genera including Bacillus and Clostridium to protect their DNA under harsh environmental conditions Spore surfaces are primarily comprised of a tough proteinaceous coat Driks 1999 Driks 2002 Gould and Hurst 1969 that may react differently with dissolved constituents relative to cell surfaces consisting of polysaccharides lipopolysaccharides and peptidoglycan among other organic molecules Although both spore and cell surfaces are porous He and Tebo 1998 found the Bacillus SG-1 spore surface area up to four times larger than its parent cell counterpart In some environments spores comprise up to 45 % of the total bacteria population Siala et al 1974 and have the potential to outnumber parent cells In fifty soil samples Hong et al 2009 determined an average aerobic spore count 105 CFU g-1 on par with vegetative cell densities In a bacterial population comprised of 50 % spores their surface area could contribute up to two times the surface area of the parent cell Spore coats like bacterial cell surfaces may host multiple chemically distinct ligands Our knowledge of spore surface complexation reactions is limited and insufficiently characterized by bulk distribution coefficients Kd describing proton and metal adsorption affinities He and Tebo 1998 Revis et al 1997 Rode and Foster 1966 Kd values defined as 31 the ratio of adsorbed to dissolved constituents oversimplify and fail to provide molecular scale insight on the adsorption reactions Bethke and Brady 2000 Unlike distribution coefficients surface complexation models SCM are based on balanced chemical equations that are mechanistically related to the adsorption reactions occurring Spectroscopic data of cell-metal adsorption supports the theory that sites derived from surface complexation models represent actual metal-active ligands on the cell surface Kelly et al 2002 More recent investigations employ calorimetric analyses that compliment SCMs and provide a more detailed understanding of the molecular scale thermodynamics associated with bacterial surface adsorption GormanLewis et al 2006 Jesperson and Jordan 1970 also utilized ITC to generate robust determinations of proton active ligands and their concentrations in proteins Together the large surface area of spores and poorly constrained spore adsorption models make it difficult to understand the influence of microbes on aqueous geochemical cycles Our research will extend beyond the scope of system specific Kd values by fitting surface complexation models to potentiometric titration and isothermal titration calorimetry ITC data describing Bacillus subtilis spore surface protonation From the SCM we will derive reactive site concentrations thermodynamic stability constants and enthalpies and entropies of protonation for a suite of potential proton adsorption sites on the spore surface The enthalpies entropies and Gibbs energies generated in this approach provide quantitative information on the thermodynamic driving forces underlying spore surfaceprotonation We will compare the thermodynamic spore-proton adsorption data to amino acid acidity constants entropies and enthalpies to better constrain which ligands may be responsible for proton adsorption Additional comparisons with B subtilis cell surface protonation data offers insight on the chemical differences between cell and spore surface adsorption behavior Acidity constants and site concentrations generated in this research will provide the necessary framework for investigating spore-metal adsorption through SCMs in the future 32 3 3 Methods 3 3 1 Spore growth and isolation We grew and isolated Bacillus subtilis spores as described in Harrold et al 2011 B subtilis was inoculated from agar plate cultures and incubated for 1 day in 3 % trypticase soy broth TSB and 0 5 % yeast extract Culture tubes were transferred to 1 or 2 L volumes of 0 3 % TSB and incubated for 6 days Spores were isolated with a two-phase polyethylene glycol 4000 and potassium phosphate buffer separatory solution Harrold et al 2011 We determined the purity of each spore harvest following ITC analysis using the method described in Harrold et al 2011 Total cell and spore counts were generated from CellC Selinummi et al 2005 batch analyses of ten fluorescence images at 1000 x magnification Cell counts were determined manually from corresponding bright-field images 3 3 2 Dipicolinic Acid DPA analysis Bacterial spores contain a large reservoir of pyridine 2 6-dicarboxylic acid also known as dipicolinic acid DPA within their cortex Nicholson et al 2000 Setlow 2003 Warth 1983 DPA released into solution during a titration has the potential to produce errors in the potentiometric data We measured the amount of DPA released from spore suspensions of 35 g L-1 and 100 g L-1 as a function of pH and time DPA was measured according to a method by Warth 1983 that utilizes the derivative of the Ca-DPA complex absorption Aliquots of spore suspensions were sampled at different time intervals and filtered with pre-rinsed 0 1 uM millipore filters The Ca-DPA complex was produced by adding 0 4 mL of 9 mM CaCl2 and 180mM Tris base to 0 5 mL of filtered sample Warth 1983 The solution absorbance was measured from 300 nm to 250 nm with a scan rate of 20 nm min-1 and 0 1 nm data intervals on a Cary 300 Bio UV-Vis spectrophotometer The difference between peak and valley values at 33 276 nm and 280 nm respectively from the derivative spectra were used to determine the concentration of DPA based on a standard calibration curve 140 120 Heat Flow uW 100 80 60 40 20 0 -20 0 5000 10000 15000 20000 25000 30000 35000 40000 Time s Figure 3 1 Heat flow from a B subtilis spore surface protonation assay measured by isothermal titration calorimetry Each peak in the heat flow corresponds to a 2 L acid injection Positive heats are exothermic Suspension pH decreases from pH 10 to approximately pH 3 with increasing time 3 3 3 Isothermal titration calorimetry We performed isothermal titration calorimetry ITC on a TAM III nanocalorimeter that measures heat flux between a reaction and reference vessel as a function of time Fig 3 1 A computer controlled Lund syringe pump delivered aliquots of acid to the reaction vessel in the calorimeter and to an identical external sample being monitored by an Orion 8103BN Ross semi-micro combination pH electrode calibrated with 4 NIST standards Spores were suspended in degassed 0 1 M NaClO4 to buffer ionic strength The spore suspension was 34 adjusted to approximately pH 10 in an anaerobic chamber using a known amount of CO2 free 1 025 M NaOH 1 mL aliquots of the suspension were pipetted into Hastelloy reaction and reference vessels for ITC analysis and an external reaction vessel for pH monitoring Upon removal from the anaerobic chamber the vessels for ITC analysis were immediately capped and placed into the reaction and reference chambers We performed the titrations by injecting 2 L of 0 143 M HClO4 into both the ITC reaction vessel and the external suspension Intervals between injections spanned 10 to 15 minutes to allow ample time for the heat signal to reach the baseline prior to the next injection Fig 3 1 The pH of the external suspension was monitored continuously and measurements were recorded every 3 seconds Temperature within the isothermal titration calorimeter was maintained at 25 oC within oC variability by a temperature controlled insulating oil reservoir The parallel potentiometric titration experiments were subject to ambient laboratory temperature maintained at 23 oC with 0 3 oC variability We report experimental temperatures of 25 oC to remain consistent with the more temperature sensitive analysis We discarded the first data point in each spore ITC analysis due to anomalous heat associated with the first titrant addition and acid diffusion into the solutions as the system equilibrates prior to initiating the experiment We determined the heat evolved from spore surface protonation reactions Qcorr n Eq 3 1 by subtracting the stepwise background heats i e heats intrinsic to the titration such as heats of dilution Qbkg n from the ITC data Qmeas n Background heats were determined as outlined above with spore-free solutions Eq 3 1 35 The average background heat was 0 1 0 03 mJ 1 Heats of base neutralization H OH- H2O were calculated from the measured pH change for each step of a titration and an enthalpy of -56 48 kJ mol-1 Gorman-Lewis et al 2006 and included in Qbkg n When loading an ITC vial the suspension was exposed to the atmosphere Consequently the spore suspensions could have absorbed some CO2 To estimate the possible heat and proton uptake by dissolved CO2 we calculated the stepwise pH dependent proton buffering capacity and heat flux for the maximum CO2 contamination from 3 mL of atmospheric headspace Both the CO2 buffering capacity and protonation heats produced from our calculations are two orders of magnitude smaller than the stepwise spore protonation buffering capacity and corrected reaction heats Maximum calculated CO2 protonation heats were endothermic 0 04 mJ CO2 contamination in the spore suspension aliquot utilized for pH measurements was eliminated by placing it under a positive pressure of N2 gas for the duration of the titration 3 3 4 Potentiometric titration reversibility We tested the reversibility of spore protonation reactions by performing multiple potentiometric titrations on the same spore suspension 35 g L-1 spore suspensions were made with N2 degassed 0 1 M NaClO4 to buffer ionic strength 1 mL aliquots of the 35 g L-1 spore suspension were adjusted to pH 10 with a known amount of CO2 free 0 143 M NaOH and subsequently titrated to pH 3 Following the first titration we readjusted the spore suspension to pH 10 with a known amount of carbon dioxide free NaOH and titrated it again to pH 3 Spores are highly resistant to acids and bases Setlow 2006 Nicholson 2000 Setlow et al 2002 studied the effectiveness of killing B subtilis spores with HCl and NaOH solutions ranging from 0 3 M to 2 M while Williams and Russell 1993 determined B subtilis spore resistance to NaOH concentrations upwards of 0 2 M Our experimental pH conditions are mild compared to these spore-killing treatments These findings combined with the DPA release see 36 Section 3 2 and reversibility titration see Section 3 3 2 data in this paper suggest that spore integrity was maintained throughout the experiments 3 4 Results and Discussion 3 4 1 Spore harvest purity Spore suspensions following ITC analysis were on average 93 3 % 1 standard deviation pure meaning cell contamination was very low We expect little deviation in the spore purity during the calorimetric titrations The flat baseline observed over the course of the ITC analysis suggests little to no spore germination outgrowth or residual cell metabolism 3 4 2 DPA release Bacillus subtilis spores contain a large reservoir of pyridine-2 6 dicarboxylic acid dipicolinic acid DPA in their cortex Setlow 2003 Warth 1983 DPA is a diprotic acid with pKa1 and pKa2 of 4 66 and 2 07 respectively Martell et al 1998 DPA released into solution can affect the proton mass balance by releasing or taking up protons over the course of an acidic ITC titration from high to low pH All B subtilis spore suspension assays slowly released DPA into solution over time irrespective of pH Low pH assays exhibited the most DPA release 35 g L-1 B subtilis spore suspensions equilibrated for 4 hrs at pH approximately 3 and 6 5 released 15 9 0 4 mol kg-1 and 4 9 1 0 mol kg-1 DPA all errors are 1 respectively DPA release from a 35 g L-1 spore assay adjusted to pH 9 and equilibrated for four hours increased with time but was below the detection limit 5-9 mol kg-1 DPA dependent on sample volume These results indicate the largest DPA release occurs at low pH DPA release from three 35 g L-1 B subtilis spore reversibility titrations ranged from 8 9 0 5 to 17 7 1 8 mol kg-1 DPA Two 100 g L-1 spore suspensions adjusted to ca pH 3 and equilibrated for approximately 2 hr and 45min released 38 3 and 84 2 mol kg-1 DPA The highest DPA release 93 2 mol kg-1 was 37 measured in a 100 g L-1 spore assay equilibrated for 3hr and 40 min circa pH 3 DPA measured in 100 g L-1 spore suspensions at pH circa 5 7 and 10 was below the experimental detection limit DPA concentrations did not plateau in any of the time dependent experiments Fig 3 2 and 3 3 35 g L 35 g L 35 g L 35 g L 20 g L 20 g L 7 6 15 5 10 pH DPA mol kg-1 20 4 5 3 0 0:00 1:12 2:24 2 4:48 3:36 time elapsed h:mm 100 7 80 6 60 5 40 4 20 3 0 0:00 0:28 0:57 1:26 1:55 2:24 2:52 3:21 3:50 pH DPA mol kg-1 Figure 3 2 DPA closed symbols release and pH open symbols change as a function of time for 20 and 35 g L-1 B subtilis spore suspensions 2 4:19 time elapsed h:mm Figure 3 3 DPA released closed symbols and pH open symbols change over time for 100 g L-1 B subtilis spore suspensions 38 A study using B megaterium showed a rapid release of spore DPA when germination was initiated with L-alanine Scott and Ellar 1978 DPA released from the germinating population reached a concentration of 450 mol g-1 spores dry weight within 20 minutes Scott and Ellar 1978 In contrast the DPA concentration of our spore assays increased much more slowly over a period of hours and only reached concentrations of approximately 0 93 mol g-1 spores wet weight in the 100 g L-1 assays Low initial DPA concentrations in our spore suspensions are most likely from incomplete removal during the spore washing process The slow rate of DPA release may suggest minimal to no germination in our spore assays This belief is further supported by a lack of common germination triggers in our spore assays aside from DPA Setlow 2003 The flat baseline observed over the course of ITC analyses suggests little to no metabolism A third line of evidence includes the 93 % average spore purity determined for the spore assays following ITC analysis Setlow et al 2002 observed DPA release from the B subtilis cortex when exposed to strong acid treatment This DPA release may be attributed to changes in the permeability of the spore inner membrane and is not associated with germination processes Setlow et al 2002 also observed significantly less DPA release from alkaline treated spores Our pH and time dependent DPA data is in direct agreement with these findings despite much less extreme alkaline and acidic experimental conditions Although limited spore germination is a potential source of DPA it is more likely that our data indicates passive DPA release from the spore cortex through process related to solution pH 3 4 3 Potentiometric Data 3 4 3 1 Proton adsorption edge Data are plotted in Fig 3 4 in terms of moles of protons adsorbed per gram of spores Hconsumed released described by Eq 3 2: 39 %& % & Eq 3 2 where Ca and Cb are the total concentration of acid and base respectively added to the spore suspension H and OH- are the suspension concentrations calculated from the pH and ms is the wet weight mass of spores in grams The spore suspension exhibited substantial buffering capacity over the entire pH range studied Average total proton uptake and 1 standard deviation from triplicate titrations was 266 10 mol g-1 The steep slope of the titration curves at low pH indicates that the spore surface is not fully protonated A fully protonated surface would produce a very shallow slope indicative of little to no pH buffering capacity mol H adsorbed g-1 spores 200 150 100 50 0 -50 -100 -150 -200 2 4 pH 6 8 10 Figure 3 4 mols of adsorbed protons per gram of B subtilis spores in 0 1 M electrolyte at 25 oC as a function of solution pH Data sets correspond to 20 30 and 35 g L-1 spore suspensions Solid and dashed curves are best fit five and four site NE-SCMs respectively for an averaged 28 3 g L-1 spore suspension Average THo values for the five and four site models are 144 mol g-1 and 132 mol g-1 respectively 40 3 4 3 2 Reversibility Triplicate reversibility titrations preformed on 35 g L-1 spore suspensions show little hysteresis between subsequent titrations on the same suspension Fig 3 5 This suggests that the protonation reactions occurring are limited to reversible adsorption reactions and not irreversible reactions that may include spore germination processes or damage to the spore surface Some disagreement between ITC and reversibility titration data is evident at high pH values Fig 3 5 We believe this is a function of the shorter injection intervals used in the reversibility titrations 1-2 minutes versus 10-15 minutes and pH drift at high pH mol of H adsorbed g-1 spores 200 150 100 50 0 -50 -100 -150 2 3 4 5 6 7 8 9 10 11 pH Figure 3 5 Duplicate 35 g L-1 B subtilis spore reversibility titrations showing the initial suspension titration closed symbols and secondary titrations open symbols following suspension readjustment to pH 10 Kapetas et al 2011 identified time dependent discrepancies between potentiometric titration data and total bacterial surface proton uptake due to dissolved organic carbon DOC release These variations in time dependent proton uptake however resulted in minimal significant differences between SCMs Kapetas et al 2011 pH dependent DPA release is the 41 most likely source of DOC contamination in our titration assays We expect significantly less DOC release from B subtilis spore assays relative to vegetative cell suspensions due to spore dormancy and their chemically resistant nature Based on this and the findings of Kapetas et al 2011 we expect longer time intervals to largely reflect the equilibrium protonation state of the B subtilis spore surface Consequently reversibility titration data is not included in the models to avoid discrepancy due to the time interval variation in the data collection method 3 4 3 3 Non-electrostatic Surface Complexation Modeling We used non-electrostatic surface complexation modeling NE-SCM to define spore surface protonation This approach has been applied extensively to vegetative bacterial cell adsorption Borrok et al 2005 Fein et al 2005 Tourney et al 2008 NE-SCM employs balanced chemical equations Eq 3 3 to describe substrate surface protonation reactions such that the total concentration of deprotonated sites on the spore surface is described in Eq 3 4 Eq 3 3 Eq 3 4 where R-Li is ligand i on the spore surface R-LiH is a proton adsorbed to spore surface ligand i H is the activity of protons in solution as determined by the pH and Ki is the stability constant defining ligand protonation The mass balance equations used to determine the moles of protons adsorbed to the spore surface in a titration defines the pH of immersion or initial surface protonation state as the zero state for each titration Eq 3 2 Figure 3 4 and 3 6 This methodology does not indicate that the spore surface is free of adsorbed protons at the pH of immersion The 42 calculated adsorbed proton concentration as a function of pH is relative to the zero state Fig 3 4 and 3 6 and indicates the extent of proton adsorption or desorption in relation to the initial total proton concentration at the pH of immersion A blank titration in contrast will pass through the zero line showing little to no proton uptake Fig 3 6 The initial total proton concentration in the system is discussed extensively by other researchers Fein et al 2005 Westall et al 1995 and defined here and in other literature as THo The mass balance for total proton concentration in the system can be written as Eq 3 5 Eq 3 5 9 00E-03 7 00E-03 Ca-Cb mol L-1 5 00E-03 3 00E-03 1 00E-03 -1 00E-03 -3 00E-03 -5 00E-03 2 3 4 5 pH 6 7 8 9 Figure 3 6 Triplicate Ca-Cb data in mol L-1 as a function of pH correspond to 20 30 and 35 g L-1 B subtilis spore suspensions in a 0 1 M electrolyte at 25 oC Solid lines show the global five-site model fit to each spore assay The dashed line shows a theoretical degassed 0 1 M electrolyte blank titration assuming an initial pH of 6 88 The pH buffering capacity of B subtilis spores is evident relative to the modeled blank titration 43 Because the SCM is based on a proton mass balance DPA contamination may affect the model results by contributing to proton uptake in the experimental assays The effects of DPA contamination in the proton adsorption data were estimated by calculating the stepwise exchange of protons over the course of the potentiometric titration assuming 20 M DPA at the start of the titration Under these assumptions there is a net uptake of protons by DPA protonation reactions over the course of an ITC analysis The proton uptake calculated for each step of a 1 mL 20 M DPA titration is circa two orders of magnitude smaller than the moles of protons adsorbed in the lowest concentration spore suspension titration data 20 g L-1 Based on our titration specific DPA models and the findings of Kapetas et al 2011 the DPA contamination levels expected in our spore suspensions should not have a significant effect on SCM model results Consequently we did not make any explicit corrections for DPA in the SCM derivation Table 3 1 F-test parameters and results comparing four and five site SCM fits The five-site heat of protonation p value model shows a statically significant better fit that cannot be determined from the spore protonation SCM fits F-test model comparison Parameter Sum-of-squares Number of model parameters Number of data points p-value Spore-Protonation NE-SCM 4 site 5 site 3 07E-6 2 97E-6 9 11 97 0 2408 Heat of protonation model 4 site 5 site 76 72 37 66 12 15 91 4 2 for solutions containing 1 mM oxalate a di-carboxylic acid DPA concentrations estimated for the highest endospore concentration assays 0 66 g L-1 range from 3 to 36 uM and are twoto three-orders of magnitude below previously described oxalate concentrations Rapid initial dissolution rates determined for dialysis and homogeneous assays with 0 66 g L-1 endospores are approximately 1-order of magnitude see section 5 4 faster than the abiotic dissolution rates Based on our estimates and compared to findings by Olsen and Rimstidt 2008 is it unlikely that DPA is a major contributor to the overall rapid initial forsterite dissolution rate observed in the biotic dissolution assays described herein 5 4 3 Dialysis assays 5 4 3 1 Aqueous Si We isolated and measured the influence of B subtilis endospore-ion adsorption on the rate of forsterite dissolution by sequestering the forsterite within dialysis tubing Duplicates of four endospore concentrations and endospore free abiotic controls for a total of 10 assays were monitored for durations ranging from 46 to 95 d Table 5 3 Average solution pH ranging from 7 41 to 7 35 show little variation between assays over the duration of experimentation The highest pHo typically occurred near the end of each experiment while the most acidic pHo was 104 observed within the first 1-2 d of dissolution pH adjustments were required at nearly every sample point for the first 3-5 days of dissolution with solution pHo often below the target pH range of 7 5 0 3 Solution pHo began to stabilize after approximately 5 days with subsequent pH adjustments made every few days on an as needed basis Dialysis tubing creates a physical barrier between the mineral grains and suspended endospores while allowing forsterite dissolution products 1000 kD MW to pass through the membrane equilibrate with the bulk solution and interact with the endospore surface Samples were taken from the bulk solution for subsequent elemental analyses to determine the rate of forsterite dissolution The forsterite powder however remains undisturbed over the course of the experiment This method of sampling results in incongruent removal of the bulk solution relative to the mineral powder effectively increasing the forsterite concentration and decreasing the endospore:forsterite ratio over time We correct for the change in effective forsterite concentration and solution volume by calculating the total moles of Si released at each time-step according to a step-wise linear integration from time t-1 to t Eq 5 1 Eq 5 1 Where nx t is the number of moles of analyte x at time t V t-1 is the total solution volume at time t-1 and is the change in analyte concentration from time t-1 to t Applying Eq 5 1 to low resolution sample sets such as the ICP-OES data n 6 data points per assay would smooth out any variation in dissolution behavior as a function of time due to the discrete stepwise integration We therefore only apply Eq 5 1 to the high-resolution n 30-40 data points per assay Si data determined from the Mo-blue method Dissolution rate is linearly related to mineral surface area White and Brantley 1995 Surface area determined by monolayer surface-gas adsorption and BET theory is commonly 105 used for normalizing mineral dissolution data White and Brantley 1995 While this approach may underestimate the reactivity of a mineral based in part on the density of highly reactive sites on the mineral surface it provides a basis for comparing dissolution rates The BET surface area of forsterite powder measured in this research however is highly variable and imparts a large error on the dissolution data and rate if used to normalize Si data We instead choose to normalize to total grams of forsterite in each assay Fig 5 3-5 Dissolution data provided in molSi gFo-1 for both dialysis and homogenous assays are directly comparable and minimize error Dissolution rates are only normalized to BET surface area following complete data processing and modeling to enable comparisons with other published dissolution rates Si aq are one order of magnitude lower in all dialysis assays Fig 5 3 and 5 4 relative to their homogeneous assay counterparts Fig 5 3 and 5 5 The dialysis membrane may slow the diffusion of dissolution products into the bulk solution and lower Si aq The average steady state abiotic dissolution rates in both homogeneous and dialysis abiotic control assays are however statistically equivalent Table 5 4 section 5 5 1 This suggests that diffusion though the dialysis membrane does not ultimately affect the dissolution rate The rate of abiotic forsterite dissolution is relatively constant over the duration of the experiment Fig 5 3 and 5 4 Dialysis assays containing endospores however show a rapid increase in aqueous Si relative to abiotic controls during the first 5 to 10 days of incubation Fig 5 4 Total aqueous Si released over time increases with increasing endospore concentration The rate of Si release and therefore the forsterite dissolution rate in each biotic assay slows drastically following the initial rapid dissolution phase We term this data region the transition point see section 5 5 1 Qualitatively the rate of forsterite dissolution following the transition point in each biotic assay parallels the dissolution behavior observed in all abiotic control assays 106 5 4 3 2 Aqueous Mg Unlike Si data Mg aq in the biotic assays parallel the behavior of Mg aq observed in abiotic assays Fig 5 6 These observations suggest endospores are adsorbing and lowering the activity of aqueous Mg in biotic dialysis assays as forsterite dissolves see Chapter 4 This behavior is in accordance with findings showing appreciable Mg-endospore adsorption at circumneutral pH and 25 mM ionic strength see Chapter 4 We refrain from using Mg aq data to determine dissolution rates since Mg aq is affected by endospore adsorption available data is at much lower resolution n 6 data points per assay and forsterite dissolution rates are typically calculated with Si dissolution Oelkers 2001 Olsen and Rimstidt 2008 Pokrovsky and Schott 2000b 6 Si mol gFo1 x 10 5 5 4 3 2 1 0 0 1 2 3 time s x 106 4 5 Figure 5 3 Si data for dialysis black diamonds and homogeneous black triangles abiotic control assays as a function of time Data points encompass 2 error The calculated transition point red x is provided for each assay Rapid initial dissolution in the homogeneous control assays is likely due to the release of highly reactive sites on the forsterite surface Rapid initial dissolution is tempered by diffusion thorough the dialysis membrane 107 Si mol gFo1 x 10 5 0 66 g L 1 endospores 0 20 g L 1 endospores 0 10 g L 1 endospores 0 05 g L 1 endospores 6 4 2 Si mol gFo1 x 10 5 0 6 4 2 Si mol gFo1 x 10 5 0 6 4 2 Si mol gFo1 x 10 5 0 6 4 2 0 0 1 2 3 6 time s x 10 4 5 Figure 5 4 Dissolution data as a function of time for dialysis assays corresponding to 4 endospore concentrations light and dark blue circles are duplicates Calculated transition points red x denote the end point for initial linear rate integrations We provide abiotic control data green diamonds for comparison Data points encompass 2 error unless otherwise marked with error bars 108 Mg aq M 200 0 66 g L 1 endospores 0 20 g L 1 endospores 0 10 g L 1 endospores 0 05 g L 1 endospores 100 Mg aq M 0 200 100 Mg aq M 0 200 100 Mg aq M 0 200 100 0 0 1 2 3 6 time s x 10 4 5 Figure 5 5 Mg aq for all biotic dialysis assays black circles 2 error compared to abiotic assay concentrations green diamonds 2 error Mg concentrations are equivalent in both biotic and abioitic dialysis assays despite rapid dissolution in the presence of endospores This is achieved though Mg2 -endospore adsorption 109 0 66 g L 1 endospores 0 20 g L 1 endospores 0 10 g L 1 endospores 0 05 g L 1 endospores Mg:Si 2 1 0 Mg:Si 2 1 0 Mg:Si 2 1 0 Mg:Si 2 1 0 abiotic control Mg:Si 2 1 0 0 1 2 3 6 time s x 10 4 5 Figure 5 6 Mg:Si ratios as a function of time for biotic black circles and abiotic black diamonds dialysis assays The Mg:Si ratio of Fo89 5 is 1 79 red line Errors are 2 110 5 4 3 3 Mg:Si ratio ICP-OES data was used to determine the Mg:Si ratio over time in each assay It was unnecessary to processes the ICP-OES data using a stepwise integration as described in section 5 4 3 1 since the ratio of aqueous Mg and Si is unaffected by sample removal The abiotic dialysis control Fig 5 7 shows an initial Mg:Si ratio below the equilibrium value corresponding to congruent forsterite dissolution 1 79:1 This is in contrast to abiotic homogeneous controls which exhibit congruent dissolution over the entire duration of incubation It is possible that the dialysis membrane selectively inhibited forsterite dissolution products from equilibrating with the bulk solution Within approximately 3 days the ratio achieves and maintains congruent dissolution for the remainder of the incubation Biotic assays show a similar trend with a low Mg:Si ratio the beginning of dissolution which trends towards the congruent forsterite dissolution ratio As endospore concentration increases the Mg:Si ratio takes longer to achieve the congruent dissolution ratio In the 0 20 and 0 66 g L-1 endospore assays the Mg:Si ratio is always lower than the congruent dissolution ratio This suggests the endospore surfaces create either a deficit of Mg an excess of Si or both relative to the 1 79 Mg:Si ratio observed within the forsterite structure 5 4 4 Homogeneous assays 5 4 4 1 Aqueous Si Homogeneous endospore dissolution assays allow both indirect endospore-ion interactions and direct endospore-forsterite adhesion to influence the rate of forsterite dissolution Samples taken from each assay removed equal parts of solution endospores and mineral powder thereby maintaining the endospore:mineral ratio as well as the original endospore and forsterite concentrations We calculate molsi gFo-1 by normalizing the Mo-blue derived Si concentrations to the concentration of forsterite Fig 5 3 and 5 5 111 Abiotic control assays exhibit an initial rapid increase in aqueous Si At the atomic scale mineral surface sites exhibit a range of reactivity related to the number of bonds remaining with the bulk mineral structure Silica tetrahedral exposed at the forsterite surface for example can maintain between 1 and 4 bonds with the forsterite structure Tetrahedra tethered by fewer bonds are more easily released from the mineral surface The observed rapid initial increase in abiotic dissolution is likely due to the release of highly reactive sites on the mineral surface Dissolution reaches a steady state once these highly reactive sites are released into solution Fig 5 3 Homogeneous biotic assays however show rapid initial dissolution beyond that observed in the abiotic controls The extent of initial dissolution increases with increasing endospore concentration After the initial dissolution phase the rate of Si accumulation in all biotic assays taper off and parallel the abiotic dissolution rate Fig 5 5 5 4 4 2 Aqueous Mg Mg aq are similar in both biotic and abiotic homogeneous assays over the duration of incubation Fig 5 7 Akin to the trends observed in the dialysis assays Fig 5 6 Mg-endospore adsorption is likely responsible for lowering the Mg aq in homogeneous assays as forsterite dissolves This interpretation is corroborated by previously discussed adsorption assays exhibiting significant Mg-endospore adsorption under equivalent aqueous conditions see Chapter 4 5 4 4 3 Mg:Si ratio Mg:Si ratios in the abiotic homogeneous assays are at or near congruent forsterite dissolution for the duration of incubation Fig 5 9 Biotic assays show Mg:Si ratios decrease with increasing endospore concentration This is the same trend observed in the biotic dialysis assays Fig 5 8 suggesting a similar dissolution mechanism involving a decrease in Mg aq increase in Si aq or both relative to congruent dissolution observed in abiotic control assays 112 Si mol gFo1 x 10 4 1 6 0 66 g L 1 endospores 0 20 g L 1 endospores 0 10 g L 1 endospores 0 05 g L 1 endospores 1 2 0 8 0 4 Si mol gFo1 x 10 4 0 1 6 1 2 0 8 0 4 Si mol gFo1 x 10 4 0 1 6 1 2 0 8 0 4 Si mol gFo1 x 10 4 0 1 6 1 2 0 8 0 4 0 0 1 2 time s x 106 3 4 Figure 5 7 Forsterite dissolution in terms of Si aq as a function of time in homogeneous forsterite-endospore assays duplicate assays in dark and light blue circles Abiotic homogeneous control data is provided for comparison dark and light green diamonds Initial rapid dissolution rate decreases with decreasing endospore concentration Calculated transition points red x for biotic assays denote the end-point for linear rate regressions Data points encompass 2 error 113 Mg aq M 200 0 66 g L 1 endospores 0 20 g L 1 endospores 0 10 g L 1 endospores 0 05 g L 1 endospores 100 Mg aq M 0 200 100 Mg aq M 0 200 100 Mg aq M 0 200 100 0 0 1 2 3 6 time s x 10 4 Figure 5 8 Mg aq for all biotic homogeneous assays black circles 2 error compared to abiotic assay concentrations red diamonds 2 error Mg concentrations are equivalent in both biotic and abioitic homogeneous assays despite rapid dissolution in the presence of endospores This is achieved though Mg2 -endospore adsorption 114 0 66 g L 1 endospores 0 20 g L 1 endospores 0 10 g L 1 endospores 0 05 g L 1 endospores Mg:Si 2 1 0 Mg:Si 2 1 0 Mg:Si 2 1 0 Mg:Si 2 1 0 abiotic control Mg:Si 2 1 0 0 1 2 time s x 106 3 4 Figure 5 9 Mg:Si ratios as a function of time for biotic black circles and abiotic black diamonds homogeneous dissolution assays The Mg:Si ratio of Fo89 5 is 1 79 red line Errors are 2 115 5 5 Modeling 5 5 1 Abiotic rate and transition point determination We calculated the final steady state forsterite dissolution rate in molSi gFo-1 s-1 for all dialysis and homogeneous assays from the slope of a best-fit linear regression line describing data from 1 5 x 106 s Table 5 4 and 1 4 x 106 s Table 5 5 respectively The average final steady state log dissolution rate for all dialysis assays is -11 33 0 15 2 Homogeneous assays show a statistically equivalent average final steady state log dissolution rate of -11 34 0 49 2 Due to the distinct similarity between all biotic and abiotic final steady state dissolution rates in both the homogeneous and dialysis assays we term this rate the abiotic dissolution rate rSi abiotic All rates are provided in log form Tables 5 4 and 5 5 The transition point TP is defined as the location where the rate of forsterite dissolution or rate of Si release transitions from the initial rapid dissolution rate to rSi abiotic We define the TP quantitatively based on a threshold deviation from the rSi abiotic regression line for data t 1 x 106 s In dialysis assays this threshold is defined as the first data point with a value that deviates from the abiotic linear regression line by 3 Fig 5 3 and 5 4 Homogeneous assays however exhibit more data scatter resulting in larger 3 rSi abiotic linear regression errors The large data scatter included in the homogeneous rSi abiotic linear regressions coupled with a 3 deviation threshold to determine the TP results in a point position far from the visually estimated TP We instead define homogeneous assay TPs as the first data point t 1 x 106 s that deviates from the respective rSi abiotic linear regression line by one tenth of the mean y value molSi gFo-1 divided by the standard deviation of the residuals Fig 5 3 and 5 5 116 5 5 2 Isolating the indirect and direct biotic rate components 5 5 2 1 Indirect endospore-ion adsorption The initial rapid dissolution rate rSi o observed in dialysis assays is a function of both abiotic and indirect endospore-ion adsorption processes We calculate rSi o from the best-fit linear regression line for data from time t 0 s up to the calculated TP tTP for all dialysis assays Table 5 4 Multivariate ANOVA tests indicate rSi o determined for the three highest endospore concentrations are statistically different p 0 05 from the average initial ro Si abiotic and steady state rSi abiotic abiotic dissolution rates The rate component associated with indirect endospore-ion adsorption rSi IS is determined by subtracting the average rSi abiotic from rSi o for each experimental assay Table 5 4 To determine the dependence of rSi IS on endospore concentration we utilize the chemical rate law as described by Eq 5 2 Nagy and Lasaga 1992 Olsen and Rimstidt 2008 : Eq 5 2 1 Where the total rate of Si release into solution Rsi is approximately equal to the forward rate of dissolution r for assays undersaturated with respect to forsterite and secondary Si precipitates see section 5 4 5 k is the rate constant of the forward reaction aj is the activity of the rate determining component j mj is the order of the reaction with respect to j is the change in Gibbs free energy of the reaction R is the gas constant and T is temperature in kelvin When -5RT 1 approaches 1 and the rate law can be simplified according to Eq 5 3 Assuming the highest observed Mg aq and Si aq of 207 and 186 M assay 3H respectively is 497 kJ mol-1 or -200RT much less than the -5RT threshold This is expected since forsterite a primary silicate dissolving at standard temperature and pressure at acidic to circumneutral pH is always far from equilibrium 117 0 65 0 66 0 20 0 20 0 10 0 10 0 05 0 05 0 00 0 00 3D 4D 5D 6D 7D 8Dc 9D 10D 1D control 2D control -10 28 0 04 -10 23 0 10 -10 49 0 10 -10 42 0 11 -10 65 0 08 -10 61 0 13 -10 87 0 08 -10 73 0 07 -11 11 0 14 -11 16 0 08 log rSi o mol gFo-1 s-1 a 11 18 11 8 11 8 10 11 8 22 nb 0 98 0 84 0 89 0 91 0 93 0 89 0 94 0 95 0 87 0 87 Mean R2 -11 37 0 05 -11 44 0 08 -11 32 0 09 -11 32 0 06 -11 29 0 07 -11 17 0 05 -11 34 0 04 -11 34 0 06 -11 35 0 06 -11 40 0 05 -11 33 0 15 log rSi abiotic mol gFo-1 s-1 a 17 19 21 21 21 13 21 21 17 19 nb b a 2 error based on the linear regression Number of data points included in linear regression c Dialysis tubing ruptured at t 3 4 x 106 s r si abiotic excludes samples taken after dialysis burst d 2 error endospore o Assay ID Table 5 4 Dialysis assays: linear regression model results 0 95 0 89 0 89 0 94 0 94 0 98 0 97 0 93 0 95 0 95 R2 -10 32 0 05 -10 27 0 11 -10 56 0 12 -10 48 0 13 -10 75 0 11 -10 70 0 16 -11 06 0 15 -10 86 0 11 n a n a log rSi IS mol gFo-1 s-1 d 118 0 66 0 66 0 20 0 20 0 10 0 11 0 05 0 05 0 00 0 00 3H 4H 5H 6H 7H 8H 9H 10H 1H control 2H control -9 91 0 11 -10 01 0 08 -10 20 0 19 -10 10 0 17 -10 24 0 09 -10 29 0 23 -10 32 0 17 -10 52 0 17 -10 61 0 16 -10 53 0 14 12 12 13 11 18 14 8 18 17 15 nc 0 85 0 92 0 78 0 86 0 90 0 70 0 90 0 75 0 69 0 77 R2 -10 71 0 21 -11 23 0 31 -11 44 0 18 -11 46 0 22 -11 35 0 53 -11 35 0 18 -11 47 0 37 -11 63 0 60 -11 44 0 30 -11 34 0 15 -11 34 0 49 log rSi abiotic mol gFo-1 s-1 a a Mean 2 error based on the best-fit linear regression describing Si dissolution data b 2 error c Number of data points included in linear regression endospore o Assay ID log rSi o mol gFo-1 s-1 a Table 5 5 Homogeneous assays: linear regression model results 17 17 16 16 16 16 16 16 15 15 nc 0 53 0 35 0 69 0 58 0 21 0 71 0 34 0 16 0 48 0 78 R2 -10 20 0 25 -10 42 0 28 -10 51 0 42 -10 32 0 31 -10 47 0 20 -10 56 0 47 -10 51 0 29 -10 89 0 50 n a n a log rSi DS ss mol gFo-1 s-1 b 119 -10 36 0 35 -10 72 0 50 -11 12 1 67 -10 60 0 59 -10 97 0 64 -11 43 3 38 -11 14 1 22 n a n a n a log rSi DS int mol gFo-1 s-1 b By taking the log of Eq 5 3 it can be re-written as Eq 5 4 which provides a linear relationship between dissolution rate and the rate-determining component in this case endospores Eq 5 3 Eq 5 4 We assume an activity coefficient of 1 for endospores and the associated surface bound reactive sites Is it likely however that ionic strength plays a role in the degree to which endospores effect forsterite dissolution Rates and rate models described herein are only valid at ionic strengths of 25 mM A more detailed discussion regarding ionic strength is provided in section 5 6 We plot versus %& % and model the data excluding the 0 05 g L-1 endospore affected rates with a best-fit linear regression Eq 5 5 Fig 5 10 The slope and intercept of the model fit provide the order and rate constant respectively describing the effect of indirect endospore-ion adsorption on the rate of forsterite dissolution as a function of endospore concentration Eq 5 5 0 52 0 06 % & 10 19 0 04 1 25 7 3 5 5 2 2 Direct endospore-mineral adhesion rSi o were determined for homogeneous assays based on the best-fit linear regression for dissolution occurring from t 0 to tTP Table 5 5 Multivariate ANOVA tests indicate rSi o determined for the three highest endospore concentrations are statistically different p 0 05 from the steady state abiotic dissolution rate The rSi o measured for 0 66 g L-1 assays are 120 statistically different p 0 05 from the initial abiotic dissolution rate observed in the homogenous abiotic controls rSi o abiotic We isolate the rate component associated with direct endospore-forsterite adhesion rSi DS ss or rSi DS int by subtracting the model derived indirect endospore affected rate rSi IS and average steady state abiotic dissolution rate rSi abiotic or initial homogeneous abiotic dissolution rate rSi o abiotic respectively from rSi o Table 5 5 The dependence of rSi DS ss and rSi DS int on endospores is modeled as previously described for rSi IS Figs 5 11 and 5 12 Models exclude 0 05 g L-1 rSi DS values Best-fit linear models describing rSi DS ss and rSi DS int are provided in Eq 5 6 and 5 7 Figs 5 11 and 5 12 Eq 5 6 0 31 0 14 % & 10 23 0 10 1 25 7 3 Eq 5 7 0 78 0 36 %& 10 38 0 25 1 25 7 3 5 5 2 3 Initial rate reconstruction The complete rate law defining the initial forsterite dissolution rate at pH 7 6 to 7 3 and I 25 mM in a homogeneous system is provided by Eq 5 8 and is the sum of rSi abiotic rSi IS Eq 5 5 and rSi DS int Eq 5 7 Eq 5 8 10 10 %& 10 %& 121 log rSi IS mol gFo1 s 1 10 0 10 5 R2 0 96 11 0 rSi abiotic 11 5 1 4 1 0 0 6 0 2 1 log endospore o wet wt g L Figure 5 10 Indirect endospore-ion affected dissolution rate as a function of endospore concentration black circles 1 error The linear regression black line solves for the simplified rate law relating dissolution rate to endospore concentration Data in open circles are excluded from the linear regression Average abiotic dissolution rate red line is provided for comparison 122 10 5 R2 0 56 log r Si DS ss mol g 1 Fo s 1 10 0 11 0 r Si abiotic 11 5 1 4 1 0 0 6 0 2 1 log endospore o wet wt g L Figure 5 11 Forsterite dissolution rate ascribed to direct endospore-mineral adhesion based on the steady state abiotic dissolution rate rSi DS ss and presented as a function of endospore concentration black circles 1 error The linear regression black line describes the dependence of rate on endospore concentration according to the simplified rate law Data in open circles are excluded from the linear regression Average steady state abiotic dissolution rate red line is provided for comparison 123 10 0 ro Si abiotic 2 R 0 54 11 0 log r Si DS int mol g 1 Fo s 1 10 5 11 5 1 4 1 0 0 6 0 2 1 log endospore o wet wt g L Figure 5 12 Forsterite dissolution rate ascribed to direct endospore-mineral adhesion based on the initial homogeneous abiotic dissolution rate rSi DS int and presented as a function of endospore concentration black circles 1 error The linear regression black line describes the dependence of rate on endospore concentration according to the simplified rate law Data in open circles are excluded from the linear regression Average steady state solid red line and initial dashed red line abiotic dissolution rates are provided for comparison 124 5 5 3 Chemical equilibrium modeling We utilized PHREEQC in conjunction with the Lawrence Livermore National Lab database to determine the saturation state of Fe Si and Mg bearing mineral phases corresponding to experimental Mg aq and Si aq data and Fe total for homogeneous and dialysis assays 3H and 3D respectively Fig 5 13 Model inputs included Mg aq and Si aq as determined from ICP-OES sample analyses Fig 5 13 panels C and F Fe total was calculated based on Si aq according to the Fe to Si ratio measured in Fo89 5 0 198:1 Homogeneous assay 3H exhibited the highest concentration data of all 20 homogeneous and dialysis assays Predominant species predicted within the assays includes SiO2 or Si OH 4 Mg2 Fe OH 3 and Fe OH 2 at one order of magnitude less than its neutral counterpart Quartz and chalcedony SiO2 became supersaturated in assay 3H after 0 5 x 106 6 d and 3 5 x 106 s 40 d respectively Dialysis assay 3D was just under quartz saturation after 45 d incubation and was always undersaturated with respect to chalcedony Amorphous silica SiO2 am was undersaturated in all assays Based on these findings is it conceivable that SiO2 underwent some form of precipitation within assay 3H during the approximately 45 d incubation period discussed herein Mg is predicted to precipitate out with iron in ferrite-Mg MgFe2O4 though the formation of this mineral requires high 90 C temperatures Omer et al 2013 Magnesite MgCO3 is undersaturated in all assays The average and maximum Fe aq measured for all dissolution assays was 1 2 0 7 M 1 and 4 8 M respectively Aqueous iron concentrations are much lower than the maximum 41 uM Fe total predicted for assay 3H suggesting iron precipitation occurred A variety of iron mineral phases were oversaturated in both assays We show the SI for minerals containing both ferric and ferrous iron since iron within forsterite is in the Fe II oxidation state Fig 5 13 panels B and E We predict ferric iron minerals in particular goethite FeOOH and Fe OH 3 are the most likely iron precipitates due to the oxidizing conditions within each assay 125 0 5 A 0 5 D quartz Saturation Index 0 0 chalcedony 0 5 1 0 1 0 SiO2 am 1 5 2 0 0 15 0 5 1 2 3 1 5 4 B 2 0 0 15 1 2 3 4 5 1 2 3 4 5 2 3 6 t s x 10 4 5 E Saturation Index hematite 10 5 0 5 0 M 10 goethite ferrite Mg magnetite Fe OH 3 5 0 magnesite 1 2 3 Fe T 4 5 0 Mg aq 250 C 250 F 200 200 150 150 100 100 50 50 0 0 1 2 6 t s x 10 3 4 0 0 Si aq 1 Figure 5 13 Saturation indices SI for a selection of mineral phases at or near oversaturation based on the Mg aq Si aq and predicted Fe total for homogeneous assay 3H panels A-C and dialysis assay 3D panels D-F Silicates are in black iron bearing minerals are in red and Mgphases are in blue expect for Ferrite-Mg MgFe2O4 126 Based on the stoichiometry and molar mass of goethite 41 M Fe total VT 0 36 L corresponds to 1 3 mg goethite Assuming the goethite has a density of 3 3 g cm-3 and is precipitated as a 1nm thick coating its maximum surface area would equate to 0 4 m2 in assay 3H The predicted maximum goethite surface area is less for all other assays relative to assay 3H based on the Si dissolution data see section 5 6 for further discussion 5 6 Discussion 5 6 1 Abiotic dissolution We normalized the average abiotic forsterite dissolution rate for all assays to the maximum 5 4 m2 g-1 and minimum 0 6 m2 g-1 BET surface area to compare our findings with others The corresponding abiotic dissolution log rates are -12 1 and -11 1 mol m-2 s-1 respectively Olsen and Rimstidt 2008 predict a log dissolution rate of -10 5 mol m-2 s-1 at pH 7 5 Pokrovsky and Schott 2000b measured dissolution log rates from -9 9 to -10 1 at similar pH and aqueous conditions Wogelius and Walther 1991 determine a log rate of -9 8 for Fo91 dissolution at pH 7 4 and standard temperature and pressure STP The log rates of abiotic dissolution from this work while slower by 0 5 to 1 order of magnitude are on par with the literature values It is possible that an overall decrease in fine particulates over the course of dissolution relative to the unreacted forsterite powder Fig 5 1 may have altered the total surface area within the early phase of incubation Furthermore the high variability in our BET data imparts a large error on the log rate values reported in mol m-2 s-1 It is pertinent to consider abiotic mechanisms of forsterite dissolution to better understand the pathways though which endospores enhance dissolution The structure of forsterite and other nesosilicates is defined by isolated Si tetrahedra linked though octahedrally coordinated metal ions This configuration makes them particularly prone to rapid dissolution since breaking weaker Mg-O bonds can undermine the entire mineral structure releasing both 127 Mg and Si into solution At pH 9 forsterite dissolution is believed to proceed via hydrogen ion attack where two H exchange for Mg2 Pokrovsky and Schott 2000a This mechanism creates an Mg leached and Si rich layer estimated at 20 thick where the Si tetrahedra are capable of undergoing dimerization Pokrovsky and Schott 2000a b Pokrovsky and Schott 2000a report a pHIEP for fresh Fo91 of 4 4 Acid reacted Fo91 exhibits a decrease in pHIEP to 2 1 which is similar to that measured for amorphous silica surfaces Pokrovsky and Schott 2000a 5 6 2 Biotic weathering Both direct endospore-mineral adhesion and indirect endospore-ion adsorption enhance forsterite dissolution at pH approximately 7 5 according to Eq 5 8 The reactive potential of endospore surfaces in our assays is likely due in part to the presence of proton active organic acid moieties Numerous organic acids and proton active moieties similar to those on the endospore surface are capable of increasing silicate dissolution rates Olsen and Rimstidt 2008 observed a 6-fold increase in forsterite dissolution in the presence of 1 mM oxalic acid at pH 4 2 Woeglius and Walther measured a 0 75 log unit increase in forsterite dissolution rate in the presence of ascorbic and pthalic acid at pH 4 Pokrovsky et al 2009 found a wide range of chelators and organic acids capable of enhancing wollastonite CaSiO3 dissolution including but not limited to chelators such as EDTA organic acids including citrate and tartrate and phosphorous ligands in the form of phosphate and metaphosphate Other research investigating quartz dissolution in the presence of organic acids suggest the formation of both aqueous and surface-bound organo-silicic complexes facilitate quartz dissolution Bennett 1991 Bennett et al 1988 5 6 2 1 Direct endospore-forsterite adhesion dissolution mechanisms The primary mechanism believed to be responsible for increased silicate dissolution rate in the presence of organic acids is the formation of ligand-mineral surface complexes that lower 128 the activation energy of dissolution Bennett et al 1988 Olsen and Rimstidt 2008 Pokrovsky et al 2009 For tectosilicates SiO2 these surface complexes must form with mineral surface reactive sites characterized by Si-OH n n-1 groups Bennett et al 1988 In silicate minerals containing metal counter ions aqueous ligands are predicted to complex with metals at the mineral surface Olsen and Rimstidt 2008 Pokrovsky et al 2009 For forsterite anionic oxygen moieties associated with deprotonated organic acids R-O- can form a reactive complex with Mg exposed at the mineral surface Mg Olsen and Rimstidt 2008 This complex shifts the electron density from the bridging oxygen in the Si-O-Mg forsterite structure to the Mgligand bond thereby weakening and ultimately breaking the bridging O bond to form Mg-O-R and Si-OH Olsen and Rimstidt 2008 For a Si tetrahedral tethered to the mineral structure by only one Si-O-Mg bond this process would result in the release of Si into solution Microbe-mineral adhesion is often discussed in terms of hydrophobic or electrostatic attraction or repulsion between the cell and mineral surface Yee et al 2000 Zheng et al 2001 Parikh and Chorover 2006 however show that bacterial cell hematite adhesion involves chemical bond formation between the two surfaces One of the identified bonds in cell hematite adhesion is consistent with inner sphere Fe phosphate or Fe phosphonate complexation between cell bound phosphate moieties and Fe at the mineral surface A second reaction carboxyl protonation is attributed to cell-bound anionic carboxyl moieties reacting with OH groups on the mineral surface Parikh and Chorover 2006 The inner sphere Fephosphate bonds described in cell-hematite adhesion are not unlike the Mg-O-R complexes attributed to enhanced forsterite dissolution Data and models provided in Chapter 4 reveal an affinity for Mg2 adsorption onto the endospore surface at sites L2 4 L3 4 and L4 4 Sites L2 4 and L3 4 are thermodynamically consistent with phosphate moieties Chapter 3 Harrold and Gorman-Lewis 2013 and proton active at the near neutral pH maintained in the forsterite dissolution assays described herein We propose that direct endospore-forsterite adhesion enhances forsterite dissolution through 129 the formation of chemical bonds between organic acid moieties particularly phosphate groups P-O- and Mg sites on the endospore and forsterite surfaces respectively The formation of P-O-Mg complexes acts to lower the activation energy of dissolution as previously described The overall surface charge of a particulate plays a large role in dictating colloidal interactions At pH above 4 the approximate pHIEP the forsterite surface has a net negative charge Repulsion between the negatively charged forsterite and endospore surfaces at pH 7 5 likely mitigates the influence of endospore-forsterite adhesion on the dissolution rate As dissolution progresses and a Si rich surface layer evolves the pHIEP of forsterite drops to 2 Pokrovsky and Schott 2000a and the surface charge at pH 7 5 likely becomes more negative relative to the fresh forsterite surface Under these conditions it is conceivable that electrostatic repulsion increases between the leached forsterite surface and endospore coat as dissolution progresses until a steady state leached layer forms An increase in endospore-forsterite repulsion may contribute to the cessation of biotically enhanced forsterite dissolution observed after approximately 9 days of incubation in the homogeneous assays 5 6 2 2 Indirect endospore-ion adsorption dissolution mechanisms Organic acids can also affect mineral dissolution rates by complexing aqueous dissolution products Bennett 1991 This pathway has the potential to enhance dissolution in accordance with Le Chatelier s principle by lowering the activity of dissolution product and pulling the reaction forward as the chemical system attempts to achieve equilibrium Based on the thermodynamics of forsterite formation and dissolution the Gibbs free energy of dissolution Gr is always far from equilibrium under standard temperature and pressure It is therefore commonly believed that the concentration of aqueous dissolution products does not affect forsterite dissolution rate Olsen and Rimstidt 2008 White and Brantley 1995 This assumption is corroborated by a variety of studies at pH 6 3 Pokrovsky and Schott 2000b 3 8 2 1 Rosso and Rimstidt 2000 and 2 Oelkers 2001 Pokrovsky and Schott 2000b 130 however observed that increasing the Si aq at pH 9 and 11 inhibits forsterite dissolution due to the formation of a Mg-OH n n-1 rich surface layer We propose that endospore-Mg2 adsorption indirectly enhances the rate of forsterite dissolution due to the removal of aqueous Mg2 from solution As forsterite dissolved over the first 1-2 days a steady state Mg-leached Si-rich layer likely formed as previously described by Pokrovsky and Schott 2000a for forsterite dissolution at pH 9 Si polymerization however is most favorable at pH above 7 Iler 1979 Consequently it is possible that the extent of polymerization and depth of the Si-rich Mg-leached layer reaches a maximum around the pH of dissolution maintained within the assays described herein 7 5 Under these conditions Mg release and therefore breakdown of the forsterite structure could be controlled in part by diffusion of Mg2 through a polymerized Si-rich layer Removal of aqueous Mg2 from solution via endospore adsorption increases the chemical gradient between the forsterite dissolution front and bulk solution This results in an increase in the rate of Mg2 diffusion though the Sirich layer As the rate of Mg2 diffusion increases Si is released from the gel-like layer into solution to maintain a steady state depth Comparable Mg aq in both biotic and abiotic assays despite rapid increases in Si aq within the biotic assays is consistent with this