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anuga_work/publications/boxing_day_validation_2008/patong_validation.tex
r7187 r7210 1 1 \documentclass[a4paper]{article} 2 % to be added when submitted to ocean dynamics 3 %\documentclass[smallcondensed,draft]{svjour3} 4 %\usepackage{mathptmx} 5 %\journalname{Ocean Dynamics} 6 2 7 \usepackage{graphicx} 3 8 \usepackage{hyperref} … … 6 11 \newcommand{\doi}[1]{\url{http://dx.doi.org/#1}} 7 12 13 8 14 %----------title-------------% 9 %\title{Inundation Modelling of the December 2004 Indian Ocean Tsunami}10 15 \title{Benchmarking Tsunami Models using the December 2004 Indian Ocean Tsunami and its Impact at Patong Beach} 11 16 12 17 %-------authors----------- 13 \author{J.~D. Jakeman\thanks{The Australian National University, Canberra, \textsc{Australia}. 14 \protect\url{mailto:john.jakeman@anu.edu.au}} 15 \and O.Nielsen\thanks{Geoscience Australia, Canberra, \textsc{Australia}} 16 \and R. Mleczko\footnotemark[2] 17 \and D. Burbidge\footnotemark[2] 18 \and K. VanPutten\footnotemark[2] 19 \and N. Horspool\footnotemark[2] 20 } 21 18 \author{J.~D. Jakeman \and O. Nielsen \and R. Mleczko \and D. Burbidge \and K. VanPutten \and N. Horspool} 19 20 % to be added when submitted to ocean dynamics 21 %\institute{J.~D. Jakeman \at 22 % The Australian National University, Canberra, \textsc{Australia}\ 23 % \email{john.jakeman@anu.edu.au} 24 % \and 25 % O. Nielsen \and R. Mleczko \and D. Burbidge \and K. VanPutten \and N. Horspool \at 26 % Geoscience Australia, Canberra, \textsc{Australia} 27 %} 22 28 %================Start of Document================ 23 29 \begin{document} … … 25 31 %------Abstract-------------- 26 32 \begin{abstract} 27 In this paper a new benchmark for tsunami model validation is proposed. The benchmark is based upon the 2004 Indian Ocean tsunami, which provides a uniquely large amount of observational data for model comparison. Unlike the small number of existing benchmarks, the proposed test validates all three stages of tsunami evolution - generation, propagation and inundation. Specifically we use geodetic measurements of the Sumatra--Andaman earthquake to validate the tsunami source, altimetry data from the \textsc{jason} satellite to test open ocean propagation, eye-witness accounts to assess near shore propagation and a detailed inundation survey of Patong Bay, Thailand to compare model and observed inundation. Furthermore we utilise this benchmark to further validate the hydrodynamic modelling tool \textsc{anuga} which is used to simulate the tsunami inundation and run rain-induced floods. 33 In this paper a new benchmark for tsunami model validation is proposed. The benchmark is based upon the 2004 Indian Ocean tsunami, which provides a uniquely large amount of observational data for model comparison. Unlike the small number of existing benchmarks, the proposed test validates all three stages of tsunami evolution - generation, propagation and inundation. Specifically we use geodetic measurements of the Sumatra--Andaman earthquake to validate the tsunami source, altimetry data from the \textsc{jason} satellite to test open ocean propagation, eye-witness accounts to assess near shore propagation and a detailed inundation survey of Patong Bay, Thailand to compare model and observed inundation. Furthermore we utilise this benchmark to further validate the hydrodynamic modelling tool \textsc{anuga} which is used to simulate the tsunami inundation and run rain-induced floods. Important buildings and other structures were incorporated into the underlying computational mesh and shown to have a large influence of inundation extent. Sensitivty analysis also showed that the model predictions are comparatively insensitive to large changes in friction and small perturbations in wave weight at the 100m depth contour. 34 % to be added when submitted to ocean dynamics 35 %\keywords{Tsunami \and modelling \and validation and verification \and benchmark} 28 36 \end{abstract} 29 37 … … 32 40 33 41 \section{Introduction} 34 Tsunami are a potential hazard to coastal communities all over the world. A number of recent large events have increased community and scientific awareness of the need for effective tsunami hazard mitigation. Tsunami modelling is major component of hazard mitigation, which involves detection, forecasting, and emergency preparedness~\cite{synolakis05}. Accurate models can be used to provide information that increases the effectiveness of action undertaken before the event to minimise damage (early warning systems, breakwalls etc.) and protocols put in place to be followed when the flood waters subside. 35 36 Several approaches are currently used to model tsunami propagation and inundation. These methods differ in both the formulation used to describe the evolution of the tsunami and the numerical methods used to solve the governing equations. The shallow water wave equations, linearised shallow water wave equations, and Boussinesq-type equations are frequently used to simulate tsunami propagation. The nonlinear nature of these equations, the highly variable nature of the phenomena that they describe and the complex reality of the geometry they operate in, necessitate the use of numerical models. These models are typically used to predict quantities such as arrival times, wave speeds and heights and inundation extents which are used to develop efficient hazard mitigation plans. Inaccuracies in model prediction can result in inappropriate evacuation plans and town zoning which may result in loss of life and large financial losses. Consequently tsunami models must undergo sufficient testing to increase scientific and community confidence in the model predictions. 37 38 Complete confidence in a model of a physical system frequently in general cannot be established. One can only hope to state under what conditions the model hypothesis holds true. Specifically the utility of a model can be assessed through a process of verification and validation. Verification assesses the accuracy of the numerical method used to solve the governing equations and validation is used to investigate whether the model adequately represents the physical system~\cite{bates01}. Together these processes can be used to establish the likelihood that that a model is a legitimate hypothesis. 