theory Endospore-Mg adsorption is the primary Mg aq sink contributing to the observed decrease in Mg:Si ratio with increasing endospore in both the homogeneous and dialysis assays Figs 5 6 and 5 9 Endospore adsorption capacity is finite meaning total Mg2 adsorbed will reach a plateau despite increasing Mg2 aq see Chapter 4 Systems containing mM of Si are capable of enhancing Mg adsorption potentially though the formation of ternary Mg-Si-Mg surface complexes see Chapter 4 Si aq observed in forsterite dissolution assays are however in the 10-6 M range making it unlikely that Si enhanced Mg adsorption is important in this system The abrupt cessation of rapid initial dissolution in dialysis as well as homogeneous biotic assays is in accordance with Mg-endospore adsorption reaching a maximum At the maximum 131 adsorption potential endospore surfaces would no longer alter Mg aq and the dissolution rate would return to a steady state abiotic dissolution rate as observed after 9 to 12 d of incubation Mg aq in biotic and abiotic dialysis and homogeneous assays are comparable over the duration of incubation due to Mg-endospore adsorption in the early rapid dissolution phase This produces equivalent Mg aq chemical gradients in both biotic and abiotic assays after the initial rapid dissolution phase and ultimately enables biotic system to return to an abiotic dissolution rate after cessation of the initial rapid biotic dissolution rate According to this mechanism the dependence of forsterite dissolution rate on the rate of Mg2 diffusion through the Si-rich layer would decrease at pH 7 where Si polymerization is slower and less favorable and the steady state Si-rich layer would be less polymerized and potentially thinner The increased activity of H and rate of 2H Mg2 exchange at more acidic pH could further dampen the affect of Mg diffusion on the dissolution rate In more alkaline solutions pH 10 the forsterite surface is characterized by a Mg-hydroxide rich Si-leached layer Pokrovsky and Schott 2000a b The influence of Mg aq on forsterite dissolution at alkaline pH would likely proceed via a different mechanism Endospore-Si adsorption is likely negligible at the ionic strength and pH of our assays see Chapter 4 Iron oxide precipitates including the formation of iron oxide coatings on B subtilis cell surfaces are known to adsorb large amounts of silicic acid at all pH Fein et al 2002 The goethite and Fe OH 3 precipitates predicted to form in all assays see section 5 4 3 are therefore capable of adsorbing aqueous Si and altering the steady state of the system A decrease in the activity of aqueous Si could act to destabilize the Mg-leached Si-rich layer at the forsterite surface and further enhance dissolution By this mechanism the rate of dissolution would also change as a function of endospore concentration since total iron precipitation will likely increase with the overall mineral dissolution rate An abundance of negatively charged endospore surfaces could also support the formation of thin iron oxide coatings Fein et al 2002 that maximize the reactive surface area of iron precipitates 132 5 7 Conclusions B subtilis endospore surface reactivity enhances the rate of forsterite dissolution through both direct and indirect pathways Direct pathways likely involve the formation of PO-Mg chemical bonds during microbe-mineral adhesion which destabilize forsterite by lowering the activation energy of dissolution Endospore-Mg adsorption enhances dissolution via an indirect pathway by lowering the activity of Mg2 aq and increasing the chemical gradient between the dissolving mineral front and bulk solution This increases Mg2 diffusion though an Mg-leached Si-rich layer thereby enhancing the rate of dissolution The influence of both indirect and direct rate determining mechanisms is dependent on the concentration of endospores in solution Forsterite dissolution in dialysis assays returns to an abiotic rate when endospore-Mg2 adsorption reaches a maximum Homogeneous assays also return to an abiotic rate when endospore-mineral adhesion becomes unfavorable A third mechanism involving Si adsorption onto trace iron oxide precipitates may also contribute to enhanced dissolution in the assays described herein While there are chemical variations between the surface chemistry of B subtilis endospores and vegetative cells the pH range and proton adsorption capacity of both surfaces are very similar Fein et al 2005 Gorman-Lewis et al 2006 Harrold and Gorman-Lewis 2013 This suggests the presence of similar surface bound organic acid moieties and cation adsorption potential Chapter 4 Borrok et al 2004 Harrold and Gorman-Lewis 2013 Further parallels between cell and endospore surface reactivity include a negligible affinity for Si adsorption see Chapter 4 Fein et al 2002 Findings by Borrok et al 2005 show 36 bacterial species including B subtilis vegetative cells exhibit remarkably similar surface reactivities Based on these lines of evidence the endospore surface serves as a first-order proxy for the surfaces of a wide range of vegetative bacterial cells We conclude that bacterial surface reactivity has the capacity to influence olivine chemical weathering rates The affect on chemical 133 weathering rates would be most pronounced in microbe-water-rock systems that support a large microbial biomass Cell surface promoted mineral dissolution may also benefit microbes in environments with trace nutrient deficiencies 5 8 References Bargar J R Tebo B M Villinski J E 2000 In situ characterization of Mn II oxidation by spores of the marine Bacillus sp strain SG-1 Geochimica Et Cosmochimica Acta 64 2775-2778 Bennett P Rogers J Choi W Hiebert F 2001 Silicates Silicate Weathering and Microbial Ecology Geomicrobiology Journal 18 3-19 Bennett P C 1991 Quartz dissolution in organic-rich aqueous systems Geochimica et Cosmochimica Acta 55 1781-1797 Bennett P C Melcer M E Siegel D I Hassett J P 1988 The dissolution of quartz in dilute aqueous solutions of organic acids at 25 C Geochimica et Cosmochimica Acta 52 15211530 Berner R A Lasaga A C Garrels R M 1983 The carbonate-silicate geochemical cycle and its effect on atmospheric carbon dioxide over the past 100 million years American Journal of Science American Journal of Science 283 641-683 Borrok D Fein J B Kulpa C F 2004 Proton and Cd adsorption onto natural bacterial consortia: Testing universal adsorption behavior Geochimica Et Cosmochimica Acta 68 3231-3238 Borrok D Turner B F Fein J B 2005 A universal surface complexation framework for modeling proton binding onto bacterial surfaces in geologic settings Am J Sci 305 826853 134 Borrok D M Fein J B 2005 The impact of ionic strength on the adsorption of protons Pb Cd and Sr onto the surfaces of Gram negative bacteria: testing non-electrostatic diffuse and triple-layer models Journal of Colloid and Interface Science 286 110-126 Daughney C J Fowle D A Fortin D 2001 The effect of growth phase on proton and metal adsorption by Bacillus subtilis Geochimica Et Cosmochimica Acta 65 1025-1035 De Vrind J P M De Vrind-De Jong E W De Voogt J -W H Westbroek P Boogerd F C Rosson R A 1986 Manganese oxidation by spores and spore coats of a marine Bacillus species Applied and Environmental Microbiology 52 1096-1100 Ehrlich H L 1996 How microbes influence mineral growth and dissolution Chemical Geology 132 5-9 Fein J B Boily J -F Yee N Gorman-Lewis D Turner B F 2005 Potentiometric titrations of Bacillus subtilis cells to low pH and a comparison of modeling approaches Geochimica et Cosmochimica Acta 69 1123-1132 Fein J B Scott S Rivera N 2002 The effect of Fe on Si adsorption by Bacillus subtilis cell walls: insights into non-metabolic bacterial precipitation of silicate minerals Chemical Geology 182 265-273 Gorman-Lewis D Fein J B Jensen M P 2006 Enthalpies and entropies of proton and cadmium adsorption onto Bacillus subtilis bacterial cells from calorimetric measurements Geochimica et Cosmochimica Acta 70 4862-4873 Harrold Z R Gorman-Lewis D 2013 Thermodynamic analysis of Bacillus subtilis endospore protonation using isothermal titration calorimetry Geochimica et Cosmochimica Acta 109 296-305 Harrold Z R Hertel M R Gorman-Lewis D 2011 Optimizing Bacillus subtilis spore isolation and quantifying spore harvest purity Journal of Microbiological Methods 87 325-329 Iler R K 1979 The chemistry of silica : solubility polymerization colloid and surface properties and biochemistry Wiley New York 135 Kohler P Hartmann J Wolf-Gladrow D A 2010 Geoengineering potential of artificially enhanced silicate weathering of olivine Proceedings of the National Academy of Sciences 107 20228-20233 Lee J -U Fein J B 2000 Experimental study of the effects of Bacillus subtilis on gibbsite dissolution rates under near-neutral pH and nutrient-poor conditions Chemical Geology 166 193-202 Mandernack K W Post J Tebo B M 1995 Manganese mineral formation by bacterial-spores of the marine Bacillus strain SG-1 - Evidence for the direct oxidation of Mn II to Mn IV Geochimica Et Cosmochimica Acta 59 4393-4408 Marczenko Z 1976 Spectrophotometric determination of elements E Horwood Halsted Press Chichester Eng New York Morris M C et al 1984 Standard x6ray diffraction powder patterns Monograph 25 Section 20 U S Dept of Commerce National Bureau of Standards : For sale by the Supt of Docs U S G P O Washington DC 71 Nagy K L Lasaga A C 1992 Dissolution and precipitation kinetics of gibbsite at 80 deg C and pH 3: The dependence on solution saturation state Geochimica et Cosmochimica Acta 56 3093-3111 Ngwenya B T Magennis M Olive V Mosselmans J F W Ellam R M 2009 Discrete Site Surface Complexation Constants for Lanthanide Adsorption to Bacteria As Determined by Experiments and Linear Free Energy Relationships Environmental Science & Technology 44 650-656 Oelkers E H 2001 An experimental study of forsterite dissolution rates as a function of temperature and aqueous Mg and Si concentrations Chemical Geology 175 485-494 Olsen A A Rimstidt D J 2008 Oxalate-promoted forsterite dissolution at low pH Geochimica et Cosmochimica Acta 72 1758-1766 136 Omer M Elbadawi A Yassin O 2013 Synthesis and Structural Properties of MgFe2O4 Ferrite Nano-particles Journal of Applied and Industrial Sciences 1 20-23 Parikh S J Chorover J 2006 ATR-FTIR Spectroscopy Reveals Bond Formation During Bacterial Adhesion to Iron Oxide Langmuir 22 8492-8500 Phoenix V R Konhauser K O Ferris F G 2003 Experimental study of iron and silica immobilization by bacteria in mixed Fe-Si systems: implications for microbial silicification in hot springs Canadian Journal of Earth Sciences 40 1669-1678 Pokrovsky O S Schott J 2000a Forsterite surface composition in aqueous solutions: a combined potentiometric electrokinetic and spectroscopic approach Geochimica et Cosmochimica Acta 64 3299-3312 Pokrovsky O S Schott J 2000b Kinetics and mechanism of forsterite dissolution at 25 C and pH from 1 to 12 Geochimica et Cosmochimica Acta 64 3313-3325 Pokrovsky O S Shirokova L S Bezeneth P Schott J Golubev S V 2009 Effect of organic ligands and heterotrophic bacteria on wollastonite dissolution kinetics American Journal of Science 309 731-772 Rogers J R Bennett P C 2004 Mineral stimulation of subsurface microorganisms: release of limiting nutrients from silicates Chemical Geology 203 91-108 Rosso J J Rimstidt J D 2000 A high resolution study of forsterite dissolution rates Geochimica et Cosmochimica Acta 64 797-811 Sacks L E Alderton G 1961 Behavior of bacterial spores in aqueous polymer two-phase systems Journal of Bacteriology 82 331-341 Setlow B Loshon C Genest P Cowan A Setlow C Setlow P 2002 Mechanisms of killing spores of Bacillus subtilis by acid alkali and ethanol Journal of Applied Microbiology 92 362-375 Setlow P 2006 Spores of Bacillus subtilis: their resistance to and killing by radiation heat and chemicals Journal of Applied Microbiology 101 514-525 137 Siala A Hill I R Gray T R G 1974 Populations of Spore-forming Bacteria in an Acid Forest Soil with Special Reference to Bacillus subtilis J Gen Microbiol 81 183-190 Song W Ogawa N Oguchi C T Hatta T Matsukura Y 2007 Effect of Bacillus subtilis on granite weathering: A laboratory experiment CATENA 70 275-281 Stumm W 1990 Aquatic chemical kinetics : reaction rates of processes in natural waters Wiley New York Vandevivere P Welch S A Ullman W J Kirchman D L 1994 Enhanced Dissolution of Silicate Minerals by Bacteria at Near-Neutral pH Microbial Ecology 27 241-251 White A F Brantley S L 1995 Chemical weathering rates of silicate minerals Mineralogical Society of America Washington D C Whitman W B Coleman D C Wiebe W J 1998 Prokaryotes: The unseen majority Proceedings of the National Academy of Sciences 95 6578-6583 Wightman P G Fein J B 2004 The effect of bacterial cell wall adsorption on mineral solubilities Chemical Geology 212 247-254 Wogelius R A Walther J V 1991 Olivine dissolution at 25 deg C: Effects of pH CO2 and organic acids Geochimica et Cosmochimica Acta 55 943-954 Yee N Fein J B Daughney C J 2000 Experimental study of the pH ionic strength and reversibility behavior of bacteria-mineral adsorption Geochimica et Cosmochimica Acta 64 609-617 Zheng X Arps P J Smith R W 2001 Adhesion of two bacteria onto dolomite and apatite: their effect on dolomite depression in anionic flotation International Journal of Mineral Processing 62 159-172 138 Chapter 6: Conclusions Microbial biomass plays a critical role in the movement and cycling of dissolved ions through the environment Divulging how and to what extent microbe-ion interactions drive low-temperature aqueous geochemical processes is instrumental to our understanding of waterrock systems Microbe-ion adsorption is one such pathway capable of influencing the activity of aqueous major and trace ions Most investigations focus on the adsorption behavior of trace metals onto vegetative bacterial cell surfaces The surface reactivity of endospores however is poorly constrained Furthermore the effect of microbial surface reactivity on major ion activities and primary silicate dissolution rates is a widely unstudied phenomenon with potentially large geochemical impacts This dissertation develops a method for generating a pure endospore biomass that enables focused experimentation regarding endospore surface reactivity in water-rock systems Endospore surface reactivity is quantified and modeled to produce a robust thermodynamic definition of discrete adsorption sites We then test the ability for endospore adsorption to impact the activities of two major ions found in forsterite Mg and Si Finally endospores are utilized as a first-order proxy to isolate the influence of microbial surface reactivity on the rate of forsterite dissolution Together this body of work fills in numerous knowledge gaps regarding microbial surface reactivity and advances our understanding of microbe-mineral interactions The culturing methods described in Chapter 2 successfully induce Bacillus subtilis sporulation and produce milligrams of endospore biomass free of vegetative cell residue Further purification is achieved using a refined version of the two-phase separatory solution described by Sacks and Alderton 1961 A semi-automated process for determining the purity of the final endospore biomass provides a method that enables quality control These methods are published in the Journal of Microbiological Methods Harrold et al 2011 Together the 139 methods described in Chapter 2 enable experimentation critical to investigating the surface reactivity of B subtilis endospores and understanding their influence on geochemical processes Chapter 3 provides the most robust analysis of endospore surface reactivity to date Data include synchronized potentiometric titration and isothermal titration calorimetry ITC data corresponding to B subtilis endospore surface protonation from pH 3 to 9 Results show net endospore proton adsorption is exothermic and occurs over the entire pH range studied We model the potentiometric titration data according to non-electrostatic surface complexation theory which defines surface protonation according to balanced chemical equations describing discrete proton active sites A four-site non-electrostatic surface complexation model NE-SCM provides the best fit to the potentiometric titration results but fails to describe the ITC data To remedy this discrepancy we use a five-site NE-SCM to describe both the potentiometric titration and ITC data A significantly better fit to the highly sensitive ITC data justifies the use of a fivesite model despite being under-constrained by the potentiometric titration results Conducting simultaneous potentiometric titration and ITC analyses is a novel approach to investigating microbial surface reactivity that provides a more robust thermodynamic definition of surface reactivity than the individual analyses The NE-SCMs describing endospore surface protonation herein include site concentrations equilibrium constants enthalpies entropies and the Gibbs free energy of protonation for discrete proton active sites on the endospore surface Site-specific thermodynamics of endospore protonation suggest the presence of reactive carboxyl phosphate and thiol groups on the endospore surface Hydroxyl phenol or amine groups may contribute to proton adsorption at high pH 7 5 Endospore adsorption capacity and behavior is comparable to their vegetative cell counterpart suggesting similar organic acid moieties are responsible for endospore and cell surface adsorption This research is published in Geochimica et Cosmochimica Acta Harrold and Gorman-Lewis 2013 and enables quantitative analysis of environmentally relevant endospore-ion interactions in both laboratory and macro-scale systems 140 Chapter 4 investigates B subtilis endospore Mg and Si adsorption over a wide range of pH and adsorbent to adsorbate ratios as well as adsorption behavior in aqueous systems containing both Mg and Si Despite exhibiting both hydrophobic and hydrophilic surface properties Si adsorption to the endospore surface is negligible under all pH and endospore to adsorbate ratios studied This behavior is similar to that observed for B subtilis vegetative cells Fein et al 2002 Mg-endospore adsorption however increases with increasing pH Mg total and Si total pH dependent Mg adsorption likely increases with increasing pH as organic acid moieties on the endospore surface sequentially deprotonate and expose anionic oxygen ligands capable of complexing Mg2 Increasing the Mg total to endospore ratio increases adsorption until maximum adsorption is achieved and the adsorption edge plateaus We modeled pH dependent Mg adsorption according to the 4-site NE-SCM described in Chapter 3 Both 1site:1Mg and 2site:1Mg stoichiometric adsorption onto sites L2 4 L3 4 and L4 4 provided a good fit to the data These models were then fit to the adsorption data from variable adsorbate to adsorbent ratio assays at pH approximately 7 2 The 1site:1Mg stoichiometry model provided a good fit to the low Mg total data but failed to describe the adsorption plateau A 2site:1Mg adsorption stoichiometry was able to describe the adsorption plateau but not the low Mg total data It is possible that both 1site:1Mg and 2site:1Mg adsorption stoichiometry contribute to overall Mgendospore adsorption behavior Systems containing both Mg and Si do not appreciably enhance Si adsorption However increases in Si total enhance Mg adsorption It is possible that ternary Mg-Si-Mg complexes are responsible for enhanced Mg adsorption in the presence of Si Assuming ternary complexes form the concomitant increase in Si adsorption is within the analytical error of the Si data rendering it undetectable Findings from Chapter 4 suggest endospore Mg and Si adsorption behavior is similar to that of their vegetative cell counterpart Endospores are more likely to affect low-temperature aqueous geochemical systems through direct Mg-endospore adsorption than direct Si-endospore adsorption Their 141 adsorptive influence on Si is likely restricted to the formation of ternary metal-Si complexes These interactions are particularly relevant to mineral dissolution and precipitation processes involving Mg and Si The metabolic dormancy and structural integrity of endospores in oligotrophic environments makes them an ideal candidate for studying the influence of microbial surfaces on low-temperature aqueous geochemical processes Chapter 5 explores the affect of microbial surfaces on the rate of forsterite dissolution at near-neutral pH by using B subtilis endospores as a first order proxy for vegetative cell surfaces Dialysis and homogeneous assays isolate the affects of both direct and indirect dissolution pathways corresponding to microbe-mineral adhesion and microbe-ion adsorption respectively The initial rate of forsterite dissolution increases in the presence of endospores in both dialysis and homogeneous assays Dissolution rates return to an abiotic steady state rate after the initial rapid biotic dissolution phase The initial biotic dissolution rate components for both indirect and direct dissolution pathways correlate with endospore concentration and are modeled according to a simplified rate law Endospore-ion adsorption likely enhances dissolution by adsorbing Mg and increasing the chemical gradient across a Si-rich Mg-leached layer that acts as a diffusion barrier between the forsterite dissolution front and bulk solution at near-neutral pH Mg-endospore adsorption data provided in Chapter 4 and Mg:Si ratios below stoichiometric forsterite dissolution in biotic assays support this theory Direct endospore-forsterite adsorption may include the formation of Mg-phosphate bonds between the endospore and mineral surfaces These bonds can shift electron density within the mineral structure destabilizing the forsterite and ultimately leading to enhanced dissolution Based on these findings microbial surface reactivity is capable of influencing the rate of primary silicate dissolution in microbe-water-rock systems at nearneutral pH This dissertation provides the first detailed thermodynamic models describing endospore surface reactivity and enabling comparison to their vegetative cell counterpart The 142 influence of direct B subtilis endospore adsorption on major element activities is most likely associated with major cation adsorption and to a much lesser extent Si adsorption Ternary metal-Si complexes are the most likely mechanism driving Si-endospore adsorption in aqueous systems These reactions have implications regarding microfossil formation and preservation In low-temperature aqueous geochemical systems B subtilis endospore-Mg adsorption and mineral adhesion are capable of enhancing forsterite dissolution at near-neutral pH Although a broad understanding of bacterial endospore coat reactivity across species and genera is still lacking this work illustrates the fundamental influence endospores can have on geochemical reactions and provides an investigative model for future studies Based on the commonalities between B subtilis endospore and vegetative cell surface reactivity it is possible that a wide range of microbial cells are capable of enhancing primary mineral dissolution rates through surface mediated pathways This suggests that the mere presence of microbes is capable of manipulating fundamental geochemical processes regardless of their metabolic activity References Fein J B Scott S Rivera N 2002 The effect of Fe on Si adsorption by Bacillus subtilis cell walls: insights into non-metabolic bacterial precipitation of silicate minerals Chemical Geology 182 265-273 Harrold Z R Gorman-Lewis D 2013 Thermodynamic analysis of Bacillus subtilis endospore protonation using isothermal titration calorimetry Geochimica et Cosmochimica Acta 109 296-305 Harrold Z R Hertel M R Gorman-Lewis D 2011 Optimizing Bacillus subtilis spore isolation and quantifying spore harvest purity Journal of Microbiological Methods 87 325-329 Sacks L E Alderton G 1961 Behavior of bacterial spores in aqueous polymer two-phase systems Journal of Bacteriology 82 331-341 143
    • Hotovec-Ellis, Alicia - Ph.D. Dissertation
      Utilizing Changes in Repeating Earthquakes to Monitor Evolving Processes and Structure Before and During Volcanic Eruptions 2014, Hotovec-Ellis, Alicia , Alicia Hotovec-Ellis Utilizing Changes in Repeating Earthquakes to Monitor Evolving Processes and Structure Before and During Volcanic Eruptions Alicia Hotovec-Ellis A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2014 Reading Committee: John Vidale Chair Joan Gomberg Seth Moran Program Authorized to Offer Degree: Department of Earth and Space Sciences Copyright 2014 Alicia Hotovec-Ellis University of Washington Abstract Utilizing Changes in Repeating Earthquakes to Monitor Evolving Processes and Structure Before and During Volcanic Eruptions Alicia Hotovec-Ellis Chair of the Supervisory Committee: Professor John Vidale Department of Earth and Space Sciences Repeating earthquakes are two or more earthquakes that share the same source location and source mechanism which results in the earthquakes having highly similar waveforms when recorded at a seismic instrument Repeating earthquakes have been observed in a wide variety of environments: from fault systems such as the San Andreas and Cascadia subduction zone to hydrothermal areas and volcanoes Volcano seismologists are particularly concerned with repeating earthquakes as they have been observed at volcanoes along the entire range of eruptive style and are often a prominent feature of eruption seismicity The behavior of repeating earthquakes sometimes changes with time which possibly reflects subtle changes in the mechanism creating the earthquakes In Chapter 1 we document an example of repeating earthquakes during the 2009 eruption of Redoubt volcano that became increasingly frequent with time until they blended into harmonic tremor prior to several explosions We interpreted the source of the earthquakes as stickslip on a fault near the conduit that slipped increasingly often as the explosion neared in response to the build-up of pressure in the system The waveforms of repeating earthquakes may also change even if the behavior does not We can quantify changes in waveform using the technique of coda wave interferometry to differentiate between changes in source and medium In Chapters 2 and 3 we document subtle changes in the coda of repeating earthquakes related to small changes in the near-surface velocity structure at Mount St Helens before and during its eruption in 2004 Velocity changes have been observed prior to several volcanic eruptions are thought to occur in response to volumetric strain and the opening or closing of cracks in the subsurface We compared continuous records of velocity change against other geophysical data and found that velocities at Mount St Helens change in response to snow loading fluid saturation shaking from large distant earthquakes shallow pressurization and possibly lava extrusion Velocity changes at Mount St Helens are a complex mix of many different effects and other complementary data are required to interpret the signal TABLE OF CONTENTS Page LIST OF FIGURES iv LIST OF TABLES vi CHAPTER 1: Strongly Gliding Harmonic Tremor During the 2009 Eruption of Redoubt Volcano 1 Abstract 1 1 Introduction 2 2 Gliding Harmonic Tremor 4 2 1 Summary of observations on Redoubt Volcano 4 2 1 1 Seismic instrumentation 5 2 1 2 Seismic signal characteristics 6 2 2 Evaluation of models 12 3 Closely Repeating Earthquakes and Harmonic Tremor 15 4 Discussion 27 Acknowledgements 32 Appendix 32 References 34 CHAPTER 2: A Continuous Record of Inter-eruption Velocity Change at Mount St Helens from Coda Wave Interferometry 44 Abstract 44 1 Introduction 45 2 Data 49 i 3 Application of Coda Wave Interferometry 50 4 Inversion Results 55 5 Seismicity Rate and Seasonal Repeaters 58 6 Interpretation 60 6 1 Seasonal variation as climatological loading 60 6 2 Response to Nisqually Earthquake 66 6 3 Long-term trends 68 7 Discussion 70 8 Conclusions 75 Acknowledgements 76 References 76 CHAPTER 3: Changes in Seismic Velocity During the 2004 2008 eruption of Mount St Helens Washington 85 Abstract 85 1 Introduction 86 2 Data 88 3 Methods 91 4 Results and Interpretations 95 4 1 Estimation of change due to deflation of magma chamber at depth 99 4 2 Velocity changes associated with vent clearing and extrusion of initial spines September 23 2004 October 25 2004 105 4 3 Velocity changes associated with recumbent growth of whaleback spines and rainstorms October 25 2004 April 19 2005 109 ii 4 4 Velocity changes associated with spines thrusting over previous spines April 19 2005 and onward 112 5 Conclusions 114 References 116 iii LIST OF FIGURES Figure Number Page Figure 1-1 Timeline of explosive events during the 2009 Redoubt eruption 5 Figure 1-2 Seismic network map for Redoubt 6 Figure 1-3 Velocity spectrograms of pre-explosive gliding harmonic tremor 7 Figure 1-4 Fundamental frequencies of consecutive gliding events 10 Figure 1-5 Representative sample of extrusive phase harmonic tremor 11 Figure 1-6 Normalized amplitude and correlation coefficient of Event 9 swarm 18 Figure 1-7 Change in period between earthquakes and tremor prior to Event 9 20 Figure 1-8 Synthetic harmonic tremor 22 Figure 1-9 Normalized spectrum of repeating earthquake and tremor 24 Figure 1-10 Repeating earthquake focal mechanism 26 Figure 2-1 Depth-time plot and cross-section of seismicity 46 Figure 2-2 Station map for Mount St Helens 49 Figure 2-3 Illustration of coda wave interferometry for velocity change 53 Figure 2-4 Inversion tests for recovering known function of velocity change 56 Figure 2-5 Inversion results for all stations 57 Figure 2-6 Seasonality of repeating earthquakes 59 Figure 2-7 Seasonality of velocity change 61 Figure 2-8 Comparison of velocity to snow load and lake elevation 64 Figure 2-9 Frequency dependence of velocity change 66 Figure 2-10 Inversion solution with greater smoothing regularization 69 Figure 2-11 Estimations of displacement strain and velocity change 74 Figure 3-1 Station map and located earthquakes for Mount St Helens 89 iv Figure 3-2 Illustration of stretching method 93 Figure 3-3 Inversion tests for recovering known function of velocity change 96 Figure 3-4 Inversion results for all stations 97 Figure 3-5 GPS N-S displacement at JRO 99 Figure 3-6 Estimations of displacement strain and velocity change 102 Figure 3-7 Comparison of mean velocity change to other data full time span 104 Figure 3-8 Comparison of mean velocity change to other data first period 106 Figure 3-9 Correlation of velocity change and RSAM 108 Figure 3-10 Comparison of mean velocity change to other data second period 110 Figure 3-11 Comparison of mean velocity change to other data third period 113 v LIST OF TABLES Table Number Page Table 1-1 Summary of gliding events 8 Table 1-2 List of first motions 27 Table 2-1 Comparison of misfit of data to different models 62 Table 2-2 Parameters for estimating surface strain due to pressure increase at depth 72 Table 2-3 Parameters for estimating the Murnaghan constant m 73 Table 3-1 Parameters for estimating surface strain due to pressure decrease at depth 101 vi CHAPTER 1: Strongly Gliding Harmonic Tremor During the 2009 Eruption of Redoubt Volcano The content of this chapter was published as part of a Special Issue in: Hotovec A J S G Prejean J E Vidale and J Gomberg 2013 Strongly Gliding Harmonic Tremor During the 2009 Eruption of Redoubt Volcano Journal of Volcanology and Geothermal Research 259 89 99 doi:10 1016 j jvolgeores 2012 01 001 The reader may also be interested in the follow-up paper: Dmitrieva K A J Hotovec-Ellis S Prejean and E M Dunham 2013 Frictionalfaulting model for harmonic tremor before Redoubt Volcano eruptions Nature Geoscience 6 652 656 doi:10 1038 ngeo1879 Abstract During the 2009 eruption of Redoubt Volcano Alaska gliding harmonic tremor occurred prominently before six nearly consecutive explosions during the second half of the eruptive sequence The fundamental frequency repeatedly glided upward from
    • Hutchins, Michael - Ph.D. Dissertation
      Source, propagation, and effects of lightning in the Earth-ionosphere system 2014, Hutchins, Michael , Michael Hutchins c Copyright 2014 Michael L Hutchins Source propagation and effects of lightning in the Earth-ionosphere system Michael L Hutchins A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2014 Reading Committee: Robert H Holzworth Chair Michael P McCarthy Abram R Jacobson John M Wallace John D Sahr Program Authorized to Offer Degree: UW Department of Earth and Space Sciences University of Washington Abstract Source propagation and effects of lightning in the Earth-ionosphere system Michael L Hutchins Chair of the Supervisory Committee: Professor Robert H Holzworth Department of Earth and Space Sciences The capabilities of the World Wide Lightning Location Network WWLLN are expanded to enable research of the source propagation and effects of lightning in the Earthionosphere system The main expansion of the network capability is the measurement of the very low frequency radiated energy from lightning the radiated stroke energy is one to one related to the canonical peak current measurements of other ground based networks Stroke energy is used to develop a model of the network relative detection efficiency this internal model rates the coverage capabilities of the network compared to the networks best regional coverage The last dataset developed and discussed is the clustering of the lightning locations into both flashes and the active lightning regions of thunderstorms These three capabilities of the network allow tracing the effects of lightning and thunderstorms from their source to a proxy for the global electric circuit and to the magnetosphere The source of lightning is investigated in two regimes: within thunderstorms and between thunderstorms Within thunderstorms the time between flashes is found to be proportional to the resulting flash energy for differing thunderstorms regions and seasons Between thunderstorms the lightning energy is shown to differ between land and ocean with oceanic thunderstorms producing stronger and fewer strokes The propagation of the radiated energy is measured using the lightning as a probe of attenuation along the different propagation paths Attenuation is seen to have an asymmetry with magnetic azimuth: eastward moving waves are attenuated less than westward moving waves The attenuation asymmetry is complimentary to the observed asymmetry in whistler and radio energy emitted through the ionosphere into the magnetosphere Thunderstorm clusters are used to estimate the total upward current contribution of thunderstorms to the global electric circuit It is shown that WWLLN can provide one of the first continuous global measurements of this current to the global electric circuit TABLE OF CONTENTS Page List of Figures iv List of Tables xi Chapter 1: Introduction 1 1 1 Background 2 1 2 Lightning Detection Systems 7 1 3 Long Wave Propagation Capability Code 12 1 4 Outline 12 Chapter 2: Stroke Energy 16 2 1 Overview 17 2 2 Instrumentation and Data Processing 2 3 Results 25 2 4 Discussion 27 2 5 Conclusion Chapter 3: 19 31 WWLLN Detection Efficiency 33 3 1 Overview 34 3 2 Minimum Detectable Energy 36 3 3 Relative Detection Efficiency 41 3 4 Analysis 43 3 5 Results 50 3 6 Conclusion Chapter 4: 52 ENTLN-LIS Detection Efficiency 54 4 1 Overview 55 4 2 Performance 57 4 3 Conclusion 62 i Chapter 5: Land-Sea Contrast 65 5 1 Overview 66 5 2 Linear Regression Analysis 5 3 Regression Slope Maps 69 5 4 Stroke Distributions 71 5 5 Regional Contrast 71 5 6 Conclusion Chapter 6: 67 74 VLF Propagation 75 6 1 Overview 76 6 2 Path Selection 6 3 Azimuthal Dependence 78 6 4 Comparisons to Theory 83 6 5 Conclusion Chapter 7: 77 84 Global Electric Circuit 86 7 1 Overview 87 7 2 Clustering 90 7 3 WWLLN thunderstorm clusters 93 7 4 Global thunderstorm activity 95 7 5 Temporal thunderstorm activity 97 7 6 Global Electric Circuit Thunderstorm Contribution 99 7 7 Conclusion Chapter 8: 101 Thunderstorms and Flashes 103 8 1 Overview 104 8 2 Data 105 8 3 Methods 105 8 4 Detection Efficiency 106 8 5 Flash Clusters 112 8 6 Conclusion Chapter 9: 115 Conclusion and Future Work 117 9 1 WWLLN Characterization 118 9 2 Thunderstorms 119 9 3 Global Electric circuit 121 ii 9 4 Other Lightning Processes 122 Bibliography 123 Appendix A: Code Repositories A 1 File Storage on Flash Machines A 2 Code Repositories A 3 Git Primer A 4 Other Useful Matlab Code 137 138 140 141 141 Appendix B: Energy Processing B 1 Code Summary B 2 LWPC B 3 Lookup Tables B 4 Matlab Code B 5 Relative Detection Efficiency Code 143 144 145 146 148 152 Appendix C: WWLLN Service Unit v4 C 1 New Design C 2 Gumstix Selection C 3 Layout and Design C 4 Construction C 5 Testing Procedures C 6 Software Setup C 7 Operations 155 156 156 157 158 165 166 171 Appendix D: Gumstix D 1 Hardware D 2 Gumstix Operating System v2 0 D 3 Software D 4 Creating Gumstix microSD Card D 5 Gumstix System Setup D 6 Common Problems 172 173 174 175 177 177 181 Appendix E: Website 182 E 1 WWLLN net 183 E 2 Lightning Maps 187 iii LIST OF FIGURES Figure Number 1 1 Page Overall thunderstorm charge structure showing a typical freezing level and tropopause hight 3 The step-leader and discharge process of cloud to ground lightning with typical times of each stage adapted from Ogawa 1995 4 Different types of lightning discharges: a negative cloud-to-ground b positive ground-to-cloud c in-cloud d positive cloud-to-ground e negative ground-to-cloud f cloud-cloud Note that a and b produce the same overall charge movement negative charge to ground and as does d and e Based on Uman 1969 5 Atmospheric temperature profile and ionospheric plasma density profile day ionosphere in black night ionosphere in red 6 1 5 Schematic of the Earth-Ionosphere Waveguide 6 1 6 a Global electric circuit model arrow correspond to currents b Very simple circuit equivalent model with representative values 7 1 7 Global WWLLN lightning stroke density for 2011 2012 9 1 8 North American ENTLN lightning stroke density for the 2011 2012 dataset Note same range as Figure 1 7 11 1 9 LIS lightning flash density for 2011 2012 Note the reduced range from Figures 1 7 and 1 8 11 1 2 1 3 1 4 1 10 LWPC generated lookup table for Dunedin station white triangle using an all day ionospheric model 0 3 km 1 and h0 74 km averaged over 8 18 kHz Each 1 by 1 bin shows the electric field seen at Dunedin if a 100kW transmitter is centered on that bin 13 2 1 WWLLN 2010 global stroke density on 1 x 1 grid station locations shown with black triangles Data processed with the Stroke B algorithm 18 2 2 The top panel shows average power spectra from 194 stroke waveforms recorded at the Tallahassee FL station between 0 and 48 kHz The strokes were located 5 Mm 10 Mm away from the station on May 3 2011 and May 9 2011 between 18:00 and 21:00 UTC The bottom panel shows the frequency response of a preamplifier 20 iv 2 3 LWPC generated lookup table for Dunedin station white triangle using an all day ionospheric model 0 3 km 1 and h0 74 km averaged over 8 18 kHz Each 1 by 1 bin shows the electric field seen at Dunedin if a 100 kW transmitter is centered on that bin 22 2 4 Method of calibrating one station to another using LWPC 2 5 An example of the bootstrapping technique showing calibration distance from the main Dunedin station Thick green lines are the first calibration stage and the thin red lines the last Stations may be unconnected due to not having common strokes being poor intermediary stations or being down for the day 24 2 6 WWLLN peak current versus NZLDN return stroke peak current for three time periods in 2009 using 5260 matches WWLLN peak current derived from Estroke 2 23 Ipeak 1 62 84% of strokes are within range of the unity line red solid line with uncertainty taken into account 86 5% of NZLDNWWLLN matched strokes shown others out of range 26 2 7 Histogram of stroke energies for 2010 with 100 logarithmically spaced bins the histogram for the globe 1 4 x 108 strokes is shown in black the Americas 6 1 x 107 strokes in blue Africa Europe 2 4 x 107 strokes in red and Asia Australia 5 0 x 107 strokes in green Error bars are too small to display 29 2 8 The cumulative probability distributions of stroke current for the best fit of the Popolansky 1972 data dashed and the 2010 WWLLN dataset solid 30 3 1 a WWLLN stroke energy distribution for the globe black the Americas blue Asia green and Aftica Europe red b WWLLN global stroke energy distribution for a year 2010 month June 2010 day 15 June 2010 and hour 09 UTC 15 June 2010 Grey lines are statistical count errors 37 3 2 a shows the evolution of the triggered RMS field strength distribution in arbitrary units for the Dunedin WWLLN station with the red line showing the 5th percentile value b shows the 9 UTC slice of the distribution with the 5th percentile value marked red line 38 3 3 a the minimum detectable energy MDE for the Dunedin station at 9 UTC on 15 June 2010 The regions of high MDE are due to poor VLF propagation over ice from those regions to Dunedin station b the minimum detectable energy MDE for the entire WWLLN network The white line shows the terminator 40 3 4 a The seven day energy distribution with the strokes above the MDE of 100 J shown in grey The fraction of strokes above 100 J to total strokes gives a relative detection efficiency of 0 9 shown as a circle in b The fraction for all possible MDE values is shown as the curve in b 42 v 23 3 5 Relative detection efficiency maps for 00 06 12 and 18 UTC on 15 June 2010 Stations are shown as triangles with operational stations in white and non-operational in black The minimum value of detection efficiency is set at 5% to prevent unphysical corrections 44 3 6 Daily average relative detection efficiency for 15 June 2010 Stations are shown as triangles with operational stations in white non operational in black and operational for part of the day in grey The minimum value of detection efficiency is set at 5% to prevent unphysical corrections 45 3 7 Median stroke energy of the 7-day distribution observed by WWLLN The relative detection efficiency of the network is based on this 7-day energy distribution Systematic changes in median stroke energy result from unaccounted for gain changes at the primary calibrated WWLLN station see Chapter 2 Tick marks correspond to the start of the listed month 46 3 8 The number of WWLLN stations operating black and the global average relative detection efficiency gray for April 2009 through October 2011 Tick marks correspond to the start of the listed month 46 3 9 Daily variation of average detection efficiency for the globe black lowlatitudes 30 N to 30 N blue over Florida at 85 E 30 N red and over South Africa at 25 E 20 N green Tick marks correspond to the start of the listed month 47 3 10 Average solar-local time variation of detection efficiency over Florida 85 E 30 N solid and South Africa 25 E 20 N dashed from 2009-2011 48 3 11 Relative detection efficiency map of 16 June 2010 for a the complete network b the network with the Hawaii station black star 158 E 21 N removed and c the network with Maitri station black star 12 E 71 N removed Stations are shown as triangles with operational stations in white non operational in black and operational for part of the day in grey 49 3 12 The difference in detection efficiency for 16 June 2010 with Hawaii a and Maitri b stations completely removed from processing 50 3 13 a The raw 2011 global stroke density measured by WWLLN b The 2011 global stroke density corrected with the relative detection efficiency model of the network 51 3 14 The increase in stroke density due to the relative detection efficiency corrections for 2011 Uncorrected and corrected stroke densities shown in Figure 3 13a and 3 13b respectively The increase is plotted on the same scale as the previous two figures 52 3 15 The distribution of lightning activity from 5 years of the Optical Transient Detector Adapted from Christian et al 2003 Figure 4 53 vi 4 1 a LIS flash density at 0 5 grid spacing for fully viewed granules and b ENTLN stroke density at 0 25 grid spacing for 2011 May 2013 Densities shown in counts km2 year grid points with less than 30 counts are shown in gray 57 4 2 Classification of a viewpoint granule 0 5 0 5 bin of LIS being in full view If all four corner granules are at least partially viewed left and center the granule is in full view if not it is only partially viewed right 58 4 3 LIS observation area for 2012 April 21 from 15:20 15:31 UTC day seconds within full view of LIS shown in grayscale a shows the LIS flashes matched by ENTLN black crosses during the overpass red crosses are LIS flashes missed by ENTLN b shows the ENTLN strokes matched by LIS black crosses during the overpass red crosses are ENTLN strokes missed by LIS 59 4 4 a ENTLN-LIS timing offset tLIS tEN T LN for the first matched stroke and b ENTLN stroke to LIS flash centroid distance for the first matched stroke Bin spacing set at a 0 25 ms and b 0 5 km 60 4 5 a ENTLN-LIS daily detection efficiency b ENTLN-LIS total matches black and total LIS flashes gray c LIS daily detection efficiency of ENTLN strokes Gaps indicate days with less than 30 LIS flashes 63 4 6 a Spatial distribution of ENTLN detection efficiency of LIS flashes and b LIS detection efficiency of ENTLN strokes Gray indicates 1 1 bins with fewer than 30 LIS flashes 64 5 1 WWLLN data from 1-15 June 2012 for global strokes grouped into land black and ocean gray to demonstrate the linear regression method a Shows two energy distributions with the corresponding energy decile bins dashed lines b is the plot of mean energy Ei in each bin with the linear regression solid lines 69 5 2 Slope of the linear regression used on the energy distribution as described in the text High slope values corresponds to a more strokes in the tails of the energy distribution 70 5 3 Ratio of the WWLLN stroke count density climatology to the LIS OTD flash count density climatology normalized by their relative total counts adapted from Virts et al 2013 70 5 4 Slope of the linear regression used on the 2011 ENTLN absolute peak current distribution as described in the text High slope values corresponds to a more strokes in the tails of the energy distribution 71 5 5 The ratio of ocean to land counts for WWLLN within each energy bin The dashed horizontal line is a ratio of 1 The vertical dashed lines show the 15th and 85th percentile levels for the distribution 72 vii 5 6 Regional maps of the linear regression slopes in the left column with respective WWLLN relative detection efficiency maps on the right Selected regions outlined in a on top of the map of the May 2009 through May 2012 average relative detection efficiency b shows the Continental United States and Gulf of Mexico c Western Africa and d Northeast Brazil The white arrows point in the direction of increasing relative detection efficiency 73 6 1 Normalized electric field values for the 315 azimuth bin for the Honolulu station during the day Counts are normalized to the maximum value in each distance bin The median solid and median absolute deviation dashed values are plotted on top of the distribution Distances with less than 15 total strokes are not plotted or used 79 6 2 Station RMS electric field vs distance for Suva Tahiti and Honolulu Electric field is normalized by the square root stroke energy and given in dB above 1 V m 1 J 1 2 Day ionosphere paths are in the left column and night ionosphere paths in the right column 80 6 3 Combined station normalized electric field for the three selected stations Shown in dB above 1 V m 1 J 1 2 81 6 4 Method for calculating the attenuation In a the normalized electric field vs distance data solid line and the fitted quadratic dashed line In b the change in electric field with distance step derivative for the data solid line and the fit dashed line normalized to dB Mm 82 6 5 Dependence of attenuation with magnetic azimuth shown as P the attenuation normalized to attenuation with no magnetic field Shown for Wait and Spies 1960 black day paths green and night paths blue The best fit curves are shown as dashed lines Day and night paths are normalized by their mean 83 7 1 DBSCAN clustering example with minP ts 3 showing the same clusters located in a latitude and longitude and b latitude and time Solid rings show the distance from core points filled dashed rings are for non-core points unfilled Triangles 1 squares 2 and stars 3 show clustered points crosses are non-clustered points 91 7 2 Variation in average thunderstorm duration rows counts left column and area right column through varying one clustering parameter with the others held constant constant set: 0 12 time 18 minutes and minP ts 2 a varies from 0 03 1 b time varies from 10 180 minutes c minP ts varies from 2 30 strokes 92 viii 7 3 Thunderstorm evolution from 2013 May 21 12 23 UTC Polygons outline active lightning regions colors correspond to thunderstorm cluster opacity increases 8% hour For clarity thunderstorms with less than 50 strokes were removed 93 7 4 WWLLN thunderstorm clusters identified by color over TRMM precipitation rate mm Hr for 2013 May 06 15:49 15:59 UTC a 17:28 17:37 UTC b 2013 May 21 10:04 10:13 UTC c 11:42 11:52 d a and b are successive passes as are c and d cluster colors are contiguous between passes Gray areas were outside the range of the TRMM radar 94 7 5 Diurnal variation of WWLLN thunderstorm 30 minute counts for 2010 2013 obtained using the DBSCAN clustering algorithm For a thunderstorms over each major lightning chimney region divided between longitudes 180 30 and 60 b all land ocean and coastal thunderstorms coastal thunderstorms have strokes over land and ocean and c the full year and each season 96 7 6 Diurnal variation of WWLLN thunderstorms for each major chimney region colors divided by hemisphere Northern Hemisphere solid line Southern Hemisphere dashed line Each panel shows two months of thunderstorm clusters averaged over 2010 2013 97 7 7 Variation in WWLLN thunderstorm count black and stroke rate red for: a daily averages 30 minute counts from 2010 June 2013 June b 30 minute counts from 2011 June 01 30 c 5 minute counts from 2011 June 15 00 23 UTC 98 7 8 Diurnal UTC variation in WWLLN 30 minute thunderstorm count for: multiyear average of Figure 7 7a solid line monthly average of Figure 7 7b dotdash line and 30 minute averages of Figure 7 7c dashed line 99 7 9 A simple model of the total global electric circuit current with contributions from land thunderstorms green solid oceanic thunderstorms blue solid land electrified storm clouds green dashed and oceanic electrified storm clouds blue dashed a shows the counts for each group and b the current contribution to the total black line 100 8 1 WWLLN detection efficiency of ENTLN thunderstorms over North America for 2011 2012 top panel with each season broken out in the lower panels 107 8 2 Spatially averaged detection efficiency of ENTLN thunderstorms over North America 108 8 3 Temporal variation in thunderstorm detection efficiency for different thunderstorm sizes: a thunderstorm area b thunderstorm stroke counts and c thunderstorm duration The distribution of thunderstorms for each parameter is shown in the right panels 109 ix 8 4 8 5 8 6 8 7 8 8 Thunderstorm detection efficiency for different thunderstorm a areas b stroke counts and c durations Area and duration plots are shown with the overall average black and for different total stroke counts colors within the thunderstorms 110 Thunderstorm comparison of matched thunderstorms for WWLLN and ENTLN for a area and b duration Note: the density levels are on a log scale 112 The inter-event times for WWLLN a and ENTLN c and the interstroke black and interflash blue time distributions for WWLLN b and ENTLN d The dashed lines correspond to the best lognormal fits of the distributions There are 20 logarithmically spaced bins per decade 113 Peak of interstroke a and interflash b times for WWLLN black WWLLN over North America blue and ENTLN red Points beyond 2th and 98th percentiles shown as dots for WWLLN North America and ENTLN 114 The interflash time since the previous flash for time-normalized thunderstorms for WWLLN a and ENTLN b with times shown for all flashes black and by stroke strength decile bins WWLLN strength is divided by flash energy and ENTLN by absolute peak current of the second flash 115 B 1 Lookup table for an all day ionosphere for Dunedin station 147 C 1 C 2 C 3 C 4 C 5 C 6 WWLLN Service Unit v4d WWLLN Service Unit v4d WWLLN Service Unit v4d WWLLN Service Unit v4d Schematic for Service Unit Schematic for Service Unit design Schematic Topside Bottomside box holes mounting holes 159 160 161 162 163 164 D 1 Pinout of the Gumstix Tobi breakout board 174 D 2 alsamixer settings for Gumstix stereo input controls the stereo gain 181 x LIST OF TABLES Table Number Page 1 1 1 2 Chapter outline 14 Appendix outline 15 3 1 Ordered list of station MDE values at 25 N 20 E and 09 UTC on 15 June 2010 The fifth lowest value in bold is the network MDE at this location 40 A 1 WWLLN Data Types 139 A 2 Git Repositories flashfile: home mlhutch Git 140 B 1 Format for lookup day dat and lookup night dat data files for a resolution of 1 147 C 1 Resolution T GPS Settings 167 xi ACKNOWLEDGMENTS I would like to thank everyone in the University of Washington Earth and Space Sciences department: colleagues classmates mentors advisors and friends I want to thank my advisor Robert Holzworth and my committee: Michael McCarthy Abram Jacobson and John Wallace who have helped throughout with discussions of ideas methods and research I would like to thank Ariah Kidder for providing guidance mentorship and much needed distractions From across campus I want to thank James Pfeiffer for the discussions of math and programming Finally I want to thank my wife Leah Ganis for the constant support and encouragement for finishing in a timely manner xii DEDICATION To Leah xiii 1 Chapter 1 INTRODUCTION 2 This thesis explores the science and capabilities of ground based lightning detection networks What are the measurement limits of lightning networks How can these networks be expanded and what are the results of the expansions Can choosing the right algorithm reveal larger structures from individual lightning locations With these questions lightning thunderstorms and the Earth-Ionosphere system are explored The electrical energy of thunderstorms is investigated in factors of production how it discharges where the energy goes and how it contributes to the Earth system as a whole 1 1 Background 1 1 1 Lightning and Thunderstorms Lightning is a process of discharging disparate charged regions in a thunderstorm When electrical charge is separated in a thunderstorm it can discharge through lightning flashes in order to neutralize the separated charge As deep convection develops in a thunderstorm moist air is lifted from below the thunderstorm through the cloud where it condenses then freezes Figure 1 1 shows the basic components of an active thunderstorm The water begins to freeze as it passes through the freezing level of the thunderstorm collisions at this freezing level occur with downwelling graupel pellets These collisions cause charge exchange between the ice particles and graupel in the upper portion of the cloud the smaller ice particles gain a positive charge and the graupel becomes negatively charged while the exchange is reversed in the lower portion of the thundercloud Saunders 1995 This leads to the gross charge structure shown in Figure 1 1 with net positive charge in the top portion of the thunderstorm and net negative charge in the bottom portion There are smaller charge layers in the thunderstorm such as screening layers but the overall charge structure is that depicted in Figure 1 1 The lightning discharge begins with the stepped-leader process While a voltage on the order of 1 MV builds up between the charge centers e g the thunderstorm and ground it is still far less than the breakdown electric field of air on the order of 1 MV m However the air can breakdown in steps between 3 200 m creating a continuous ionized plasma 3 Thunderstorm Motion Tropopause 11 km Freezing Level 5km -20 C Charge Separation Region -10 C Cloud Base 2 km Figure 1 1: Overall thunderstorm charge structure showing a typical freezing level and tropopause hight channel the steps occur until an oppositely charged region is connected Ogawa 1995 An example of stepped leader breakdown is shown at the beginning of Figure 1 2 For the first 10 ms the leader streamer steps down from the cloud creating an ionized channel to ground or to another charge region Once the channel is established the return stroke discharges the charge from to ground from the cloud over the course of 70 s the return stroke labeled in Figure 1 2 After the return stroke occurs the top of the ionized channel can connect to other charge regions through subsequent positive streamer processes producing multiple return strokes along the same ionized channel The total process from step-leader through multiple return strokes is considered a single lightning flash Lightning can discharge in several configurations with the most common shown in Figure 1 3 Lightning predominately occurs either between clouds or within the same cloud: cloud-to-cloud lightning in-cloud lightning or cloud lightning Figure 1 3c and 1 3f Lightning between the thunderstorm and ground is more powerful easier to detect and less common It can occur in 4 combinations of positive or negative charge in the cloud dis- 4 10 Time ms 40 2 Figure 1 2: The step-leader and discharge process of cloud to ground lightning with typical times of each stage adapted from Ogawa 1995 charging to ground with the discharge beginning in the cloud or on the ground Figure 1 3a 1 3b 1 3d and 1 3e Negative cloud to ground lightning moving negative charge from the cloud to ground Figure 1 3a is the most common cloud-to-ground discharge at a negative : positive ratio of 10 : 1 It is estimated that there are 4 in-cloud IC strokes or flashes for every cloud-to-ground CG stroke Uman 1969 There are other sources for large electrical discharges that produce electromagnetic waves similar to thunderstorm lightning For example: terrestrial gamma ray flashes terrestrial luminous events volcanic lightning and compact intra-cloud discharges However these events are less common than typical lightning and will not be discussed in this work 1 1 2 The Ionosphere The ionosphere is the plasma environment located between 80 km and 1000 km altitude it is a highly conductive region within the exponentially decreasing atmospheric neutral density It forms from the ionization of the background neutral particles by extreme ultraviolet sunlight During the day the ionospheric extends farther down in altitude with the D- and E-regions during night the ions in these regions recombine seen in Figure 1 4 At higher altitudes the F-region remains through the night as the neutral particle density is much lower preventing significant recombination For very low frequency waves VLF 1 kHz to 24 kHz the conductive ionosphere and 5 a b c d e f Figure 1 3: Different types of lightning discharges: a negative cloud-to-ground b positive ground-to-cloud c in-cloud d positive cloud-to-ground e negative ground-to-cloud f cloud-cloud Note that a and b produce the same overall charge movement negative charge to ground and as does d and e Based on Uman 1969 ground are good reflectors and form the Earth-Ionosphere Waveguide EIWG The EIWG allows for propagation of VLF waves from natural sources e g lightning and artificial sources e g Navy VLF transmitters to propagate large distances 5000 km VLF waves above 5 kHz propagating in the waveguide undergo loss on the order of 1 dB Mm with the lost energy heating the waveguide and generating plasma waves in the ionosphere Figure 1 5 VLF wave attenuation is greatest over ice then continents with the lowest attenuation over the oceans 1 1 3 Global Electric Circuit The global electric circuit is the multiply connected current system formed by thunderstorms charging the ionosphere which leaks through the conductive atmosphere like a leaky spherical capacitor to ground as shown in Figure 1 6a with a very simple equivalent circuit shown in Figure 1 6b Thunderstorms are the primary drivers of the global electric cir- 6 Altitude km 1000 Thermosphere 100 Mesosphere Stratosphere 10 Troposphere 1 1000 Night 100 D Day F E 10 1 0 400 800 1200 1600 Temperature K 103 104 105 106 Plasma Density cm-3 Figure 1 4: Atmospheric temperature profile and ionospheric plasma density profile day ionosphere in black night ionosphere in red 1000 km 100 km Ground Figure 1 5: Schematic of the Earth-Ionosphere Waveguide cuit with the charged ionosphere discharging through fair weather atmosphere The global circuit was first proposed after observing diurnal variation in global thunderstorm activity along with fair weather electric field measurements originally observed by Wilson 1921 and Whipple 1929 Strong correlations between thunderstorm activity and fair weather return current led to the present model of the global electric circuit The global electric circuit activity changes on short time scales that are not resolved with past models or with 7 long term averaged observations Holzworth et al 1984 The global electric circuit is an important component to the solar-terrestrial system creating a link between solar activity the ionosphere aerosols cloud microphysics thunderstorms weather and climate Tinsley et al 2007 Holzworth and Volland 1986 a b Ionosphere 80km Fair Weather 250kV Equivalent Circuit 0 105 200 Thunderstorm Generators 10km 0 km 2 pA m2 0 7 F 1250 A 0 kV 0 Current Figure 1 6: a Global electric circuit model arrow correspond to currents b Very simple circuit equivalent model with representative values 1 2 Lightning Detection Systems There is a growing importance both scientifically and operationally of ground based lightning detection networks Lightning detection networks are being used in a larger gamut of research areas including: terrestrial gamma ray flashes Dwyer 2012 Gjesteland et al 2011 Connaughton et al 2010 lightning climatology Virts et al 2013 2011 B urgesser et al 2012 ionospheric disturbances and probing Jacobson et al 2010 Singh et al 2011b transient luminous events Soula et al 2011 global electric circuit Holzworth et al 2005 and whistler observation Collier et al 2010 2011 Burkholder et al 2013 This is in conjunction with the extended usage of lightning networks operationally in weather 8 prediction and tracking Fierro et al 2012 Pan et al 2010 Thomas et al 2010 volcano monitoring Doughton 2010 and hazard estimation Altaratz et al 2010 With growing usage it is necessary to understand and improve the capabilities and efficiencies of the various available lightning networks Ground based total lightning networks distinguish themselves from other ground based networks and satellites by detecting and identifying in-cloud IC discharges as well as cloud to ground CG strokes Lightning type is critical in understanding thunderstorm dynamics Williams et al 1989 with real time monitoring of sudden increases of IC activity able to predict severe weather events Rudlosky and Shea 2013 Darden et al 2010 Metzger and Nuss 2013 Schultz et al 2009 2011 The higher operational frequencies of total lightning networks are also useful for researching narrow bipolar events Suszcynsky 2003 and large scale lightning behavior Hutchins et al 2013a Lightning mapping arrays are able to locally detect locate and distinguish IC activity however total lightning networks have the advantage of much larger spatial coverage 1 2 1 World Wide Lightning Location Network The World Wide Lightning Location Network WWLLN see http: wwlln net determines the location for nearly all lightning producing storms around the globe in real time Jacobson et al 2006 WWLLN has been generating global lightning locations starting in 2004 Rodger et al 2006 2009 since then the network has grown from 18 stations to over 70 as of April 2014 Knowledge of individual stroke locations with high temporal accuracy and within a fraction of a wavelength is beneficial for both scientific and technical uses WWLLN lightning location data have recently been used for advances in space science Lay et al 2007 Kumar et al 2009 Collier et al 2009 Holzworth et al 2011 Jacobson et al 2011 meteorology Price et al 2009 Thomas et al 2010 detailed lightning physics Connaughton et al 2010 and volcanic eruption monitoring Doughton 2010 The observed global lightning stroke density for 2011 2012 is shown in Figure 1 7 The network uses a time of group arrival TOGA technique originally developed by Dowden et al 2002 to locate strokes by analyzing the sferic waveforms at each station 9 90 60 30 0 -30 -60 -90 -180 -120 -60 0 60 0 001 0 01 0 1 1 120 Lightning Stroke Density strokes km year 10 180 100 2 Figure 1 7: Global WWLLN lightning stroke density for 2011 2012 using the Stroke B algorithm as discussed by Rodger et al 2006 2009 WWLLN locates strokes by analyzing the TOGA of the sferic wave packet in the 6 18 kHz band Dowden and Brundell 2000 The TOGA of the VLF wave packet is used rather than the trigger time to produce more uniform arrival times across the network A recent upgrade to the network allows for the measurement of the radiated VLF energy of located strokes within the 8 18 kHz VLF band see Chapter 2 The stroke energy is calculated from the square root of the time-integrated squared electric field of the VLF sferic at each WWLLN station it uses the Long Wave Propagation Capability code Ferguson 1998 see Section 1 3 to estimate the sferic attenuation and calculate the radiated energy Hutchins et al 2012b As stations are added the accuracy and detection efficiency of the network improves In 2010 the network locates most strokes to within 5 km and 30% for more powerful strokes Abarca et al 2010 Rodger et al 2009 The network improves in accuracy and detection efficiency with added stations for example an increase in the number of WWLLN stations from 11 10 in 2003 to 30 in 2007 led to a 165% increase in the number of lightning strokes located Rodger et al 2009 However the WWLLN does not observe lightning with the same detection efficiency everywhere This is due to variable WWLLN station coverage and the strong effect on VLF radio propagation from surface electrical conductivity and ionospheric conditions along the great-circle path of the wave 1 2 2 Earth Networks Total Lightning Network The Earth Networks Total Lightning Network ENTLN is a ground based network that began in 2009 as the Weatherbug Total Lightning Network WTLN It has two operational regimes: short range using broadband sferic waveforms 5 kHz 12 MHz and long range with only VLF LF waveforms 1 Hz 256 kHz Heckman and Liu 2010 Correlations of the stroke waveform and amplitude from multiple stations determines the time location altitude peak current polarity and type of the located stroke Liu and Heckman 2011 The network utilizes a time of arrival method to determine the location of each stroke where a minimum of 8 stations is required to produce a valid solution To compress the broadband waveforms each station removes the necessary amount of low-amplitude signal to reach the requisite packet size In the continental United States CONUS the network has approximately 530 operational stations in September 2013 A comparison to the Oklahoma Lightning Mapping Array OKLMA in 2010 demonstrated the ability to discriminate between CG and IC strokes Beasley et al 2010 The observed stroke density over North America for 2011 2012 is shown in Figure 1 8 1 2 3 TRMM LIS The Lightning Imaging Sensor LIS 1997-present is a satellite-based lightning detector flown onboard the Tropical Rainfall Measurement Mission TRMM satellite orbiting at a 35 inclination and 402 km altitude Christian et al 1999 In low earth orbit it observes the total lightning activity from individual thunderstorms for 90 sec in each 0 5 0 5 viewtime granule LIS is useful as it is an optical lightning detection system without the spatial dependency inherent with ground based networks and the sensor performance has 11 60 45 30 15 -120 -90 -60 0 001 0 01 0 1 1 10 100 Lightning Stroke Density strokes km2 year Figure 1 8: North American ENTLN lightning stroke density for the 2011 2012 dataset Note same range as Figure 1 7 not changed over time The LIS data are available at several processed levels throughout this work the flash level data are used The LIS flash density for 2011 2012 is shown in Figure 1 9 30 0 -30 -180 0 0001 -120 -60 0 60 0 001 0 01 Lightning Flash Density flashes km2 year 120 180 0 1 Figure 1 9: LIS lightning flash density for 2011 2012 Note the reduced range from Figures 1 7 and 1 8 12 1 3 Long Wave Propagation Capability Code The Long Wave Propagation Capability code LWPC is used to model the VLF attenuation between WWLLN located lightning and the network stations The LWPC code was developed by the Space and Naval Warfare Systems Center by Ferguson 1998 and has most recently been validated by McRae and Thomson 2000 and Thomson et al 2011 In this research we made use of an adapted LWPC version 2 1 available online see Appendix A LWPC can be used to model the attenuation along a mixed day night ionospheric path however due to computational limitations a lookup table is used instead The lookup tables model the received electric field at a given station for a 100 kW transmitter in each grid cell A 1 by 1 grid is used for either an all day 0 3 km 1 and h0 74 km or an all night f 0 3 0 8 km 1 and h0 87 km ionospheric model where and h0 are the slope of the conductivity is frequency dependent at night and the reference height The ionospheric models are the default models of LWPC and fully described in Ferguson 1998 For each grid cell the electric field is averaged over the 8 18 kHz band capturing the frequencies of the peak radiated power from lightning Volland 1995 An example of the day ionosphere lookup table for the Dunedin station is shown in Figure 1 10 The discontinuity of electric field over Greenland and in the South Atlantic is caused by the high attenuation rate of VLF propagating over ice Using the lookup tables assumes that the attenuation rates do not vary greatly within a given grid cell and that the frequency response of a sferic is relatively flat within the band considered 1 4 Outline An outline of this work is provided in Table 1 1 along with the corresponding publications adapted for each chapter Chapters 2 4 cover the technical improvements and analysis of the networks used work that is necessary for Chapter 5 8 The appendices discuss the code implementation of the techniques described in a few of the chapters along with the construction design and operation of the WWLLN stations The descriptions are given in Table 1 2 Notably the code for the energy calculations Chapter 2 relative detection efficiency model Chapter 3 and thunderstorm clustering 13 90 Latitude 60 30 0 -30 -60 -90 -180 -40 -120 -60 0 60 Longitude 120 -20 0 20 40 60 E field in dB above 1 V m 180 80 Figure 1 10: LWPC generated lookup table for Dunedin station white triangle using an all day ionospheric model 0 3 km 1 and h0 74 km averaged over 8 18 kHz Each 1 by 1 bin shows the electric field seen at Dunedin if a 100kW transmitter is centered on that bin Chapter 7 are available online as described in Appendix A The same appendix contains the schematics EAGLE files parts list and software for the WWLLN Service Units 14 Table 1 1: Chapter outline Chapter 2 Describes the process for calculating the far-field radiated Hutchins et al 2012b VLF energy of lightning with WWLLN Chapter 3 Discusses the relative detection efficiency model of WWLLN Hutchins et al 2012a Chapter 4 Examines the detection efficiency between the ENTLN and Under Review LIS lightning data over North America Chapter 5 Examines the energy contrast between oceanic and continen- Hutchins et al 2013a tal lightning Chapter 6 Estimates the VLF attenuation rates over ocean under the Hutchins et al 2013b day and night ionosphere Chapter 7 Develops WWLLN thunderstorm clusters to create a prediction of the global electric circuit activity Chapter 8 The thunderstorm clustering is expanded to flash clustering and explored in the context of thunderstorm accuracy Chapter 9 Explores the future work that can be carried forward from this work Hutchins et al 2014 15 Table 1 2: Appendix outline Appendix A Describes the different types of WWLLN data files available their location and the common code used in this thesis Appendix B Describes the WWLLN stroke energy processing code and operations enabling reproduction or reprocessing of the energies Appendix C Describes the development design and construction of the WWLLN Service Unit v4 Appendix D Describes the software and operations of the WWLLN Service Unit v4 computers Appendix E Outlines the new WWLLN website structure and operation along with the realtime lightning display 16 Chapter 2 STROKE ENERGY 17 2 1 Overview The World Wide Lightning Location Network WWLLN is a long range network capable of locating lightning strokes in space and time While able to locate lightning to within a few kilometers and ten microseconds the network currently does not measure any characteristics of the strokes themselves The capabilities of the network are expanded to allow for measurements of the far-field energy from the root mean square electric field of the detected strokes in the 6 18 kHz band This is accomplished by calibrating the network from a single well calibrated station using a bootstrapping method With this technique the global median stroke energy seen by the network is 1 3 x 103 J with an average uncertainty of 17% The results are validated by comparing to return stroke peak current as measured by the New Zealand Lightning Detection Network and to previous energy measurements in the literature The global median stroke energy is found to be 2% of past estimates of the average radiated electromagnetic energy Accounting for the different observational distances we find our far-field observations of the waveguide mode are consistent with the previous literature This study demonstrates that the WWLLN determined energies can be used to estimate the return stroke peak currents of individual lightning strokes occurring throughout the globe As only the spectral variations through the sferic wave packet are needed for determining the TOGA the absolute electric field amplitude is unnecessary to accurately locate lightning Due to this the network does not currently report other characteristics of strokes such as peak field However each WWLLN station does record the root mean square RMS electric field value of the sferic waveform used in the TOGA calculation but these values need to first be calibrated The station operated by the University of Otago near New Zealand s Antarctic station Scott Base was calibrated by a field team in December 2009 The field team injected a series of calibration signals ramped progressively in frequency through the crossed magnetic loops of the Scott Base antenna and computed the calibration from the equivalent electric field This calibration of a single station allows for the calculation of stroke energy as seen by the network 18 90 60 Latitude 30 0 -30 -60 -90 -180 10-4 -120 -60 0 Longitude 60 120 10-3 10-2 10-1 1 Stroke density strokes km2 year 180 10 Figure 2 1: WWLLN 2010 global stroke density on 1 x 1 grid station locations shown with black triangles Data processed with the Stroke B algorithm A previous study by Rodger et al 2006 attempted to calibrate the network through observations of narrow-band VLF communication transmitters at each WWLLN station These observations were combined with the U S Navy Long Wave Propagation Capability LWPC code described by Ferguson 1998 to predict what the received amplitude should be in order to calibrate each station However the study assumed that the frequency response and calibration of the sound cards was the same across the network assumptions that are false In fact the sound cards preamplifier and antenna can vary in their sensitivity by a factor of 10 The current study utilizes a broader range of frequencies and calibrates each station such that differing frequency responses are accounted for in the calibration Measuring stroke energy is an important step forward as it allows the network to make real time measurements of the strength of lightning worldwide Measuring characteristics of the strokes will allow for insights into thunderstorm evolution large scale storm phenomena and global effects of lightning For example stroke energy values could help current research on terrestrial gamma ray flashes by Briggs et al 2011 constraining efficiencies and source 19 mechanisms and tropical hurricanes by Thomas et al 2010 could utilize the energy in analyzing eyewall replacement As we will show in this Chapter the network measures a median global VLF energy in the far-field waveguide mode of 1 3 103 J with an average uncertainty of 17% Previous measurements have shown the energy radiated by strokes is often near 7 0 104 J Taylor 1963 Past measurements were measured much closer to that strokes 100 km and normalize to closer distances resulting in a measurement of both the sky- and ground-wave of the sferic WWLLN measures the RMS electric field at distances where only the waveguide mode of the sferic remains When these factors are accounted for the median energy from WWLLN located strokes is comparable to the previously reported value of 7 0 104 J electromagnetic energy 2 2 Instrumentation and Data Processing In order to calculate the stroke energy from WWLLN three steps are necessary: calibrate each station in the network measure RMS electric field of a stroke at each station and calculate the stroke energy needed to produce the electric field at each station 2 2 1 Station Electric Field Each WWLLN station consists of four main components: the antenna a preamplifier a service unit for signal and power management and the sound card that digitizes the measured fields The difficulty in making an energy measurement with the network arises in calibrating for the coupling between a short 2m station antenna to a signal with an approximately 10 km wavelength When a station digitizes the electric field waveform it stores it in uncalibrated sound card units SCU Additionally the effective gain and calibration differs at each station due to the preamplifier antenna construction soundcard sensitivity and local environmental conditions This results in the RMS electric field being reported in station specific sound card units The average power spectra from 194 stroke waveforms recorded at the Tallahassee Florida station are shown in figure 2 2 along with the frequency response of a typical preamplifier The strokes used were located at distances of 5000 km to 10000 km from the station 20 and were recorded between 18:00 and 21:00 UTC on May 3 and May 9 2011 As can be seen in the figure the average power peaks between 6 18 kHz with the analog response remaining relatively flat through the entire frequency range The spikes in the power spectra Analog Response dB Average Power dB are a result of manmade VLF communication transmitters 15 10 5 0 10 5 0 -5 -10 0 5 10 15 20 25 30 Frequency kHz 35 40 45 48 Figure 2 2: The top panel shows average power spectra from 194 stroke waveforms recorded at the Tallahassee FL station between 0 and 48 kHz The strokes were located 5 Mm 10 Mm away from the station on May 3 2011 and May 9 2011 between 18:00 and 21:00 UTC The bottom panel shows the frequency response of a preamplifier The waveforms used are 1 33 ms long with 0 33 ms pre-trigger samples and 1 ms posttrigger samples Prior to processing the waveform is put through a 6 18 kHz 16 point finite impulse response FIR bandpass filter The RMS value of the resultant waveform is stored in uncalibrated sound card units After being calibrated to the 10 km wavelength signal the SCU measurement can be converted into the RMS electric field of the sferic 2 2 2 LWPC and Energy To calculate the stroke energy based on the RMS electric field at a station the LWPC code is used to model the attenuation as a function of frequency between a transmitter at the stroke location and the receiving station The LWPC code was developed by the Space and 21 Naval Warfare Systems Center by Ferguson 1998 and has most recently been validated by Thomson et al 2011 In this research we made use of LWPC version 2 1 With a known conversion from a station s SCU value to V m 1 Alocal of the lightning waveform power is calculated using equation 2 1 The ratio from LWPC between a 100 kW transmitter and the modeled field given in dB above 1 V m 1 is used to account for the sferic attenuation along the path for every grid location for every detector Since energy of the stroke is proportional to the time integrated square electric field and the power measurements are from the RMS electric field value the energy of the stroke can be found from the size of the recording window: Ustroke Pstroke trecord with the current recording window set at 1 33 ms WWLLN stroke strength values measured and recorded in terms of radiated energy Pstroke 2 Escu 100kW 2 20 Alocal 10 V m 2 Ustroke Pstroke trecord 2 Escu 100kW trecord 2 20 Alocal 10 V m 2 2 1 2 2 Due to computing limitations running the LWPC code we cannot conduct a full run for every stroke-station pair in real time Instead a lookup table is used which breaks stroke locations into 1 by 1 bins and uses either an all day 0 3 km 1 and h0 74 km or an all night f 0 3 0 8 km 1 and h0 87 km ionospheric model where and h0 are the slope of the conductivity is frequency dependent at night and the reference height in the ionospheric model The ionospheric models are the default models of LWPC code and fully described in Ferguson 1998 To account for transitions across the terminator a weighted average of the day and night electric field values are used The lookup tables give the electric field averaged over the 8 18 kHz band which captures the frequencies of the peak radiated power from lightning 6 7 kHz omitted due to code limitations Volland 1995 An example of the day ionosphere lookup table for the Dunedin station is shown in figure 2 3 the discontinuity of electric field over Greenland and in the South Atlantic is caused by the high attenuation rate of VLF propagating over ice 22 90 Latitude 60 30 0 -30 -60 -90 -180 -40 -120 -60 0 60 Longitude 120 -20 0 20 40 60 E field in dB above 1 V m 180 80 Figure 2 3: LWPC generated lookup table for Dunedin station white triangle using an all day ionospheric model 0 3 km 1 and h0 74 km averaged over 8 18 kHz Each 1 by 1 bin shows the electric field seen at Dunedin if a 100 kW transmitter is centered on that bin 2 2 3 Calibration and Bootstrapping With one calibrated station it is possible to find the calibration of other nearby stations the process is shown in figure 2 4 Using a well calibrated station on the right the stroke energy of a given stroke is found using LWPC for the same stroke The uncalibrated station also finds the energy using LWPC however instead of an energy in joules it measures the energy in sound card energy SCE The ratio between the two energy values will give the calibration factor A2local of the second station This is repeated for many strokes with the median of the conversion factors used as the conversion factor between the two stations To calibrate the entire network off of a single station a bootstrapping method is used Station to station calibrations are done using strokes that have all day paths to both stations and are within 1000 8000 km of both stations All day paths were chosen as the daytime ionosphere is modeled more accurately by LWPC than the night ionosphere McRae and Thomson 2000 The first set of calibrations are done between the well calibrated station and those with common strokes that have the desired path characteristics Once calibrated these stations 23 10 SCE 103 J LWPC LWPC m 1000 SCU k 00 0 3 12 00 0k m 0 5 mV m 10 SCE x103 103 E -3 2 ASCU 10 SCE J Figure 2 4: Method of calibrating one station to another using LWPC are used to calibrate the next set of stations and these newly calibrated stations are used to find the next set This process is repeated until no further stations can be calibrated Figure 2 5 is an example of this process Not all stations are calibrated for each day they may not be calibrated if they do not see any common strokes with another station that match the path requirements or if their calibration to the next set of stations does not match direct calibrations For example if station A calibrates B and then B calibrates C then if the calibration path ABC does not match the well calibrated path of AC it is determined that B is not well calibrated so it is not used for the day 2 2 4 Energy Calculation The fully calibrated WWLLN network is used to calculate the stroke energy for each station participating in a TOGA event using equation 2 2 with the Alocal values known for a majority of the stations Of the participating stations the median of their energy measurements is used as the final energy value for the event The uncertainty in the energy is the median absolute deviation MAD of the participating station energy measurements the MAD is the method of getting standard deviation of median values MAD median Ui median Ui On average 96 7% of WWLLN strokes have an energy value even with only an average of 2 3 of stations being well calibrated and participating in energy calculations The 3% of 24 90 60 Latitude 30 0 -30 -60 -90 -180 -120 -60 0 Longitude 60 120 180 Figure 2 5: An example of the bootstrapping technique showing calibration distance from the main Dunedin station Thick green lines are the first calibration stage and the thin red lines the last Stations may be unconnected due to not having common strokes being poor intermediary stations or being down for the day strokes without energy values either were not reported by any well calibrated stations or had an uncertainty greater than 100% and are removed The last step in calculating the energy per stroke is an iterative technique to improve accuracy The first set of energy values are used as a basis to recalibrate all of the stations in the network These new values are used to recalibrate again with this process repeating several times until the station calibrations converge to a stable and final value Currently the station calibrations along with this iterative technique are performed once a day for calculating the stroke energies of that day The bootstrap method of calibration is an internally consistent method of determining the conversion factors at each station The iterative technique allows for a convergence of calibrations to reduce the uncertainty in the energy measurements Even the original calibrated station is updated in each iteration removing errors that may be introduced by local effects since the initial ground truth calibration However the internal consistency could be improved and monitored through the introduction of a second well-calibrated station such a station would enable additional diagnostics and error correction not possible with a single starting station 25 2 3 Results 2 3 1 Validation A study was conducted comparing the stroke energy values determined by WWLLN to the ground based NZLDN estimates of return stroke peak current NZLDN described in Rodger et al 2006 The comparison was done using three periods of high lightning activity over New Zealand: 25 27 August 2009 26 27 September 2009 and 21 October 2009 WWLLN strokes were considered to match NZLDN strokes if they occurred within 0 5 ms and 400 km of a NZLDN detector the same criteria used by Rodger et al 2006 From the comparison the empirical relation between return stroke peak current and 6 18 kHz radiated energy was found to be: Ustroke 2 23 Ipeak 1 62 2 3 where Ustroke has units of joules and Ipeak has units of kA In figure 2 6 the WWLLN peak current using the inverse of equation 2 3 is shown against the NZLDN absolute peak current When taking the uncertainties of the energy values converted to peak current and an assumed 30% uncertainty in the NZLDN data 84% of the matched strokes have equivalent peak currents The peak current values fit close to the unity line with a robust linear fit of IW W LLN 0 93 IN ZLDN 1 93 with an R2 value of 0 92 a robust fit is used due to the lognormal behavior of the WWLLN energy data Of the matched strokes 86 5% are shown in figure 2 6 with the remaining 13 5% out of the plotted bounds This strong relationship confirms that the energy values measured are directly related to the physical properties of the stroke i e the return stroke peak current 2 3 2 Error and Uncertainty The model used in relating the stroke energy to the peak current uses the 2010 average stroke uncertainty of 17% from the median of the MAD distribution of all strokes in the year If a stroke has an uncertainty greater than 100% that value is thrown out doing so only decreases the number of stroke energies by 3% 26 WWLLN Peak Current kA 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 NZLDN Return Stroke Peak Current kA 0 5 10 Counts 15 20 Figure 2 6: WWLLN peak current versus NZLDN return stroke peak current for three time periods in 2009 using 5260 matches WWLLN peak current derived from Estroke 2 23 Ipeak 1 62 84% of strokes are within range of the unity line red solid line with uncertainty taken into account 86 5% of NZLDN-WWLLN matched strokes shown others out of range The largest source of uncertainty in the calculations arises from the assumptions that are made using the LWPC code and in the calibration process The lookup tables used to calculate attenuation on a given stroke are gridded into 1 by 1 bins and averaged over the 8 18 kHz frequency range This assumes that the attenuation rates do not vary greatly within a given grid and that the frequency spectra of a sferic is relatively flat within the band considered The ionospheric models used within the code assume a perfectly smooth day or night ionosphere paths crossing the terminator are weighted averages of these values These issues arise from the inherent speed limitations of the LWPC code A secondary source of uncertainty manifests as variations in the WWLLN station cali- 27 bration factors These are not caused by drift in the electronics but from variations in the local station environment and the ionosphere along the path Local weather could change the gain at a station for example through water or ice on an antenna or if there are significant changes in conductivity of the ground or ionosphere Since the LWPC code results are fixed the only free variable in the bootstrapping process are the station conversion factors so variations in the propagation path manifests within these factors These uncertainties are mitigated by performing a seven day running average of the calibration values but they are still present as daily variations in the calibrations Uncertainties that arise through the use of the LWPC model and through the station calibrations are seen through the MAD of each stroke Without these uncertainties each stations should agree on the detected stroke energy however the variations between each station due to changes in the propagation path or in the calibration appear as differences in reported stroke energy Even with these differences the overall 17% uncertainty of the WWLLN energy measurements is comparable to the 13% uncertainty in the peak current estimates of the U S National Lightning Detection Network NLDN Nag et al 2011 2 4 Discussion 2 4 1 Comparison to Literature The current method of measuring stroke energies using WWLLN results in a global median energy of 1 33 103 J for 2010 However it has been shown in past literature that the average radiated energy for a typical stroke is 6 9 104 J Taylor 1963 A 17 2 dB increase is needed to bring the WWLLN stroke energies into the range of those in the literature The main difference in the measurement method is the difference in attenuation between nearby measurements of the sferic with measurements made at a larger distance The analysis of this difference was done using the raw waveform data from three stations: the secondary Seattle station the Canaveral station and the Tallahassee station Data was taken from between 20 April 2011 and 9 May 2011 In this interval 198 events were selected that had a clear waveform at the network trigger time The biggest effect on the received stroke energy is caused by the distances involved in 28 the measurements Particularly the difference between the ground and sky wave near the stroke and the wave propagating in the waveguide Most of the VLF energy measurements in the literature have measured waveforms near 100 km distance from the stroke At larger distances only the lowest order mode is propagating in the Earth-ionosphere waveguide at near distances other modes have not been attenuated by the structure of the waveguide To measure the effect that the nearby high attenuation will have compared to a signal in the waveguide the difference in received power of the VLF transmitter near Seattle NLK 250 kW radiated power at a frequency of 24 8 kHz i e Clilverd et al 2009 was compared to the same signal seen at two stations in Florida A second transmitter in Hawaii NPM 500 kW radiated power at a frequency of 21 4 kHz was used as a reference for both stations The two Florida stations were chosen as they are far from both VLF transmitters with a sampling frequency of 96 kHz Nyquist frequency of 48 kHz well above the frequencies of the lightning peak power and the VLF radio transmitter frequencies The LWPC code estimate for the transmitter signal at the WWLLN stations is compared to the measured transmitter signal to determine the conversion factor for each event The conversions are found to be consistent with calculations and calibrations reported in this study for broadband lightning produced signals Based on the verification of the LWPC code performed by Thomson 2010 LWPC is confidently used as a ground truth for this comparison The conversion factors from the NLK and NPM signals present in the selected waveforms were used to calculate the power of the two transmitters using the same method as the WWLLN energy calculations Equation 2 2 To determine the importance of the ground wave the ratio of estimated NLK to NPM powers at Seattle were divided by the NLK to NPM ratio at the two Florida stations This ratio is necessary instead of just the Seattle NLK to actual NLK power ratio in order to normalize out any intrinsic errors in the calculation process Measuring the waveguide signal causes a loss of 17 9 dB to 23 8 dB on the signal power as seen by WWLLN compared to the corresponding nearby ground and sky wave measurements This loss is near the 17 2 dB difference between the measured WWLLN stroke energies and those made by Taylor 1963 This analysis leads to the conclusion that the energy being measured by WWLLN is 29 not the total radiated energy of the stroke rather it is the energy radiated into the Earthionosphere waveguide in the 6 18 kHz band 2 4 2 Energy Distribution Stroke energy in a given thunderstorm region or time span closely follows a lognormal distribution Golde 1977 Figure 2 7 shows the stroke energy distribution for all strokes seen by WWLLN in 2010 along with the distributions for the three major chimney regions of the Americas Africa Europe and Asia Australia The Americas and Asia Australia show similar distributions likely a result of having similar WWLLN coverage while Africa Europe differ possibly due to uneven network coverage 6 Counts x106 5 4 3 2 1 0 1 10 102 103 104 105 106 Stroke Energy J Globe Africa Europe Americas Asia Australia Figure 2 7: Histogram of stroke energies for 2010 with 100 logarithmically spaced bins the histogram for the globe 1 4 x 108 strokes is shown in black the Americas 6 1 x 107 strokes in blue Africa Europe 2 4 x 107 strokes in red and Asia Australia 5 0 x 107 strokes in green Error bars are too small to display When the energy distribution of figure 2 7 is converted to peak current using equation 2 3 it can be compared to earlier measurements of peak current distributions We can compare 30 the WWLLN peak current distribution to that of Popolansky 1972 as shown in Golde 1977 That study used peak current data from 624 return strokes to create a cumulative probability distribution of stroke currents as shown in Figure 2 8 A similar frequency distribution was created using the WWLLN peak current estimates and is shown in the same figure As can be seen the WWLLN distribution is shifted by a factor of two compared to the previous distribution which is expected as WWLLN is known to preferentially detect higher current strokes when compared to what is seen by regional ground based networks Abarca et al 2010 In a comparison to the NLDN those authors found that the probability distribution function of the WWLLN coincident strokes was similarly of an order two higher than the distribution for all NLDN strokes These comparisons further validate the stroke energy to peak current relation of equation 2 3 and demonstrates this relationship is likely valid for the entire global network and not just the New Zealand region Cumulative Probability Percent 100 Popolansky 1972 90 WWLLN 2010 80 70 60 50 40 30 20 10 0 1 10 102 Stroke Current kA 103 Figure 2 8: The cumulative probability distributions of stroke current for the best fit of the Popolansky 1972 data dashed and the 2010 WWLLN dataset solid Africa has a lower detection efficiency in the network due to the small number of stations on the continent With a lower detection efficiency only the strongest strokes are seen by the more distant stations while the weaker strokes are not seen by these stations due to the stronger attenuation of VLF over continents than for propagation paths over water Wait 31 1970 An initial effort to model the detection efficiency of WWLLN showed this effect very strongly Rodger et al 2006 Fig 11 This results in the distribution of figure 2 7 with fewer low energy strokes occurring over Africa compared to the other regions Without a full understanding of the regional detection efficiency of the network it cannot be determined whether every region follows the same lognormal energy distribution or whether local environments affect the energy of strokes in the region However the bootstrap calibration process described in the current study allows new estimates of the global variation in WWLLN detection efficiency in Chapter 3 2 5 Conclusion A new method of measuring the VLF waveguide mode energy radiated from lightning using the WWLLN has been shown and validated While not the total radiated energy of the strokes the energy measured is directly related to the peak current and therefore to inherent properties of the strokes Our study shows that WWLLN observations can provide realistic return stroke peak current measurements in addition to the timing and location of global lightning activity The method developed here can be applied to similar ground based lightning detection networks The key components in applying this method are the availability of a propagation model in the frequency range of the sensors LWPC in the case of WWLLN a measure of stroke strength e g peak electric field and at least one well-calibrated station Finally the station density needs to be high enough such that the average inter-station distance is within the applicable range of the propagation model used An enhanced WWLLN allows for a global real time view of lightning with the ability to distinguish between weak and strong strokes This will allow for future research into areas such as the long range evolution of thunderstorms over oceans wider surveys of terrestrial gamma ray flashes and with a more complete understanding of detection efficiency an analysis of global lightning energy output 32 Acknowledgments for this Chapter We are grateful to the New Zealand MetService Ltd for collecting the NZLDN data and to Antarctica New Zealand for supporting the operation of the Scott Base WWLLN station This research in this chapter was supported in part by the National Science Foundation Grant AGS-0809988 33 Chapter 3 WWLLN DETECTION EFFICIENCY 34 3 1 Overview Using the detected energy per strokes of the World Wide Lightning Location Network WWLLN we calculate the relative detection efficiency for the network as if it had a uniform detection efficiency The model uses the energy statistics of located strokes to determine which stations are sensitive to what stroke energies We are then able to estimate the number of strokes that may be missing from any given regions as compared to the best most sensitive regions of the WWLLN network Stroke density maps can be corrected with the knowledge of how sensitive various regions of the network are operating This new model for the relative WWLLN detection efficiency compensates for the uneven global coverage of the network sensors as well as variations in very low frequency VLF propagation The model gives a way to represent the global distribution of strokes as if observed by a globally uniform network The model results are analyzed in spatial and temporal regimes and the effects of a single VLF detector going offline are investigated in areas of sparse and dense detector coverage The results are also used to show spatial temporal and energy distributions as seen by the detection efficiency corrected WWLLN The WWLLN network does not observe lightning with the same detection efficiency everywhere This is due to variable WWLLN station coverage and the strong effect on VLF radio propagation from surface electrical conductivity and ionospheric conditions along the great circle path of a wave This chapter demonstrates a technique which only uses data collected by the WWLLN network itself to estimate the relative detection efficiency of each 1 x 1 pixel over the earth compared to the best average WWLLN detection efficiency For instance the lightning stroke density over central Africa where WWLLN station density is sparse can now be compared to the region of the Earth with the best detection efficiency such as North America This chapter does not provide an absolute detection efficiency calculation A concern for all VLF networks is the non-uniform propagation of VLF waves due to changing ionospheric and surface conditions this is true for networks monitoring lightning produced VLF signals like WWLLN or those monitoring fixed-frequency communication transmitters like AARDDVARK Clilverd et al 2009 During the day there is a larger 35 ionospheric electron density at lower D-region altitudes this lowers the effective reflection height of the sferics increasing the attenuation rate of the sferics This increase in electron number density is also seen in the change of the reference ionospheric height h0 Wait and Spies 1960 during the day h0 74 km compared to during the night h0 87 km There is a similar change in attenuation over the path of the sferic from the differences in the conductivity of the oceans 4 S m continents 10 2 10 4 S m and Antarctic Arctic ice 10 5 S m The many path parameters for a given sferic result in a highly variable attenuation Volland 1995 Thus independently determining the real-time detection efficiency has always been a challenging topic Several studies have been conducted comparing WWLLN to other ground based networks or satellite measurements Lay et al 2004 Jacobson et al 2006 Rodger et al 2009 Abarca et al 2010 Abreu et al 2010 These studies tend to be limited in either scope or in time due to the availability of data from other lightning detection networks Past work by Rodger et al 2006 attempted to determine the global detection efficiency of WWLLN using a theoretical model linked to observations from a ground based commercial lightning network in New Zealand In this chapter a new method is developed for determining the relative detection efficiency of WWLLN based upon the recent network expansion of measuring the radiated energy of detected strokes Chapter 2 Hutchins et al 2012b Developing a model of detection efficiency expands the capabilities and uses for WWLLN In particular a model that does not rely on external comparisons to other networks or sensors is critical for obtaining a dynamic global view of network performance Such a view will enable the network to be used with more confidence in areas of lower coverage and enable the network to be utilized with uniform detection efficiency in work requiring lightning rates and densities This uniform performance will allow for more accurate studies of global phenomena such as the short time 500 strokes hour The four major competing effects on the detection efficiency are the day night terminator local stroke activity station density and station performance The day night terminator effect can be seen as it moves from 00 UTC Figure 3 5a through 18 UTC Figure 3 5d An increase in local stroke activity in North American afternoon Figure 3 5a causes a decrease in detection efficiency as nearby stations raise their triggering thresholds Station density is coupled with station performance since when a station is not operating optimally it has a similar effect as removing that station the effect of station performance is discussed in Section 3 4 3 Figure 3 6 shows the daily relative detection efficiency from the average of the hourly maps here grey stations were only operational part of the day This average map is more representative of the relative detection efficiency for the day and it shows behavior that is expected based on the distribution of stations: lower detection efficiency over most of Africa with higher detection efficiency over and around the Pacific and North America The low detection efficiency over Antarctica parts of Siberia and Greenland are due to the high attenuation of VLF propagating subionospherically over ice Conversely the high detection efficiency over North America Western Europe and Oceania are due to the high station density and low attenuation of VLF over ocean In order to prevent unphysical overcorrections a minimum relative detection efficiency of 5% has been set for all of the relative detection efficiency maps 3 4 3 4 1 Analysis Distribution Changes As shown in the previous sections the relative detection efficiency values in a given day are derived from the WWLLN observed stroke energy distribution from the previous seven days this allows for direct comparisons within a day and for nearby days but it does not take into account the changing distribution from changes in the network As more stations are added to the network additional low-energy strokes will be detected and the overall 44 00 UTC Latitude 90 60 60 30 30 0 0 -30 -30 -60 -60 -90 -180 -120 -60 60 120 180 12 UTC 90 Latitude 0 -90 -180 60 30 30 0 0 -30 -30 -60 -60 -120 -60 0 60 Longitude 0 -120 -60 10 120 180 -90 -180 0 60 120 180 0 60 Longitude 120 180 18 UTC 90 60 -90 -180 06 UTC 90 -120 20 30 40 50 60 70 80 Relative Detection Efficiency % -60 90 100 Figure 3 5: Relative detection efficiency maps for 00 06 12 and 18 UTC on 15 June 2010 Stations are shown as triangles with operational stations in white and non-operational in black The minimum value of detection efficiency is set at 5% to prevent unphysical corrections energy distribution will shift towards lower values When the overall network distribution changes between years then for a given region the relative detection efficiency can change even if that region of the network has detected the same distribution of strokes One way to examine the change in the distribution of energy is to examine the temporal variability of the median of the global WWLLN energy distribution The median of the seven day distribution is shown in Figure 3 7 The median energy varies from the three year median by 52% with the daily median value ranging from 400 J to 2000 J The variability is caused by ionospheric changes not accounted for in the ionospheric model used Several jumps in the median energy e g Dec 2009 and Dec 2010 are caused by changes in the 45 90 Latitude 60 30 0 -30 -60 -90 -180 0 -120 10 -60 0 60 Longitude 120 20 30 40 50 60 70 80 Relative Detection Efficiency % 180 90 100 Figure 3 6: Daily average relative detection efficiency for 15 June 2010 Stations are shown as triangles with operational stations in white non operational in black and operational for part of the day in grey The minimum value of detection efficiency is set at 5% to prevent unphysical corrections primary calibrated WWLLN station e g gain changes The slow increase to Aug 2011 was due to a change of the primary calibrated station from the Dunedin New Zealand station to the Scott Base Antarctica station It is important to note that since the detection efficiency is relative to the past seven days the relatively slow changes in median energy do not strongly affect the detection efficiency and highlight how the relative detection efficiency cannot correct for absolute overall network performance 3 4 2 Temporal Variability The evolution of the network can be seen as an increase in the global average relative detection efficiency calculated by averaging all grid cells of each hourly map for a day While no region can have a relative detection efficiency over 100% as regions improve with more stations they will approach 100% and increase the global average detection efficiency The global average relative detection efficiency from April 2009 through October 2011 is shown as the green line in Figure 3 8 In the Figure the total number of operational stations 46 Median Energy J 104 103 102 Apr Aug Dec Apr Aug Dec Apr Aug Dec 2009 2010 2011 Figure 3 7: Median stroke energy of the 7-day distribution observed by WWLLN The relative detection efficiency of the network is based on this 7-day energy distribution Systematic changes in median stroke energy result from unaccounted for gain changes at the primary calibrated WWLLN station see Chapter 2 Tick marks correspond to the start of the listed month is shown as the black line and it has a strong correlation to the global averaged detection efficiency with a correlation value of 0 86 With more stations strategically added to the network the 7-day energy distribution will also change to include more low energy strokes Relative detection efficiency and increase the average relative detection efficiency 1 50 0 8 40 0 6 Operational Stations 60 30 Apr Aug Dec Apr Aug Dec Apr Aug Dec 2009 2010 2011 0 4 Figure 3 8: The number of WWLLN stations operating black and the global average relative detection efficiency gray for April 2009 through October 2011 Tick marks correspond to the start of the listed month While Figure 3 8 shows an overall increase in the number of network stations and hence 47 detection efficiency Figure 3 9 shows similar curves for just low-latitude regions 30 N to 30 N blue a single location near Florida at 85 E 30 N red and a single location near South Africa at 25 E 20 N green Removing high latitude regions which have small contributions to lightning increases the overall detection efficiency but does not change the overall upward trend shown by the blue curve in Figure 3 9 When the region near Florida is examined it can be seen that it remains fairly close to 1 0 for the entire dataset with downward trends during local summer months due to increased local lightning activity The region near South Africa has a steady increase in detection efficiency except during a large drop out which occurred in the middle of 2011 caused by one of the African stations going offline This shows the global detection efficiency tracks the network as a whole but it Relative Detection Efficiency cannot be used as an accurate proxy for smaller spatial scales 1 0 8 0 6 0 4 0 2 0 Apr Aug Dec Apr Aug Dec Apr Aug Dec 2009 2010 Globe Low-latitude 2011 Florida S Africa Figure 3 9: Daily variation of average detection efficiency for the globe black low-latitudes 30 N to 30 N blue over Florida at 85 E 30 N red and over South Africa at 25 E 20 N green Tick marks correspond to the start of the listed month The local time variability over the region near Florida is shown in black in Figure 3 10 and shows a total variability of about 4 9% The largest drop in the relative detection efficiency occurs in the afternoon near the peak in local lightning activity at 3pm This drop is due to the nearby stations raising their detection threshold in response to detecting more local strokes For this location the effects of local activity dominates over the expected 48 S Africa Relative Detection Efficiency Florida Relative Detection Efficiency day night effect due to changes in VLF propagation 1 0 7 0 98 0 6 0 96 0 5 0 94 0 4 0 92 0 3 0 3 6 9 12 15 18 21 Local Time Florida S Africa Figure 3 10: Average solar-local time variation of detection efficiency over Florida 85 E 30 N solid and South Africa 25 E 20 N dashed from 2009-2011 The variability for the region near South Africa is shown as the dotted line in Figure 3 10 there is a total variability of 25 5% There is an overall decrease in relative detection efficiency during the day when the sferics are propagating over the continent The best relative detection efficiency occurs in the middle of the night when the stations in Africa have less nearby activity and sferics are able to propagate more readily under a night ionosphere Compared to the Florida region there is a much higher dependence on day and night conditions as well as a much wider range of variability 3 4 3 Station Outage Effects While the overall performance of the network trends along with the total number of stations a single station turning on or off can affect a large region with only a small effect on the network as a whole To test the influence of single stations a day of data was randomly selected 16 June 2010 and the entire data were reprocessed with just the Honolulu Hawaii station 158 E 21 N removed from the raw data and again with just the Maitri Antarctica station 12 E 71 N removed The maps of the daily average with and without these 49 stations are shown in Figure 3 11 For Hawaii the change is fairly local to its region in the Pacific Ocean but leads to little effect across the entire network In the case of Maitri there is a larger effect as it is located in a region of sparse detector coverage and covers much of the southern Atlantic a 90 Latitude 60 30 0 -30 -60 -90 b -180 90 -120 -60 0 60 120 180 -120 -60 0 60 120 180 -120 -60 0 60 Longitude 120 180 Latitude 60 30 0 -30 -60 c -90 -180 90 Latitude 60 30 0 -30 -60 -90 -180 0 10 20 30 40 50 60 70 80 Relative Detection Efficiency % 90 100 Figure 3 11: Relative detection efficiency map of 16 June 2010 for a the complete network b the network with the Hawaii station black star 158 E 21 N removed and c the network with Maitri station black star 12 E 71 N removed Stations are shown as triangles with operational stations in white non operational in black and operational for part of the day in grey 50 The daily average global relative detection efficiency dropped from 64% to 63% without Hawaii and from 64% to 53% without Maitri The detection efficiency in the grid cell over Hawaii dropped from 85% to 78% and from 45% to 7 4% in the grid cell over Maitri A plot of the total change between the daily averages in Figure 3 11 is shown in Figure 3 12 Latitude a b 90 90 60 60 30 30 0 0 -30 -30 -60 -60 -90 -180 -120 -60 0 60 Longitude -20 120 180 -90 -180 -120 -60 -15 -10 -5 Relative Detection Efficiency Change % 0 60 Longitude 120 180 0 Figure 3 12: The difference in detection efficiency for 16 June 2010 with Hawaii a and Maitri b stations completely removed from processing 3 5 Results The detection efficiency model can be applied to global maps of stroke density to estimate or correct for the global stroke density which would be seen if WWLLN had a uniform spatial and temporal coverage This does not correct for the overall absolute detection efficiency 11% for CG flashes in the United States see Abarca et al 2010 rather it corrects for the areas with less WWLLN coverage The hourly stroke density plots are corrected by dividing the counts in each grid cell by the relative detection efficiency of that cell For example a grid cell with 100 strokes and an efficiency of 80% would be corrected to 125 strokes The stroke density from 2011 Figure 3 13a had the model corrections applied hourly with the condition that a 1 x 1 grid cell needed at least two strokes to have a correction applied A second condition was that a minimum relative detection efficiency of 5% was set for the model 51 Latitude a b 90 90 60 60 30 30 0 0 -30 -30 -60 -60 -90 -180 -120 -60 0 60 Longitude 10-4 120 180 -90 -180 -120 10-3 10-2 10-1 1 Stroke density strokes km2 year -60 0 60 Longitude 120 180 10 Figure 3 13: a The raw 2011 global stroke density measured by WWLLN b The 2011 global stroke density corrected with the relative detection efficiency model of the network The total number of strokes for 2010 was 1 4 108 4 4 strokes second and after applying the model the total was 2 0 108 strokes 6 3 strokes second In 2011 the total number of strokes was 1 5 108 4 8 strokes second with a model-corrected value of 1 9 108 6 0 strokes second In 2010 63% of the global area between 60 latitude had a relative detection efficiency of at least 80% and in 2011 this area increased from 66% to 72% If we assume that the global lightning flash rate was a constant 46 flashes second as determined by satellite measurements using the Optical Transient Detector and Lightning Imaging Sensor Cecil et al 2011 Christian et al 2003 for both years this would imply a corrected global absolute detection efficiency for cloud to ground and in-cloud flashes of 13 7% for 2010 and 13 0% in 2011 The slight decline in overall detection efficiency in 2011 compared to 2010 is likely caused by the temporay decrease in the number of operational WWLLN stations during 2011 seen in Figure 3 8 The corrected yearly density is shown in Figure 3 13b aside from the overall increase in number counts the important feature is the relative count rates over the US Africa and Southeast Asia In the uncorrected Figure 3 13a the peak stroke density in Asia and America are similar while Africa is about 1-10% of these values also shown in Figure 3 1a In the corrected maps we can see that the peak density in Africa is much closer in magnitude to 52 that seen for America and Asia and the relative densities match the distributions seen by OTD see Figure 3 15 from Christian et al 2003 Figure 4 The total increase in stroke counts is shown in Figure 3 14 with the greatest increases occurring over land in particular central Africa 90 Latitude 60 30 0 -30 -60 -90 -180 -120 10-4 -60 0 60 Longitude 120 10-3 10-2 10-1 1 Stroke density strokes km2 year 180 10 Figure 3 14: The increase in stroke density due to the relative detection efficiency corrections for 2011 Uncorrected and corrected stroke densities shown in Figure 3 13a and 3 13b respectively The increase is plotted on the same scale as the previous two figures 3 6 Conclusion A relative detection efficiency model is developed for WWLLN based on the WWLLN observed stroke energy distribution The model is examined on various temporal scales as well as performance changes due to station outage effects The model is applied to the 2011 WWLLN dataset to produce a corrected map of stroke activity matching the satellite optical flash incidence distribution Work on comparing distant regions is now possible as the network data can be corrected to a uniform global level of performance The model developed can be used for other lightning detection networks given similar operations Another network would need some way to determine the detection threshold at each stations an available propagation model and a measure of the stroke or flash 53 CHRISTIAN ET AL : GLOBAL FREQUENCY AND DISTRIBUTION OF LIGHTNING ACL 4-5 Figure 4 The annualized distribution of total lightning activity in units of fl km 2 yr 1 Figure 3 15: The distribution of lightning activity from 5 years of the Optical Transient Goodman et al 1988 Thomas et al 2000 and unreported contain a strong diurnal bias if the data are not smoothed analysis of data presented Boccippio et et al al 2001b A over 55 day intervals Detector Adapted frombyChristian 2003 Figure 4 A period of 55 days is required for the minimum cutoff value of 140 arbitrary units was estab- OTD instrument to observe most locations on the Earth at lished for this metric as the most tolerant filter level that least once in each local hour of the diurnal cycle due to the removes clearly SAA-related radiation noise this value is precession of the satellite s orbit around the Earth s polar the same used in the validation and science studies of axis Since lightning activity is more frequent during the late Boccippio et al 2000a 2000b 2001a afternoon hours the slow but constant orbital precession of 18 Orbital precession of the OTD instrument relative to the satellite relative to the Sun significantly biases flash strength WWLLN uses the determining triggering threshold each asof reported in the the Sun was accounted for when the flash rate rates at derived fromstation brief subsets OTD data Annual cyclesTOGA for the globe Flash rates computed from OTD data will presented in this paper are constructed by summing all packets the LWPC model and the energy of each stroke Figure 5 Mask used for land gray ocean white and zonal and meridional band definitions as used in this analysis Figures 7 8 and 9 Elevation contoured every 500 m 54 Chapter 4 ENTLN-LIS DETECTION EFFICIENCY 55 4 1 Overview Performance of the Earth Networks Total Lightning Network ENTLN is evaluated with respect to the TRMM Lightning Imaging Sensor LIS ENTLN lightning strokes are matched to LIS lightning flashes from 2011 2013 over the continental United States and within the 35 orbital inclination of LIS ENTLN matched 1 4 105 of the 2 1 105 LIS flashes with a total of 4 8 105 strokes giving an average multiplicity of 3 5 and 66% detection efficiency of all flashes over the course of the evaluation period the average daily detection efficiency was 69 14% The median timing offset from the first ENTLN stroke was 2 4 ms LIS leading with a sharp peak at -1 9 ms the median distance offset was 7 0 km from the flash centroid The sharp peak at -1 9 ms is likely caused by inherent differences in the detection techniques: LIS observes light emitted from the tops of the clouds and ENTLN measures the radio signals from the return stroke The performance of LIS relative to ENTLN is also evaluated by finding all ENTLN strokes located within the LIS field of view LIS matched 68% of the 7 1 105 ENTLN strokes in the LIS field of view The 70 12% daily average LIS detection efficiency of ENTLN strokes demonstrates that neither system detects every flash or stroke located by the other Assuming a 3 5 multiplicity of ENTLN unmatched strokes LIS did not detect 6 6 104 flashes or 31% of all flashes The ENTLN-LIS matched strokes were 20 3 0 6% cloud to ground and unmatched strokes were 21 8 0 8% cloud to ground There is a marginal difference in the lightning populations sampled by both systems LIS is slightly biased towards cloud flashes There is a growing importance both scientifically and operationally of ground based lightning detection networks Lightning detection networks are being used in a larger gamut of research areas including: terrestrial gamma ray flashes Dwyer 2012 Gjesteland et al 2011 Connaughton et al 2010 lightning climatology Virts et al 2013 2011 B urgesser et al 2012 ionospheric disturbances and probing Jacobson et al 2010 Singh et al 2011b transient luminous events Soula et al 2011 global electric circuit Holzworth et al 2005 and whistler observation Collier et al 2010 2011 Burkholder et al 2013 This is in conjunction with the extended usage of lightning networks operationally in weather 56 prediction and tracking Fierro et al 2012 Pan et al 2010 Thomas et al 2010 volcano monitoring Doughton 2010 and hazard estimation Altaratz et al 2010 With growing usage it is necessary to understand the capabilities and efficiencies of the various available lightning networks Ground based total lightning networks distinguish themselves from other ground based networks and satellites by detecting and identifying in-cloud IC discharges as well as cloud to ground CG strokes Lightning type is critical in understanding thunderstorm dynamics Williams et al 1989 with real time monitoring of sudden increases of IC activity able to predict severe weather events Rudlosky and Shea 2013 Darden et al 2010 Metzger and Nuss 2013 Schultz et al 2009 2011 The higher frequencies of total lightning networks are also useful for researching narrow bipolar events Suszcynsky 2003 and large scale lightning behavior Hutchins et al 2013a Lightning mapping arrays are able to locally detect locate and distinguish IC activity however total lightning networks have the advantage of much larger spatial coverage To evaluate the ENTLN performance it is compared against the Lightning Imaging Sensor LIS onboard the Tropical Rainfall Measurement Mission TRMM satellite orbiting at a 35 inclination Christian et al 1999 LIS is used as a reference system as the sensor performance has not changed over time and it uses a different detection method optical than ground networks The LIS data are available at several processed levels the 2011 2013 flash level data are used for this comparison The comparison with LIS is made over North America and within the inclination of LIS the area covered is shown in Figure 4 1 In this region LIS located 2 1 105 flashes with the distribution shown in Figure 4 1a and ENTLN located 3 1 108 strokes shown in Figure 4 1b ENTLN detected 1 4 105 strokes within the field of view of LIS Utilizing lightning networks requires a thorough understanding of what the networks detect and their limitations Examining detection efficiencies is one method to characterize the performance of networks however such measures need to be used carefully as they often necessitate the assumption that the reference system is uniform constant and complete Using the LIS instrument allows for a robust and standard analysis of the ENTLN efficiency and accuracy 57 a 35 30 25 -120 0 0001 b -110 -100 -90 -80 0 001 0 01 LIS flash density flashes km2 year 0 1 35 30 25 0 01 -120 -110 -100 -90 -80 0 1 1 10 100 1000 ENTLN stroke density strokes km2 year Figure 4 1: a LIS flash density at 0 5 grid spacing for fully viewed granules and b ENTLN stroke density at 0 25 grid spacing for 2011 May 2013 Densities shown in counts km2 year grid points with less than 30 counts are shown in gray 4 2 Performance 4 2 1 Matching ENTLN strokes are matched to LIS flashes when the ENTLN stroke is within a 0 5 box around the flash centroid and within 10 ms of the flash duration If multiple strokes are matched to a single LIS flash the timing and location of the stroke closest in time to the start of the flash is used as the best match for the case of multiple flashes matched to a single stroke only the flash closest in time to the stroke is matched Matches between ENTLN-LIS had 30% of LIS flashes matched to a single ENTLN stroke with an overall mean multiplicity of 3 5 Days with less than 30 total LIS flashes over North America are not used in this evaluation Evaluation of the effectiveness of LIS at observing ENTLN strokes utilizes the viewpoint granule data available with the flash level data The viewpoint granules give the start and end times of LIS observation for 0 5 0 5 bins Full coverage for a given viewpoint 58 granule is determined by the start and end times of the adjacent corner granules as shown in Figure 4 2 When LIS has at least partial coverage of the four corner viewpoint granules the center viewpoint granule is guaranteed to be in full view of the sensor The latest start time and earliest end time of the adjacent corner granules determines the time when the viewpoint granule is in full view of LIS Only ENTLN strokes and LIS flashes within viewpoint granules with full LIS coverage are used in this evaluation This restriction reduces the total number of LIS flashes by 30% from 3 0 105 to 2 1 105 flashes this ensures that all ENTLN strokes are within full view of LIS removing edge and partial view cases Full View Partial View Out of View Figure 4 2: Classification of a viewpoint granule 0 5 0 5 bin of LIS being in full view If all four corner granules are at least partially viewed left and center the granule is in full view if not it is only partially viewed right An example of a single LIS overpass full coverage field of view determined by the viewpoint granules is shown in Figure 4 3 This overpass occurred on 2012 April 21 from 15:20 15:31 UTC Within the field of view LIS observed 220 flashes of which ENTLN matched 66% shown in Figure 4 3a ENTLN strokes are considered within the field of view of LIS if they occur within the bounds of the viewpoint granule and between the start and end time of full LIS coverage In the pass shown in Figure 4 3b ENTLN detected 773 strokes where 67% were matched to LIS flashes In both cases the missed events are shown 59 a 35 30 b 25 35 30 25 -100 0 15 -90 Matched -80 Missed 30 45 60 75 Full Granule Viewtime s 90 Figure 4 3: LIS observation area for 2012 April 21 from 15:20 15:31 UTC day seconds within full view of LIS shown in grayscale a shows the LIS flashes matched by ENTLN black crosses during the overpass red crosses are LIS flashes missed by ENTLN b shows the ENTLN strokes matched by LIS black crosses during the overpass red crosses are ENTLN strokes missed by LIS as red crosses 4 2 2 Accuracy System accuracy is measured by the timing and spatial offset between the lightning locations The timing offset tLIS tEN T LN Figure 4 4a is sharply peaked at -1 9 ms with ENTLN occurring before the LIS flash time the median timing offset is 2 4 ms The LIS flash time is the time of the first LIS event in the flash group 42% of ENTLN strokes occurred 0 4 ms before the start of the LIS flash the remaining strokes correspond to subsequent discharges of the flash The median distance offset from the flash centroid is 7 0 km as seen Figure 4 4b slightly above the LIS spatial resolution of 3 6 km Christian et al 1999 The location offset 60 b 12 8 4 0 -4 -2 0 2 4 Timing Offset ms 12 Counts x1000 Counts x1000 a 8 4 0 0 5 10 15 20 Distance Offset km Figure 4 4: a ENTLN-LIS timing offset tLIS tEN T LN for the first matched stroke and b ENTLN stroke to LIS flash centroid distance for the first matched stroke Bin spacing set at a 0 25 ms and b 0 5 km can be given in either kilometers from the flash centroid or in units of the estimated flash radius the radius is calculated by considering the given LIS flash area as a circle Using the flash radius for distance results in a median offset of 0 80 flash radii 65% of the strokes are located within the visible extent of the flash A more refined location accuracy of ENTLN cannot be determined with LIS due to the spatial accuracy of the LIS pixels 4 2 3 Detection efficiency During the 2011 2013 evaluation period the average daily detection efficiency of LIS flashes by ENTLN was 69% 14% The detection efficiency was marginally higher during the day at 72 14% and lower during the night at 65 16% The ENTLN decrease at night likely stems from the increased detection efficiency of LIS at observing lightning against a non-sunlit ground The spatial distribution of detection efficiency is shown in Figure 4 6a with the daily variability shown in Figure 4 5a The spatially averaged detection efficiency is 61 16% due to the uneven distribution of ENTLN stations with fewer stations in the West ENTLN detected 66% of the 2 1 105 LIS flashes within those flashes ENTLN detected 7 4 105 strokes 0 15% of total ENTLN strokes ENTLN has a spike of low detection efficiency in mid-June 2012 that is reflected in the LIS detection efficiency this temporary decrease is likely due to a short-term issue with the network Within the LIS field of view ENTLN detected 7 1 105 strokes of these strokes 4 8 105 were matched to LIS flashes for an overall LIS detection efficiency of ENTLN strokes of 68% 61 The spatial distribution of LIS detection efficiency of ENTLN strokes is shown in Figure 4 6b and the daily detection efficiency is shown in Figure 4 5c The average spatial detection efficiency of LIS is 67 13% with an average daily detection efficiency of 70 12% Assuming the same multiplicity of 3 5 for the unmatched ENTLN strokes LIS missed 6 6 104 or 31% of all flashes To test for the possibility that the strokes not detected by LIS were improperly located the waveforms for a random subset for ENTLN strokes were examined and the locations were found to be correct Over land the highest ENTLN detection efficiency can be seen to occur in the Great Plains Florida and Texas There is decreased detection efficiency over both the Rocky and Appalachian Mountains possibly caused by the lower sensor density in these regions While the mountain regions show lower detection efficiency with lower sensor density there is a higher and more uniform detection efficiency within 450 km off the coasts The increased detection efficiency off of the coasts is a combined effect of fewer and stronger lightning strokes Hutchins et al 2013a Rudlosky and Fuelberg 2010 LIS has a more uniform detection efficiency than ENTLN as is expected from the imaging system On a daily scale the ENTLN-LIS detection efficiency seen in Figure 4 5a is fairly high through this time period with brief periods of decreased performance The average daily detection efficiency is 69 15% with a 5th to 95th percentile range of 48% 87% Some of the larger decreases in detection efficiency match with the increased LIS flash counts in Figure 4 5b such as early April 2012 late May 2012 and mid-July 2012 On days with low LIS flash counts 40th percentile ENTLN detects 71 16% of flashes while on days with high LIS flash counts 70th percentile ENTLN detects 65 10% of flashes During these times of increased lightning activity the ENTLN would need to raise the data compression threshold causing it to miss weaker strokes that are still detected by LIS resulting in the suppressed detection efficiency 4 2 4 Observation bias Two populations of ENTLN strokes are found with the comparison to LIS: the strokes matched to LIS flashes and the strokes that are unmatched Characteristics of these popu- 62 lations should show any bias of the flashes that are observed by LIS As ENTLN is a total lightning network it has the capability to detect and distinguish between CG and IC strokes To get a statistically robust measure of the percentage of cloud to ground strokes observed by LIS the matched LIS-ENTLN stroke data was randomly subdivided into 100 subsets of approximately 4 8 103 matched strokes Averaging these subsamples results in a statistically robust measure of the matched stroke CG percentage The populations of matched and unmatched LIS-ENTLN strokes are very similar matched strokes are 20 3 0 6% CG and unmatched strokes are 21 8 0 8% CG The small difference between the populations shows that there is only marginal detection efficiency bias between lightning observed by LIS and ENTLN with LIS slightly biased towards cloud flashes 4 3 Conclusion Characterizing the ENTLN and other ground based networks relative to a uniform detection system is critical in enabling the application of these networks in scientific and operational uses The Earth Networks Total Lightning Network was compared to the TRMM LIS instrument on a stroke to flash matching level An average daily detection efficiency of 69 14% was found for the continental United States for January 2012 May 2013 for 2 1 105 LIS flashes The relative location accuracy with respect to the flash centroid is 7 0 km and a timing offset to the start of the flash of 2 3 ms Within the LIS field of view ENTLN located 7 1 105 strokes and 3 1 108 strokes within the entire evaluation region Of those located ENTLN strokes LIS had a 70 12% detection efficiency leading to an estimated 6 6 104 flashes 31% of total flashes not detected by LIS Long range ground networks have the advantage of continuous real-time coverage of their encompassed region resulting in more strokes detected along with capabilities such as stroke type discrimination and peak current estimation Acknowledgments for this Chapter The LIS flash data were obtained from NASA s Global Hydrology Resource Center http: thunder msfc nasa gov 63 100 Detection Efficiency % a 80 60 40 20 0 Counts x1000 b 3 6 9 12 3 2011 6 9 12 3 2012 6 9 12 2013 3 6 9 12 3 2011 6 9 12 3 2012 6 9 12 2013 6 9 12 3 2011 6 9 12 3 2012 6 9 12 2013 3 2 1 0 -1 -2 -3 ENTLN LIS LIS Detection Efficiency % c 100 80 60 40 20 0 3 Figure 4 5: a ENTLN-LIS daily detection efficiency b ENTLN-LIS total matches black and total LIS flashes gray c LIS daily detection efficiency of ENTLN strokes Gaps indicate days with less than 30 LIS flashes 64 a 35 30 b 25 35 30 25 -120 0 -110 20 -100 -90 -80 40 60 80 Detection Efficiency % 100 Figure 4 6: a Spatial distribution of ENTLN detection efficiency of LIS flashes and b LIS detection efficiency of ENTLN strokes Gray indicates 1 1 bins with fewer than 30 LIS flashes 65 Chapter 5 LAND-SEA CONTRAST 66 5 1 Overview A global contrast between oceanic and continental lightning very low frequency energy is observed using the World Wide Lightning Location Network WWLLN Strokes over the ocean are found to be stronger on average than those over land with a sharp boundary along a majority of coastlines A linear regression method is developed to account for the spatial and temporal variation of WWLLN in order to perform a multi-year and global analysis of stroke energy distributions The results are corroborated with data from the Lightning Imaging Sensor the Optical Transient Detector and the Earth Networks Total Lightning Network These systematic comparisons lead to the conclusion that there exists a strong difference in the energetics between land and ocean thunderstorms that results in a higher fraction of more powerful strokes over the oceans Global surveys of lightning climatology have routinely shown more lightning activity over continents than over oceans Christian et al 2003 The difference in activity is often attributed to changes in the convective regimes in the clouds Williams and Stanfill 2002 and Williams et al 2005 discuss aerosol concentration wet bulb temperature and cloud base height as dominant mechanisms of the difference in cloud electrification Zipser 1994 suggests updraft velocity due to differential surface heating may lead to the difference in observed flash rates Boccippio et al 2000 shows the total flash counts may be due to a lesser frequency of occurrence of oceanic storms and not a difference in the storms themselves Along with the difference in flash rates there have been several observations suggesting an inherent difference in the lightning peak currents and optical radiance between land and ocean storms Seity et al 2001 Ishii et al 2010 The U S National Lightning Detection Network NLDN observed higher average peak currents for negative cloud to ground CG strokes off of the coast but the NLDN is limited in range for oceanic strokes near to coastlines Rudlosky and Fuelberg 2010 Lyons et al 1998 Boccippio et al 2000 observed with LIS OTD an increase in the optical radiance and extent of oceanic flashes compared to those over land It was suggested that either a more energetic lightning generation process 67 or a reduced cloud optical depth for the oceanic storms could produce the increased optical radiance However using just the available satellite data it could not be be determined whether the more radiant flashes were caused by changes in the flashes or in the cloud optical depth A comparison is made between the global stroke count climatologies of WWLLN and the 13-year Lightning Imaging Sensor LIS and 5-year Optical Transient Detector OTD flash count climatologies The LIS 1997-present and OTD 1995-2000 are nearly identical satellite-based lightning detectors flown in low earth orbit that observe total lightning activity from individual thunderstorms for 90 sec and 2 min respectively as the satellite passes overhead The LIS observes storms from an inclined orbit of 35 at an altitude of 402 km while the OTD observed storms from an inclined orbit of 70 at an altitude of 740 km Christian et al 1999 2003 Since WWLLN preferentially detects high-energy strokes Hutchins et al 2012a a direct comparison between the two systems as described in Virts et al 2013 gives a comparison between high and low-energy strokes because of the detection biases of the two systems 5 2 Linear Regression Analysis In order to compare WWLLN energy data over large spatial and temporal scales the data needs to be processed to account for the regional variations in detection efficiency and temporal changes in network performance To examine the spatial changes in stroke energy while accounting for network variability a linear regression method is developed Energy data for each day is binned every 0 5 in latitude and longitude The strokes in each bin are split into 10 energy deciles each containing J strokes with the mean energy of each decile i given by: PJ Ei j 1 Ei j J 5 1 Ei has a power law dependence on decile number due to the lognormal distribution of stroke energies In order to make a regression between Ei and decile number i the log10 of Ei is used This allows for a simple linear regression between the two variables instead of a 68 power regression in linear space this prevents overweighting of the high energy values of the distribution A linear regression is found between log10 E i and i to get an approximation of the mean energy with decile: log10 E i C log10 Ei i i 5 2 The first parameter from the fit C is related to the overall mean of the stroke energies in the particular spatial bin It is not used in this analysis as C greatly depends on the network coverage at the time and location where it calculated C will be larger where coverage is lower WWLLN detecting only strong strokes and lower with high coverage WWLLN detecting both strong and weak strokes By using the regression method the network coverage and variable detection efficiency is factored out of the energy distribution into C allowing for the shape of the energy distribution to be examined directly The second parameter log10 Ei i is the slope of the regression and will be used to study the energy changes between land and ocean regimes log10 Ei i is the measure of how much logarithmically the average stroke energy changes from one decile to the next So a value of log10 Ei i 0 1 at a location will increase the mean stroke energy by 100 1 25% per decile while a value of 0 2 will increase by 100 2 58% per decile The regression slope will be higher for either relatively more high-energy or low-energ strokes corresponding to greater variance in the distribution The low-energy tail of the energy distribution is mostly set by the detection efficiency of the network where a higher detection efficiencies result in an overall shift of the distribution to lower energies while the high end is always well detected even where the network has low station density As C captures the effects of the network performance the slope of the regression will be mainly set by the energy of the strokes in the tails of the distribution Detecting more low energy strokes will shift the distribution but not change the shape or variance of energies An example of the linear regression method is shown in Figure 5 1 using 15 days of data from 1 15 June 2012 separated into land black and ocean gray strokes The stroke counts are split into the ten decile bins outlined in Figure 5 1a Ei is shown in Figure 5 1b with the corresponding regressions plotted on top of the points Departures 69 from the regression are acceptable as only the trend of increasing energy is important and not an exact fit a b 8 104 4 Energy J Counts x103 6 2 0 103 6 4 2 0 102 1 10 102 103 104 Energy J 105 106 0 2 4 6 8 Decile Number i 10 Figure 5 1: WWLLN data from 1-15 June 2012 for global strokes grouped into land black and ocean gray to demonstrate the linear regression method a Shows two energy distributions with the corresponding energy decile bins dashed lines b is the plot of mean energy Ei in each bin with the linear regression solid lines 5 3 Regression Slope Maps This technique is applied over 3 years of WWLLN data from May 2009 through May 2012 on a 0 5 grid the resulting regression slopes are shown in Figure 5 2 For this analysis the calculated regressions must have an R-square value of at least 0 80 to be used In general higher slopes are seen over oceans and lower slopes over land except for several regions of low detection efficiency e g off the shore of Madagascar and regions such as the Andes mountain range The map is similar to Figure 5 3 adapted from Virts et al 2013 which shows the ratio of the WWLLN normalized stroke climatology to the LIS OTD normalized flash climatology The climatologies are normalized by their total stroke and flash counts respectively Figure 5 3 is the spatial distribution of where WWLLN preferentially detects more strokes than LIS OTD due to the bias of WWLLN towards detecting the most energetic strokes Comparing the stroke and flash data directly is possible as a majority of flashes have only the first and strongest stroke detected by WWLLN Abarca et al 2010 70 90 0 25 0 2 Latitude 30 0 15 0 -30 0 1 -60 -90 -180 Linear Regression Slope 60 -120 -60 0 Longitude 60 120 180 0 05 Figure 5 2: Slope of the linear regression used on the energy distribution as described in the text High slope values corresponds to a more strokes in the tails of the energy distribution 90 2 log10 WWLLN to LIS OTD ratio 60 1 Latitude 30 0 0 -30 -1 -60 -90 -180 -120 -60 0 Longitude 60 120 180 -2 Figure 5 3: Ratio of the WWLLN stroke count density climatology to the LIS OTD flash count density climatology normalized by their relative total counts adapted from Virts et al 2013 The same linear regression was applied to the 2011 ENTLN data for a region over North America The absolute peak current was used for the regression instead of the stroke energy with the results in Figure 5 4 The land-ocean contrast is seen strongly in the ENTLN dataset particularly over Mexico Cuba and Haiti The difference also exists off the coast of the southeastern United States but the contrast is not as strong slope increase on the order of 0 01 instead of 0 1 For the ENTLN data the linear regression slopes only range from 0 05 to 0 15 compared to 0 05 to 0 25 for the WWLLN regressions Since energy is related to peak current by 71 30 -120 0 10 Linear Regression Slope Latitude 0 15 0 05 Longitude Figure 5 4: Slope of the linear regression used on the 2011 ENTLN absolute peak current distribution as described in the text High slope values corresponds to a more strokes in the tails of the energy distribution Estroke 2 23 Ipeak 1 62 Hutchins et al 2012b log10 Ei will be 1 62 times higher than log10 Ipeak i The range of the slopes for the ENTLN regression should then be correspondingly lower by a factor of 1 62 or from 0 03 to 0 15 matching the range seen by WWLLN 5 4 Stroke Distributions The global ratio of the land and ocean stroke distributions clearly shows the prevalence of higher energy strokes over oceans The energy distribution of the WWLLN data is found for the set of strokes occurring over land and for the strokes occurring over oceans The ratio of these ocean and land energy distributions is shown in Figure 5 5 The ocean-land ratio starts increasing quickly with increasing energy at 3000 J showing there are relatively more high-energy top 15% of stroke energy strokes over the oceans than over land Similarly there is a general decrease in the ratio for decreasing strokes energies with the downward trend interrupted with a small bump near 10 J 5 5 Regional Contrast In Figures 5 2 and 5 3 there is an evident overall difference between land and ocean strokes and it can be seen to vary sharply across most coastlines This raises the question of whether 72 Count Ratio 2 1 0 1 10 102 103 Energy J 104 105 106 Figure 5 5: The ratio of ocean to land counts for WWLLN within each energy bin The dashed horizontal line is a ratio of 1 The vertical dashed lines show the 15th and 85th percentile levels for the distribution network detection efficiency across the coastline should be considered as a potential cause for the change Three regions are chosen for closer examination shown outlined by the white boxes on top of a map of the WWLLN relative detection efficiency in Figure 5 6a: North America Western Africa and Northeastern Brazil WWLLN has an inherent bias towards more readily detecting low energy strokes over oceans than over land This is due to lower VLF wave attenuation over oceans low-energy strokes propagating over the ocean can reach more WWLLN stations compared to the same stroke traveling over land Hence WWLLN is naturally biased to predominately detect only the highest energy strokes over land and relatively more lower energy strokes over water Hutchins et al 2012b The method of linear regression described in Section 5 2 should remove most of this bias in WWLLN this can be checked in part by the recent work on relative detection efficiency Hutchins et al 2012a The three regions chosen in Figure 5 6 were chosen such that the gradient of relative detection efficiency is changing parallel to the coastline Over North America and the Gulf of Mexico Figure 5 6b the strokes over Mexico Florida Cuba and Haiti are all weaker than those over the nearby ocean This is also seen with the ENTLN in Figure 5 4 The relative detection efficiency see Hutchins et al 2012a is fairly uniform over this region with the largest change occurring over the Atlantic where there is no change to the regression slope Over the central United States there is 73 Latitude 90 100 60 80 30 60 0 40 -30 20 -60 -90 -180 b -120 -60 0 60 Longitude 0 25 20 20 -110 -100 -90 -80 20 0 15 10 d -40 10 -30 -20 -10 0 120 0 100 80 -110 -100 -90 -80 60 10 40 -40 10 0 180 Relative Detection Efficiency % 30 Linear Regression Slope 30 c 20 Relative Detection Efficiency % a -30 -20 -10 0 20 0 -60 -50 -40 -30 0 05 -60 -50 -40 -30 0 Figure 5 6: Regional maps of the linear regression slopes in the left column with respective WWLLN relative detection efficiency maps on the right Selected regions outlined in a on top of the map of the May 2009 through May 2012 average relative detection efficiency b shows the Continental United States and Gulf of Mexico c Western Africa and d Northeast Brazil The white arrows point in the direction of increasing relative detection efficiency a large region of high stroke energies this is also observed in the ENTLN regression slope Figure 5 4 and LIS OTD count ratio Figure 5 3 data In Western Africa Figure 5 6c there is a clear difference between the land and the ocean the coast shows a very sharp change in the stroke strength The changing detection efficiency in this case is parallel to the coast and would not affect the variation in stroke energy at the coastline The difference in Brazil shown in Figure 5 6d is similar to that over Western Africa with the exception of the increased stroke energies seen over Amazon River delta Even with the increase over the delta there is still a contrast off of the coast with the change in regression slope comparable to the coastline northwest of the delta 74 5 6 Conclusion A linear regression method is developed and applied to the WWLLN dataset in order to examine global and regional changes of lightning stroke strength over several years of network data Through comparing WWLLN ENTLN and LIS OTD the difference between stroke strength is seen to be highly dependent on whether the storms occur over land or over ocean with a sharp boundary occurring along most coastlines Smaller regions are examined to show that the contrast along coastlines is not due to abrupt changes in the detection efficiency of the networks The sharpness of the coastal changes less than 100 km suggests the effect is due to a local phenomena and not be caused by large scale changes in the convective land-ocean regions Changes exist within continental regions but these transition were not examined as the underlying change between regimes is not as sharp as for coastlines 75 Chapter 6 VLF PROPAGATION 76 6 1 Overview The World Wide Lightning Location Network WWLLN is used to measure the normalized lightning electric field at three network stations in order to examine the sferic attenuation between the stroke and the station The electric field measurements are normalized to the square root radiated very low frequency VLF stroke energy to allow direct comparisons of the many stroke-station paths seen by WWLLN WWLLN observes a strong dependence of VLF propagation on magnetic azimuth similar to past work From WWLLN the average attenuation over the water of eastward-propagating sferics is found to be 1 13 0 35 dB Mm during the day and 0 71 0 68 dB Mm at night with westward-propagating sferics having average attenuation rates of 2 98 0 68 dB Mm and 2 66 0 39 dB Mm for day and night respectively The propagation dependence on magnetic azimuth stems from the polarization of the VLF wave with respect to the electron motion in the ionosphere Ionospheric electrons are constrained to gyrate in one direction for VLF waves propagating eastward the polarization of the wave is in the same direction as the electrons providing more efficient propagation the opposite in the case for westward propagating waves There is then no change in propagation for waves aligned with the magnetic field e g northward or southward propagating waves Past experimental work has shown a strong dependence of VLF attenuation on the magnetic azimuthal angle of propagation Wait and Spies 1960 provide an in-depth analysis of the theoretical background present a theoretical background for why the attenuation changes with azimuth By measuring the signal strength from the same nearly antipodal transmitter along the short and long great circle path Crombie 1958 found less attenuation for the eastward propagating signals Similarly Taylor 1960 showed that eastward propagating VLF waves have 1 3 dB Mm less attenuation than westward propagating waves Recently Jacobson et al 2012 used negative cloud-to-ground strokes to examine ionospheric reflectance and also found a strong azimuthal dependence to the measurements The past work has examined stationary VLF transmitters with either a few receivers or one moving receiver Recent work by Burkholder et al 2013 utilized the World Wide Lightning Location Network WWLLN to examine how eastward and westward propa- 77 gating VLF sferics couple into the ionosphere This work motivated us to use the many stroke-receiver paths of WWLLN to study the azimuthal dependence of VLF propagation within the Earth-ionosphere waveguide The global coverage of the network allows for many long range stroke-receiver paths with which to estimate VLF attenuation rates The sferic attenuation for a single station can be found with WWLLN by comparing the stroke energies measured by the network to the RMS electric field measured at a single WWLLN station Using WWLLN allows for the azimuthal propagation effects to be examined at all magnetic azimuths for both all-night and all-day paths The measured electric fields and observed attenuation rates can be directly compared to the theoretical predictions of Wait and Spies 1960 and Taylor 1960 By examining the propagation it is shown that WWLLN captures the effects of propagation and that the theories are applicable for non-stationary transient sources 6 2 Path Selection To examine eastward and westward propagation three WWLLN stations were chosen based on their island locations: Suva Tahiti and Honolulu These stations were selected as a majority of their stroke-receiver paths are over water so the effects of variable ground conductivity can be ignored The WWLLN energy calculation uses the LWPC code that accounts for eastward and westward propagation However each WWLLN energy measurement is the median energy of several WWLLN stations so by selecting strokes with a similar number of stations to the east and west the azimuthal dependence computed by LWPC can be minimized There is allowed to be at most 25% more WWLLN stations to the east or west of a located stroke where this abundance is defined by: neast nwest n For example a located stroke with 1 station to the north 2 east and 3 west will have a westward abundance of 16 7% and would be included in the analysis With these three stations the WWLLN data are reduced to only consider sferics that crossed at most 5% land and propagated in either at least 95% day or night ionospheric conditions The stroke energy uncertainty median absolute deviation of contributing stations see Hutchins et al 2012b is limited to a maximum of 10% Further the data are reduced 78 by selecting only strokes with a similar number of locating WWLLN stations situated to the east and west as described above These requirements reduce the stroke-receiver paths in the WWLLN dataset to 0 2% of the total paths for each station where 87% occur during the day and 13% occur at night This resulted in over 2 106 total stroke-receiver paths used in this Chapter The subset of data contains the RMS electric field at each station the distance to the strokes and the VLF energy of the stroke VLF stroke energies and station measured electric fields both vary over several orders of magnitude All station electric fields in units of 1 V m 1 are normalized by the square root of the stroke energy in J to allow for direct comparisons between differing source energies The stroke energy normalization gives the electric field in dB above 1 V m 1 J 1 2 Changes in the normalized electric field with stroke distance gives the attenuation of the lightning sferic for that distance interval reported as the dB Mm decrease Normalized field values are grouped into 45 azimuth and 500 km distance bins An example of all of the distance bins for a given azimuth for one station is shown in Figure 6 1 northwestward-propagation during the day for Honolulu station Each distance bin has a distribution of normalized field values with the spread a result of differing ionospheric conditions uncertainty in the energy measurements and changes in ground conditions at the station Because of this spread the median value of the normalized field is used for each distance-angle combination shown as the solid black line At least 15 strokes are required for each distance bin at a given azimuth in order to calculate a reasonable median The magnetic azimuth used is the average magnetic azimuth over the path of wave propagation 6 3 Azimuthal Dependence For the three stations data were used from May 2009 to May 2013 resulting in 2 1 106 stroke-station paths to analyze The results are split into the 8 azimuth octants for day paths and night paths as shown in Figure 6 2 For the three stations the westward propagating waves green show higher attenuation electric field change per unit distance than for the eastward propagating waves red The attenuation is also seen in the maximum distance that strokes are detected with night eastward paths detectable at farther distances than Normalized E-field dB 79 60 50 40 30 20 10 0 0 4 12 8 Distance Mm 0 5 Normalized Counts 16 1 0 Figure 6 1: Normalized electric field values for the 315 azimuth bin for the Honolulu station during the day Counts are normalized to the maximum value in each distance bin The median solid and median absolute deviation dashed values are plotted on top of the distribution Distances with less than 15 total strokes are not plotted or used day westward paths For some stations such as Honolulu in Figure 6 2 the difference between eastward and westward sferics is quite clear during the day at all distance ranges and between day and night For other stations such as Suva the difference in propagation direction is not distinct for all azimuths Suva and Tahiti stations do not show a differentiation in attenuation until the waves have propagated some distance from the stroke for example the night strokes for Suva in Figure 6 2 are indistinguishable until 4 Mm In all cases the slopes of the field strength curves in Figure 6 2 show that the eastward sferics exhibit less attenuation than westward sferics away from the stroke In cases like Honolulu the westward sferics initially have a lower normalized electric field but the attenuation rate of these sferics is still lower than the eastward sferics The overall behavior of the VLF waves observed by WWLLN can be seen in the combined station data The station-stroke pairs were combined for all stations to give a single dataset of paths shown in Figure 6 3 The westward sferics in both day and night have similar electric field to the eastward sferics with the distinction developing at greater than 4 Mm 80 Suva Day Night 50 40 30 Normalized E-field dB 20 0 4 8 12 16 0 Tahiti 4 8 12 16 0 4 8 12 16 0 Honolulu 4 8 12 16 0 4 8 12 16 0 4 Distance Mm 8 12 16 50 40 30 20 50 40 30 20 0 45 90 135 180 225 270 315 Magnetic Propagation Azimuth degrees Figure 6 2: Station RMS electric field vs distance for Suva Tahiti and Honolulu Electric field is normalized by the square root stroke energy and given in dB above 1 V m 1 J 1 2 Day ionosphere paths are in the left column and night ionosphere paths in the right column from the stroke There is a small upturn in field strength as the sferics propagate past 10 Mm because the waves are re-focusing when they cross the halfway point to their antipode The method for estimating the attenuation and the uncertainty is outlined in Figure 6 4 using the station averaged eastward-propagating electric field values as an example red line Normalized E-field dB 81 Day Night 50 50 40 40 30 30 20 20 0 4 8 12 0 16 0 Distance Mm 4 8 12 16 45 90 135 180 225 270 315 Magnetic Propagation Azimuth degrees Figure 6 3: Combined station normalized electric field for the three selected stations Shown in dB above 1 V m 1 J 1 2 in Figure 6 3 The following fitting and smoothing method is used to estimate the attenuation to remove the noise in the direct attenuation Figure 6 4b First the normalized electric field versus distance curves are smoothed and fitted to quadratics for the bins that have data as shown with the dashed line in Figure 6 4a Second the attenuation between each bin of the fit the slope of Figure 6 4a is found and shown in Figure 6 4b Lastly the attenuation for a given electric field curve is calculated by the mean of the fitted attenuation where positive attenuation corresponds to a signal loss over distance The standard deviation of the attenuation is taken as the uncertainty in the attenuation measurement In the example of Figure 6 4 the fitted attenuation is 1 13 0 35 dB Mm whereas the attenuation directly from the data solid line in Figure 6 4b is 0 79 2 34 dB Mm The increased uncertainty in the direct attenuation is due to the variations in attenuation between successive 500 km distance bins The fitted attenuation is used for all of the following attenuation values There is an inherent geometric factor to the measured attenuation values As the wave expands radially out from the lightning source it is moving through the spherical waveguide of the Earth and Ionosphere This expansion adds in a factor of wave power at a station or 1 sin d R 1 2 1 sin d R to the received to the measured electric field In the geometric factor 82 d is the great circle distance from the wavefront to the lightning source and R is the radius of the Earth Because past models such as Wait and Spies 1960 include the effects of the geometric factor in their predictions and past measurements do not correct for it the measured attenuations will not be corrected for the geometric effect Attenuation dB Mm Normalized E-field dB a b 50 40 30 20 0 4 0 4 8 12 16 4 2 0 -2 -4 -6 8 12 Distance Mm 16 Figure 6 4: Method for calculating the attenuation In a the normalized electric field vs distance data solid line and the fitted quadratic dashed line In b the change in electric field with distance step derivative for the data solid line and the fit dashed line normalized to dB Mm Overall there is an average attenuation of 1 87 1 06 dB Mm for all azimuths and times Within the first 4 Mm of the stroke the attenuation is fairly high for both day and night with 2 08 0 90 dB Mm during the day and 2 09 1 02 dB Mm at night Beyond 4 Mm the attenuation decreases to 1 29 1 09 dB Mm for day and 0 24 0 48 dB Mm for night The 4 Mm cutoff was chosen based on Figure 6 2 and 6 3 where the eastward and westwardpropagating sferics start to clearly differentiate The increased attenuation near the stroke is likely due to the fast decay of higher order modes that cannot propagate far from their 83 source Wait 1970 For eastward sferics the average attenuation is 1 13 0 35 dB Mm and 0 71 0 68 dB Mm for day and night for westward sferics attenuation is higher with rates of 2 98 0 68 dB Mm and 2 66 0 39 dB Mm for day and night paths The difference in attenuation between eastward and westward-propagating sferics is an increase of 1 9 dB Mm for day and 2 0 dB Mm for night 6 4 Comparisons to Theory The azimuthal variability of the WWLLN normalized electric-field attenuation is directly compared to the azimuthal variance predicted by Wait and Spies 1960 in Figure 6 5 The azimuthal variation P is found by comparing the attenuation with the presence of a magnetic field to the attenuation without For the WWLLN data the average attenuation of all azimuths is taken as representative of the attenuation with no magnetic field The variability of the attenuation rate in dB Mm with magnetic azimuth from Wait and Spies 1960 is approximated as P 0 3 sin 1 P 2 1 0 360 0 90 180 270 Magnetic Propagation Azimuth degrees Theory Day Night Figure 6 5: Dependence of attenuation with magnetic azimuth shown as P the attenuation normalized to attenuation with no magnetic field Shown for Wait and Spies 1960 black day paths green and night paths blue The best fit curves are shown as dashed lines Day and night paths are normalized by their mean The average attenuation azimuthal variation was fit to the same form as the theory 84 P a sin b 1 with the resulting fits shown in Figure 6 5 The leading coefficient a gives the relative variation in attenuation with azimuth how much attenuation rates will change between northward southward and eastward westward propagating sferics The day attenuation best fit is P 0 58 sin 348 1 and the night attenuation best fit is P 0 76 sin 344 1 Both day and night paths show twice the amplitude relative to the theory atheory 0 3 with a weaker day dependence and a stronger night dependence a 0 58 0 18 and a 0 76 0 26 respectively On average the day measurements vary from the theory by 19% and the night measurements by 34% In previous measurements of 3 30 kHz VLF attenuation Taylor 1960 observed westward VLF paths to exhibit 1-3 dB Mm more attenuation than eastward paths This is in line with the WWLLN measured increase of 1 9 2 0 dB Mm from eastward to westwardpropagating sferics Similarly the LWPC model shows an attenuation increase of 2 dB Mm from eastward to westward-propagating sferics for equatorial day paths over the Pacific Ocean The model also gives a 28% to 37% variability of attenuation between propagation directions relative to northward propagation compared to 30% for Wait and Spies 1960 and 58% to 77% for WWLLN The measured attenuation rates of WWLLN are within the previously measured ranges of attenuation and within the same difference between propagation directions However the total azimuthal dependence of VLF propagation has been observed to be greater than that of the theoretical model of Wait and Spies 1960 and the propagation model LWPC The inconsistency may stem from the WWLLN measurements being the average over a range of frequencies while past measurements and models are for specific narrow frequencies usually VLF transmitters 6 5 Conclusion Four years of WWLLN data were used to analyze the normalized VLF electric field from lightning at three island stations with the variation with magnetic azimuth compared to theoretical results The electric fields were used to calculate the average attenuation in the 8 18 kHz band at different propagation azimuths The stroke-receiver paths were selected for sferics propagating over at least 95% water and under either 90% day or 90% night 85 ionospheric conditions It was found that compared to day propagation night propagating sferics have higher attenuation close to the stroke 2 09 1 02 with less attenuation farther out 0 24 0 48 Similarly attenuation of night sferics have a higher dependence on magnetic azimuth compared to day sferics Variations with magnetic azimuth showed that westward propagation had 1 9 2 0 dB Mm more attenuation than eastward propagation for both day and night ionospheric conditions Combining three optimally placed WWLLN stations allowed for this examination of the azimuthal dependence of VLF attenuation Utilizing more of the 70 stations will allow for further investigation of VLF attenuation rates with other path parameters such as ocean salinity ice and ground conductivity 86 Chapter 7 GLOBAL ELECTRIC CIRCUIT 87 7 1 Overview The diurnal variation of the global electric circuit is investigated using the World Wide Lightning Location Network WWLLN which has been shown to identify nearly all thunderstorms Jacobson et al 2006 using WWLLN data from 2005 To create an estimate of global electric circuit activity a clustering algorithm is applied to the WWLLN dataset to identify global thunderstorms from 2010 2013 Annual seasonal and regional thunderstorm activity is investigated in this new WWLLN thunderstorm dataset in order to estimate the source behavior of the global electric circuit Through the clustering algorithm the total number of active thunderstorms are counted every 30 minutes creating a measure of the global electric circuit source function The thunderstorm clusters are compared to precipitation radar data from the Tropical Rainfall Measurement Mission satellite and with case studies of thunderstorm evolution The clustering algorithm reveals an average of 660 70 thunderstorms active at any given time with a peak-to-peak variation of 36% The highest number of thunderstorms occurs in November 720 90 and the lowest number occurs in January 610 80 Thunderstorm cluster and electrified storm cloud activity are combined with thunderstorm overflight current measurements to estimate the global electric circuit thunderstorm current contribution to be 1090 70 A with a variation of 24% By utilizing the global coverage and high time resolution of WWLLN the total active thunderstorm count and current is shown to be less than previous estimates based on compiled climatologies Diurnal variation in global thunderstorm activity was original observed by Wilson 1921 and Whipple 1929 through a combination of thunderstorm day and electric field measurements Strong correlations between thunderstorm activity and fair weather return current led to the model of the global electric circuit a system of ionospheric charging and discharging through thunderstorms and fair weather return currents Studies to date have estimated that globally there are 1000 2000 thunderstorms active at any one time most concentrated over tropical landmasses covering 1 10% of Earth s surface Markson 1978 Rycroft and Harrison 2011 Singh et al 2011a Previous work on diagnosing the generator source of the global electric circuit used several methods: long time scales Tinsley et al 88 2007 Liu et al 2010 mathematical models Kasemir 1977 Hays and Roble 1979 Roble 1991 engineering models Ogawa 1985 Kartalev et al 2004 Rycroft 2006 parameterization Price and Rind 1992 Williams 1985 and thunderstorm overflight estimates Mach et al 2011 Most work with the global electric circuit uses long term averaging to recreate the known Carnegie curve of Whipple 1929 yet short time scales do not match the long term averaging Holzworth et al 1984 The variation of the global electric circuit changes on short time scales that is not resolved in past models or with long term averaged observations The global electric circuit is an important component to the solar-terrestrial system creating a link between solar activity the ionosphere aerosols cloud microphysics thunderstorms weather and climate Tinsley et al 2007 Holzworth and Volland 1986 Individual lightning strokes and flashes are not yet a reliable method of characterizing the source of the global electric circuit but global thunderstorm activity is a reliable measure Ruhnke 1969 proposes that the conduction and displacement currents above thunderstorms are the global electric circuit generators source as they vary slowly through the evolution of a thunderstorm and the currents are fairly independent from impulsive events like lightning Krider and Blakeslee 1985 looked at displacement currents below a thunderstorm to find them steady with abrupt but insignificant changes due to lightning Rycroft et al 2000 created an engineering model with three different regions for the the return current concluding that sprites lightning and other transients will have little direct effect on the global electric circuit Stergis et al 1957 showed that cloud to ground lightning is not necessary for upward current from thunderstorms With a numerical model of a dipolar thunderstorm Tzur and Roble 1985 estimated the average upward current contribution of a thunderstorm to the global electric circuit to be 0 7 A per thunderstorm Similarly with a combination of numerical and analytical models of dipolar thunderstorm Driscoll et al 1992 estimated a total contribution of 0 4 A to the global circuit per thunderstorm Unlike the other models Mareev et al 2008 estimated a 50 400 A current contribution directly from global lightning with a similar model Mallios and Pasko 2012 investigated the efficiency of lightning and found lightning only contributed 1% 3 A of the total 300 A contribution from thunderstorms These models show that thunderstorms contribute an appreciable upward current to the global electric circuit with a wide range of 89 estimated current contributions Balloon and aircraft overflights have been used to estimate the total current contributions from thunderstorms to the global electric circuit Stergis et al 1957 found thunderstorm currents ranging from 0 6 4 3 A with an average of 1 3 A these estimates are the lower bound with uncertainties of up to 50% Blakeslee et al 1989 shows the upward current generated by a thunderstorm to range between 0 1 6 A with an average current between 0 5 1 A Other studies show current density over thunderstorms ranging from 10 40 pA m2 Holzworth 1981 to 20 33 nA m2 Mach et al 2009 The overflights in previous research found no consistent parameterization between lightning rates and fair weather return current but recent balloon work found strong correlation between global lightning activity and the fair weather return current on short time scales Holzworth et al 2005 Lightning stroke activity and locations cannot directly provide estimates of the global circuit however they can be used for directly locating and defining active thunderstorm areas and relative intensities Compared to satellite and balloon observations ground based lightning networks have the advantage of continuous observation of large regions Global very low frequency networks such as the World Wide Lightning Location Network WWLLN are capable of locating lightning around the entire globe Holzworth et al 2005 compared the stroke counts of a nascent WWLLN to the fair weather return current and found strong temporal correlation between the measurements A better measure of global circuit activity is the total number of active thunderstorms around the globe applying clustering algorithms to lightning network data enables the network to locate track and monitor global thunderstorm activity The WWLLN data are clustered into thunderstorms with the Density-Based Spatial Clustering of Application with Noise DBSCAN algorithm Ester et al 1996 Kriegel et al 2011 DBSCAN was chosen as the clustering algorithm for several key features: the capability to handle noise no requirement to specify the number of clusters arbitrary cluster shapes and the insensitivity to the ordering of the data Clustering lightning strokes into thunderstorms cannot require a designated number of clusters before clustering as the total number of thunderstorms is not known before clustering Similar algorithms such as Ward s 90 Method cluster into large unphysical thunderstorms due to noise Ward 1963 In another approach Mezuman 2013 used a connected components methods to cluster the WWLLN data They found global thunderstorm activity to average near 1000 thunderstorms with significant daily variability The resulting WWLLN lightning clusters are representative of the lightning active stage of the thunderstorm Even though the electrically active portion of a thunderstorm extends beyond the active lightning stage Jacobson and Krider 1976 Stolzenburg et al 2010 the clustered lightning active stage in this work will be referred to as the clustered thunderstorm or thunderstorm clusters 7 2 Clustering 7 2 1 DBSCAN DBSCAN clusters n-dimensional points based on the distance between the points a length scale and the minimum number of points necessary to form a cluster minP ts Kriegel et al 2011 Points in a cluster are either core points or non-core points a point is a core point of a cluster if there are minP ts 1 other points within distance of that point resulting in minP ts points within distance In Figure 7 1 the distance is represented by the circle around each point lines connect points within of each other and core points are shown as filled symbols Points that are within of one core point but less than two core points minP ts 3 are added to the cluster as non-core points and cannot be used to add more points into the cluster For example the unfilled triangle symbol in Group 1 of Figure 7 1 is within of one core point and clustered into the group as a non-core point but cannot connect further unclustered points crosses into the cluster WWLLN lightning strokes are separated by three dimensions: latitude longitude and time With time as a consideration two clusters that appear to overlap in Figure 7 1a group 2 blue and group 3 green are separated by in time and are distinct groups as seen in Figure 7 1b DBSCAN is a physically realistic algorithm for clustering lightning data such as WWLLN data as the core points of a thunderstorm are the intense lightning centers while edge points are clustered but do not connect disparate lightning centers 91 a b Latitude 2 1 Longitude 3 2 1 3 Time Figure 7 1: DBSCAN clustering example with minP ts 3 showing the same clusters located in a latitude and longitude and b latitude and time Solid rings show the distance from core points filled dashed rings are for non-core points unfilled Triangles 1 squares 2 and stars 3 show clustered points crosses are non-clustered points 7 2 2 Clustering WWLLN Accurate thunderstorm clustering of WWLLN data requires optimizing the clustering parameters and minP ts WWLLN requires a second parameter time for clustering in time The parameter corresponds to the physical extent of an average thunderstorm time the duration and minP ts the number of lightning strokes necessary to consider a thunderstorm electrically active As the clustering parameters are varied the total number of thunderstorms the average thunderstorm area and the average thunderstorm duration change In Figure 7 2a it can be seen that has a high degree of control over thunderstorm area and total thunderstorms To balance the total number of thunderstorms average area 320 km2 and percentage of strokes clustered 89% not shown the best value is found to be 0 12 or about 13 km To prevent consecutive thunderstorms from being clustered e g one thunderstorm occurring in the same area as a previous distinct thunderstorm storm time Figure 7 2b needs to be smaller than average duration of a thunderstorm With this requirement the value of time 18 minutes is found giving an average thunderstorm cluster duration of 16 minutes The minimum number of strokes needed to produce a cluster is set at minP ts 2 as two 92 detected WWLLN strokes confirms the presence of a thunderstorm A sharp drop in the total number of thunderstorms can be seen in Figure 7 2c when minP ts moves from 2 to 3 To get a majority of strokes included in the thunderstorm clusters while retaining reasonable physical attributes of the thunderstorms the parameters 0 12 time 18 minutes and minP ts 2 strokes were chosen 1 0 8 30 0 6 0 4 15 0 0 2 4 6 101 Total Clusters x1000 102 103 Area km2 104 0 03 180 time minutes Duration minutes b 45 0 2 degrees Duration minutes a 45 30 120 15 60 30 10 0 0 2 4 6 101 Total Clusters x1000 104 30 30 20 15 12 8 0 0 2 4 6 101 Total Clusters x1000 102 103 Area km2 104 minPts Duration minutes c 45 102 103 Area km2 2 Figure 7 2: Variation in average thunderstorm duration rows counts left column and area right column through varying one clustering parameter with the others held constant constant set: 0 12 time 18 minutes and minP ts 2 a varies from 0 03 1 b time varies from 10 180 minutes c minP ts varies from 2 30 strokes 93 7 3 WWLLN thunderstorm clusters Using the DBSCAN algorithm the individual WWLLN lightning strokes from 2010 June - 2013 June are clustered into active thunderstorms Clustered WWLLN strokes allow for simple thunderstorm tracking as shown in Figure 7 3 here the strokes comprising a thunderstorm are outlined with polygons every hour and plotted with opacity increasing with time Figure 7 3 shows several active thunderstorms on 2013 May 21 12 23 UTC For clarity clustered thunderstorms with less than 50 strokes were removed from the plot The thunderstorm opacity increases at 8% per hour with each color corresponding to a single thunderstorm cluster Latitude 40 35 30 -100 -95 -90 Longitude -85 Figure 7 3: Thunderstorm evolution from 2013 May 21 12 23 UTC Polygons outline active lightning regions colors correspond to thunderstorm cluster opacity increases 8% hour For clarity thunderstorms with less than 50 strokes were removed The cluster results can be directly compared to active precipitation regions as seen by the TRMM Precipitation Radar Kawanishi et al 2000 Rainfall rates from the TRMM data product 2A25 were used as binned rates on a 0 25 grid in Figure 7 4 the TRMM rainfall data are shown as the background image gray areas are not in view of the satellite WWLLN strokes are shown in Figure 7 4 if they occur between the start and end times of the TRMM regional overpass In Figure 7 4 two sets of consecutive overpasses are used the first on 2013 May 06 from 94 a b 36 36 34 34 32 c -80 -75 32 d 36 36 34 34 32 32 -100 -95 -90 0 -80 -100 2 4 6 8 Precipitation Rate mm Hr -75 -95 -90 10 Figure 7 4: WWLLN thunderstorm clusters identified by color over TRMM precipitation rate mm Hr for 2013 May 06 15:49 15:59 UTC a 17:28 17:37 UTC b 2013 May 21 10:04 10:13 UTC c 11:42 11:52 d a and b are successive passes as are c and d cluster colors are contiguous between passes Gray areas were outside the range of the TRMM radar 15:49 15:59 UTC 7 4a and 17:28 17:37 UTC 7 4b the second in on 2013 May 21 from 10:04 10:13 UTC 7 4c to 11:42 11:52 UTC 7 4d These passes were selected as they passed over the same thunderstorms twice with an appreciable amount of lightning activity in view of the satellite Unlike Figure 7 3 the clustered WWLLN strokes are shown as individual strokes in the thunderstorm with many of the strokes overlapping each other in the center of the clustered regions The clustered thunderstorms match up well with the TRMM precipitation regions and clearly track the same thunderstorm between the consecutive overpasses Thunderstorms continue and are clustered by WWLLN well after TRMM no longer observes the area green thunderstorm in Figure 7 4c and 7 4d There 95 were no previous or later TRMM overpasses of these thunderstorms 7 4 Global thunderstorm activity Original estimates of global thunderstorm activity show afternoon peaks in lightning activity for each of the major lightning chimney regions: the Americas Africa Europe and Asia Wilson 1921 The global averaged WWLLN thunderstorm clusters show the previously measured long term averaged diurnal behavior of the global electric circuit activity with a diurnal variation of 36% The three year average of thunderstorm activity is shown in Figure 7 5 for different regions 7 5a for thunderstorm type 7 5b and for seasons 7 5c with the global average displayed in each panel black Averages of thunderstorm activity are calculated from the total number of unique thunderstorms every 30 minutes Each chimney region is separated in Figure 7 5a with peaks in thunderstorm activity occurring in the local afternoon Americas 19 UTC Africa 15 UTC and Asia 8 UTC then a slow decrease during the night until a minimum in the early hours of the morning A strong diurnal variation is evident for thunderstorms over land seen in Figure 7 5b with little diurnal variation in oceanic thunderstorm activity On average WWLLN observes a total of 660 70 thunderstorms on any given day of the year while the total is lower than previous estimates in the 1000 2000 thunderstorm range those estimates were made using partial or extrapolated datasets For each chimney region the average number of thunderstorms are 280 80 for the Americas 140 60 for African and Europe and 240 50 for Asia and the Maritime Continent The long-term thunderstorm behavior observed by WWLLN resembles the previous measurement of global electric circuit behavior Of the clustered thunderstorms 350 70 were continental and 300 10 were oceanic This is in contrast to the disparity in the distribution of individual lightning strokes where a majority are continental the continental thunderstorms tend to be larger with higher stroke rates than those over the oceans There are slight changes in the overall diurnal behavior between each season shown Figure 7 5c The contribution of each chimney region divided by northern and southern hemisphere is shown in Figure 7 6 The overall seasonal change in thunderstorm activity is clearly seen with the change in dominant contributor from the northern hemisphere in 96 Thunderstorm Counts a b c 800 600 400 200 0 800 600 400 200 0 900 800 700 600 500 Global Americas Africa Asia 0 3 6 9 12 15 18 21 All Land Ocean Coast 0 3 6 9 12 15 18 21 Annual JJA SON DJF MAM 0 3 6 9 12 15 18 21 Hour UTC Figure 7 5: Diurnal variation of WWLLN thunderstorm 30 minute counts for 2010 2013 obtained using the DBSCAN clustering algorithm For a thunderstorms over each major lightning chimney region divided between longitudes 180 30 and 60 b all land ocean and coastal thunderstorms coastal thunderstorms have strokes over land and ocean and c the full year and each season May August to the southern hemisphere in November February In the shoulder seasons March April and September October the different chimneys are closer in activity levels to each other The shift in peak activity times for each chimney region between northern and southern summer reflects the difference in longitudinal landmass distribution of each region For example the North America peak occurs at 23:30 UTC while the South America peak occurs at 18:30 UTC since the South American lightning regions are in general farther east than the North American ones This time change in regional contributions has been seen in other global circuit measurements in the Vostok Antarctica electric field measurements 97 of the fair weather field the peak changes from 18:00 UTC in January to 21:00 UTC in August Burns et al 2005 2012 January February 400 Thunderstorm Counts 200 0 200 0 3 6 400 9 12 15 18 21 May June 200 0 400 0 0 3 6 400 9 12 15 18 21 July August 200 0 3 6 9 12 15 18 21 September October 200 0 March April 400 0 0 3 400 6 9 12 15 18 21 November December 200 0 3 6 9 12 15 18 21 Hour UTC Americas Africa Asia 0 0 3 6 9 12 15 18 21 Hour UTC North South Figure 7 6: Diurnal variation of WWLLN thunderstorms for each major chimney region colors divided by hemisphere Northern Hemisphere solid line Southern Hemisphere dashed line Each panel shows two months of thunderstorm clusters averaged over 2010 2013 7 5 Temporal thunderstorm activity As a result of a constantly growing number of WWLLN stations the number of WWLLN strokes detected increases with time due to improvements in the network and the detection efficiency As a result long term tracking of stroke rate cannot be used without deconvolving detection efficiency improvements However thunderstorm counts have remained relatively constant while stroke rate has increased WWLLN has been capable of detecting almost every thunderstorm since 2005 Jacobson et al 2006 In Figure 7 7a the daily average 98 30 minute thunderstorm counts black are plotted alongside the daily average stroke rate red It can been seen that the stroke rate has increased relatively steadily while the thunderstorm count has remained relatively stable Jul Jan Jul Jan Jul Jan b 2010 2011 2012 2013 1000 800 600 400 200 0 1 4 7 10 13 16 19 22 25 28 c 2011 June 300 10 8 6 4 2 0 10 8 6 4 2 0 Stroke Rate 1 s Thunderstorm Counts a 1000 800 600 400 200 0 6 250 5 200 4 150 0 3 6 9 12 15 18 21 2011 June 15 Thunderstorm Counts Stroke Rate 3 Figure 7 7: Variation in WWLLN thunderstorm count black and stroke rate red for: a daily averages 30 minute counts from 2010 June 2013 June b 30 minute counts from 2011 June 01 30 c 5 minute counts from 2011 June 15 00 23 UTC The daily average thunderstorm count remains relatively constant during 2010 2013 while the stroke rate increases during the same time span The thunderstorm count increased an average of 3% per year while the stroke had a much higher yearly increase of 13% Similarly 90% of the daily thunderstorm averages are within 20% of the mean for the three years Previous work has suggested that changes in climate will cause a change in global thunderstorm behavior Williams 2005 Price 2009 During 2010 2013 the average 99 global surface temperature and thunderstorm count have both remained relatively constant Hansen et al 2013 but future changes in global temperature may be reflected in the global average thunderstorm count Figure 7 8 shows that the typical diurnal behavior of Figure 7 5 emerges only after long term averaging When examining the thunderstorm counts on a monthly scale Figure 7 8 dot-dash line the long term average begins to emerge while over a single day Figure 7 8 dashed line the expected diurnal behavior is missing Similarly on the daily scale of Figure 7 7c it can be seen clearly that stroke rate does not follow thunderstorm counts as located by WWLLN Despite the short time scale variation the overall average of the data still accurately reproduces the expected global thunderstorm activity in Figure 7 5 With such short time scale variations global observations of the global electric circuit source mechanism be it with ground lightning networks or several geostationary satellites need to occur along with an accurate measure of the return current to better understand the charging of the global electric circuit Thunderstorm Counts 900 700 500 0 3 6 9 12 15 Hour UTC 18 21 2010 June 2013 June 2011 June 2011 June 15 Figure 7 8: Diurnal UTC variation in WWLLN 30 minute thunderstorm count for: multiyear average of Figure 7 7a solid line monthly average of Figure 7 7b dot-dash line and 30 minute averages of Figure 7 7c dashed line 7 6 Global Electric Circuit Thunderstorm Contribution With the WWLLN thunderstorm clusters a simple model is made to estimate the total contribution of thunderstorms and electrified storm clouds to the global electric circuit 100 Mach et al 2011 considered LIS OTD observed land thunderstorms with less than 1 7 flashes min 1 and ocean thunderstorms with less than 0 33 flashes min 1 electrified storm clouds For an average storm duration of 15 minutes these cutoffs are 26 flashes for land and 5 flashes for oceanic electrified storm clouds ESCs With a WWLLN-LIS OTD detection efficiency of 6 4% over land and 17% over oceans Rudlosky and Shea 2013 WWLLN would expect cutoffs of 2 strokes per thunderstorm over land and 1 stroke per thunderstorm over oceans Given the clustering parameters used in this work requires a minimum of 2 strokes to be considered a thunderstorm every un-clustered WWLLN stroke is considered a single ESC The daily average of thunderstorms and ESCs observed by WWLLN are shown in Figure 7 9a Since not all ESC will produce lightning the counts shown in Figure 7 9a should be considered a low estimate Counts a 600 400 200 b 0 3 6 0 3 6 9 12 15 18 21 Current A 1200 800 400 0 Total 9 12 15 18 21 Hour UTC Land Ocean Land ESC Ocean ESC Figure 7 9: A simple model of the total global electric circuit current with contributions from land thunderstorms green solid oceanic thunderstorms blue solid land electrified storm clouds green dashed and oceanic electrified storm clouds blue dashed a shows the counts for each group and b the current contribution to the total black line 101 The average thunderstorm and ESC current contribution is taken from the overflight data of Mach et al 2010 Average current contribution for land thunderstorms is 1 0 A for oceanic thunderstorms 1 7 A for land ESCs 0 41 A and for oceanic ESCs 0 13 A The total current for each contributor and the total current is shown in Figure 7 9b The average thunderstorm current is found to be 1090 70 A with a total peak-to-peak variability of 24% The largest contributor are oceanic thunderstorms 47% with 510 10 A followed by land thunderstorms 32% with 350 70 A overall ESCs contribute 21% to the thunderstorm global circuit current With a similar model based on the TRMM LIS OTD data Mach et al 2011 found ocean thunderstorms contribute 32% and land thunderstorms 55% with a total ESC contribution of 13% to the total mean current of 2 04 kA Their difference in current and contributing fraction stems from an increased count of land thunderstorms This highlights a shortcoming of this simple model: land thunderstorms tend to be larger than oceanic storms thunderstorm area should be taken into account along with overall counts However to validate any global circuit model a comparison needs to be made with simultaneous fair weather return current measurements in order to constrain the models 7 7 Conclusion Global thunderstorm count is a good measure of global electric circuit activity and for a simple model of the circuit the location and size of thunderstorms is necessary along with totals to create a more accurate model of the real time fair weather return current WWLLN strokes are successfully clustered into thunderstorms using the DBSCAN clustering algorithm with appropriately chosen clustering parameters The clustered thunderstorms were compared against the TRMM Precipitation Radar and a case study of thunderstorm tracking and evolution When the three years of WWLLN data were averaged the diurnal behavior of global thunderstorm activity aligned with the expected behavior of both thunderstorms and the fair weather return current The results of global thunderstorm and electrified storm cloud activity are combined with upward thunderstorm current averages to create an estimate of the fair weather return current The model found an average thunderstorm current contribution of 1090 70 A This and future estimates of the current can 102 be validated against an accurate fair weather return current measurement Acknowledgments for this Chapter The TRMM data used in this effort were acquired as part of the activities of NASA s Science Mission Directorate and are archived and distributed by the Goddard Earth Sciences GES Data and Information Services Center DISC 103 Chapter 8 THUNDERSTORMS AND FLASHES 104 8 1 Overview Application of clustering algorithms to ground based lightning detection networks expands the real time global observations of lightning from strokes to flashes and strokes to thunderstorms Lightning detection networks such as WWLLN or ENTLN are then able to identify locate and analyze nearly every active thunderstorms within their operational range Global thunderstorm information allows for research into the climatological structures of thunderstorm behavior on large spatial and temporal scales Flash clustering allows for new network diagnostics such as flash multiplicity and thunderstorm detection efficiency The DBSCAN algorithm is used to cluster strokes to flashes and thunderstorms for both the WWLLN and ENTLN Cross validation of the networks is performed with the located thunderstorms and comparisons of their inferred areas and duration Overall WWLLN detects 61% of all ENTLN thunderstorm clusters and 80% of thunderstorms larger than 103 km2 In the reverse analysis ENTLN detection of WWLLN thunderstorms ENTLN detects 86% of all WWLLN thunderstorms over North America On average WWLLN observes thunderstorm clusters lasting 10 minutes and spanning 66 km2 ENTLN observes averages of 10 minutes and 60 km2 Within thunderstorms the average time between flashes is 21 seconds as seen by WWLLN and 10 seconds by ENTLN with a strong dependence on season Clustering algorithms applied to lightning detection networks allow for a new range of analysis from thunderstorm effects network performances to the links between lightning and thunderstorms properties Lightning network detection efficiency is often measured in terms of relative stroke or flash performance through pair-wise comparisons of different systems For example comparing two ground based networks Abarca et al 2010 a ground based network with a satellite Chapter 4 Rudlosky and Shea 2013 or a network to an actual ground truth such as rocket-and-wire triggered lightning Nag et al 2011 In some cases such as examining the global electric circuit Hutchins et al 2014 Chapter 7 it is the location and properties of the thunderstorms generating the lightning that are important The thunderstorm detection efficiency for a lightning location system is then important in these applications both the location duration and extent of the thunderstorm 105 Within known thunderstorms the time between successive flashes can be used to examine further properties of the thunderstorm such as charging rate controls on lightning strength life cycle and dynamics of the thunderstorm Zoghzoghy et al 2013 examined the effect of the time between flashes as a measure of thunderstorm discharging in terms of the supression of future flashes Zipser 1994 examined the relation between the flash rate in a thunderstorm with the updraft velocities which in turn are controlled by the differential surface heating below the thunderstorm Only after considering and validating the performance of lightning detection networks can the effects of a flash be directly related to properties and behaviors of the parent thunderstorm Inferring thunderstorm properties based on the observed lightning flash rates can benefit regions with low availability of direct or continuous observations e g radar over oceans 8 2 Data The global WWLLN data will be used everywhere in this work unless specifically restricted to a given region the ENTLN data used will only be the North American subset of the data The data are from 2011 and 2012 with the exception of Section 8 5 which extends through June 2013 8 3 Methods Clustering the located strokes of both networks provides the thunderstorm and flash data The clustering is performed with the DBSCAN algorithm Ester et al 1996 Kriegel et al 2011 following the application methodology discussed in Chapter 7 Hutchins et al 2014 DBSCAN is used over other clustering methods as it clusters based on the spatial and temporal distance between strokes with robust handling of noise e g nearby thunderstorms The flash clustering uses the same algorithm as the thunderstorm clustering with adjustment of the spatial and temporal clustering parameters For thunderstorms WWLLN strokes are clustered together if they occur within 0 5 and 18 minutes for ENTLN it is 0 25 and 15 minutes The tighter restraints on the ENTLN clustering stem from the increased network performance of by ENTLN compared to WWLLN notably a better location accuracy 1 km compared to 5 km For flash 106 clustering the strokes of both networks are clustered if they are within 0 12 and 1 second of each other the 1 second timing is based on the natural inflection point observed in the WWLLN data see Figure 8 6 in Section 8 5 The thunderstorm area is estimated by the best fit ellipse encapsulating all of the strokes in the cluster This will not be the areal extent of the thunderstorm system rather just the electrified lightning region of the thunderstorm Similarly thunderstorm duration is taken to be the time from the first stroke in a thunderstorm cluster to the last With these thunderstorm clustering parameters both networks observe similar average thunderstorm size and durations over North America WWLLN observes a median area and duration of 66 km2 and 10 minutes while ENTLN observes an average of 60 km2 and 10 minutes Two parameters used throughout this chapter are the times between successive strokes or flashes This interstroke time will refer to the time since the previous stroke in the parent thunderstorm cluster interflash time will refer to the time since the start of the previous flash in the thunderstorm cluster When discussing interflash time in relation to flash energy or peak current the values refer to the strength of the second flash 8 4 Detection Efficiency The WWLLN thunderstorm detection efficiency is examined by comparing the located thunderstorm clusters with those located by ENTLN ENTLN does not have 100% detection efficiency of strokes it is used as a readily available baseline to compare to as a nominal ground truth for WWLLN Two thunderstorm clusters are considered to be matches if the convex hull of their constituent strokes overlap to within 5 km and 5 minutes Using a convex hull method requires at least three strokes in a thunderstorm for it be considered a match this creates an artificially lower detection efficiency for WWLLN for the cases where only 1 2 strokes are detected in a thunderstorm Over the 2011 2012 period in North America the average thunderstorm detection efficiency of WWLLN compared to ENTLN was 61% while ENTLN has a detection efficiency of WWLLN of 86% Similar to how detection efficiency varies with stroke strength WWLLN has a higher detection efficiency of larger thunderstorms than smaller ones The spatial distribution of the detection efficiency is shown in Figure 8 1 In the southern regions 107 where there is typically higher thunderstorm activity WWLLN has a detection efficiency above 70% In regions with few thunderstorms e g the West there is a lower detection efficiency possibly due to a lower detection efficiency of both networks in that region 50 40 30 20 DJF 50 -120 -100 50 40 40 30 30 20 -120 50 -100 JJA -80 -60 20 40 30 30 -120 0 -100 10 -80 20 -60 20 -60 MAM -120 -100 SON -80 -60 -120 -100 -80 -60 50 40 20 -80 30 40 50 60 70 Thunderstorm Detection Efficiency % 80 90 100 Figure 8 1: WWLLN detection efficiency of ENTLN thunderstorms over North America for 2011 2012 top panel with each season broken out in the lower panels The seasonal behavior shows a similar overall distribution of detection efficiency with an overall increase in winter DJF and spring MAM compared to summer JJA and fall SON A winter increase 68% compared to 56% in summer is tied to the decreased occur- 108 rence of thunderstorms during the cold season On a regional scale a decrease in activity allows for the networks to lower their detection thresholds and increase the sensitivity of the nearby stations In all seasons WWLLN has the highest detection efficiency over the oceans Increased detection efficiency at the limits of the ETNLN detection range e g in the center of the Atlantic Ocean is convolved with the decreased efficiency of ENTLN and not solely an increase in the WWLLN detection efficiency The daily spatially averaged detection efficiency is shown in Figure 8 2 Here the seasonal variation is evident the high variation in the winter reflects the lower overall thunderstorm counts during these months With fewer lightning strokes and thunderstorms during the winter both networks are able to lower the detection threshold at the nearby stations and increase their detection sensitivity The annual variation in detection efficiency is imprinted on the dependence of detection efficiency with thunderstorm area size and duration the relative scale and behavior of the annual signal is seen in every other detection efficiency Detection Efficiency % relation 100 50 0 3 6 9 2011 12 3 6 9 2012 12 Figure 8 2: Spatially averaged detection efficiency of ENTLN thunderstorms over North America The temporal distribution of thunderstorm detection efficiency can be split into different thunderstorm sizes Figure 8 3a total counts Figure 8 3b and durations Figure 8 3c The daily detection efficiency increases for larger productive and longer thunderstorms For thunderstorms larger than 102 km2 the detection efficiency is 53% while for those larger than 103 km2 it is 80% In a similar vein thunderstorms with more than 102 strokes are 109 detected with 75% efficiency and for more than 103 strokes at 94% efficiency Almost all thunderstorms observed are less than 1 hour in duration Figure 8 3c right for those lasting more than 2 hours the detection efficiency increases to 93% a 100 50 6 9 2011 12 3 6 9 2012 12 50 0 3 12 3 6 9 2012 12 1 10 102 103 104 105 106 Area km2 60 40 20 0 1 10 102 103 104 105 Stroke Counts 40 20 3 6 9 2011 12 3 6 9 2012 12 0 105 1 10 102 103 60 50 0 104 0 1 2 3 4 5 6 7 8 Duration hours 104 1 2 3 4 5 6 7 8 Duration hours c 100 6 9 2011 Counts x1000 b 100 3 103 Stroke Counts Detection Efficiency % 0 1 10 102 Area km2 8 6 4 2 0 Figure 8 3: Temporal variation in thunderstorm detection efficiency for different thunderstorm sizes: a thunderstorm area b thunderstorm stroke counts and c thunderstorm duration The distribution of thunderstorms for each parameter is shown in the right panels Removing the temporal variation demonstrates the trend of increasing detection efficiency for each thunderstorm parameter In Figure 8 4 the black lines represent all thunderstorms and the colored lines split the thunderstorms by total counts detected by WWLLN in these thunderstorms Thunderstorm area Figure 8 4a shows a gradual increase in detection efficiency from 40% to near 100% efficiency above 103 km2 the total number of 110 strokes does not have an independent effect from area of the thunderstorm Similarly the longer a thunderstorm is active the more likely it is to be detected by WWLLN shown in Figure 8 4c On short time scales the thunderstorm detection efficiency is lower than the previous estimates of Jacobson et al 2006 but for thunderstorms lasting more than 1 hour the average detection efficiency is 91% Unlike area duration is convolved with the lightning count of the thunderstorm: smaller thunderstorms have lower detection efficiency regardless of duration and larger thunderstorms are easier to detect a 100 50 Detection Efficiency % 0 1 b 100 10 102 103 104 105 Thunderstorm Area km2 106 50 0 c 100 0 1 2 3 4 5 6 7 8 Thunderstorm Duration hours 50 0 1 10 102 103 104 Thunderstorm Stroke Count 105 Figure 8 4: Thunderstorm detection efficiency for different thunderstorm a areas b stroke counts and c durations Area and duration plots are shown with the overall average black and for different total stroke counts colors within the thunderstorms Matching thunderstorms between the networks shows the overall performance of the 111 networks but not how the characteristics of the thunderstorms agree between the two networks If the thunderstorm clusters are capturing intrinsic properties of the thunderstorms independent of the overall detection efficiency then the properties should be same between both networks For example if WWLLN measures a thunderstorm cluster to have an area of 66 km2 with 50 strokes and ENTLN measures an area of 60 km2 with 200 strokes it can be said that both measure the actual estimated area of that thunderstorm cluster The properties of the matched thunderstorm between WWLLN and ENTLN can be directly compared for thunderstorm area and duration Density plots of the two networks estimation for each matched thunderstorm are shown in Figure 8 5 the counts in each bin are displayed on a log scale Each characteristics in Figure 8 5 shows a strong distribution along a single 1-to-1 line Area Figure 8 5a has good agreement between both networks with 46% of matches within 25% of each other there is increased deviation for smaller thunderstorms compared to larger ones The WWLLN overestimation compared to ENTLN thunderstorm area may be caused by incorrect matches or accidental merging between two thunderstorm clusters The thunderstorm duration has the stronger relation of the two parameters with 33% of matches falling within 25% of the 1-to-1 line There is fairly good agreement between the two networks on thunderstorm properties despite the differences in overall detection efficiency The overall detection efficiency of WWLLN for ENTLN thunderstorms is lower than previous estimates of the networks thunderstorm detection performance on the order of 90% Jacobson et al 2006 in this case it likely stems from only 67% of WWLLN strokes clustered into thunderstorms The remaining 33% of total strokes would increase the overall detection efficiency of thunderstorms for the cases where only 1 2 WWLLN strokes match ENTLN thunderstorms In contrast ENTLN had 96% of strokes clustered into thunderstorms due in part to the higher overall efficiency of the network The identified WWLLN thunderstorms exhibited similar characteristics to their corresponding ENTLN thunderstorms 112 a b ENTLN Duration hours ENTLN Area km2 106 105 104 103 10 2 10 1 1 10 102 103 104 105 106 WWLLN Area km2 1 10 6 5 4 3 2 1 0 0 1 2 3 4 5 6 WWLLN Duration hours 102 Matches per Bin 103 104 Figure 8 5: Thunderstorm comparison of matched thunderstorms for WWLLN and ENTLN for a area and b duration Note: the density levels are on a log scale 8 5 Flash Clusters Within a thunderstorm cluster lightning detection networks are able to measure two additional properties: the interstroke and interflash timing The full WWLLN interstroke time Figure 8 6a shows two distinct peaks: one at 40 ms and another at 100 seconds with a clear minima at 1 second With ENTLN the interstroke distribution does not show the same distinct peaks Figure 8 6c because it is able to locate more strokes in each flash the tail of the interstroke time distribution overlaps the interflash time distribution In the WWLLN interevent time distribution there is a spike of events near 10 s shown as points caused by the same event recorded twice by the network this also occurs less frequently with ENTLN After the network events are clustered into flashes the time distributions can be split into the time between strokes in the same flash black and time between flashes blue shown in Figure 8 6b and 8 6d The stroke and flash distributions can be fit as lognormal distributions for each day of the year an example set of fits is shown with the dashed 113 Counts 106 10 8 6 4 2 0 10-5 10-4 10-3 10-2 10-1 1 10 102 103 104 b Counts 106 10 8 6 4 2 0 10-5 10-4 10-3 10-2 10-1 1 10 102 103 104 Time seconds Interstroke Counts 107 c 2 1 0 10-5 10-4 10-3 10-2 10-1 1 10 102 103 104 d Counts 107 a 2 1 0 10-5 10-4 10-3 10-2 10-1 1 10 102 103 104 Time seconds Interflash Figure 8 6: The inter-event times for WWLLN a and ENTLN c and the interstroke black and interflash blue time distributions for WWLLN b and ENTLN d The dashed lines correspond to the best lognormal fits of the distributions There are 20 logarithmically spaced bins per decade lines in Figure 8 6b and 8 6d This fitting allows for the daily tracking of the interstroke Figure 8 7a and interflash Figure 8 7b times for both networks With WWLLN the global distributions black remain relatively centered at 71 ms and 100 seconds over North America WWLLN averages blue are 60 ms for interstroke and 39 seconds for interflash times ENTLN red has lower daily averages of 53 ms and 17 seconds due to detecting more strokes within each thunderstorm The North American WWLLN distribution more closely matches the seasonal behavior present in the ENTLN distribution with a small offset in timing the average daily offset in interflash timing is 14 seconds with WWLLN detecting flashes further apart than ENTLN The longer interflash time is directly related to the detection efficiency of both networks with the longer WWLLN interflash time reflecting the lower detection efficiency of the network a b 103 1 0 1 0 01 1 4 7 10 1 2011 4 7 10 1 2012 WWLLN 4 7 2013 Peak Location sec Peak Location sec 114 102 10 1 1 4 7 10 1 2011 WWLLN North America 4 7 10 1 2012 ENTLN 4 7 2013 Figure 8 7: Peak of interstroke a and interflash b times for WWLLN black WWLLN over North America blue and ENTLN red Points beyond 2th and 98th percentiles shown as dots for WWLLN North America and ENTLN Directly comparing the time evolution of a thunderstorm will not work with thunderstorms of differing durations To account for this the thunderstorm life cycle is normalized by the duration of the thunderstorm Each thunderstorm is broken into 9 time segments where the first flash in the thunderstorm is at time 1 and the last flash at time 9 With this normalization the average interflash time is found at each step for all thunderstorm clusters located by the two networks shown in black in Figure 8 8 The interflash time can be seen to decrease to the center of a thunderstorms life cycle before increasing at the end this is consistent with the known life cycle of a thunderstorm Peckham et al 1984 Rakov and Uman 2003 The interflash time for different energy Figure 8 8a and absolute peak current Figure 8 8b deciles are also shown energy and peak current from the second flash The interflash values shown are the median values of the interflash distribution e g Figure 8 6c blue with median absolute deviations of 74% for WWLLN and 98% for ENTLN All flashes follow the same behavior regardless of energy or peak current however there are offsets in interflash time for different strength strokes As seen with WWLLN Figure 8 8a the interflash time increases for more energetic strokes for ENTLN Figure 8 8b the interflash time increases for absolute peak current Between normalized time 1 and 5 Interflash time s 115 a b 40 40 30 30 20 20 10 10 0 1 2 3 4 5 6 7 8 Normalized Time 9 0 1 Percentile 2 3 4 5 6 7 8 Normalized Time 9 0 10 20 30 40 50 60 70 80 90 All Figure 8 8: The interflash time since the previous flash for time-normalized thunderstorms for WWLLN a and ENTLN b with times shown for all flashes black and by stroke strength decile bins WWLLN strength is divided by flash energy and ENTLN by absolute peak current of the second flash the interflash time for the 90th percentile and above stroke strengths decreases by 21% for WWLLN and 11% for ENTLN compared to the median interflash time This shows that longer times between flashes is associated with stronger flashes more charge separation can occur in the thunderstorm resulting in the stronger flashes In Figure 8 8 the separation between different flash strengths is consistent at all points in the thunderstorm life cycle It is not a constant offset but increases at the weaker stages of the thunderstorm beginning and end where longer time is necessary for a stronger flash caused by a decreased charge separation rate The time between flashes is a parameter associated with the strength of the resulting flash 8 6 Conclusion When compared to ENTLN WWLLN performs better when detecting large and active thunderstorm regions The lower performance for smaller thunderstorm clusters may be due to the cutoff in the clustering that requires at least 3 strokes for a cluster removing 39% of strokes from the analysis Including these strokes would lead to less robust matches between 116 the networks and conflate a stroke to thunderstorm detection efficiency and the thunderstorm to thunderstorm detection efficiency For the thunderstorms WWLLN does detect the characteristics of the thunderstorm are on par with those of ENTLN As WWLLN does not detect every ENTLN thunderstorm ENTLN does not detect every WWLLN thunderstorm So assuming ENTLN as a ground-truth leads to lower estimates of the WWLLN performance as ENTLN only detects 86% of WWLLN thunderstorms On a global scale there is little change in the time between successive strokes and flashes within thunderstorms but locally there are strong seasonal variations Both ENTLN and WWLLN observed the same seasonal variation in North America with a small offset in their times possibly due to the general detection efficiency differences in the networks The seasonal behavior shows a decrease in interflash times from the end of winter to the beginning of summer thunderstorms in these times have higher flash rates compared to thunderstorms during the rest of the year The charging rate for thunderstorms evolves through the lifecycle of the thunderstorm with the highest lighting flash rate during the middle of a thunderstorm The observed change in interflash time reflects the changes in the charging rate of the thunderstorm the resulting flash strength depends on the charging rate and the total time charging between flashes If charging rate was constant with time then flash strength would be constant with interflash time through the life of a thunderstorm For a given thunderstorm the flash strength depends in part on the time since the previous flash and the current convective activity of the thunderstorm 117 Chapter 9 CONCLUSION AND FUTURE WORK 118 My work in this dissertation started with the WWLLN producing only lightning stroke locations and uncalibrated RMS energy values of the detected strokes To enable new and extended analysis with the dataset I developed techniques to measure the energy per stroke model the relative detection efficiency of the network and cluster lightning into flashes and thunderstorms To prove and validate the new techniques they were applied to problems and questions that have only been addressed with limited extent or duration the new techniques allowed for broader longer and more detailed analysis The new analysis were: an examination of the difference between continental and oceanic thunderstorm energies the dependence of VLF propagation on magnetic azimuth a model of the thunderstorm contribution to the global electric circuit and an analysis of observed thunderstorm and flash properties These analysis were made using WWLLN by itself or in conjunction with other lightning detection systems Most of the research completed here naturally leads to future projects and research avenues that can be explored in the context of this work Several of the possibilities for research with WWLLN are: network characterization thunderstorms the global electric circuit and other lightning processes are discussed in this chapter 9 1 WWLLN Characterization The relative detection efficiency model developed in Chapter 3 provides one view of the WWLLN network performance but it relies on several assumptions Either the model can be advanced to not rely on these assumptions or those assumptions themselves can be directly monitored The main assumption is that the distribution of lightning energy is the same everywhere this was seen not to hold in Chapter 5 between land and oceanic thunderstorms The model can take into account the varying energy distributions or the expected variance through the variability of the observed regional energy distributions over time A promising method for examining the energy detection efficiency is to check how the measured energy values change when the station configuration changes For example processing the energy data after artificially removing a few stations to quantify how the energy distributions change Compare the two energy distributions to the change in detection ef- 119 ficiency relative to a reference network e g ENTLN or LIS to better parameterize the model Similarly the accuracy of the energy measurements themselves can be improved by adapting the energy per stroke processing to include multiple well calibrated WWLLN stations In the processing described in this work the entire network calibration is bootstrapped from one station the addition of a second well calibrated station can improve the energy measurements and help quantify the regional variation in energy uncertainty This can address the uncertainty that is introduced in the station calibrations for stations far from the first station Finally other network characterizations can be developed based on the clustering results The number of thunderstorms the average number of strokes per thunderstorm average flash multiplicity or time between flashes within a single thunderstorm can be routinely monitored for network health 9 2 Thunderstorms 9 2 1 Cluster Validation The thunderstorm clustering discussed in Chapter 7 and 8 can benefit from additional validation Two potential methods for validation are large scale comparisons to TRMM precipitation rates and case studies against regional weather radars The TRMM comparison would require grouping of the precipitation data to compare to the estimated thunderstorm extents Weather radar comparisons would provide detailed ground truth of the thunderstorm cluster areas and durations further weather radar would allow for a measure of thunderstorm tracking accuracy Aside from comparisons to other systems the properties measured by the thunderstorm clustering can be tracked over spatial and temporal scales For example: the average thunderstorm duration interannual variability in a given region or the overall network observed thunderstorm area This can explore the changes in the clustering values and accuracy as the stroke rate detected by WWLLN changes with time 120 9 2 2 Parameterization Thunderstorm parameterizations are functional relationships between different properties of thunderstorms Using lightning detection networks allows for the development of these relationships that infer thunderstorm properties based on the observed lightning flash rates of particular benefit for regions with low availability of direct observations e g radar satellite Zipser 1994 examined the relation between the flash rate in a thunderstorm with the updraft velocities which in turn are controlled by the differential surface heating below the thunderstorm Parameterization of flash rate based on other observations has led to simple models of global lightning behaviour Price and Rind 1992 used cloud height parameterization for flash rate These empirical parameterizations can help in the development and validation of models e g Baker et al 1999 of thunderstorm electrification and enable or expand prediction of the global electric circuit NOx production and weather forecasting Investigating the parameterization of lightning behavior in relation to the properties of a thunderstorm on a large scale can create better and more robust parameterizations The WWLLN thunderstorm clustering can be compared to other networks and systems in order to develop and validate new parameterizations 9 2 3 Thunderstorm Properties The WWLLN thunderstorm clustering can be used to investigate global and regional thunderstorm properties and their distributions Thunderstorm area and duration are briefly discussed in Chapter 8 but can be explored in more depth and in more regions These two properties can be measured over different spatial and temporal scales For example the distribution of winter thunderstorms over the Sea of Japan Ishii et al 2010 or the South American green ocean phenoma Williams and Stanfill 2002 Alternatively more complex measures of thunderstorms can be developed: the average stroke count per thunderstorm the peak flash rate or the electrical activity The electrical activity can be measured as the total flash energy per unit area per unit time for the thunderstorm: the sum of measured flash energies within the thunderstorm This measure and others may be highly dependent on the network performance or may not be absolutely 121 calibrated however they can still allow for relative comparisons between thunderstorms in a limited temporal or spatial scope e g North America in July 2013 The thunderstorm dataset can also be advanced by classifying thunderstorms into different thunderstorm types While this may only work for small case studies it may be possible to use more advanced machine learning classifiers to automatically assign cloud types to thunderstorm clusters 9 3 Global Electric circuit The global electric circuit model presented in Chapter 7 provides an estimate of the thunderstorm contribution to the circuit based on the WWLLN thunderstorm clusters It is shown that the model is able to reproduce the expected Carnegie curve over long time scales and has the capability to provide current estimates on shorter time scales The model can be improved for a more accurate measure of the current contribution but without any validation it cannot be reliably used To improve the model there are several underlying assumptions that can be factored in The main one is that all thunderstorms produce the same upward current to the ionosphere regardless of their size or activity The estimates used in the model from Mach et al 2010 can be scaled by either the thunderstorm cluster activity or the estimated cluster size Since the development of the model the thunderstorm cluster area was validated against ENTLN in Chapter 8 giving confidence to the area measurements The second assumption is that WWLLN detects on the order of 90% of all thunderstorms an assumption explored in Chapter 8 The third assumption is that all thunderstorm currents are the same everywhere This assumption is harder to address as it relies on direct measurements of the current made in different regions Regardless of the model improvements made the model needs to be compared against a ground truth measurement Further comparison to a ground truth will allow for tuning of the model to better fit the observed measurements or if adjustments cannot be made then other components of the global electric circuit need to be included in the model For the ground truth a balloon campaign needs to be conducted to measure the fair weather return current over the span of one to several weeks With a reliable and clean measurements of 122 the return current the model can be validated on a very short time scale instead of relying on long term averages 9 4 Other Lightning Processes WWLLN is able to measure and detect more than just the main discharge of a lightning stroke The network is able to directly detect terrestrial gamma-ray flashes TGF and their related strokes it is also able to detect whistler waves at the individual stations For TGFs WWLLN has been used to geolocate the TGF itself and the originating thunderstorm Connaughton et al 2010 2013 WWLLN can be used to create an estimate of the global TGF 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data files summarized in Table A 1 The example filenames given in the table are for 31 December 2013 5:10 UTC Most of the file types with exception of WB-files are located on flashfile on wd1 wwlln Each file type has it s own directory denoted Afiles AEfiles etc with flat file structures except for R-files R-files due to the large number generated are broken into yearly and monthly folders of the form: Rfiles R YYYY R YYYY MM Some but not all of the WWLLN data file directories have been copied to the other flashes on a need-basis and so the other flashes should not be considered a backup of the flashfile dataset An example line from each of the R A AP and AE files are given below with descriptors for each file R-files are the simplest with each line containing three columns: 10 3000 015563 2668 The first number is the station ID the second is the seconds from the start of the hour and the last is the root integrated square electric field at the station in uncalibrated sound card units For A-files each line if of the form: 2013 01 31 16:18:54 103460 9 0621 -117 8276 19 9 9 The first six numbers are the date YYYY MM DD and UTC time of the stroke hh mm ss The next two are the stroke location in degrees north latitude and east longitude The final two are the timing uncertainty in microseconds and the number of WWLLN stations that participated in the stroke location AP-files are similar to A-files with additional information after the stroke location: 2013 02 12 00:00:07 142335 -10 4622 26 453 53 225 64 2263 20 0863 13 4 5 17 600 19 2084 139 Table A 1: WWLLN Data Types File Type Name Description R-files R20121231051000 Raw packets sent by stations A-files A20121231 loc Lightning locations generated in real time AP-files AP20121231 loc Location data with station and E-field data of each stroke solution generated daily with relocate-B AE-files AE20121231 loc Location and stroke energy data generated daily by Bootstrap DE-files DE20121231 mat Relative detection efficiency maps as Matlab data S-files S201212310510 loc Waveform data for strokes located near a given station WB-files WB201212310510 dat Continuos wideband field data output by toga -r T-files T20131114 Single dat Station packet count record TCurrent dat is the current running record Starting at 17 600 are pairs of numbers that give the station ID 17 and the field strength 600 in sound card units the same value as in the R-files Finally AE-files are similar to A-files but with three additional numbers: 2013 2 12 00:00:07 142335 -10 4622 020 0863 13 4 5 448 86 114 87 4 The last three numbers correspond to the radiated VLF stroke energy in joules 448 86 the median absolute deviation of the energy value in joules 114 87 and the subset of stations that participated in the energy value solution 4 T-files are records of how many packets a given station sent to flash4 during the history of WWLLN Unlike the other files it is not automatically generated rather it is written whenever it is updated through the TfileUpdater m script in the functions git repository Each line contains the date in days since 01 01 0000 and the counts for each station 140 where column 2 corresponds to station 0 A 2 Code Repositories All of my code should be stored on flashfile at home mlhutch The operational code running every day is stored on flash5 at home mlhutch matlab bootstrap with a nonoperational copy on flashfile The exact details of where the energy processing code is located the necessary files and similar code for the relative detection efficiency processing is covered in Appendix B Aside from being stored in plaintext scripts all of the code is also stored in a Git repository located on flashfile: home mlhutch Git and hosted online on github com mlhutchins The Git repositories have the advantage of multiple back ups version control easily portable and easy to use A list of the WWLLN processing code and corresponding git repository is given in Table A 2 A basic primer on how to use git is given in Section A 3 online resources are also readily available Table A 2: Git Repositories flashfile: home mlhutch Git Code Repository Notes Energy Processing bootstrap git Requires process git and functions git LWPC lwpc git LWPC and Matlab implementation AP Processing process git Relocate files required for energy processing MATLAB Functions functions git Various Matlab functions required by other scripts SU Eagle Files eagle git Eagle files for WWLLN SU and Pre-amps includes Erin Lay s files Gumstix gumstix git Files for building and configuring Gumstix microSD cards 141 A 3 Git Primer Git http: git-scm com is an open source distributed version control system available on all operating systems with very little system resources required Most often git is accessed through the command line but there are many graphical interfaces available I chose git for my research and code since it allows easy branching constant backups locally and on remote servers and helps to organize code and projects A brief tutorial on git is available online: http: git-scm com book en Getting-Started and http: try github com Once git is installed on a host machine http: git-scm com apt-get install git or yum install git-core repositories can be downloaded with the command: git clone user server : repository This will copy clone the repository to the current directory as a folder of the same name as the repository For example to copy over the energy processing repository listed in Table A 2 to the matlab directory: cd matlab clone sferix flash5 ess washington edu: home mlhutch Git bootstrap git Where the user can be anyone with permission to access that directory More information on how to use git for source control instead of downloading the repositories can be found in the online resources A 4 Other Useful Matlab Code Some of the functions present in the functions git repository are very useful and often critical to the routine WWLLN processing The function terminator m is used to calculating the percentage of a VLF path that is in daylight and the percentage that is nighttime conditions It is written to take into a either a vector or scaler initial location time and end location The function vdist m is from the MathWorks file exchange and calculated the great circle distance between two points on the ellipsoidal Earth 142 Aside from these three functions there is a directory in the functions git repository dedicated to reading and writing WWLLN file types In the directory functions IO are a set of import functions to import A AP AE R T and DE files There are also functions to read and write tab delimited data the LWPC lookup tables described in Appendix B and WWLLN stations dat data All of these functions take in a given date and possibly time to find and load the desired file The file dataPath dat lists locations that the import functions check for the data folders of the particular file type The default is to look for either flashfile: wd1 wwlln or wd2 drives but other locations can be added to this list as needed 143 Appendix B ENERGY PROCESSING 144 The process for bootstrap calibrating the WWLLN stations and how the energy is calculated is described in Hutchins et al 2012b This section walks through the code used in the processing along with the decisions behind various checks and adjustments made in the processing B 1 Code Summary There are 8 main sections to the bootstrap processing: Process R-files into AP-files Calculate LWPC attenuation coefficients for each stroke-station pair Bootstrap calibrate the network Calculate stroke energy using LWPC and calibration Iterative re-calibrate the network Final energy calculation Run Relative Detection Efficiency Model Move files to storage locations This processing requires several files locations given relative to ml- hutch flash5 ess washington edu Process relocate-B31Jan2013 x86-64 James Brundell s relocate program used to process R-files into AP-files this version compiled for Linux 64-bit systems stations dat list of current WWLLN stations copied over from flash4 at the start every processing run 145 lwpcv21 directory containing a working compiled version of the LWPC code Used in generating new lookup tables as stations are added a parallelized matlab implementation is discussed below Provided as a sub-module of the Bootstrap directory matlab Bootstrap directory containing the necessary matlab files available as a git directory see Appendix A matlab functions directory of necessary matlab functions used by the Bootstrap code files also available as a git directory see Appendix A B 2 LWPC The Long Wave Propagation Capability code is a codebase developed by Ferguson 1998 that is used to calculated the electric field at a given location for a VLF transmitter at another location For the WWLLN energy processing it is used to estimate the attenuation between a stroke treated as a transmitter and a station The original LWPC code has been altered in two ways: first the Windows-compiler specific code has been replaced with GCC compilable code second all warning have been removed to produce output of a constant shape for reading into MATLAB All edits in the source code have been marked by my initials of MH B 2 1 Compiling To recompile LWPC two bash scripts need to be run The first is BuildData cmd BuildData recompiles the data files that contain the surface parameters such as ground conductivity and coastlines The second step is to run buildlwpc cmd this should compile the program and result in an executable called LWPC To test a successful compile run the script run bench cmd if it runs successfully it is compiled if not consult the Readme Unix txt file that has some common troubleshooting steps The last step in setting up LWPC is to set the lwpcDAT loc file to point towards the data folder 146 B 2 2 Running LWPC is run from the command line with the structure: LWPC test1 inp Where test1 inp is formatted as per the structure in User manual pdf The matlab implemtations discussed below automatically generate formatted input files The result of running LWPC is an output file the specifies the electric field at various distance along the path from the transmitter to receiver It is also capable of outputting plots azimuthal dependence and many other features not utilized in this research B 2 3 Matlab Function A matlab implementation of LWPC is available as a git repository see Appendix A This implantation allows for LWPC to called in matlab with: LWPCpar freq lat long time stat_lat stat_long model Where freq is the transmitter frequency lat long is the transmitter location time is the date and time stat lat stat long are the receiver locations and model is the ionospheric model used If model is set to time then day and night is considered in the calculation if it is set to day or night an all day or all night ionosphere will be used LWPCpar as the advantage of being runnable within matlab parallelized loops parfor While LWPC itself cannot be run in parallel this method simply copies the LWPC directory to allow each matlab instance it s own copy B 3 Lookup Tables While LWPC can be parallelized it is still too slow to run faster than realtime for WWLLN processing As a result two sets of lookup tables are generated for each station with the pre-calculated LWPC electric field values The lookup tables are part of the main Bootstrap directory under the names lookup day dat and lookup night dat Each of these files are tab-delimited text with 147 the format given in Table B 1 The tables list the electric field measured the the station given a 100 kW transmitter in each grid point on the globe The latest lookup tables are at a resolution of 2 Station Name Station North Latitude Station East Longitude E-field at -179 89 E-field at -178 89 E-field at -177 89 E-field at -179 88 E-field at -178 88 E-field at -177 88 E-field at -179 87 E-field at -178 87 E-field at -177 87 Table B 1: Format for lookup day dat and lookup night dat data files for a resolution of 1 An example of a lookup table for the all day ionosphere for Dunedin station is shown in Figure B 1 90 Latitude 60 30 0 -30 -60 -90 -180 -40 -120 -60 0 60 Longitude 120 -20 0 20 40 60 E field in dB above 1 V m 180 80 Figure B 1: Lookup table for an all day ionosphere for Dunedin station 148 B 3 1 Generation The LWPC lookup tables are generated automatically with the matlab script Bootstrap Lookup automation m that is called at the start of the daily energy processing The script checks the current number of stations in the dat files and compares it to the most recent stations dat file If there are a new entries in the stations dat then the script proceeds to make the lookup tables The automatic script calculates the electric field at every grid point for 11 frequencies ranging from 8 kHz to 18 kHz and averages them together to add to the dat files The same script can be run for specific stations with the matlab lwpcpar lwpc generate m script Tables generated with either script can be validated with the matlab Bootstrap lookup validation m scipt This script checks each grid point to ensure there is a real number there sometimes LWPC generates errors for very specific locations If there is no valid electric field value at that spot it is reprocessed by offsetting the transmitter by a fraction of a degree B 4 Matlab Code The main matlab script to run the entire energy calculation process is Boostrap automation m This script: 1 Defines the dates to run in case past days need to be rerun 2 Sets the system path parameters from data path m 3 Updates stations dat and the lookup tables Lookup automation m 4 Generate the current AP-file with generate ap m 5 Calculate the energies and station calibrations using wwlln energy m 6 Generates the relative detection efficiency map with de mapper m 149 7 Calculates network statistics with network statistics m 8 Generate and amend T-files to TCurrent dat 9 Saves and archives all of the resulting data files In order to rerun lost days the only change necessary for Bootstrap automation is to change the rundate from: RUNDATE floor now - 1 to the day or dates that need to be rerun The LIVE variable and second part of the if clause is for rerunning previously processed data If LIVE is set to false then the script runs and stores in an alternative directory with a copy of the resulting calibration file For the case of restarting the script on the same day it failed to run no changes need to be made B 4 1 data path m It is important to correctly set up the data path m script Aside from the storage paths it is important to set how the script should obtain the stations dat and R-files from flash4 The transfer type can either be cp if the computer has flash4 network mounted or scp if passwordless scp is setup The r path flat variable determines whether the R-files are stored in one directory or with a hierarchal structure e g wd2 Rfiles R2013 R201304 R201304 Additionally the location of the bootstrap processing folder itself as well as the TOGA relocate script B 4 2 Lookup automation m The Lookup automation m script compares the current number of entries in the lookup day dat data file and compares it to the latest stations dat file If stations dat has new entries then the script generates the corresponding LWPC lookup tables for those new stations 150 Using the current lookup spatial resolution LWPCpar is called for each grid point at 11 frequencies 8 11 kHz for both day and night The 11 values in each grid point in dB are averaged together and added to the existing lookup data files This code takes about twelve hours to run using a single core due to calling the LWPC code The LWPCpar m function is set up to run in parallel it copies the LWPC code to new locations however the Lookup automation m script has not be parallelized B 4 3 generate ap m generate ap m copies over the R-files to the TOGA relocate folder and processes them with the -e flag This generate the normal WWLLN A-file structure with the addition of the participating stations and their RMS electric field values at the end of each line The RMS electric field as mentioned elsewhere is in the uncalibrated sound card units where the calibration is the main part of the wwlln energy m code The script ends with moving the new AP file and R-files to their storage locations B 4 4 wwlln energy m The wwlln energy m function runs the subfunctions described below in order to calculate the stroke energies Unless it is set otherwise which it should be the script sets the default master station to use to be Scott Base with the most recent calibration The master station is one with a known calibration that is used to bootstrap the calibrations for the rest of the network One future upgrade to the code would be the ability to include multiple master stations and combine their results for a better system-wide calibration The script also generates and saves two sets of station ratios The first is the station conversion file the values in this file give how to convert the sound card units at the master station to the sound card units at the other stations It is saved in the case that the master calibration requires a retroactive change The calibration file gives the values to convert from individual station sound card units to RMS electric-field values The station calibration incorporates both the actual station calibration and any environmental changes near the station 151 apply lwpc m applies the LWPC lookup tables to each sound card value in each strokestation pair The day and night lookup table values are weighted by the percent of the path in daytime and nighttime There is also a distance range restriction where only strokestation values between 1 and 8 Mm are calculated otherwise they are given a value of zero cross calibration m finds all strokes common to each pair of stations and uses them to create a conversion ratio between every pair of stations Only if the two stations have common strokes in all day paths and are within the same 1 8 Mm distance restriction The median value of every common stroke value is used as the resulting station-pair conversion ratios bootstrap m solves the connected graph of station-pair conversions to find the valid calibration paths from the master station to every other possible station There are two ways for a station to be added as a well calibrated station First it can have common strokes between itself and the master station this would result in a single hop conversion The second way is to be calibrated off of one of the previously calibrated stations In this case a secondary or tertiary etc calibration is validated by comparing it s direct conversion with a conversion using it as an intermediary So to test if the calibration of A to B is valid B is used in the A to B to C calibration If the ABC calibration matches the direct AC calibration to within 75% then B is considered well calibrated This bootstrapping is conducted for 5 hops so any converted station is at most 4 intermediary stations away from the master station conversion check m takes the resulting calibration paths from bootstrap m and performs the bootstrap calibration using the initial calibration of the master station and the conversion ratios of cross calibration m It also requires that the master station is included in the case where it becomes excluded in the bootstrap m subfunction To prevent sudden changes in gain or wildly varying station from being included conversion mean m checks the new calibration values against the previous 7 days of calibrations If the new calibration is not drastically different then the average of the previous 7 days of calibration values is used as the calibration value otherwise it is excluded A station is deemed unstable if one of the past seven days is either larger or smaller than the median 152 by a factor of 10 normalized by Scott Base Dunedin and Seattle stroke energy m applies the calibration values from conversion mean m to the LWPC corrected data from apply lwpc m to get the stroke energy The stroke energy is the median of the individual station values and the uncertainty is the median absolute deviation of the values The values are stored as the 11th and 12th column in the resulting AE-file The 13th value is the number of stations that participated in the calculation The final step is to iterate the entire process 5 times with energy iterate m Here the stroke energies are taken to be ground truths from which all of the calibration values are recalculated The new calibrations are then used in stroke energy m to get a new set of energy calculations After 5 iterations the values start to converge and the resulting calibrations and values are used as the final values The iteration is performed to remove far outliers 2-4 order of magnitude larger or smaller than other values and get a more stable result Once the final energy and calibration values are found the data is written to both loc and mat files for the AE-files and the txt files for the calibration and conversion values The conversion file is only used within the processing internally and with reprocessing for any station level calibration work the calibration file should be used Then the de mapper m function is called to get the relative detection efficiency for the day the results stored as a DE-file Finally a set of network statistics are stored in a file for quick reference currently this file is not being ingested or incorporated anywhere such as the WWLLN management page B 5 Relative Detection Efficiency Code The overall description of the relative detection efficiency model is given in Hutchins et al 2012a B 5 1 de mapper m de mapper m creates the relative detection efficiency model for each hour in the day currently the code is written such that this step is parallelized if the parallel toolbox is 153 available and running Within each hour the subset of operational stations 500 stroke solutions are used to create the model For each station the stroke-station pairs are found that are between 0 5 20 Mm these are used to determine the station detection threshold for the current hour The threshold is determined as the 5th percentile value of the local electric field value in uncalibrated soundcard units from the stroke-station pairs This is converted into a minimum stroke energy for an array of potential attenuation rates to serve as a lookup table Using the current station calibration averaged over the past 7 days The terminator m program is used to determine the percent day and night paths between the station and every grid point on the globe These ratios are combined with the LWPC lookup tables to determine the attenuation at every grid point Finally the attenuation values are used to index the potential stroke energy lookup to get the minimum detectable stroke energy at each grid point After this is performed for each station the 5th lowest value is found at each grid point The 5th lowest is chosen as at least 5 stations are required to locate a WWLLN stroke if that requirement ever changes then it would need to be changed in this code as well The 5th lowest value corresponds to the minimum detectable energy of the network for the given hour The minimum detectable network energy is compared to the energy distribution of the past 7 days For this distribution only strokes with energy solutions using 2 or more stations are totaled The percentage of strokes above the minimum is called the relative detection efficiency for that grid point B 5 2 Output Interpretation The output of the model is a n m 24 array where n and m are determined by the resolution of the lookup tables For example if the lookup tables have a resolution of 2 then n 180 and m 90 The third dimension of the array corresponds to the UTC hours 0 23 In each grid cell is the relative detection efficiency of the network on a 0 1 scale The 1 154 corresponds to locations that could detect 100% of the past 7 day distribution and are the best performing regions of the network Other locations will have values below 1% such as Antarctica It is recommended that prior to use a minimum relative detection efficiency such as 5% is set on the maps to prevent unphysical stroke density counts In the automated Boostrap processing the resulting relative detection efficiency maps are expanded to a 1 grid and smoothed to give a standardized size in the case that the lookup tables change their resolution In the unlikely case that the resolution goes below 1 the maps should then be downsampled to recreate this resolution 155 Appendix C WWLLN SERVICE UNIT V4 156 C 1 New Design The WWLLN service unit was redesigned due to the obsolescence of the previous Trimble GPS unit this redesign allowed for several other major revisions to the board: Built in USB-Serial conversion On board computer Remote controlled pre-amp power system Remove inline preamp LEDs Increased stereo driving power Two-way GPS serial communication The biggest change is the addition of the onboard computer eliminating the need for a separate CPU to be installed with every service unit The Gumstix WaterStormCOM with Tobi breakout board was chosen for the onboard computer An on board computer is able to toggle the preamp power supply remotely communicate with the GPS engine via TSIP and standardize the host computer capabilities The USB-serial convert is used to output GPS messages to an external computer if desired and two-way communication can be switched from the GPS to the USB port via the use of an onboard jumper Finally the system is designed to be operated remotely via SSH but it does have the ability to use a keyboard mouse and monitor through a powered USB hub and HDMI capable display C 2 Gumstix Selection There are a few important aspects of the Gumstix WaterStormCOM that makes it suitable as a WWLLN service unit computer Other compact computers meet most if not all of these requirements and they should be satistifed for future upgrades and revisions to the design The primary requirements are: 157 48 kHz stereo input Ethernet connection Linux OS Once these are met the secondary requirements are: Serial input GPS comminication 8 GB of memory 512 MB of RAM USB Video out VGA DVI HDMI Low power 1 A Low cost 3 Satellites Packet Masks 0x8F-AB Table C 1: Resolution T GPS Settings 168 C 6 2 Network Configuration The WWLLN Service Unit v4 runs a customized version of the Angstrom Linux distribution for ARM processors For additional help contact Michael Hutchins mlhutch uw edu or Bob Holzworth bobholz ess washington edu WWLLN Service Unit v4 Initial Setup Method 1: SSH Setup The SSH setup method requires: Ethernet cable SSH capable computer 1 Connect SU to a host computer directly with an ethernet cable 2 Set host computer ethernet network settings to: address: 192 168 10 1 gateway: 192 168 10 100 netmask: 255 255 255 0 3 SSH into the SU from host computer: ssh -p 7777 sferix 192 168 10 2 password: 4 Set desired static ip configuration in file networkSetup sh 5 sudo networkSetup sh 6 Switch SU to main network ethernet within 1 minute of running networkSetup sh 169 7 Test connection by SSH ing into SU with new IP address 8 a If successful: set new IP setting in etc network interfaces b If unsuccessful: power cycle SU and check settings starting with step 3 9 Reset SU and confirm new settings Method 2: Workstation Setup The Workstation setup method requires: HDMI Monitor and cable Powered USB Hub USB Keyboard USB Mouse Connect the powered USB hub to the back USB port of the service unit and attach the keyboard and mouse to the hub Connect a monitor to the HDMI port DVI - HDMI adapters work as well Power on the box it will take a few minutes for the login screen to show up Select Other and login with the username host Wait a few more minutes for the graphical display to load Adjust the network settings by either changing the files listed in Method 1 or by logging in as root as adjusting them through System Network in the top menu bar 1 Connect an HDMI display keyboard and mouse 2 Set network information through GUI Method 3: Manual microSD Editing The file that need to be edited on the rootfs partition are: etc network interfaces etc resolv conf etc init d dropbear 170 The interfaces file lists the IP information of the machine whole the resolv conf file is for the DNS information The sshd config file on line 13 sets the port with which SSH is allowed The last step if a non-standard port is being used is to also alter the built in firewall of iptables and netfilter The firewall settings are stored in: etc iptable rules and can be edited as a standard iptables configuration file Website Setup Starting apache2 To get apache2 running only one change needs to be made in the etc apache2 httpd conf file Line 96: ServerName www example com:80 Needs to be uncommented and changed to the hostname of the computer e g : Line96: ServerName gumstix ess washington edu:80 Then httpd needs to be restarted: sudo httpd -k restart Setting up the website All changes to the website need to be made in the home sferix public html static folder this folder is copied to home sferix public html during start up Changes to public html are not saves as the folder is located in system RAM due to SD card read write limitations A restart in not necessary if the public html static contents are copied to public html 171 C 7 C 7 1 Operations LED Signals The two sets of front facing LEDs can be used to diagnose most issues with a given Service Unit The left two red lights correspond to the status of the GPS receiver and the right two yellow lights with the Gumstix and Preamp The bottom red LED lights up when the GPS engine is sending a serial packet to the Gumstix and USB serial out port on the front The packet is a TSIP packet 9600 801 that can be read on the Gumstix with readTSIP py python program on a connected computer with the same program or on a Windows computer with the Trimble Studio Software The red LED lights up for every pulse per second If the GPS is not synced with three or more satellites the engine will not send a pulse per second The two yellow LED s correspond to the 15 V preamp power supply output The default setting for no Gumstix attached is to turn the preamp power supply on When the Gumstix is booting it first turns the preamp off default behavior and then turns it on during the boot process The power can be manually toggled with the preampOn sh and preampOff sh scripts If the Gumstix does not turn the preamp on after a minute then there is something wrong with the Gumstix or the operating system If none of the LEDs turn on then the fuse has likely blown and needs to be replaced 172 Appendix D GUMSTIX 173 D 1 Hardware The WWLLN Service Unit uses a Gumstix WaterStormCOM mounted on a Tobi breakout board as the on-board computer to run the WWLLN software D 1 1 Hardware Summary The Gumstix WaterStormCOM is part of the Overo COM series and has the following features: 1 GHz ARM Cortex-A8 CPU 512 MB RAM microSD Card Slot OpenGL POWER SGX graphics Aaccelerator C64x Fixed Point DSP Max: 660 800 MHz The Tobi breakout boards adds: HDMI video Out 1 USB port 1 USB console connection Stereo in out Ethernet 174 Figure D 1: Pinout of the Gumstix Tobi breakout board D 1 2 Pinouts The Gumstix COM has direct pinouts to the processor however as it is not used without the Tobi breakout board only the Tobi pinout is shown in Figure D 1 In the service unit only pins 1 GND 9 RXD1 10 TXD1 28 GPIO145 and 40 V BATT are used RXD1 and TXD1 are used for the serial communication with the GPS GPIO145 is used to control the pre-amp power supply V BATT is the 5 V power for the Gumstix D 2 D 2 1 Gumstix Operating System v2 0 Gumstix-Yocto The Gumstix used in the service unit is running a custom Linux distribution created using the Yocto Project build system This OS runs similar to most unix operating systems with the main difference being the smart package manager instead of yum or apt-get A useful resource in setting up and configuring the Gumstix software is the Gumstix developer site http: gumstix org and the mailing list archive forum http: gumstix 8 x6 nabble com 175 D 2 2 Distribution Location The operating system used is the Yocto Project Gumstix Layer v1 5 available on flashfile or in the Git repository: home mlhutch Git gumstix git repository on flashfile in the image folder D 2 3 Building Building the operating system can be done by following the instructions at: https: github com gumstix Gumstix-YoctoProject-Repo With the final configuration image yocto local conf in the Git repository on flashfile in If rebuilding use the local conf file in the build conf folder and run the bitbake target bitbake gumstix-xfce-image With either a newly made OS image or the one in the gumstix git repository follow the install instructions in INSTALL md for setting up a new microSD card to run with WWLLN D 3 D 3 1 Software WWLLN Software The WWLLN software is provided by James Brundell and compiled specifically for the ARM process The three programs are toga ntpcheck and GDspectro toga is the main WWLLN processing programming that reads in the VLF and GPS signals to produce the UDP packets sent on to the main WWLLN processors It should be always running on the system with a crontab entry such as: 0 5 10 15 20 25 30 35 40 45 50 55 toga -s 100 -a 3 -j 1 -g -o & This will try to start it every 5 minutes in case it stops for any reason The ntpcheck and GDspectro and programs used by toga but do not need to be called or run on their own 176 D 3 2 Hardware Controls Pin GPIO145 is the pin that controls whether the preamp power supply is turned on or off When the pin is held low value of 0 the power supply is on when it is set high value of 1 it is turned off The command to change a GPIO pin value is: echo 0 sys class gpio gpio145 value The two scripts preampOn sh and preampOff sh can be used to easily toggle the preamp power supply The default value for GPIO pins is to hold them high so during boot the preamp turns off until the preampOn sh script can be called at the end of the boot sequence D 3 3 GPS Interface The Trimble GPS communicates with the TSIP protocal compared the NMEA of the previous GPS engine used The pythons script readTSIP py interprets the TSIP messages and reports the GPS status to the file gps log and prints them to the console The console printing can be turned off by changing the variable print to console to False The program can be started and run in the background to produce a continues record of GPS activity The default location for the gps log file is in the public html folder where it can be remotely checked through the service unit website D 3 4 RAM Disk The Linux distribution for Gumstix automatically sets up a RAM disk for users It is created at var volatile with half of the available RAM 256 MB It needs to be used for the running of the WWLLN software as the microSD card is too slow At start-up the public html folder logs and spectrograms and sferics folder are created in the ram disk and symlinked to the main sferics directory For this reason all permanent edits to the Service Unit website should be made in the public html static directory 177 D 4 Creating Gumstix microSD Card There are two methods for configuring a new microSD card for use with the service unit Gumstix computer Either a card can be formatted and loaded with the latest software following the INSTALL md instructions or an existing installation disk image can be copied over located on flashfile and flash5 D 4 1 Card Duplication Once a new card is created it is advised to make an exact copy of the card to allow for duplication onto new cards Since the partitioning and bit location on the card is critical for the Gumstix the direct copy program dd should be used to make the copy To copy a card to a disk image the command will look like: sudo dd if dev sdb of Path To Target gumstix iso bs 512 And the command to copy a microSD image back to a new card in the same slot as the previous card: sudo dd if Path To Target gumstix iso of dev sdb bs 512 A word of warning: the dd command can overwrite and destroy hard drives if they are incorrectly targeted Always double check the mount point of the microSD card before running the dd command D 5 Gumstix System Setup Subsection D 5 1 gives the setup instructions for a new station namely setting the IP address so it can be added to the network A more up to date version is available in the gumstix git repository in the user manual folder Also included in the station setup instructions are how to setup and customize the service unit webpage as described in Subsection D 5 2 178 D 5 1 Connecting to the Gumstix Method 1: SSH Setup The SSH setup method requires: Ethernet cable SSH capable computer 1 Connect SU to a host computer directly with an ethernet cable 2 Set host computer ethernet network settings to: address: 192 168 10 1 gateway: 192 168 10 100 netmask: 255 255 255 0 3 SSH into the SU from host computer: ssh -p 7777 sferix 192 168 10 2 password: 4 Set desired static ip configuration in file networkSetup sh 5 sudo networkSetup sh 6 Switch SU to main network ethernet within 1 minute of running networkSetup sh 7 Test connection by SSH ing into SU with new IP address 8 a If successful: set new IP setting in etc network interfaces b If unsuccessful: power cycle SU and check settings starting with step 3 9 Reset SU and confirm new settings 179 Method 2: Workstation Setup The Workstation setup method requires: HDMI Monitor and cable Powered USB Hub USB Keyboard USB Mouse Connect the powered USB hub to the back USB port of the service unit and attach the keyboard and mouse to the hub Connect a monitor to the HDMI port DVI - HDMI adapters work as well Power on the box it will take a few minutes for the login screen to show up Select Other and login with the username host Wait a few more minutes for the graphical display to load Adjust the network settings by the steps listed in Method 1 or 3 1 Connect an HDMI display keyboard and mouse 2 Follow Method 1 or Method 3 Method 3: Manual microSD Editing The files that need to be edited on the rootfs partition are: etc network interfaces etc resolv conf etc systemd system sshd socket The interfaces file lists the IP information of the machine whole the resolv conf file is for the DNS information The sshd socket file sets the port with which SSH is allowed The last step if a non-standard port is being used is to also alter the built in firewall of iptables and netfilter The firewall settings are stored in: 180 etc iptable rules and can be edited as a standard iptables configuration file D 5 2 Website Setup Starting apache2 To get apache2 running only one change needs to be made in the etc apache2 httpd conf file ServerName www example com:80 Needs to be uncommented and changed to the hostname of the computer e g : ServerName gumstix ess washington edu:80 Then httpd needs to be restarted: sudo httpd -k restart Setting up the website All changes to the website need to be made in the home sferix public html static folder this folder is copied to home sferix public html during start up Changes to public html are not saves as the folder is located in system RAM due to SD card read write limitations A restart in not necessary if the public html static contents are copied to public html D 5 3 Sound Settings The Gumstix a myriad of analog inputs that are all controlled with alsamixer For the WWLLN service unit the stereo input is controlled by the input as shown highlighted in Figure D 2 and a digital gain through Included in the installation files is the default alsa profile asound state 181 Figure D 2: alsamixer settings for Gumstix stereo input controls the stereo gain D 6 Common Problems The network icon in the top menu bar says the network connections are disabled The GUI network manager is disabled but the network settings set as above still work The GPS pulse per second is not working with the TOGA program it lists PPS bad for most lines Adjust the gain on the pulse per second with Alsamixer TX1 Digital right channel usually lowering it will resolve the problem 182 Appendix E WEBSITE 183 This appendix discusses operations of the updated WWLLN website and the real-time lightning map E 1 WWLLN net The new WWLLN website uses Wordpress as the content management system for every webpage The structure of the webpage e g headers footers titles spacing are stored in the Wordpress theme while the content is for the most part stored in either the MySQL database or in three list files Editing the files in the theme will change every corresponding page of the website while content edits will just change that page E 1 1 Directory Structure The website directory looks like: backup sh hosts_list htm index php map map_demo publications_list htm README txt spectra_list htm volcanoMonitor html wordpress The three files hosts list htm spectra list htm and publication list htm are used to generate the list content on their respective pages hosts spectra publications backup sh is a script to backup the Wordpress database to a file called wwlln site bak sql bz2 that is discussed below index php redirects the user to the Wordpress based pages and generally should not be changed 184 map and map demo are the folders containing the scripts and data for the WWLLN lightning maps The htaccess file in each directory should be used to control who can access them this data access is completely separate from Wordpress The htaccess is currently set to use the htpasswd file at home mlhutch sites htpasswd volcanoMonitor html is used to redirect users to the new volcano monitor page other previous permanent links e g wwlln net climate were replaced more easily and did not need a redirect file Finally there is the wordpress directory This contains all of the support files used to power the wordpress aspects of the website including the admin page the blogs the MySQL database settings and WWLLN theme page settings Outside of the website directory is the MySQL database This is stored by the MySQL program running on webflash and does not have an exact file location How to backup and restore the content from the MySQL database is covered below E 1 2 Wordpress Files Inside the wordpress directory there are only a few files that will ever need to be changed or that even should be changed The main file is the wordpress wp-config php file this file contains the information for connecting to the MySQL database including the user name and password in plain text It is important to note that access to this file non-locally e g through the website is not allowed and it can only be seen with a local connection e g ssh The other set of files in the wordpress directory are the WWLLN theme files These files control how the website looks and feels with some content stored in the files themselves They are located in the non-intuitive location of wordpress wp-content themes wwlln Editing these files will change how the corresponding pages look In general only the style files css files should be changed to alter the website appearance The other files that may be changed is the header php file this is where you can change the items and order of the menu bar 185 Admin The admin panel for Wordpress is used to create content alter the site if the user is an administrator To access the admin panel go to wp-admin php from the main page of the website e g wwlln net wp-admin php From here new pages can be made new blog posts website settings and user control Content Creation Wordpress content comes in two forms: blog posts and static pages Blog posts show up in reverse chronological order on the blog newest first and the first few are listed on the front page of the website Blog posts are created with the Wordpress tools and text editor and support embedding pictures and videos Pages are similarly created but use different templates instead each described below Both can be drafted edited published deleted and generally controlled through the admin page If other users are added say other management team members they can add blog posts as well Page Templates There are 6 page templates depending on the template the content will be placed in different locations All pages can be written with the text editor provided or HTML Default Template content is placed inside a white box exactly like the blog posts HTML Content Page blank page below the header that uses the HTML given to create the page Home page main index page entirely in HTML Editing using the visual editor may break the page Lightning map page specifically designed to show the WWLLN lightning maps The content is placed below the inset lightning map Note: there needs to be a folder with the same URL as the listed page with the lightning code in it see the existing pages folders for examples 186 List Uses a name list htm file to generate a single list of that data below the content where name is the post URL The file format is one line per list item with a blank line in between List Two-Column same as List but uses two columns Two lines between spaces where the second line is the second column entry See hosts list htm as an example E 1 3 MySQL The MySQL server can be backed up with the backup sh script or with the command: mysqldump --add-drop-table -h localhost -u wwlln -p wordpress bzip2 -c wwlln_site bak sql bz2 To restore the Wordpress database from a back up file is relatively easy use the command: mysql -h localhost -u wwlln -p wordpress wwlln_site bak sql Which will then prompt for the password located in the wp-config php file and perform the backup This does not require any special sudo permissions to run E 1 4 Moving Wordpress Moving the Wordpress directory is a more involved process and is not recommended to do casually First backup the current Wordpress directory along with the htaccess and index php files in the root directory Then go to the settings page on the websites wp-admin php page here change the website and Wordpress directories to what they will be after the move After saving the site will stop working Move the Wordpress directory to the new location listed on the admin page and move the htaccess and index php files to the root of the website page that was also listed Now the admin page should work Back on the admin page go to the Permalinks page on the settings menu and at the bottom will be the updated htaccess file listed Propagate the changes over to the root htaccess file and the wordpress htaccess file After that the website should be working as before 187 E 2 Lightning Maps A WWLLN http: wwlln net visualization tool to show realtime lightning activity The map displays WWLLN data viewed in realtime or at other speeds The user can pause the display return to the start of the loaded data jump around by 30-seconds resume playing or return to real time data display where available There are options to show a Google Map cloud layer only shows current cloud conditions a density map of all loaded strokes place a selection box for more refined statistics and an option to clear the loaded strokes in memory Users can also load their own WWLLN loc files for playback and viewing There is a load limit of 25 000 strokes to prevent slow playback due to too many strokes Loading a file larger than 25 000 will only load the first 25 000 strokes and ignore the rest Loaded data files play from the beginning of the file The terminator code is taken from https: github com marmat google-maps-api-addons Login in controlled by the htpasswd file specified in htaccess An htpasswd file is created with: htpasswd -c htpasswd new user And amended with: htpasswd htpasswd new user 188 VITA Michael Hutchins was born in Santa Rosa California in 1987 He had an uncomplicated childhood set amidst the vineyards of the Sonoma wine country Without any inherent struggles or tragedies in his life to fuel an artistic career he left Northern California to attend the University of California Santa Barbara for a BS in Physics He spent his third year at UCSB abroad studying Astrophysics at the University of Edinburgh Scotland where a chance assumption directed him to graduate school In 2009 he eschewed a move away from the West Coast to attain his PhD in Earth and Space Sciences studying lightning at the University of Washington Seattle
    • Huybers, Kathleen - Ph.D. Dissertation
      Relationships between climate and geophysical processes: what climate histories can be inferred from glaciers, lakes, and ice streams? 2014, Huybers, Kathleen , Kathleen Huybers Copyright 2014 Kathleen Huybers Relationships between climate and geophysical processes: what climate histories can be inferred from glaciers lakes and ice streams Kathleen Huybers A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2014 Reading Committee: Gerard Roe Chair Howard Conway Summer Rupper Program Authorized to Offer Degree: University of Washington Department of Earth and Space Sciences University of Washington Abstract Relationships between climate and geophysical processes: what climate histories can be inferred from glaciers lakes and ice streams Kathleen Huybers Chair of the Supervisory Committee: Professor Gerard Roe Earth and Space Sciences This dissertation aims to characterize the present and future variability of the Earth s climate by putting it in the context of past variations in climate Herein I explore how the spatial and temporal fluctuations of climate variables such as temperature precipitation evaporation and sea level are filtered and integrated by the geophysical systems that they influence I use relatively simple models to explore the scale over which a paleoclimate proxy record is relevant the physics and parameters to which the system is most sensitive and how one can distinguish a climate signal from noise The three geophysical systems explored in this work are detailed below: 1 Glaciers: Glaciers integrate interannual variations in precipitation and temperature and respond with kilometer-scale multi-decadal terminus fluctuations Oerlemans 2000 Reichert et al 2002 Roe and O Neal 2009 My work extends these studies and uses reanalysis data and correlation analysis to establish how patterns in precipitation temperature and glacier geometry give rise to patterns in glacier advance and retreat Using a linearized glacier model I also derive analytic expressions to calculate the expected coherence of regional glacier advance and retreat and to assess the sensitivity of these glaciers to temperature and precipitation changes By focusing on how climatic and geometric heterogeneity affect patterns of regional glacier length variations I isolate the parameters that exert the most influence on the timing and magnitude of glacier response to temporal variations in the climate 2 Lakes: Like mountain glaciers lakes integrate year-to-year climate fluctuations to produce large persistent surface fluctuations on timescales of decades or longer Using the Great Salt Lake as a case study I model lake-level variability in response to perturbations in evaporation and precipitation Though there already exists a body of work that has characterized persistence in observed lakelevel variations Mason et al 1994 Lall and Mann 1995 Abarbanel and Lall 1996 Mohammed and Tarboton 2011 my research shows that this persistence not only reflects any autocorrelation in the climate but is also intrinsic to the dynamics of the lake system My work also shows how the geometry of the lake influences the magnitude and persistence of lake level fluctuations These results develop a null hypothesis in expected lake-level variability which can be compared to the magnitude and frequency of paleo lake-level variations 3 Ice streams: Previous studies have used flowline models to understand the behavior of ice streams on idealized bed geometries Schoof 2007 Docquier et al 2011 This work applies the flowline model approach to a realistic basal topography beneath the West Antarctic Ice Sheet WAIS and evaluates changes in grounding line positions and upstream ice profiles in response to changes in model physics and environmental factors These sensitivity studies demonstrate that the present positions of many Wed- dell Sea-sector grounding lines lie within an asymmetric trench implying a strong stability to retreat but also creating the potential for significant advance due to either sea-level lowering on the order of tens of meters or conceivably from precipitation increases of less than 10% My evaluation reaffirms that the greatest concerns for WAIS retreat or collapse are locations of reverse slopes muted basal topography and limited lateral support This dissertation uses models of low complexity allowing for a complete understanding of the system and providing a deeper and richer understanding of the temporal and spatial patterns of Earth s limitless complexity TABLE OF CONTENTS Page List of Figures iii List of Tables v Chapter 1: Introduction 1 1 Glaciers 1 2 Lakes 1 3 Ice Streams 1 4 Conclusion 1 3 5 6 8 Patterns in 10 10 13 16 19 27 29 45 45 47 50 53 55 Chapter 2: 2 1 2 2 2 3 2 4 2 5 2 6 Spatial Patterns of Regional Climate Introduction Setting and data A linear glacier model Results Small-scale patterns Summary and discussion Glaciers in Response Chapter 3: Geometric Influences on Glacier 3 1 Introduction 3 2 Mount Baker glaciers 3 3 Glacier model 3 4 Model application and results 3 5 Discussion and summary to Spatial Variability Chapter 4: Lake Level Changes in Response to Interannual Climate Variability 66 4 1 Introduction 66 i 4 2 4 3 4 4 4 5 4 6 The Great Salt Lake Model Lake-level statistics Alternative lake hypsometries Discussion and summary 68 72 79 84 87 Basal topographic controls on the long-term stability of the West Antarctic Ice Sheet Introduction Model Results: Foundation Ice Stream Discussion Conclusions 107 107 108 111 113 114 Chapter 5: 5 1 5 2 5 3 5 4 5 5 Chapter 6: Conclusions 121 Bibliography 124 Appendix A: Interpreting Temporal Variability 140 Appendix B: Autocorrelation: Determining the Degrees of Freedom 143 Appendix C: Standard deviations in lake level 146 Appendix D: Ice Stream Model Methods 148 ii LIST OF FIGURES Figure Number Page 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 Glaciers of the Pacific Northwest Climate of the Pacific Northwest Linear glacier schematic Climate correlations Sensitivity ratios Standard deviation in glacier length Glacier correlations Geometric sensitivity MM5: climate of the Pacific Northwest MM5: ratio of sensitivity MM5: standard deviation of glacier length 34 35 36 37 38 39 40 41 42 43 44 3 1 3 2 3 3 3 4 Mount Baker map view Glacier profiles and map view Mount Baker glacier time series Altered geometry glacier time series 60 61 63 64 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 Great Salt Lake map view and geometry Great Salt Lake historical climate and lake level Autocorrelation of Great Salt Lake climate and lake Great Salt Lake schematic Great Salt Lake e-folding timescale Great Salt Lake model statistics Model lake level and area distributions Maximum and minimum lake-level excursions Alternative lake model statistics level 93 95 97 98 99 100 101 103 105 5 1 Antarctic ice stream catchments and flowlines 116 iii 5 2 5 3 5 4 Foundation Ice Stream profile and model results Weddell-Sea sector ice-stream profiles Ross and Amundsen Sea sector ice-stream profiles iv 118 119 120 LIST OF TABLES Table Number Page 2 1 2 2 Glacier geometry parameters Key glacier correlations 32 33 3 1 3 2 Mount Baker glacier geometry Mount Baker glacier correlations 58 59 4 1 4 2 Great Salt Lake parameters and historical values Parameters and model output for alternate geometry experiments 91 92 v ACKNOWLEDGMENTS This work would not have been possible without the many people who have supported me during my studies and research Gerard Roe has been an incredible mentor He is my greatest ally and has pushed me further than I thought possible I am forever grateful for his insights patience encouragement friendship and brilliance I also deeply appreciate the tremendous support of my committee: Howard Conway Summer Rupper Ed Waddington Claire Todd and Greg Balco I have learned how to learn from this team Several other faculty members at the University of Washington have also been instrumental to my growth as a scientist and as a person Many thanks are owed to Steve Warren Eric Steig Dargan Frierson Cecilia Bitz David Battisti Abby Swann Al Rasmussen and LuAnne Thompson My community of graduate students in the department of Earth and Space Sciences and the Program on Climate Change is incredible and I am honored to have worked with and among them Michelle Koutnik Emily Newsom Mike Town Shelley Kunaseck Perry Spector Joe MacGregor Julia Jarvis Lora Koenig Nicole Feldl Nick Siler Kevin Wood Steve Po-Chedley Adam Campbell Stu Evans Clement Miege Peter Neff Jessica Lundin and the Graduate Climate Conference 6 organizing committee are among the most incredible scientists and friends I could imagine vi I am grateful for my communities in Seattle Cambridge and elsewhere including Lisa Ciecko Brendan O Donnell Jodi Wellman the BAD co-op my friends from USF and my Friday group My ice community has taught me so much about humanity and humility and I am forever changed by my experiences in Greenland and Antarctica: thank you especially to Jake Speed Kathy Blumm Kathy Young Andrea Isgro James Ken Jessen and Sandy Starkweather I want to thank my family for their incredible and unwavering love and support Mom Dad Pete Downing Pax and Kai have inspired me cheered for me and have been with me all the way I admire each member of my family greatly and am humbled to be among their lot And finally to Matt Smith words cannot express my love gratitude and admiration vii DEDICATION I dedicate this work to my partner Matt Smith and to my family: Mom Dad Pete Downing Pax and Kai viii 1 Chapter 1 INTRODUCTION Paleoclimate proxies provide a wealth of information about Earth s history far beyond what is available from the instrumental record However proxies are not equivalent to instruments the nature of what and how a proxy is deposited must be understood before any meaningful climate information is extracted In most instances the proxy record is not a direct history of climate but rather of some other geophysical sub-system i e a tree a lake a glacier an ice sheet or a soil that itself has a dynamical response to climate The size shape local climatology internal dynamics and non-climatic external forcings of the system all determine the time that it takes to respond to a climatic forcing and the magnitude of that response Further the proxy record left by the geophysical system may represent a spatial integration of climatic effects This delayed smoothed and integrated response to a climate signal is a hallmark of many geophysical systems with memory such as the ocean s mixed layer Hasselmann 1976 Frankignoul and Hasselmann 1977 glaciers e g Oerlemans 2000 Roe 2011 lakes e g Mason et al 1994 ice sheets e g MacAyeal 1992 Huybrechts and de Wolde 1999 and permafrost soils e g Romanovsky et al 2007 see Appendix A Both the spatial and temporal integration of the climatic forcings can complicate the interpretation of a proxy record giving rise to several questions: 1 What climatic variables represented by the climate proxy are well preserved 2 by the geophysical system 2 On what timescale is climatic information well preserved 3 Over what spatial scale does the proxy represent relevant information 4 How can one distinguish a climatic signal from noise in the proxy record 5 What physics and parameters is the system most sensitive to This dissertation explores three geophysical systems from which paleoclimate proxy records are often derived: Glaciers whose length variations are influenced by patterns of accumulation and ablation Lakes whose extent and surface elevation vary in response to evaporation and precipitation Ice streams whose shape and extent are sensitive to changes in sea level accumulation and ice-shelf buttressing These geophysical systems are studied by applying climatic forcings to relatively simple models that capture the systems behavior Despite the models simplicity they retain the most essential behaviors of the systems that are being studied Though the models do not capture all of the nuances of the systems behavior their simplicity is also their strength: a thorough understanding of the behavior of the governing equations leads to physical understanding of the system in nature To some degree each chapter in this dissertation addresses each of the five questions posed above though 3 the emphasis varies for each of the three systems 1 1 Glaciers Mountain glaciers are key indicators of regional and global climate change and variability responding sensitively to changes in precipitation and temperature However internal dynamics cause glaciers to integrate variations in precipitation and temperature over timescales longer than a year The timescale and magnitude of a glacier s response to climate perturbations are functions of both the geometric and climatic setting of the glacier It is therefore difficult to diagnose whether discrepancies in glacier behavior are due to geometric or climatic heterogeneity Glaciers respond to variations in the climate through changes in both the profile and length of the glacier Because the length of the glacier is relatively simple to diagnose through terminal moraine deposits or aerial photographs variations in a glacier s length offer the most straightforward way to track its response to variations in the climate Nye 1960 showed that these terminal variations are driven by not only the direct effects of snowfall and ice melt but also to the arrival of ice from the upper part of the glacier Nye estimated that the time it takes to transfer snowfall to the terminus of an alpine glacier is between 3 and 30 years With this understanding much work was done to understand what climatic forcings determine the timing and magnitude of variations in glacier length e g Nye 1961 1963 J ohannesson et al 1989 Oerlemans et al 1998 Harrison et al 2001 Weber and Oerlemans 2003 Roe 2011 Oerlemans 2012 Harrison 2013 Reichert et al 2002 and Roe and O Neal 2009 each recognized that in addition to responding to climatic change glacier lengths also vary in response to interannual climate variations Their work determined the expected amplitude of glacier varia- 4 tion in response to interannual variations in precipitation and temperature Length variations that exceed the bounds of this range are indicative of a glacier that is responding to a true climatic shift rather than a short-term variation in precipitation or temperature The shape of the underlying bed and the distribution of ice also control the timing and size of a glacier s response to changes or variations in the climate These geometric effects can be large For example Kessler et al 2006 showed that 97% of the disparity between the lengths of glaciers flanking the east and west side of California s Sierra Nevada range during the most recent glacial period is attributed to the topographic asymmetry of the mountains Oerlemans et al 1998 concluded that while there is no straightforward relationship between glacier size and fractional change in ice volume hypsometry plays an important role in determining the variability of a glacier and that in general smaller glaciers are more likely to lose a higher percentage of their mass However the tendency of larger glaciers to have lower slopes can also expose a large fraction of a large glacier to ablation for the same warming or same ELA rise This can be a compensating factor Given that both the regional climate and the regional mountain topography are non-homogeneous it is therefore expected that regional glacier advance and retreat should also be non-uniform Regional correlations in glacier lengths that are apparent in the historical or proxy record reflect the influence of three factors: spatial correlations in precipitation and melt-season temperature the climatic setting of the glaciers e g a maritime or continental climate and a similarity between the glaciers geometric setting and hypsometric distribution Chapters 2 and 3 explore the influence the factors on setting the patterns of regional glacier advance and retreat 5 1 2 Lakes Many of the same issues that affect the interpretation of glacier-length records also apply to lake-level records Lakes that do not have efficient drainage outlets integrate year-to-year climate fluctuations to produce large persistent fluctuations in lake levels on timescales of decades or longer A lake integrates climatic information over its entire catchment area reflecting regional climate signals with a rise or fall in the lake s level Langbein 1961 noted that closed-basin lakes which lack drainage outlets i e endorheic basins fluctuate more than open lakes because changes in the inflow or outflow of the lake can be compensated only by a change in the lake s surface area Therefore closed lakes are particularly sensitive to climate fluctuations and have been the subject of many paleoclimate studies Street-Perrott and Harrison 1985 One such lake that is particularly well-studied is the Great Salt Lake GSL It is tempting to attribute decadal-scale variations in the GSL s lake level to decadalscale climatic forcings Mann et al 1995 Lall and Mann 1995 Moon et al 2008 and Wang et al 2010 invoke low-frequency climate phenomena to explain the lowfrequency response of the GSL and aim to predict future lake levels from the periodicity of the atmospheric indices However Kite 1989 proposed that the changes and apparent periodicity in the GSL s record are within the range of normal fluctuations and cannot be cited as an indication of climatic change Mohammed and Tarboton 2011 showed that the timing of increases and decreases in lake level are directly related to the GSL s bathymetry Because the area of the lake controls the outgoing flux a shallow lake like the GSL is quickly stabilized and modulated by the available evaporative surface In related work they used a model to calculate the sensitivity of the GSL to changes in the historical inflow precipitation and air temperature and use these historical records 6 to predict possible future lake-level scenarios Mohammed and Tarboton 2012 Mason et al 1994 derived general solutions to the water-balance equation that characterized the lake-level response to idealized climate forcings showing how closedbasin lakes act as low-pass climate filters In Chapter 4 I apply a similar model putting the historical record of the GSL into context by considering the natural variability of the lake s level which occurs in response to the year-to-year fluctuations in weather that occur even without any climate change or persistence in the climate I derive analytic solutions for the standard deviation of lake-level changes the threshold-crossing frequency of a lake and the sensitivity to variations in precipitation versus temperature Chapter 4 also demonstrates the important role of lake bathymetry on integrating natural lake-level variability 1 3 Ice Streams Advances in the physical understanding of marine ice sheet stability coupled with evidence that the West Antarctic Ice Sheet WAIS has collapsed in the past Hillenbrand et al 2012 have led to recent concerns about the WAIS s future stability The total potential sea-level contribution from the WAIS is 4 3 m Fretwell et al 2013 and recent work suggests that Antarctica could contribute 0 15 to 0 62 m to global sea-level rise in the next century Solomon et al 2007 Pfeffer et al 2008 Joughin et al 2010 Gladstone et al 2012 Mouginot et al 2014 Joughin et al 2014 Similarly the distribution of ice on the Antarctic continent during the last glacial period as well as a comprehensive understanding of its retreat to the present state remains unknown e g Anderson et al 2002 Clark et al 2009 The difficulty in predicting future change or resolving past change stems in part from the complexity of ice ocean dynamics Joughin and Alley 2011 Nowicki et al 2013 7 However recent advances in remote sensing offer an unprecedented insight into the present state of the ice sheet including observations of ice-thickness basal topography and surface velocity Fretwell et al 2013 Rignot et al 2008 Le Brocq et al 2010 Rignot et al 2011 Fretwell et al 2013 These data sources in combination with advances in the theoretical understanding of ice-sheet-shelf-ocean interactions allow us to gain perspective on the stability of the WAIS using numerical models Schoof 2007 Gagliardini et al 2010 Drouet et al 2012 In an idealized steady state the flux of ice from the margins of the ice sheet is balanced by the accumulation integrated over the upstream catchment area In reality the mass balance of the ice sheet is continuously being modified by changes in the activity of fast-flowing outlet glaciers and ice streams The volume of ice that is discharged from these outlets is determined by changing conditions at the grounding line the transitional area between the grounded ice sheet and the floating ice shelf The grounding line in turn is highly sensitive to changes in sea-level and the melting freezing of buttressing ice shelves Payne et al 2004 Joughin et al 2010 Pritchard et al 2012 Shepherd et al 2012 Schoof 2007 showed that the grounding-line position is determined by the basal topography and is therefore extremely sensitive to changes in the bed beneath and extending outward from the grounded ice The position of the grounding line exerts a strong control over the inland iceelevation profile Glacial erratics which are collected from nunataks and dated with cosmogenic nuclide techniques can offer evidence of past ice-thickness changes e g Balco et al 2008 This paleo-evidence coupled with physical understanding from a model can inform us how ice streams respond to changes in the grounding line In Chapter 5 I use an idealized flowline model to assess the relative importance 8 of environmental variations and physical parameters on ice-stream thickness profiles Sub-glacial and sub-marine basal topography together with the assumed form of the grounding-line flux controls the grounding-line sensitivity to change Results emphasize that differences in the basal relief beneath present-day ice streams will cause the Weddell Amundsen and Ross Sea sectors of Antarctica to respond with varying sensitivity to similar environmental perturbations 1 4 Conclusion I return now to the initial five questions that motivate this work and detail how each chapter of my dissertation will answer each of these questions: 1 What climatic variables represented by the proxy are well preserved by the geophysical system I derive linearized formulas for the ratio of sensitivity of glaciers lakes to changes in accumulation precipitation and mass loss melt evaporation The icestream chapter uses sensitivity analyses to characterize the potential changes in ice thickness due to changes in accumulation sea level and ice shelf buttressing 2 On what timescale is climatic information well preserved Characteristic response times are derived from the linearized glacier and lake level models The sensitivity of the ice-stream model to physical and environmental factors enhances our understanding of how well ice-stream models can capture the changes observed in exposure-age data 3 Over what spatial scale does the proxy represent relevant information The mountain glacier work expressly answers this question with correlation analysis Similar work could be done with the lake model but is not part of 9 this dissertation For the ice stream my results imply that the near-groundingline elevations will reflect regional ice sheet shelf condition 4 How can one distinguish a climatic signal from noise in the proxy record Roe and O Neal 2009 used statistical analysis to estimate the variability of glaciers due to climate variability alone I have used a similar approach in my work with lakes For ice streams I compare the ice-profile response to variations in accumulation bed slipperiness and relative sea level This intra-model comparison can then be compared to the magnitude of ice-thickness changes from the Last Glacial Maximum to the present 5 What physics and parameters is the system most sensitive to All three chapters identify the primary sensitivity of the systems that are addressed The main advantage to my idealized modeling approach is that the physics and parameters are easily identified and altered and that comparisons between model configurations are straightforward allowing for clear interpretations of the modeling results 10 Chapter 2 SPATIAL PATTERNS OF GLACIERS IN RESPONSE TO SPATIAL PATTERNS IN REGIONAL CLIMATE Chapter 2 in full is a reprint of Spatial Patterns of Glaciers in Response to Spatial Patterns in Regional Climate authored by K Huybers and G H Roe This is the author s version of the work It is posted here by permission of the American Meteorological Society AMS for personal use not for redistribution The definitive version was published in Journal of Climate 22 17 in 2009 and AMS holds the copyright The dissertation author was the primary investigator and author of this paper 2 1 Introduction A major goal in current climate research lies in understanding patterns in climate and how they translate to climate proxies Glaciers are among the most closely studied of these proxies because they respond directly to both snow accumulation and surface energy balance These in turn reflect the precipitation and melt-season temperature of the regional climate Ohmura et al 1992 A glacier s response to this climate is most often characterized by a change in the position of its terminus Records of terminus advance and retreat are readily available in both the geological and historical record through the formation of moraines lichenometry aerial photography cosmogenic dating and satellite imagery Beyond the period of the instrumental record well-dated glacial deposits often serve as the primary descriptor of the climate history of a region 11 Despite the direct nature of a glacier s response to climate both the current nearglobal retreat and past glacier variations present complicated pictures Though there is strong evidence that glaciers worldwide are presently retreating e g Oerlemans 2005 individual glaciers vary in the magnitude of response In a few locations glaciers have even advanced during the past decades as is the case in Norway and New Zealand e g Nesje 2005 Chinn et al 2005 Moreover some well-documented retreats like that on Mount Kilimanjaro have complicated causes that are not easily explained e g M olg and Hardy 2004 While there is often local coherence among glacial advances and retreats it has proven harder to extrapolate these results across continental-scale regions e g Rupper and Roe 2008 The difficulty in interpreting terminus advance and retreat is threefold First glaciers are not indicators of a single atmospheric variable They reflect the effect of many atmospheric fields primarily accumulation and temperature but also cloudiness wind longwave and shortwave radiation balances the turbulent fluxes of sensible and latent heat and humidity among others Second each glacier is subject to a particular combination of the bed slope hypsometry accumulation area debris cover local shading etc creating a setting that is unique to each glacier Finally glaciers integrate the interannual variability of the climate over many years or even decades the advance or retreat of a glacier cannot be traced to a single years climate Hence in order to understand how spatial patterns in climate variability translate into spatial patterns of glacial response we must systematically analyze patterns in regional climate and model a glacier s response to the dominant variables These patterns of climate variability and glacier response must be understood in order to establish the natural variability of a glacier i e the variability in the absence of an external climate forcing It is only when observed responses exceed this expected natural variability that glaciers can be said to be recording a true regional hemi- 12 spheric or global climate change e g Reichert et al 2002 Roe and O Neal 2009 hereafter RO The goal of this paper is to derive and analyze a model of the expected regionalscale correlations of glacier length variations in response to interannual variability in precipitation and melt-season temperature We take a first-order approach to this problem using the simplest model framework capable of representing how glaciers amalgamate different aspects of climate to produce terminus variations In particular we address the following questions: 1 What are the spatial patterns of variability in precipitation and melt-season temperature 2 How do these patterns of intrinsic climate variability translate into patterns of glacier advance and retreat 3 Over what spatial extent can we expect these intrinsic natural fluctuations of glaciers to be correlated We use a simple linear glacier model that has been shown to adequately capture recent glacier variability RO J ohannesson et al 1989 Oerlemans 2005 The patterns we find in our results are consistent with those of other glacier mass balance studies Harper 1993 Bitz and Battisti 1999 The advantage of our approach is that it allows us to explore such patterns on a wider regional scale and to understand in detail the relative importance of the different causes Our modeled patterns of glacier advance and retreat are not intended to simulate either the recent or the paleorecord of glacier advance and retreat First this is because we have chosen to explore only the interannual variability of climate and have 13 removed any trend from the data Second and more fundamentally accounting for the processes that build up and deposit moraines on the landscape and particularly the time scale of their formation is beyond the scope of our chosen model e g Putkonen and O Neal 2006 We regard our results therefore as a means to explore how climate patterns are combined through the dynamical glacier system and as an aid in the interpretation of glacial landscape features 2 2 Setting and data Our study area is the Pacific Northwest covering the northwestern United States British Columbia and southern Alaska This region is ideal because of the large number of well-documented glaciers the different climatic environments and the range of glacier sizes that exist in the region The dominant climate patterns in the area are also well understood Figure 2 1 maps the locations of all major glaciers in the region Our principal climate data set is that of Legates and Willmott 1990a b hereafter LW50 which provides 50 years of worldwide temperature and precipitation station data interpolated onto a 0 5 0 5 grid We extract from this data set two atmospheric variables that reflect the most important climatic forcing for glaciers The first variable is the melt-season temperature which we define as the average surface temperature between June and September JJAS For simplicity we assume that the ablation rate is directly proportional to the melt-season temperature as suggested by observations e g Paterson 1994 Ohmura et al 1992 The second variable is the mean annual precipitation which again for simplicity we assume reflects the accumulation of snowfall on a putative glacier within any grid point Approximately 80% of precipitation in this region comes in the fall and wintertime e g Hamlet et al 2005 To distinguish in more detail between precipitation and snowfall would require extrapolation onto high-resolution topographic digital elevations models The data 14 are linearly detrended in order to identify the internal variability in these climate variables and so neglect any recent warming These simplifications are appropriate for the first-order approach in this study its focus on the regional-scale response and the relatively coarse 0 5 -resolution data that does not reflect detailed small-scale orographic features We discuss refinements of the model framework in section 5 and the discussion 2 2 1 Climate in the Pacific Northwest Figures 2 2A and B depict the mean annual precipitation and the mean melt-season temperature over the region The Cascade Olympic Coast and St Elias Mountains are important influences on the regions climate These mountain ranges partition the setting into a generally wet region on the upwind flank of the mountains and a dry region toward the leeward interior On a smaller scale not resolved in Fig 2 there are distinct patterns in climate over the peaks and valleys in the mountain ranges giving rise to rich and intricate local weather patterns e g Minder et al 2008 Anders et al 2007 We address the important effect of these small-scale patterns in section 2 5 For mean melt-season temperature the pattern is characterized by the north-south gradient though cooler temperatures at higher elevations can also be seen The major feature of the regional atmospheric circulation pattern is the Aleutian low pressure system The effects of the dominant modes of climate variability influencing the region e g El Ni no e g Wallace et al 1998 the Pacific decadal oscillation e g Mantua et al 1997 and Pacific-North American pattern e g Wallace and Gutzler 1981 can all be understood in terms of how they shift the position and intensity of the Aleutian low These shifts result in a dipole-like pattern with storms having a tendency to track either north or south depending on the phase of the mode 15 and leaving an anomaly of the opposite sign where the storminess is reduced The natural year-to-year variation observed in the region s climate system is well characterized by the standard deviations in annual temperature and precipitation from LW50 Figure 2 2C shows a simple relationship: the interannual variability of precipitation is higher where the mean precipitation is also high However for meltseason temperature the picture is different Whereas the mean was dominated by the north-south gradient the variability of melt-season temperature Fig 2 2D is higher inland reflecting the continentality of the climate 2 2 2 Glaciers in the Pacific Northwest The high annual precipitation totals and widespread high-altitude terrain within this area are conducive to the existence of glaciers The region s glaciers have been extensively mapped as have their changes over recent geologic history e g Harper 1993 Hodge et al 1998 ONeal 2005 Pelto and Hedlund 2001 Post 1971 Porter 1977 Sapiano et al 1998 Sidjak 1999 The glaciers in the region range from the massive tidewater glaciers in southern Alaska to small ice patches in steep terrain In this study we focus on the many temperate alpine glaciers in the area because these are the best suited to reflect a clean signature in their response to climate Even among these temperate glaciers there is a wide range in size and shape giving rise to individual variations in advance and retreat These advances and retreats cannot be interpreted as responses to long-term climate changes alone Climate is by definition the statistics of weather In other words it is the probability density distribution of the full suite of variables that describe the state of the atmosphere over some specified period of interest The World Meteorological Organization defines climate as the statistics within any 30-yr period 16 A stationary climate therefore has constant statistics with a given mean standard deviation and higher-order moments Glaciers are dynamical systems that integrate this natural year- to-year climate variability This integrative quality of glaciers means that even in a constant climate the length of glaciers will vary on decadal and centennial time scales e g RO Reichert et al 2002 Roe 2009 2 3 A linear glacier model A schematic of the linear model employed in this study is shown in Fig 2 3 The model is from RO which is based on that of J ohannesson et al 1989 The model neglects ice dynamics and assumes that any imbalance between snow accumulation and ice ablation is immediately expressed as a rate of change of the terminus position Other aspects of the glacier geometry are specified The absence of glacier flow dynamics means that the linear model is not damped enough on short time scales e g RO but on decadal time scales and longer this model and similar ones are able to reproduce realistic glacier variations for realistic climate forcings RO Oerlemans 2001 Harrison et al 2001 Climate is specified by an annual accumulation rate of P m yr-1 and an average melt-season temperature T Ablation is assumed to be linearly proportional to T C where the constant of proportionality is given by the melt-rate factor Observations suggest that ranges from 0 50 to 0 84 m yr-1 C-1 water equivalent e g Paterson 1994 The lapse rate is taken to be a constant 6 5 C km-1 be the equilibrium glacier length that would result from constant T and Let L P the long-term averages of the melt-season temperature and the precipitation The model calculates the time evolution of perturbation in glacier length L0 that arises from the interannual anomalies in the melt-season temperature T 0 and annual pre- 17 cipitation P 0 From here on we drop the prime symbol and use L T and P to represent the anomalies in length melt-season temperature and precipitation RO show that perturbations in glacier length L away from the equilibrium glacier length for a given constant climate can be described by the following equation: Lt t tan Aabl t AT 0 t Atot t 1 Lt Tt Pt Lt Tt Pt wH wH wH 2 1 The model geometry and parameters are defined in Fig 2 3 t is time in years and t is the interval between successive time steps which we take to be one year Most of the correlations presented in this paper are calculated with respect to Mount Baker in the Cascade Mountains of Washington state 48 7 N 121 8 W Mount Baker is a large stratovolcano flanked by eight glaciers with a broad range of sizes and shapes Mount Baker was chosen because the history of its glaciers is well documented ONeal 2005 its climatic setting is well understood and its glaciers generally fit well into the simple geometrical constraints of the model i e no sharp corners Doing so also complements the analysis in a companion study RO Table 2 1 shows the range in the model parameters and geometry that is reasonable for typical Alpine glaciers in this region taken from RO Ablation areas are calculated from the total area using the accumulation area ratio AAR the ratio of 1 Aabl to Atot which has been shown to vary from 0 6 to 0 8 in this region e g Porter 1977 For simplicity we group the parameters for the three terms in eq 2 1 into the coefficients and respectively Here ranges between 0 81 and 0 97 and is unitless between 9 and 81 m C-1 and between 85 and 240 yr depending on the choice of parameters and the size of the glacier Note that has the largest 18 uncertainty owing to the large uncertainties in and in the AAR both of which in principle can be observed and therefore constrained much better for any specific glacier Table 2 1 also shows a standard set of typical parameters which we use for all calculations from now on unless otherwise stated Equation 2 1 describes a glacier that advances retreats if melt-season temperatures are anomalously low high or if the accumulation is anomalously high low It is the discrete form of a simple first-order ordinary differential equation that has a characteristic response time In the absence of any climate anomalies the glacier asymptotes exponentially back to its equilibrium length with a characteristic e-folding time scale of: t 1 wH tan Aabl For Mount Baker glaciers ranges from 5 to 30 yr Table 2 1 consistent with other estimates for these small mountain glaciers In the presence of climate forcing represents the decorrelation time scale or memory of the glacier RO and Roe 2009 demonstrate that because of this memory a fundamental property of glaciers is that they will naturally undergo persistent multidecadal and centennial fluctuations even in the absence of any persistent climate anomalies RO also show that this linear model is able to capture typical magnitudes of glacier variations in the Cascade Mountains of Washington State and so is adequate to capture the approximate response of glacier length to large-scale patterns of P and T Caveats and possible improvements to the model are noted in the discussion 19 2 4 2 4 1 Results Glacier correlations The aim of this study is to explore how patterns of glacier-length variations are driven by patterns of climate From eq 2 1 an expression can be derived for the correlation between the length variations of two glaciers located at two different locations denoted A and B in terms of the correlations between T and P : LA t 1 A LA t A TA t A PA t 2 2a LB t 1 B LB t B TB t B PB t 2 2b The expected value denoted by angle brackets of the correlation between glaciers A and B is hLA t 1 LB t 1 i A B hLA t LB t i A B hTA t TB t i A B hPA t PB t i A B hLA t TB t i A B hLA t PB t i A B hTA t LB t i A B hPA t LB t i 2 3 Cross terms in temperature and precipitation i e hTA t PB t i have been neglected in eq 2 3 because calculations show that in this region they are not statistically significant at a 95% confidence level Here hLA t LB t i is the covariance of LA and LB which is in turn equal to the correlation between LA and LB rL A B our desired answer multiplied by the standard deviations of LA and LB The covariances hTA t TB t i and hPA t PB t i can be calculated from observations However the other terms in 3 are in need of additional manipulation We elaborate below on hLA t TB t i The other terms can be derived in a similar 20 fashion From the definition of the correlation between TA and TB we can write hTA t i 2 1 2 1 rT t hTB t i T B rT T A 2 4 where rT is the correlation of melt-season temperature between points A and B T is the standard deviation of T at point and we assume that the residual t t is a Gaussian-distributed random number of unit variance at time t Using the right-hand side of eq 2 4 the value for hLA t TB t i can be rewritten as hLA t TB t i rT T B hLA t TA t i T A 2 5 where we have used the fact that there is no correlation between a random number and LA t That is hLA t t i 0 So to find hLA t TB t i we need hLA t TA t i First TA can be written in terms of its autocorrelation T A and the residuals which we assume are governed by another Gaussian-distributed white noise process t : 1 TA t T A TA t 1 1 2T A 2 t 2 6 Therefore using eqs 2 6 and 2 2a we can write 2 hLA t TA t i A T A hLA t 1 TA t 1 i A T A hTA t 1 i 2 7 21 where again we use the fact that hLA t t i 0 Since the expected value of a distribution of numbers is independent of the time step hLA t TA t i hLA t 1 TA t 1 i we rewrite eq 2 7 as 2 A T A T A hLA t TA t i 1 A T A 2 8 Therefore the expected correlation between Lt and Tt is a function of the magnitude of T T the autocorrelation of T T and the memory of the glacier A Finally inserting the right hand side of eq 2 8 into eq 2 5 yields hLA t TB t i A rT T A T A T B 1 A T A 2 9 Derivations directly analogous to the above can be used for the remaining terms in eq 2 3 and yield an equation for the correlation of glacier lengths between A and B: rL A B 1 A T A B T B rT A B T A T B 1 1 A B L A L B 1 A T A 1 B T B B P B A P A rP A B P A P B 1 1 A P A 1 B P B 2 10 The terms relating to climate rT rP T P T P can all be calculated from observations 22 Equation 2 10 reveals that the correlations between the lengths of glaciers in different places are dependent on both the relationships between climate variables and the geometries of the glaciers in question The variables and parameters are the correlation of the climate variables rT rP the standard deviations of the glacier length L precipitation P and melt-season temperature T the memory of the glacier and climate T P and finally the size and shape of the glacier We will now discuss each of these factors in turn and how their respective ranges of uncertainty affect the correlations between glaciers 2 4 2 The spatial correlation of the climate variables Spatial correlations between glacier behavior are fundamentally driven by spatial correlations in the climate: eq 2 10 shows that rL A B is equal to a linear combination of rT A B and rP A B From LW50 we calculate at each grid point the correlations of T and P with their values at Mount Baker Fig 2 4 As expected rT and rP are high in areas surrounding Mount Baker However the spatial extent of significant rT is much greater than that of rP Variations in T are dependent on the perturbations in the summertime radiation balance which appear to be fairly uniform over the region A striking feature of rP is the anti-phasing between Washington and southeastern Alaska The dipole pattern results from the tendency of storms to be more prevalent in one of the two regions leaving the other relatively dry The smaller area of significant values of rP reflects the smaller spatial scale of precipitation patterns 2 4 3 The relative importance of T and P for a glacier While the correlations in T and P are the main factors in correlations in L the relative importance of T or P for glacier length also matters In what follows we determine 23 the ratio of length variations forced only by T denoted as L T to length variations forced only by P denoted as L P These expressions can be derived from eq 2 1 Setting P 0 the expected value of a glaciers length forced only by T is hL2t 1 i 2 hL2t i 2 hTt2 i 2 hLt Tt i 2 11 Using our derivation for hLt Tt i from eq 2 8 the variance of the expected length can be written L2 2 L2 2 T2 2 2 T T2 1 T 2 12 Rearranging eq 2 12 the standard deviation for a glacier forced only by T is s L T T T 1 1 2 2 T 1 1 T Similarly the expression for a glacier forced only by P is s 1 2 P L P P P 1 1 2 1 P 2 13 2 14 The ratio R between the two is therefore R L T L P v u 1 T u t P 1 From eq 2 1 can be rewritten as 2 T 1 T 2 P 1 P AT 0 Atot 2 15 and the ratio of the glacier length sensitivity to melt-season temperature and precipitation fluctuations can also be written: L T R L P v u 1 AT 0 T u t Atot P 1 2 T 1 T 2 P 1 P 2 16 24 The terms 2 T 1 T and 2 P 1 P in eqs 2 15 and 2 16 are similar to one another Because is always less than one and calculations not given show that values for T P are typically close to 0 2 - 0 3 the ratio of these terms will be close to one To convey a clear sense of the regional coherence of glacier patterns we present our analyses as if there were a hypothetical glacier at each grid point in the figure In other words we imagine that within each grid point in the LW50 there is a mountain high enough to support glaciers This is simply a device for clarity of presentation comparison with real glaciers comes directly from Fig 2 1 Figure 2 5A shows R for the standard set of parameters To convey a sense of the uncertainty in R we also combine the highest melt rate with the lowest AAR and the lowest melt rate with the highest AAR Figs 2 5B and C Overall the calculations suggest that over most of the area glaciers are more sensitive to melt-season temperature than to precipitation except for a narrow coastal band where glaciers are always more sensitive to P because of the high precipitation variability and muted melt-season temperature variability i e Fig 2 2 However the extent of T dependence varies greatly depending on the choice of parameters Glaciers with a high melt factor or a large ablation area are much more likely to be affected by variations in T In section 2 5 we explore how small-scale patterns of climate not resolved at this scale can affect this answer 2 4 4 Standard deviations From eq 2 10 it can be seen that the standard deviation of T or P and the standard deviation of L affect rL A B directly Because T and P also strongly influence the sensitivity of glacier length changes section 4c their magnitudes can greatly increase or decrease the importance of R and L 25 We derive a formula for L from the root of the sum of the squares of eqs 2 13 and 2 14 : L 1 2 2 T 2 P 1 2 2 2 2 T 1 P 1 1 2 1 T 1 P 2 17 Figure 2 6 shows L for standard parameters values range from 100 to over 300 m Along the coasts L is high and P is also high Southeast British Columbia also has above-average values in L corresponding to high values in T 2 4 5 Correlations between glaciers with the same geometry We now apply eq 2 10 to each grid point in LW50 and correlate a hypothetical glacier at that point with a glacier that rests on Mount Baker We begin by imposing the same and at each point taking values characteristic for a Mount Baker glacier Table 2 1 to eliminate differences in correlation due to geometry and thus isolate the effect of spatial patterns in climate The effect of differences in geometry and choices in parameters will be addressed in the following section Figure 2 7 shows the expected correlations between a theoretical glacier at each point and a glacier resting on Mount Baker The correlations between glaciers are strongest where both T and P are well correlated with Mount Baker On the southeast coast of Alaska rL is somewhat negative where P is most strongly anticorrelated with Mount Baker and the glaciers are most sensitive to P These results are consistent with those of Bitz and Battisti 1999 There are also regions where T dominates For example the strong sensitivity to T northeast of Mount Baker Fig 2 5 where rT is also high Fig 2 4B gives rise to strong glacier correlations Little to no correlation can be expected in regions where both the T and P correlations with Mount Baker 26 are low and the value of R is ambiguously close to one such as is the case in northern British Columbia and the Yukon Territory of Canada Inferences of the spatial extent of past climate changes are often made by comparing the reconstructed dates of relict moraines Given the point made in this study that regional correlations in glaciers also arise from natural interannual variability alone i e in a constant climate there is some chance that concurrent advances would be misinterpreted Furthermore the statistical significance of a hypothesized change in climate is difficult to establish from the few points that are typically available from even well-dated moraines The integrative nature of a glacier gives it a memory of previous climate states and means that the number of independent observations is much lower than the number of years in a record In Appendix B we show calculations for deriving the appropriate number of degrees of freedom using our model given the autocorrelation of both the glaciers and the T and P values 2 4 6 Correlations between glaciers with differing geometries Assuming that all glaciers have the same geometry is clearly a simplification We expect the spatial correlation between glaciers to weaken if we compare glaciers of different geometries Because we cannot present the full range of glacier geometries at every point we focus on locations that are representative of the range of different climatic correlations with Mount Baker These locations shown in Fig 2 1 were chosen to encompass as large a range as possible for this region of rP rT and R values and are detailed in Table 2 2 We consider five combinations of glacier parameters the five main glaciers of Mount Baker given in Table 2 1 and three values for the AAR at each of the five points Then we correlated the terminal advance and retreat with that of a typical 27 glacier on Mount Baker with an AAR of 0 7 and of 0 67 m yr-1 C-1 The values of rL calculated with respect to Mount Baker as well as rT and rP are shown in Fig 2 8 The correlations are strikingly insensitive to this range of parameter variations Here rT and rP are the main drivers of the correlation between glaciers Differences in the basic geometry are of secondary importance To the extent that parameters do matter the variations in the AAR and are of most importance RO 2 5 Small-scale patterns While the LW50 data set has the advantage of a long record it lacks the small-scale detail of climate patterns due to individual mountain peaks and valleys that strongly influence the behavior of individual glaciers Since 1997 the fifth-generation Pennsylvania State UniversityNational Center for Atmospheric Research Mesoscale Model MM5 Grell et al 1994 has been run by the Northwest Regional Modeling Consortium at the University of Washington at 4-km horizontal resolution over the Pacific Northwest Mass et al 2003 Anders et al 2007 Minder et al 2008 Though the short interval of the model output makes statistical confidence lower it is instructive to evaluate the patterns of temperature and precipitation over the region on such a fine grid and repeat the calculations that we performed using LW50 RO find good correspondence between the MM5 output and snowpack telemetry SNOTEL observations in the vicinity of Mount Baker The performance of the MM5 model in this region relative to observations has also been evaluated by Colle et al 2000 The patterns in the mean annual precipitation in Washington State Fig 2 9A are dominated by the Olympic and Cascade Mountains Localized maxima in precipitation near individual volcanic peaks can be identified The pattern of interannual variability of annual precipitation measured by the standard deviation is similar to 28 the pattern of the mean precipitation Mean melt-season temperatures in the region Fig 2 9B are dominated by elevation differences with colder temperatures recorded in the mountains Interannual variability in the mean melt-season temperature in contrast with precipitation is fairly uniform over the region Fig 2 9D but the amplitude is increased somewhat and exceeds 18 C yr-1 in places Fig 2 9B Using eq 2 15 the spatial pattern in R can be plotted for the standard set of parameters Fig 2 10 Owing to the high interannual variability in annual precipitation the variability of glaciers in the Cascades and Olympic Mountains is predicted to be most sensitive to variability in precipitation This is confined to the high elevations Lower elevation points dominated by temperature variability are not able to sustain actual glaciers in the modern climate The high levels of precipitation variability in the mountains also drive high values of the standard deviation in glacier length exceeding 1400 m in places Fig 2 11 By definition of the standard deviation the glacier would spend approximately 30% of its time outside of the 1 variations Thus over the long term fluctuations of 2 3 km in glacier length should be expected driven solely by the interannual variability inherent to a constant climate RO This result highlights the crucial importance of knowing small-scale patterns of climate in mountainous regions in determining the response of glaciers On this spatial scale interannual climate variations from the MM5 model output are very highly correlated in space This translates into very high spatial correlations in glacier response not shown 29 2 6 Summary and discussion A simple linear glacier model has been combined with climate data to address how regional-scale patterns in precipitation and melt-season temperature combine to produce regional-scale patterns in glacier response In our model framework correlations in the glacier lengths are a linear combination of the spatial correlations in the climate variability The climate correlations are modified by the relative importance of temperature and precipitation to the glacier response which in turn is a function of the glacier geometry and mass balance parameters In coastal regions high precipitation variability and low melt-season temperature variability mean that the patterns of glacier response are controlled by the patterns of precipitation variation Conversely in continental climates patterns of glacier response are most influenced by the patterns in melt-season temperature Results are quite insensitive to variations in glacier geometry it is the spatial patterns in T and P that are the key drivers of spatial patterns in glacier variations Finally using seven years of archived output from a high-resolution numerical weather prediction model shows that the increased total precipitation and precipitation variability characteristic on individual coastal mountain peaks will give rise to large variations in glacier advance and retreat The correlations calculated in this study are derived using a simple model and a grid size larger than the area of a single glacier and so should be regarded as providing insight and not predictions In exchange for being able to understand and analyze the results of the system we have neglected many of the complications that exist in true dynamical glacier systems and mountain climates We feel confident that our choice in LW50 is adequate as the North American Regional Reanalysis model 30 and the 40-yr European Centre for Medium-Range Weather Forecasts ECMWF Re-Analysis ERA-40 grid-spaced data set produced very similar results However climate data with a resolution of 0 5 cannot capture the full gamut of climatic effects in mountainous terrain The unresolved details of small-scale precipitation patterns will not change the results regarding the overall contrast between maritime and continental climates or the general northsouth trends due to the inherent spatial scale of the regional climate patterns It is likeliest to make a difference in the predicted sensitivities of and spatial correlations among the coastal Pacific Northwest glaciers The lesson from the MM5 results about the importance of knowing small-scale orographic precipitation patterns is one of the key findings of this study We also opted to present results in terms of the correlation between glaciers An alternative would have been to calculate empirical orthogonal functions EOFs to find the modes that account for the largest proportion of the variance in glacier advance and retreat Different treatments for the mass balance are also possible: we could have chosen to use a positive degree-day model e g Braithwaite and Zhang 2000 or a full surface energy balance model e g Rupper 2007 to calculate glacier mass balance The assumption that all precipitation is accumulation over the glacier could be relaxed by including a temperature-dependent threshold for snow We feel that this would be unlikely to make any important difference in our main results We have also made significant assumptions regarding glacial processes Chief among these assumptions is the neglect of glacier dynamics However several studies have shown that the linear model is capable of reproducing reasonable variations in glacier length e g RO J ohannesson et al 1989 Oerlemans 2005 and so is adequate for the purposes of the present study Glacier geometry is also highly simplified in the linear model Tangborn et al 1990 concluded that area distribution of each glacier was the main distinguishing characteristic accounting for difference in mass 31 balance on two adjacent glaciers in the North Cascade Range of Washington State between 1947 and 1961 highlighting the complexities in small-scale geometric and climatic factors relevant to glaciers Finally we have focused on glaciers for which the connection with temperature and precipitation is clear and well understood Our framework cannot be directly applied to tropical or tidewater glaciers glaciers with a history of surging or large ice caps or ice sheets where the physics of that connection is more complex Further work should be performed understanding not only spatial patterns in glacial correlation but temporal patterns as well The model can also readily be used to evaluate when and where a climatic trend in glacier length can be detected against the background interannual climatic variability 32 Boulder Deming Coleman Easton Rainbow Typical Atot km2 4 30 5 4 2 1 3 6 2 7 4 0 Aabl km2 1 3 1 6 0 64 1 1 0 81 1 2 tan 0 47 0 36 0 47 0 34 0 32 0 4 w m 550 450 650 550 300 500 H m 50 50 39 51 47 50 yr 10 9 20 17 13 12 0 90 0 89 0 95 0 94 0 92 0 92 m C-1 32 48 17 26 39 77 yr 160 240 85 130 190 160 Table 2 1: Values for geometric parameters that are used in eq 2 1 for five glaciers on Mount Baker Washington RO For the values shown here an accumulation area ratio AAR 0 7 was assumed Here Atot is the total glacier area m2 and Aabl the area over which there is net ablation m2 is the melt-rate factor a standard value of 0 67 and a range of 0 5 to 0 84 m yr m-1 C m-1 was used the atmospheric lapse rate 6 5 C km-1 the slope of the bed w the average width of the ablation area H the uniform height or thickness of the glacier and t is the e-folding relaxation time scale yr unitless a m C-1 and yr are combinations of the above variables as prescribed in 1 In the last column values are generally representative of the Mount Baker glaciers and are used for the standard calculations unless otherwise noted in the text 33 Point Lat N Lon W Nearest Mountain rP rP R A 47 3 123 7 Olympus 0 85 0 92 0 39 B 49 8 120 2 Girabaldi 0 75 0 82 2 10 C 53 3 116 8 Columbia Ice Field 0 40 0 26 2 00 D 46 3 119 8 Adams 0 19 0 85 2 40 E 60 3 142 7 Wrangell -0 37 0 22 0 41 Table 2 2: Key points to correlate with Mount Baker over a variety of glacier geometries: the latitude and longitude of each point are listed as well as the correlations in precipitation rP and temperature rT and the sensitivity ratio R See Fig 2 8 34 E C B A D Figure 2 1: Glaciers in the Pacific Northwest shown in red Data from the Global Land Ice Monitoring from Space GLIMS project http: www glims org The location of Mount Baker is denoted with a star Also indicated in the figure are the locations where glacier model sensitivity is tested Figure courtesy of Harvey Greenberg 35 a 60 N 3 b 2 5 60 N 2 55 N 20 15 55 N 1 5 50 N 50 N 1 ave annual precipitation 45 N 150 W 0 5 120 W 135 W 45 N 0 150 W m yr-1 c 0 4 5 oC 1 1 1 60 N 0 5 55 N 120 W 135 W d 0 6 60 N 10 ave melt-season temperature 0 9 55 N 0 8 0 3 50 N 0 7 50 N 0 2 1S annual precipitation 45 N 150 W 0 1 120 W 135 W 0 m yr-1 1Smelt-season temperature 45 N 0 6 0 5 150 W 120 W 135 W 0 4 oC Figure 2 2: Climate mean and variability in the Pacific Northwest from LW50: a mean annual precipitation m yr-1 b mean melt-season JJAS temperature C and interannual standard deviation of c mean annual precipitation m yr-1 and d melt-season temperature in C 36 Total Area Atot Melt Area AT 0 ELA Ablation Area Aabl H t gh ei H Width w Slope tan F Figure 2 3: Schematic of linear glacier model based on J ohannesson et al 1989 Precipitation falls over the entire surface of the glacier Atot Melt is linearly proportional to the temperature and a constant lapse rate is assumed The basal slope is tan Melt occurs over the lower reaches of the glacier where melt-season temperature exceeds 0 AT 0 and net mass loss occurs over a smaller area where melting exceeds precipitation Aabl The upper boundary of this latter region is known as the equilibrium line altitude ELA The thickness H of the glacier and the width of the ablation area w remain constant by assumption 37 Figure 2 4: Correlation in annual mean precipitation between each grid point and Mount Baker from LW50 data set note the dipole of correlations between Alaska and Washington b As in a but for the correlation of melt-season temperature note the widespread correlation of uniform sign over the region Correlations exceeding about 0 28 would pass a t-test at greater than 95% confidence 38 a 5:1 4:1 O 60 N 3:1 O 55 N 2:1 1:1 O 50 N O 45 N 1:2 AAR 0 7 M 0 67 m yr-1 oC-1 1:3 1:4 O 150 W 120 W O 135 W b c O O 60 N 60 N O O 55 N 55 N O O 50 N O 45 N 1:5 50 N AAR 0 6 M 0 84 m yr-1 oC-1 O O 150W O 45 N O 135W 120W AAR 0 8 M 0 5 m yr-1 oC-1 O O 150W O 135W 120W Figure 2 5: Ratio of sensitivities to temperature and precipitation for a typical glacier geometry at each grid point for different choice of model parameters Warm colors denote temperature sensitivity while cool colors denote sensitivity to precipitation a The standard parameters b the largest ablation area and melt rate factor and c the smallest values of the ablation area and melt rate factor 39 300 280 O 60 N 260 240 O 55 N 220 200 O 50 N 180 160 O 140 45 N 120 O O 150 W O 135 W 120 W m 100 Figure 2 6: Standard deviations of glacier length at each grid point if a typical glacier exists at each grid point calculated from 17 Large standard deviations in length are driven by large standard deviations in either precipitation or temperature cf with Fig 2 2 40 1 0 8 O 60 N 0 6 0 4 O 55 N 0 2 0 O 50 N -0 2 -0 4 O -0 6 45 N -0 8 O O 150 W O 120 W -1 135 W Figure 2 7: Correlations between a typical glacier at each grid point and at Mount Baker calculated from eq 2 10 41 1 Correlation coefficient 0 8 T P T T P 0 6 0 4 P T 0 2 P 0 0 2 T 0 4 P A B C Location D E Figure 2 8: Sensitivity test of correlations at selected locations see Fig 1 to varying the glacier geometry and parameters: T and P denote melt-season temperature and annual precipitation correlations between that location point and Mount Baker Colored symbols represent the correlation of glacier length between that location and Mount Baker and the range arises from using the five different parameter sets applying to the different Mount Baker glaciers given in Table 2 1 Finally the different colors mean a different AAR was used: green AAR 0 6 red AAR 0 7 and blue AAR 0 8 42 a ave annual precipitation o 50 N 6 5 5 b 24 ave melt-season temperature o 50 N 22 5 20 4 5 18 4 o 3 5 48 N o 16 48 N 3 14 2 5 12 2 o 1 5 46 N 10 o 46 N 8 1 o 124 W o 122 W 0 5 o 120 W m yr-1 c 1S annual precipitation o 50 N 1 4 o 124 W o 120 W o 1 4 1S melt-season temperature 50 N 1 2 1 0 8 o 48 N 6 C d o 1 2 o 122 W 1 o 48 N 0 8 0 6 0 6 0 4 o o 46 N 0 2 o 124 W o 122 W o 120 W 0 m yr-1 46 N 0 4 o 124 W o 122 W o 120 W oC 0 2 Figure 2 9: Archived output from the MM5 numerical weather prediction for the Pacific Northwest at 4-km scale: a mean annual precipitation b mean melt-season temperature and standard deviation of c precipitation and d melt-season temperature Contours of the model surface elevation are also plotted every 500 m the location of Mount Baker is indicated with a star Note the small-scale patterns of climate associated with the mountainous terrain in particular the high rates of orographic precipitation 43 5:1 O 50 N 4:1 3:1 2:1 O 48 N 1:1 1:2 1:3 O 46 N 1:4 O 124 W O 122 W O 120 W 1:5 Figure 2 10: Ratio of sensitivities to temperature and precipitation of a glacier length with a typical Mount Bakerlike geometry calculated at every model grid point from eq 2 16 Blue indicates a greater sensitivity to precipitation The mountainous regions of the Olympics and Cascades where glaciers in the region actually exist are dominated by sensitivity to variation in the precipitation 44 1400 O 50 N 1200 1000 800 O 48 N 600 400 O 46 N 200 O 124 W O 122 W O 120 W m 0 Figure 2 11: The standard deviation of glacier length calculated from eq 2 17 using the 4-km resolution MM5 output This fine-resolution scale shows that in the mountainous regions where glaciers exist the standard deviation in glacier length is much higher than in lower elevations The high standard deviations are driven by the high variability in precipitation there 45 Chapter 3 GEOMETRIC INFLUENCES ON GLACIER VARIABILITY 3 1 Introduction As discussed in Chapter 2 mountain glaciers are often cited as indicators of climatic variability and change They directly integrate changes in snowfall temperature which drives ice melt Glaciers dynamically thicken thin or advance retreat in response to climatic variations Because evidence for glacier change is often derived from terminal moraine deposition historical records or aerial photography the variations in length are the most straightforward way to track a glacier s health Nye 1960 described how variations in the lower part of a glacier respond both to the direct effects of snowfall and ice melt and to the arrival of material from the upper part of the glacier which can take between 3 and 30 years Following on this much work was done to understand what drives the timing and magnitude of variations in glacier length e g Nye 1961 1963 J ohannesson et al 1989 Oerlemans et al 1998 Harrison et al 2001 Weber and Oerlemans 2003 Roe 2011 Oerlemans 2012 Harrison 2013 Reichert et al 2002 and Roe and O Neal 2009 specifically studied how glacier lengths vary in response to interannual climatic forcing Their work determined the expected range of glacier variation in response to interannual variations in precipitation and temperature Variations that exceed the bounds of this range indicate that a glacier is responding to a true climatic shift rather than a short-term variation in precipitation or temperature Further Huybers and Roe 2009 showed that a glacier s latitude and proximity to the ocean correlates with whether these changes 46 are more sensitive to variations in temperature or precipitation Along with the mean state of the climate the steepness shape and makeup of the bed the size of the catchment area the width of the tongue and the elevation of the glacier contribute to determining the mean length and thickness of a glacier These geometric effects can be large For example Kessler et al 2006 showed that 97% of the disparity between the lengths of glaciers flanking the east and west side of California s Sierra Nevada range during the Last Glacial Maximum is attributed to the topographic asymmetry of the mountains alone These geometric characteristics will also determine the amplitude and timing of a glacier s response to climatic variations Oerlemans et al 1998 concluded that while there is no straightforward relationship between glacier size and fractional change in ice volume hypsometry plays an important role in determining the variability of a glacier and that in general smaller glaciers fractionally lose more mass Kuhle 1988 showed that glacier geometry and mass balance both correlate with deviations in the Equilibrium Line Altitude ELA For this work I use a dynamic flowband model which incorporates width variations to compare length variations between glaciers with unique geometric characteristics as they respond to identical climate forcings The geometric setting is based on Mount Baker a glaciated volcanic peak in the Cascade Range of Washington State USA Fig 3 1 The glacier models are forced with randomly generated perturbations in precipitation and temperature based on the local present-day means and standard deviations The model is run repeatedly altering the slope shape width bed roughness and area for each experiment The correlation coefficients are calculated for pairs of the resulting glacier-length time series The main purpose of this work is to determine the geometric parameters that most affect the magnitude of glacier variability and the temporal coherence between pairs of glaciers 47 3 2 Mount Baker glaciers Continuing the work of Roe and O Neal 2009 Huybers and Roe 2009 and Roe 2011 I have chosen Mount Baker as my study area Mount Baker is a large stratovolcano located in the Cascade Mountains of Washington state U S A 48 7 N 121 8 W It is flanked by eight glaciers with a broad range of shapes and sizes whose history and geometry have been well-documented and studied The glaciers on Mount Baker have undergone large variations during the Holocene e g Thomas et al 2000 and a large body of research has been done to understand the general pattern of retreat since the local Little Ice Age Harper 1992 1993 Pelto and Riedel 2001 Pelto and Hedlund 2001 ONeal 2005 and the individual glacier dynamics e g Harrison 1970 Harper 1993 discussed the historical variations on Mount Baker All of the glaciers exhibit a general retreat prior to 1940 an advance after 1940 and a subsequent retreat though the timing and magnitude of these advance and retreats vary He observed that Easton and Rainbow Glaciers responses lag behind the Coleman and that the total magnitude of Coleman Glacier s response is larger than Easton and larger than Rainbow with the exception of the initial retreat 3 2 1 Climate The present-day climate of the Pacific Northwest is strongly affected by the peaks and valleys of several mountain ranges giving rise to rich and distinct weather patterns e g Bitz and Battisti 1999 Minder et al 2008 Despite important mountain-scale precipitation patterns Pelto and Riedel 2001 show that the glacier mass balance throughout the major North Cascadian glaciers is highly correlated indicating that large-scale climate conditions can explain much of the regional glaciers mass-balance profiles 48 As noted in the previous chapter the major feature of the region s atmospheric circulation pattern is the Aleutian Low pressure system which responds to the dominant modes of climate variability in the region e g ENSO Zhang et al 1997 the PDO Mantua and Hare 2002 and the PNA Renwick and Wallace 1996 Though these modes of variability lend some memory to the climate system the year-to-year variation in the region is well characterized by the standard deviations from the mean in annual temperature and precipitation Annual mean precipitation at Diablo Dam near Mount baker is equal to P 1 89 m yr-1 with a standard deviation of P 0 36 m yr-1 The values for temperature are T 16 8 C and T 0 78 C I assume a steady atmospheric lapse rate of -6 5 C km-1 and relate the annual melt rate to temperature through an empirical melt factor which is equal to 0 65 m yr 1 C 1 3 2 2 Geometry I model three of Mount Baker s glaciers chosen for their distinct size shape and bed slope see Fig 3 1 and Table 3 1 from Harper 1992 Roe and O Neal 2009 Easton Glacier is mid-sized with an accumulation area that is only slightly wider than its ablation area which has a characteristic width1 of 420 m It rests on a bed with a slope of 18 with a modern length of 4 2 km and area of 3 3 km2 Though its bedslope is similar to that of Easton Glacier Rainbow Glacier is smaller its area covering 2 1 km2 over a length of 3 2 km Rainbow Glacier s area widens near the middle of its present-day length and tapers in the ablation zone where its characteristic width is 315 m Coleman-Roosevelt Glacier heretofore referred to as Coleman Glacier has a similar length to Easton 4 9 km but has a much wider catchment zone and therefore a much larger area 10 6 km2 It rests on a slope of 25 which is steeper 1 i e average width of the ablation area 49 than either Rainbow or Easton Glacier and its characteristic ablation width is 630 m This work does not aim to capture the true behavior of a specific set of glaciers but rather to gain insight into the nature of a general glacier s response I therefore approximate each glacier s footprint as symmetric around a flowline and assume a linearly sloping bed When the modeled glaciers grow beyond their present-day position the ice is directed down a rectangular channel that is a continuation of the present-day glacier tongue 3 2 3 Altering the glacier geometry To isolate the geometric factors that have the strongest influence on decorrelating neighboring glaciers I use the model described in the following section to capture the behavior of Easton Coleman and Rainbow Glaciers I then alter a single geometric parameter for each of these glaciers and run the new glacier to steady state The length of the domain and therefore the baseline T at the end of the domain is also changed so that the altered glacier has the same steady-state length as its original counterpart The glacier configurations are as follows: Original Glaciers: Easton Eorig Rainbow Rorig and Coleman Corig Glaciers are the baseline glacier models which capture the thickness and length profile of the present-day glaciers on Mount Baker Fig 3 5A E and I using their width distribution I assume a planar bed both because bed geometry is not readily available and for comparative simplicity The map view of each of these glaciers from Fig 3 1 is also shown in Fig 3 5D F and J for Easton Rainbow and Coleman glaciers respectively Width: Each of the glacier s width variations are removed so the glacier is described by a flowline of uniform width These experiments are referred to as 50 Ew Rw and Cw to denote an Easton Rainbow and Coleman Glacier with an unchanging width The bed geometry remains as shown in Fig 3 5A E and I glacier profiles not shown Slope: Easton and Rainbow Glaciers are set to a 25 slope which is Coleman s original slope E25 and R25 respectively Coleman glacier likewise is set to Rainbow and Easton s 18 slope C18 The width profile remains as in Fig 3 5D F and J glacier profiles not shown Easton Area: The aspect ratio of Easton Glacier is preserved but the length is increased or decreased by 50% Elarge and Esmall See Fig 3 5 panels G H K and L Bed Shape: The cross-sectional shape of Easton Glacier s bed slope is altered to reflect a parabolic divot into the longitudinal valley profile similar to those seen in nature Anderson et al 2006 Ecurve Fig 3 5B Bed roughness is added by imposing a sine wave with an amplitude of 5 m on a linear bed E 5sin x not shown and another with an amplitude of 10 and a wider spacing E 10sin 5x Fig 3 5C These profiles have the same width distribution with the original Easton Glacier profile Fig 3 5D 3 3 Glacier model Glaciers are deformable bodies that can be described by the physical laws of conservation and thermodynamics Glacier models span many levels of complexity from analytical steady-state profiles to full 3D Navier-Stokes simulations For this work I use a flow-band finite-volume model which responds to perturbations in melt-season temperature and annual mean precipitation Leysinger-Vieli and Gudmundsson 2004 compared a two-dimensional numerical model which solve to full equations for velocity and stress fields to a shallow-ice model and show that there is no significant difference 51 in advance or retreat rates between the two Further they found only a slight change in steady-state lengths I therefore proceed with using a shallow-ice approximation SIA model Hutter et al 1981 Hutter 1983 The glacier is assumed to have an accumulation area with a fixed size and shape Any loss or gain of mass is realized either in the thickness profile of the glacier or at the glacier s tongue advancing down slope through a rectangular channel The length variations are departures from an equilibrium steady-state value and the length and profile thickness anomalies are direct responses to anomalies in melt and precipitation alone the effects of wind redistribution and refreezing of meltwater and sublimation are not taken into account The model solves the continuity equation using finite-volume methods Patankar 1980 Assuming constant ice density the glacier s thickness evolution is described using a standard differential equation for conservation of mass: H q b t x 3 1 H x t is the thickness of the ice where t is time x is the longitudinal distance t is the accumulation ablation rate written from the head of the glacier and b x in terms of precipitation P and melt which is a function of temperature T The flux of ice q x t through each control volume in the glacier model is defined by the depth-averaged velocity u x t that the ice flows through a cross-sectional area of the glacier s width times height w x H x t q x t w x u x t H x t 3 2 The total velocity is the sum of the velocity due to the internal deformation of the ice ud and the sliding velocity us To determine ud the SIA assumes that longitudinal stresses can be ignored and that all stress is due to basal shearing stress 52 The SIA relates the vertical gradient in velocity in the bed-parallel vertical profile to the to the driving shear stress d raised to some power n an empirical value chosen to be 3 as per convention The driving stress is a function of both the ice s thickness and the surface slope of the ice profile: d gH dh where is the density of ice dx g is the acceleration due to gravity and h x t is the ice-elevation H x t plus bed elevation zb The depth-averaged horizontal velocity in the ice is then: u us ud us 2 AH d n 1 d n 2 3 3 where A is a function of ice temperature and describes the ice s softness For this work A is assumed to be constant The sliding speed is derived from a Weertman-style law where the basal water pressure is assumed to be a function of the ice load above Following Oerlemans 2001 : us fs dm H 3 4 where fs is a constant chosen to approximate observed present-day glacier thicknesses The exponent m like its deformational counterpart n is chosen to be 3 after Oerlemans 2001 When Eq 3 1 is rewritten as a diffusion equation it can be solved for using finite-volume methods: dH dt x h b x 3 5 where q x t h 1 x is not a constant but is itself a function of the ice thickness Therefore this model solves for the ice surface elevation implicitly and the length of the glacier is tracked at each time step 53 3 4 Model application and results Because this work aims to characterize the correlation between glaciers as they experience interannual climate variability rather than the true history of the glaciers no trends are applied to the climate forcings Instead the glaciers are forced with 1000-year stochastic time series of precipitation and temperature with standard deviations reflecting those from the historical climate records described above The variations in the precipitation and temperature time series are shown in Fig 3 3A & B The precipitation is assumed to be uniform over the length of the glacier and all precipitation falls as snow This is a reasonable approximation since as discussed in Chapter 2 about 80% of the Pacific Northwest s regional precipitation occurs during the months of October-March when high-elevation temperature is below freezing The temperature profile itself decreases linearly with height and so varies along the glacier s length and between glaciers These forcings are applied to each of the model configurations described in Section 3 2 3 and the modeled length variations are recorded over time The standard deviation of each glacier terminus position L and the correlation coefficient r between pairs of glaciers are computed see Table 3 2 3 4 1 Original Glaciers The time series for Corig Eorig and Rorig are shown in Fig 3 3C Though the glaciers are responding to the same climate forcing the Coleman Glacier varies with a higher amplitude and with higher frequency than the Easton or Rainbow glaciers L C 269 m L E 188 m L R 230 m The r-value of the time series of Corig and Eorig is 0 79 while Eorig and Rorig are correlated at 0 87 The time series of Corig and Rorig have a correlation coefficient of 0 54 54 3 4 2 Width When the width variations of the glaciers are removed the correlation coefficients increase: the correlation between Cw and Ew is 0 82 Ew and Rw is 0 97 and Cw and Rw is 0 72 The correlation between each of these uniform-flowband model runs with their corresponding original glacier model runs is above r 0 9 see the grey lines in Fig 3 5A B and C although the pair of Rainbow Glacier models has the lowest r indicating that its irregular hypsometry can strongly effect its pattern of advance and retreat Without width variations less snow is fluxed through the system and so each glacier s standard deviations are all substantially smaller than the standard deviations of the original models L C 103 m L E 111 m L R 107 m 3 4 3 Slope When Coleman Glacier is set to 18 C18 the same angle as Eorig the correlation between the two is nearly perfect: r 0 99 The correlation between C18 and Rorig is also improved with r 0 85 Likewise the correlation between Corig and the higher-sloped E25 and R25 is also very high: r 0 99 Conversely the correlation between the original glaciers and their new-slope counterparts is relatively low: for Coleman Glacier r18 orig 0 78 Easton Glacier r25 orig 0 83 and Rainbow Glacier r25 orig 0 82 see the green lines in Fig 3 5A B & C This indicates that bedslope has a very strong effect on the timing of the glacier advance and retreat The smallest r for the Rainbow Glacier pair is still high compared to the correlation between Corig and Rorig The variations of C18 are larger than the original model and the variations of E25 and R25 are smaller than the original models L C 310 m L E 167 m L R 203 m 55 3 4 4 Easton Area The time series of Eorig Esmaller and Elarger are shown in Fig 3 5D It is apparent that the amplitude of the variation for all three models is comparable L larger 206 m L smaller 160 m This may not be intuitive given that the length of Elarger is twice as long and that and 6 times larger in area than Eorig and that Esmaller is half the length and 2 5 times smaller in area than Eorig The correlations between the similarly shaped glaciers are comparable to those of the correlations between Easton Glacier and Rainbow or Coleman Glaciers Eorig and Esmall have a correlation of r 0 86 and Eorig and Elarge have a correlation of r 0 87 The correlation between Esmall and Elarge is 0 65 The larger glacier which accumulates more snow also loses ice more readily the converse is true for the smaller glacier Therefore hypsometrically similar glacier distributions may yield a similar amplitude of variability but will respond with a different time scale of variability Further the fractional variations in length are much larger for the smaller glacier 3 4 5 Bed Roughness Introducing Easton Glacier to a parabolic bed Ecurve or a sinusoidally roughened bed E5sin x E10sin 5x does little to changes the amplitude of the variations L curve 179m L 5sin x 188 m L 10sin 5x 186 m The correlation between each of these glaciers and Eorig is r 0 99 3 5 Discussion and summary The experiments described above explore the sensitivity of glacier response to each of these factors Bed slope hypsometry and the overall size of the glacier all affect the timing of glacier advance and retreat My model experiments are consistent with the observations of Harper 1993 showing a lagged response of Easton and Rainbow Glaciers behind Coleman Glacier and a larger magnitude of variability from Coleman 56 in comparison to the other two glaciers For each experiment larger glaciers respond on shorter timescales than smaller glaciers The linear formula for from Roe and O Neal 2009 shows that the timescale of response is inversely proportional to the ablation area of the glacier The Coleman Glacier and its altered counterparts indeed have larger ablation areas than the Easton or Rainbow glaciers allowing warmer temperatures to melt more ice away and more snowfall to be caught when the precipitation increases This reasoning also explains why removing width variations increases the glacier correlations for the non-varying width experiments only variations in ablation-area length affect the net accumulation or melt whereas in the original experiments differences in width alter the amount of ice collected or removed from the glacier Similarly the largest glaciers Elarge and the suite of Coleman-like glaciers all have high correlation coefficients even when their values for L differ from one another Glaciers with the same bed slope tend to have high correlation coefficients This is unsurprising because again Roe and O Neal 2009 showed that the timescale is inversely proportional to the tangent of the bed slope A notable exception to this general rule is the correlation between Elarge and Rorig which both lie on 18 slopes but are have an r-value of 0 65 This relatively low correlation shows how the overall size and hypsometry of the glaciers also affect the timescale of response There are some r-values that are surprisingly high because the glaciers being compared appear to have very few common characteristics For example R25 and C18 have a near-perfect correlation The slope and ablation area appear to balance one another in this case Similarly R25 has high correlations with the Cw and Ew which reinforces the idea that the hypsometry of the Rainbow glacier strongly affects its timescale of response 57 To look for evidence of shorter timescale variability researchers should look to records of glaciers on steeper slopes or glaciers with large ablation areas It is important to note that comparable magnitudes of variability is not predictive of the correlation of advance and retreat of the glaciers Long records of such detailed temporal or spatial information about glacier length variations are rare However this work complements Chapter 2 allowing us to freely explore the effect of geometric differences in glacier length agreement informing the observations of regional glacier advance and retreat that do exist When comparing the advance or retreat of glaciers one must take into account these best-case length correlations before interpreting a regional climatic signal The temperature or precipitation time series will be uniquely integrated by glaciers with their own array of geometric parameters Detecting a coherent regional climatic signal requires this preliminary understanding of how the glacier dynamics filter the climate 58 Coleman Easton Rainbow units Atotal 10 6 3 3 2 1 km2 Aabl 4 0 1 4 1 1 km2 L 4 89 4 35 3 0 km 25 18 5 18 5 Wchar 630 420 315 m Hchar 43 49 39 m char 3 5 10 8 yr C Table 3 1: Default geometric inputs to glacier models Length and area are based on values for the 1990 s Harper 1992 The estimates for come from the linear formula in Roe and O Neal 2009 59 Corig Eorig Rorig C18 E25 R25 Cw Ew Rw Elarge Esmall Corig 1 0 Eorig 0 79 1 0 Rorig 0 54 0 87 1 0 C18 0 78 0 99 0 85 1 0 E25 0 99 0 83 0 58 0 82 1 0 R25 0 99 0 77 0 82 0 99 0 87 1 0 Cw 0 97 0 73 0 52 0 71 0 96 0 77 1 0 Ew 0 88 0 98 0 81 0 98 0 91 0 99 0 82 1 0 Rw 0 77 0 99 0 91 0 99 0 81 0 98 0 72 0 97 1 0 Elarge 0 98 0 87 0 65 0 86 0 99 0 89 0 93 0 85 1 0 Esmall 0 55 0 86 0 99 0 84 0 59 0 81 0 53 0 81 0 90 0 65 1 0 L m 269 188 230 310 167 203 103 111 107 206 160 Table 3 2: Correlations between glacier lengths All runs are done with the same random 1000 year precipitation and temperature time series C Coleman Glacier E Easton Glacier R Rainbow Glacier orig original model configuration w no width variations 18 and 25 refer to the altered bed slope large and small refer to glaciers that have the same shape as Easton Glacier but are double and half the length respectively L is the standard deviation in glacier length 60 Figure 3 1: Major glaciers of Mount Baker Washington State U S A Figure is modified from Roe and O Neal 2009 The outlines represent the width variation used in the glacier modelling Advances beyond the present-day length of the glacier follow a rectangular channel that is equal to the width at the end of the ablation area referred to in the text as the characteristic width 61 Figure 3 2: Glacier and bed profiles as well as map view widths for several of the model experiments A: Original Easton Glacier B: Easton Glacier with a linear bedslope that has been modified with a sine wave with amplitude 10 and phase 5x C: Parabolic bed with Easton Glacier D Map view of Easton glacier as in Fig 3 1 and applied to glaciers in panels A-C E: Original Rainbow Glacier F: Map view of Rainbow glacier as in Fig 3 1 and applied to the glacier in panel E G Smaller version of Easton glacier with half the length and a proportionally smaller width H Map view of glacier in panel G I Original Coleman Glacier J Map view of Coleman glacier as in Fig 3 1 and applied to the glacier in panel J K Larger version of Easton glacier with half the length and a proportionally larger width L Map view of glacier in panel K 62 Width m 2 5 2 1 5 0 2 2 0 500 1 5 2 2 Length km G 2 5 2 1 5 3 2 5 2 1 5 0 2 4 H 500 0 500 2 4 Length km L 500 0 500 0 2 4 Length km 4 0 1000 0 2 4 Length km 5 K 4 D 0 2 1000 4 Elevation km 3 2 2 4 Elevation km Elevation km 500 0 3 1 0 4 J Width m 2 5 0 Width m 2 F 3 0 C 4 1 5 1 0 Width m Elevation km B 2 Width m Width m 3 I 2 5 Width m E Width m A 4 3 2 1 0 2 4 6 8 1000 0 1000 0 2 4 6 Length km 8 63 A meters Precipitation Variations 1 0 1 B Temperature Variations C 2 0 2 C Glacier Length Variations 1 Coleman Easton Rainbow kilometers 0 5 0 0 5 1 200 400 Time 600 years 800 1000 Figure 3 3: The top two panels show 1000 years of random precipitation and temperature variations applied to the glacier models P 0 36m T 0 78 C in agreement with historical records from the nearby Diablo Dam weather station The bottom panel shows the glaciers length variations in response to the precipitation and temperature forcings Note that the frequency of glacier response is much lower than that of the climate forcings 64 Figure 3 4: A B C: The original altered slope and uniform-flowband time series of glacier length variability for the Coleman Easton and Rainbow Glaciers respectively D: The glacier length response for the original Easton Glacier as well as the smaller and larger versions of the glacier B Glacier Length km Glacier Length km E25 1000 1 0 5 0 400 600 Time yr 1000 Ew 800 800 0 5 400 600 Time yr Eorig 200 200 Cw C18 Corig 1 1 0 5 0 0 5 1 C D Glacier Length km Glacier Length km A 200 400 600 Time yr 800 200 400 600 Time yr 800 1 0 5 1000 Elarger 0 5 0 Eorig Esmaller 1000 1 1 0 5 0 Rw 0 5 R25 Rorig 1 65 66 Chapter 4 LAKE LEVEL CHANGES IN RESPONSE TO INTERANNUAL CLIMATE VARIABILITY Chapter 4 in full is currently being prepared for publication as Lake Level Changes in Response to Interannual Climate Variability authored by K Huybers S Rupper and G H Roe The dissertation author was the primary investigator and author of this paper 4 1 Introduction Lakes are important archives of climate history responding sensitively to variations in evaporation and precipitation A lake integrates climatic information over its entire catchment area reflecting regional climate signals with a simple volumetric response Langbein 1961 noted that closed-basin lakes which are found in semi-arid regions and lack drainage outlets fluctuate more than open lakes because variations in the inflow can only be compensated by a change in the lake s surface area Therefore closed lakes are particularly sensitive to climate fluctuations and have been the subject of many paleoclimate studies Street-Perrott and Harrison 1985 The integrative nature of lakes also complicates the interpretation of a region s climatic history A lake proxy record does not distinguish between an increase in precipitation and a decrease in evaporation Moreover lakes act as low-pass temporal filters on the climate For example if a lake that is initially in steady state experiences a spike in precipitation its level rises and spatial extent increases With a larger surface area the net evaporation also increases and the lake gradually low- 67 ers and returns to its original size The size and shape of the lake and the mean climatic state determine the time it takes to return to equilibrium This delayed and smoothed response to a climate signal is a hallmark of other geophysical systems with memory such as the ocean s mixed layer Hasselmann 1976 Frankignoul and Hasselmann 1977 and glaciers Oerlemans 2000 Roe 2011 In terms of lakes both the spatial and temporal integration of evaporation and precipitation can complicate the attribution of a lake-level change to a single climatic event In this study we develop a lake-level model to characterize the nature of a lake s response to climate variations aiming to improve interpretations of lake-level changes in relation to climate and quantify the integrative nature of lakes We choose to focus on the closed-basin Great Salt Lake GSL because of its long historical lake-level and climate records and detailed bathymetry though this work can be applied to any other closed-basin lake system The model is validated against historical measurements In order to estimate the lake-level response to interannual variability alone we drive the lake model with a synthetic record of year-to-year fluctuations based on modern instrumental observations of precipitation and evaporation that occur even without a climate change Using a mass-conservation model we calculate the principal metrics of lake variability: the standard deviation and autocorrelation of the lake-level record and the expected frequency with which a lake exceeds or falls below a given level We also create a linearized version of the lake-level model for which analytic expressions for the above metrics can be derived and which capture much of the behavior of the full model The differences between the two models highlight the non-linear aspects of the lake s response We find that the magnitude of the GSL s historical lake-level fluctuations is consistent with a system driven purely by interannual variability 68 Finally we emphasize the importance of lake geometry on the integration of climate by contrasting lake-level response to interannual climate variability for three distinctly-shaped closed-basin lakes Their divergent responses highlight the importance of understanding how a lake s unique geometry and mean climatic state integrates the regional climate history 4 2 The Great Salt Lake The GSL is located to the northwest of Salt Lake City Utah USA It is bounded by the West Desert to the west the Wasatch Range to the east and is one of the largest terminal lakes in the world with a surface area averaging 4300 km2 including evaporation ponds for mineral recovery over the past 166 years see Fig 4 6A The GSL is filled predominantly by inflow from surrounding rivers 66% and direct precipitation 31% with groundwater accounting for the small balance of the input Arnow 1985 Water is lost primarily through evaporation Despite its vast area the lake is quite shallow with a maximum depth of 10 meters e g Arnow and Stephens 1990 This aspect ratio is summarized in the lake s hypsometry Fig 4 6B taken from Loving et al 2000 These dimensions mean that even a small imbalance between inflow and outflow can drive large changes in lake area The GSL has a long historical record of lake level Fig 4 6A From 1847-1874 lake levels were estimated by observing the water depth over sandbars in the lake Arnow and Stephens 1990 Since 1875 the United States Geological Survey USGS has been collecting water-surface elevation data directly After linearly detrending the time series of interannual lake level the standard deviation is 1 14 m We will characterize lake level by the elevation of the lake surface above sea level a s l Over the historical record the average lake level has been 1280 4 m a s l The record low in 1963 was 1277 5 m a s l corresponding to a maximum depth of 8 m and a surface 69 area of 2500 km2 In contrast the lake s historical high in 1987 of 1283 8 m a s l corresponds to a depth of 14 m and a surface area of 6200 km2 This high stand required an expensive pumping project to relocate the excess water Loving et al 2000 Thus lake area has varied by a factor of approximately 2 5 over the historical record 4 2 1 Climate Precipitation The catchment basin of the GSL is large 5 5 104 km2 and topographically varied so a single rain gauge does not reflect the entire basin s precipitation Given sparse and sometimes noncontinuous records there will be some uncertainty in the precipitation history For this work we choose to use the University of Delaware s monthly gridded precipitation product which provides a continuous record from 1900 2010 based on an interpolation onto a 0 5 by 0 5 latitude longitude grid Matsuura and Willmott 2012 We sum the monthly totals into an annual record based on the water year from October to September Arnow 1985 Arnow and Stephens 1990 Fig 4 6B Based on this data set the mean P and standard deviation P in precipitation for the GSL are 0 37 m yr-1 and 0 08 m yr-1 respectively Evaporation Because it is difficult to directly measure evaporation data is sparse and unreliable Overlake evaporation is a function of temperature wind relative humidity and salinity e g Morton 1986 Among these variables only temperature has a long and reliable record The average yearly summer JJA temperature record is shown in Fig 4 6C from Willmott et al 2012 T 21 3 C T 0 91 C Evaporation 70 records of the GSL have been derived through mass-balance modeling and a modified Penman-Montieth equation though each of these has drawbacks Mohammed and Tarboton 2012 The mass balance approach assumes that all other quantities are perfectly known while the modified Penman equation may not properly apportion the system s available energy and is more appropriate for timescales on the order of a day We follow Waddell and Barton 1980 Arnow 1985 and Arnow and Stephens 1990 in estimating overlake evaporation on the basis of nearby pan-evaporation data We piece together the temporal variations in evaporation using pan-evaporation records from two sites near the GSL: Saltair 1957-1990 and Logan Farm 1971-2000 data from Western Regional Climate Center www wrcc dri edu We align these records setting the mean to E 1 m yr-1 and the standard deviation to E 0 1 m yr-1 in agreement with the water-balance model of Mohammed and Tarboton 2012 Fig 4 6D Pan-evaporation records are subject to significant uncertainty but are reasonable if imperfect estimates of overlake evaporation capturing the relative changes over time We will later show that evaporation is of secondary importance to precipitation in driving the GSL s lake-level changes and so our analysis is not critically dependent on the evaporation record 4 2 2 Persistence in the lake and the climate time series It is clear even visually from Fig 4 6 that the time series of precipitation temperature and evaporation have much less persistence than that of the lake itself Persistence can be explicitly quantified by calculating the autocorrelation function of a time-series Fig 4 3 One simple test of whether there is any significant persistence in a time series is whether the lag-1 autocorrelation exceeds 2 N where N is the number of points in the time series e g Von Storch and Zwiers 2001 These threshold levels are shown for their respective time series in Fig 4 3 Based on this test we conclude 71 that no significant persistence exists for temperature and evaporation Some slight interannual persistence may be indicated for the precipitation record though its significance is marginal Fig 4 3 demonstrates that the lake-level fluctuations themselves do exhibit significant persistence and further that this persistence is characterized by an exponential fit with a characteristic e-folding timescale or memory of approximately 8 years The exponential fit underestimates the autocorrelation at lags less than five years a discrepancy which we explore later in this chapter Because there is little to no persistence in the climate variables the lake s memory must arise from the dynamics of lake adjustment rather than being intrinsic to the climate The main point of the present study is that the lake exhibits memory that is not present in the climate Analysis of the lake models that we develop below explain much of this behavior 4 2 3 Previous research Prior research has characterized the GSL as a low-order dynamical system and suggests that the lake s volume anomalies slightly lag the regional precipitation and temperature anomalies Abarbanel and Lall 1996 Abarbanel et al 1996 Sangoyomi et al 1996 Lall et al 1996 Related research invokes low-frequency climate phenomena to explain the low-frequency response of the GSL Mann et al 1995 Lall and Mann 1995 Moon et al 2008 Wang et al 2010 These studies aim to use some combination of atmospheric indices to predict the GSL lake levels In this study we aim to put these explanations into context by considering the natural variability of lake level that occurs in response to white noise the stochastic year-to-year fluctuations in weather that occur even without any climate change or persistence in the climate 72 Other studies have considered the inherent lake dynamics of GSL Kite 1989 proposed that the changes and apparent periodicity in the GSL s record are within the range of normal fluctuations and are not ascribed to climatic change Mohammed and Tarboton 2011 refer to the lake s bathymetry to explain the large and long excursions of the lake record They note that the area of the lake controls the outgoing flux and therefore a shallow lake like the GSL is quickly stabilized and modulated by the available evaporative surface In subsequent work Mohammed and Tarboton 2012 use a simple lake model to calculate the sensitivity of the GSL to changes in inflow precipitation and air temperature and use variations of historical climate input to predict possible future lake-level scenarios Our work is similar in spirit to that of Mohammed and Tarboton 2011 2012 but rather than being predictive our goal is to understand the natural lake variability in order to put past and anticipated future fluctuations in context We also extend this work by considering the role of lake alternate bathymetries on natural lake-level variability 4 3 Model In the following section the full and linearized models are described The full model is similar to that of Mason et al 1994 who derive general and comprehensive timedependent solutions to a lake s water balance They explore the response of lake level and area to step changes single brief excursions and sinusoidal variations in the climate In contrast our focus here is on the lake s response to the continuous random perturbations in forcing that occur even in a constant climate 73 4 3 1 Full model The rate of volumetric change for a closed-basin lake such as the GSL is determined by the balance of inflow into and evaporation out from the lake illustrated in Fig 4 4 The mass budget can be described by a straightforward differential equation: dV P AL I EAL dt 4 1 where VL t is the lake s volume AL t is the lake s surface area P t is the annual regional precipitation rate I t is the total annual river inflow from the surrounding basin and E t is the annual evaporation rate over the lake all functions of time t Eq 4 1 can be rewritten in terms of lake-level variations The volume of water is a unique function of lake level: V V h which can also be written as V h Rh AL z dz Hence 0 dV dV dh dh AL h t 4 2 dt dh dt dt Substituting eq 4 2 into eq 4 1 yields: dh 1 P AL I EAL dt AL 4 3 is proportional to the product We assume that the long-term mean of the inflow I of the long-term mean of the annual regional precipitation rate P and the area over which runoff is collected i e the area of the catchment basin excluding the direct precipitation over the lake : I P AB A L 4 4 where AB is the entire catchment area of the lake The parameter reflects the fact that much of the precipitation that falls into the basin is lost to evapotranspiration or groundwater percolation Some of the uncertainty in regional precipitation 74 may also be subsumed into We set so that the lake level matches its long-term mean For the GSL an of 0 13 yields an I of 2 5 km3 yr-1 which is close to the values estimated from stream gauges by Arnow and Stephens 1990 2 3 km3 yr-1 and Mohammed and Tarboton 2012 2 8 km3 yr-1 The fluctuations in inflow I 0 are parametrized as I 0 P 0 AB AL 4 5 where P 0 denotes the variations away from P We have introduced a tunable parameter which ensures that the interannual fluctuations in inflow are the same as observed We find we need 0 40 in order to emulate the observed standard deviation of inflow which is 1 5 km3 yr-1 Mohammed and Tarboton 2012 That we require different values for and suggests that there is some slow-timescale process in the region s groundwater that is neglected in our model For the purposes of our study here our goal is to drive the lake model with interannual variability in inflow whose magnitude is consistent with observations Our use of allows us to do that We use the time series of P and E shown in Fig 4 6B & D to force eq 4 3 using the parameter values shown in Table 4 1 starting in 1901 with the initial condition of h 1280 m a s l consistent with the observations This initial lake level corresponds to a volume of 18 4 km3 and an initial area of 4100 km2 From 1901-1956 there is no evaporation data and so for this interval we force the lake with variations in precipitation only keeping the evaporation rate at its long-term mean of 1 m yr-1 The simulated lake-level history is shown in Fig 4 6A Despite its crude treatment of inflow and incomplete evaporation record the detrended interannual standard deviation of model lake level 1 19 m agrees well with that of observations 1 14 m The model time series correlates with observations at r 0 85 The fact the model does a good job in the early part of the record despite the absence of evaporation variations 75 suggests that the precipitation is of primary importance in driving lake-level fluctuations a result we confirm in the next section 4 3 2 Linear model In the following section we develop a linear version of the lake-level model From it we derive analytical solutions for the lake s relaxation timescale the relative importance of P and E and the variance of the lake level in response to stochastic climate forcing The analytic expressions allow us to characterize the behavior of the lake without a complete knowledge of lake bathymetry and to clearly understand the parameters that drive the lake-level responses to climate variations Eq 4 3 is linearized by rewriting all time-varying fields using overbars to denote long-term means and primes to denote anomalies from that mean: P t P P 0 t h0 t E t E E 0 t I t I I 0 t AL t A l A0L t and h t h Using eq 4 4 and eq 4 5 for I and I 0 eq 4 3 becomes: h0 d h 1 P P 0 A L A0L P P 0 AB A L A0L 0 dt AL AL 4 6 0 0 E E AL A L Because AL is a function of h we rewrite it using a first-order Taylor Series expansion: h0 AL h dAL h h0 A L dAL h0 AL h AL h dh dh 4 7 76 Substituting dA l 0 h dh for A0l and considering only first-order terms eq 4 6 becomes: dh0 h0 AB P 0 E 0 1 dt AL 4 8 where A L dA L E P 1 dh 4 9 The value for represents the characteristic e-folding timescale on which perturbations in lake level will relax towards the mean A large A L implies that will also be large because all else being equal for a given h0 there is a large anomalous volume A L h0 that must be either filled or evaporated to return to equilibrium A large value of dA dh is associated with smaller because it means that an increase in h0 leads to a large increase in evaporating area enabling the excess volume of water to be more rapidly removed Likewise a decrease in h0 significantly decreases the evaporating area reducing the total evaporation and allowing the lake to return more rapidly to equilibrium Finally a large difference between E and P 1 indicates that the lake is in an arid region and that the restoring tendency of E is relatively efficient Aridity therefore also tends to shorten the response time of a lake However as we discuss below in a given setting these three factors influencing cannot be considered independent of each other The GSL is a large shallow lake in an arid environment and so there are trade-offs between the factors that determine For the values shown in Table 4 1 eq 4 9 predicts that 10 yrs Our falls within the range of 4 17 years cited by Mason et al 1994 who estimate several equilibrium e-folding response times for different historical levels of the GSL Further our value for compares quite well with the e-folding time suggested from observations 8 yrs Fig 4 3 77 From eq 4 9 we see that is a function of the mean lake level since A L and dA L dh are functions of h and the mean climatic setting is therefore a function of a particular mean state of the lake The black line in Fig 4 5 shows how varies for the GSL keeping E P and fixed Over the historical range of GSL lake with h levels 1277 5 to 1283 8 m a sl ranges from as low as 5 years at 1280 m a s l to as long as 26 years at the historical high The 5-year response time is due to a large value of dA L dh indicating that the basin area is changing rapidly at these elevations evident in Fig 4 6B The 26-year response time corresponds to a large value for A L as well as a relatively small value for above 1284 m a sl because dAL dh dAL dh The timescale plummets for elevations increases allowing the lake to quickly adjust to anomalies in the water balance independently since a long-term lake-level However it is not consistent to vary h change also requires an accompanying change in P or E to maintain the new mean lake level For example an increase in A L only happens if also accompanied by a decrease in E or an increase in P These both work in the same direction as an increase in A L acting to increase Thus it is more realistic to constrain through consistent P and E that ensure the lake is in equilibrium i e combinations of h dV dt 0 for a Fig 4 5 shows two examples For the first blue line we vary P keeping given h E fixed so that dV dt keeping P fixed 0 in eq 4 3 For the second red line we vary E When the parameters covary like this the basic pattern of the variation of re on its own However confirming sponse time with lake level is the same as varying h the reasoning given above the variations in are amplified reaches 40 yrs for 1284 m a sl when h and E covary Fig 4 5 h the linear model eq 4 8 does Despite the large changes in as a function of h 78 a remarkably good job of emulating the historical lake level record when it is driven by the historical variations in P 0 and E 0 Fig 4 6A The correlation with the observations is 0 83 only slightly smaller than that for the full model The results lend confidence that we can use the linear model to derive analytical expressions for some useful metrics of the lake response Response to step changes in P and E Let E be a step-change in evaporation rate From eq 4 8 and assuming P 0 0 the resulting equilibrium change in lake level i e when dh dt 0 is hE E 4 10 Similarly for a step-change in the precipitation rate P the resulting change is AB hP 1 P 4 11 AL A simple measure of the relative importance of P and E for the lake level is the ratio of hE and hP : R h hE E hP 1 AB P A 4 12 L In other words R h is proportional to the ratio of the two climate changes modified by the lake geometry and evapotranspiration in the catchment basin Standard deviation in lake level As was argued in the introduction and as was supported by an analysis of the instrumental climate record a sensible null hypothesis is that interannual climate variability 79 can be characterized by stochastic normally-distributed white noise with standard deviations in P 0 and E 0 of P and E respectively Analytical solutions for the standard deviation in lake response L can be derived for the lake-level response to the stochastic variability from eq 4 8 and are presented in the Appendix C For lake-level variability driven by E 0 t alone we find r t hE E 2 Lake-level variability driven by P 0 t alone is r t AB hP P 1 2 AL 4 13 4 14 Combining eqs 4 13 and 4 14 we get: 2 2 h2 hE hP 4 15 For the GSL hP 1 04 m hE 0 24 m and h 1 07 m meaning that P 0 contributes 95% of the variance in fluctuations in h0 This confirms our earlier result Fig 4 6A that lake level fluctuations in the GSL are predominantly driven by precipitation variability A more comprehensive study of lake geometry and climatic conditions would be needed to establish whether this is generally true or whether under some conditions evaporation variability dominates The predominant importance of precipitation and inflow for the GSL is also noted by Mohammed and Tarboton 2012 4 4 Lake-level statistics To this point we have demonstrated that both the full and linear models can capture the general behavior of the GSL s historical lake-level variations We now turn to 80 characterizing the lake s behavior beyond the historical record: its variance power spectrum lake-level threshold-crossing probabilities and evaluating the analytical expressions derived from the linear model when forced with stochastic climate variations The differences between the models highlight the capacity of the analytic solutions to describe the behavior of the lake and the degree to which changes in the geometry of the lake basin and bathymetry are important We force the full and linear models with long 106 yr realizations of P 0 t and E 0 t generated from normally distributed white-noise processes that have the same mean and variance as the observations detailed in Table 4 1 A 300-year snapshot of the resulting lake-level time series is shown in Fig 4 6A with the full model in grey and the linear model in blue The full time series correlate highly with one another r 0 89 but there are also notable differences For example because the full model resolves changes in dA L dh which decreases below the present lake level the full model s response time is longer at lake levels just slightly lower than the mean lake level Therefore the full model s lake level is consistently lower than that of the linear 4 4 1 Standard deviations For the full model we find h 1 1 m in close agreement with the linear model also h 1 1 m The probability density functions PDFs are shown in Fig 4 6A The PDF of the lake levels for the linear model is normal by construction but the actual hypsometry of the GSL introduces a significant degree of skewness in the full model skewness -0 4 kurtosis 3 9 Therefore the full model is not consistent with a normal distribution at p 0 05 based on a Kolmogorov-Smirnov test e g Von Storch and Zwiers 2001 Relative to the mean the full model s lake-area extremes are skewed towards neg- 81 ative excursions Fig 4 6B The area that is associated with 3 h is 6000 km2 and covers about 2 5 times the area associated with 3 h 2300 km2 Fig 4 6C and D This range is comparable to the difference between the highest and lowest areas in the historical record and describe the expected extremes seen in a thousand-year period if there was no climatic change 4 4 2 Power spectral density The power spectra of lake level for the models and the historical record are shown in Fig 4 6B The spectrum for the linear model is calculated using a standard formula for eq 4 8 e g Box et al 2013 which applies to frequencies 0 f P0 t 2 P f 1 2 1 t cos 2 f t 1 t 2 1 : 2 t 4 16 where P f is the power spectral density P0 4 h2 and h is taken from the linearized model i e eq 4 15 The area beneath the power spectrum is the variance of the time series and so the similarity of the power spectra of the full and linear models is consistent with their values for h also being similar There are however some noteworthy differences between the models and the observations While the spectral power at low frequencies is quite similar the observations are more damped than the models at high frequencies The power spectrum is the Fourier transform of the autocorrelation function e g Box et al 2013 Therefore the extra damping at high frequencies in observations above that predicted by eq 4 16 is consistent with the observed autocorrelations at short lags being higher than predicted by a simple exponential function Fig 4 3 Similar behavior was found recently for the glaciers by Roe and Baker 2014 82 For the GSL these results suggests that neither eq 4 3 nor eq 4 8 are complete descriptions of the lake response In particular groundwater dynamics likely impacts lake-level variability at higher frequencies Further development of the model might better emulate the observed autocorrelation power spectrum structure These differences notwithstanding the results confirm the basic principle embodied in the models For the historical record persistence in lake level fluctuations is associated with the dynamic memory of the lake system rather than persistence in climate 4 4 3 Threshold crossing statistics Often it is the extrema of lake level i e a flood or extreme lowering that have the highest impacts on water resources and are most evident in proxy records A metric of particular importance then is the likelihood that a given lake level is reached in a given period of time Given interannual climate variability the question is inherently a statistical one For the full model the statistics can be estimated from the long idealized simulations of lake level For the linear model the statistics can be derived analytically from the statistics of a Poisson distribution e g Von Storch and Zwiers 2001 Roe 2011 The probability of the lake level exceeding a given threshold h0 above or below the long-term average at least once in a given interval of time tf ti is given by: tf ti p N tf ti 1 1 exp 2 2 t 21 e 12 h0 h 2 4 17 Eq 4 17 shows that the longer the time interval tf ti the higher the probability of exceeding a given threshold This probability depends on but is especially sensitive to the ratio of h0 and h Fig 4 6A shows results for time intervals of of 100 500 and 1000 years For the 83 full model we randomly sample these intervals 105 times from the long model integration and collate the statistics of how often a give lake level is crossed As an example for the full model in any 1000 yr period it is extremely likely 98% to find the lake level exceeding 2m and extremely unlikely 1% to find the lake level exceeding 4m The threshold-crossing probability curves show that the full and linear models diverge at the extremes For the linear model the maxima and minima curves are symmetric about the mean lake level as expected from the probability distribution function of the lake levels Fig 4 6A However for the full model a large lake-level minimum is more likely than a lake-level maximum of the same magnitude This is also apparent in Fig 4 6A where the full model s lake levels are consistently lower than those of the linear model and in Fig 4 6B which shows differences between the spectra of each model Though the standard deviations of the models are quite close the linear model overestimates the frequency of a lake-level maximum and underestimates the frequency of a lake-level minimum relative to the full model Fig 4 6B shows the full model s frequency-crossing distribution for the total excursion of a given time slice i e the maximum - minimum values within tf ti This illustrates total expected spread in the the lake level on the order of 100 500 or 1000 years The GSL has a higher than 50% probability of varying more than 4 meters within a century more than 6 meters every 500 years and more than 7 meters every millennium Interestingly Karl and Young 1986 inspected the return times for precipitation records alone and found that there was greater than 50% probability of having a wet spell as extreme as the 1986 floods in any hundred year period with a return time of 120 years The similarity between the high precipitation probability and flood probability is unsurprising given how sensitive the lake is to changes in precipitation 84 4 5 Alternative lake hypsometries We have focused on the GSL because of its long lake-level history relatively short response time and detailed hypsometric information However the framework developed above can be used to characterize any closed-basin lake s response to variations in the climate This response will be dependent on the lake s unique hypsometry and regional climate To understand the extent of geometric influence on the timescale and magnitude of lake-level variability we create simple hypsometric profiles that are approximations to the bathymetry of three closed-basin lakes: the extensive and shallow GSL the extensive and deep Lake Titicaca on the border of Bolivia and Peru and the areally small and deep Lake Bosumtwi in Ghana Fig 4 6A B and C In the following calculations we do not try to simulate historical or projected future variations of these lakes but aim to isolate the impact of different lake geometries on lake-level response The simple functions used to describe the bathymetry allow dA L dh to vary smoothly in turn smoothing the lake-level response The GSL and Lake Titicaca s hypsometric curves are concave down and can be idealized as an inverted rectangular pyramidal frustum: AL h LW h z0 z0 z1 2 4 18 where again AL is the lake area and h is the lake level L and W are the length and width of the basin at some known elevation z1 above the bottom of the frustum and z0 is the vertical distance from the bottom of the frustum to the point that would complete a full pyramid Lake Bosumtwi s hypsometric curve is concave up and is idealized as a tri-axial 85 half-ellipsoid: AL h LW z0 h 2 1 z02 4 19 where L W and z0 are the lengths of the semi-principal x y and z axes and h 0 at z z0 The values for each lake s parameters are given in Table 4 2 and are compared with the known hypsometric profiles in Fig 4 6 Estimates for E and P for lakes Titicaca and Bosumtwi are available from the literature Table 4 2 Turner et al 1996 Richerson et al 1977 For each idealized lake geometry we set so as to match the modern lake levels By analogy with the GSL we set 3 In order to focus solely on the impact of the different basin geometries on lake-level variability we apply the same E 0 t and P 0 t to all three idealized lake geometries as were applied to the GSL see section 4 4 We integrate the full lake model eq 4 3 with each of the idealized lake geometries and use the linear model solutions to calculate h and P f for each lake All parameters are provided in Table 4 2 A 2000-year slice of each lake s time series is shown in Fig 4 6D It is clear that the lakes respond to the same perturbations at different timescales and with different amplitudes The analytic solutions to the linear model allow us to link the differences in lake response to each lake s parameter values 4 5 1 Response time The response time for each lake is calculated using eq 4 9 The idealized GSL has the fastest response time with a 10 years because of its large dA L dh The shape of Lake Bosumtwi is very different with a relatively small area of 48 km2 but a modern 86 depth of 79 m Its geometry means that if Lake Bosumtwi experiences a brief increase in P the lake level will increase but the lake s surface area only increases slightly Hence it takes many years for a steady E to remove the excess water and return the lake to its original level Therefore though the surface area of Lake Bosumtwi is much smaller than that of Lake Titicaca or the GSL its small dA L dh gives the lake a long memory with an e-folding time of 209 years Lake Titicaca is much larger 280 than the GSL or Lake Bosumtwi However A L 6700 km2 and deeper h Lake Titicaca s ratio of A L : dA L dh and therefore its 201 yrs is similar to that of Lake Bosumtwi also affect as does the ratio of A L and AB The mean climatic differences P E through the needed to ma