39 40 The sources of data used to validate and verify a model can be separated into three main categories; analytical solutions, scale experiments and field measurements. Analytical solutions of the governing equations of a model, if available, provide the best means of verifying any numerical model. However analytical solutions to the governing equations used here are frequently limited to a small set of idealised examples that do not completely capture the more complex behaviour of `real' events. For tsunami inundation, scale experiments, typically in the form of wave-tank experiments, provide a much more realistic source of data that better captures the complex dynamics of natural tsunami, whilst allowing control of the event and much easier and accurate measurement of the tsunami properties. However comparison of numerical predictions with field data provides the most stringent test of model veracity. The use of field data increases the generality and significance of conclusions made regarding model utility. However the use of field data also significantly increases the uncertainty of the validation experiment that may constrain the ability to make unequivocal statements~\cite{bates01}. 42 Tsunami are a potential hazard to coastal communities all over the world. A number of recent large events have increased community and scientific awareness of the need for effective detection, forecasting, and emergency preparedness. Probabilistic, geological, hydrodynamic, and economic models are required to predict the location and likelihood of an event, the initial sea floor deformation and subsequent propagation and inundation of the tsunami, the effectiveness of hazard mitigation procedures and the economic impact of such measures and the event itself. Here we focus on modelling of the physical processes. For discussion on economic and decision based models refer to~\cite{} and the references therein. 43 44 Various approaches are currently used to assess the potential impact of tsunami. These methods differ in both the formulation used to describe the evolution of the tsunami and the numerical methods used to solve the governing equations. However any legitimate model must address each of the three distinct stages of tsunami evolution--- generation, inundation and propagation. Geological models must be used to provide estimates of initial sea floor and ocean surface deformation. The complexity of these models range from empirical to non-linear three-dimensional mechanical models. The shallow water wave equations, linearised shallow water wave equations, and Boussinesq-type equations are frequently used to simulate tsunami propagation. These models are typically used to predict quantities such as arrival times, wave speeds and heights, and inundation extents which are used to develop efficient hazard mitigation plans. 45 46 Inaccuracies in model prediction can result in inappropriate evacuation plans and town zoning which may result in loss of life and large financial losses. Consequently tsunami models must undergo sufficient end-to-end testing to increase scientific and community confidence in the model predictions. 47 48 Complete confidence in a model of a physical system cannot be established. One can only hope to state under what conditions the model hypothesis holds true. Specifically the utility of a model can be assessed through a process of verification and validation. Verification assesses the accuracy of the numerical method used to solve the governing equations and validation is used to investigate whether the model adequately represents the physical system~\cite{bates01}. Together these processes can be used to establish the likelihood that that a model is a legitimate hypothesis. 49 50 The sources of data used to validate and verify a model can be separated into three main categories; analytical solutions, scale experiments and field measurements. Analytical solutions of the governing equations of a model, if available, provide the best means of verifying any numerical model. However analytical solutions are frequently limited to a small set of idealised examples that do not completely capture the more complex behaviour of `real' events. Scale experiments, typically in the form of wave-tank experiments, provide a much more realistic source of data that better captures the complex dynamics of natural tsunami, whilst allowing control of the event and much easier and accurate measurement of the tsunami properties. Comparison of numerical predictions with field data provides the most stringent test. The use of field data increases the generality and significance of conclusions made regarding model utility. However it must be noted that the use of field data also significantly increases the uncertainty of the validation experiment that may constrain the ability to make unequivocal statements~\cite{bates01}. 41 51 42 52 Currently the extent of tsunami related field data is limited. The cost of tsunami monitoring programs, bathymetry and topography surveys prohibits the collection of data in many of the regions in which tsunamis pose greatest threat. The resulting lack of data has limited the number of field data sets available to validate tsunami models. Synolakis et. al~\cite{synolakis07} have developed a set of standards, criteria and procedures for evaluating numerical models of tsunami. They propose three analytical solutions to help identify the validity of a model and five scale comparisons (wave-tank benchmarks) and two field events to assess model veracity. … … 44 54 The first field data benchmark introduced by Synolakis compares model results against observed data from the Hokkaido-Nansei-Oki tsunami that occurred around Okushiri Island, Japan on the 12th of July 1993. This tsunami provides an example of extreme runup generated from reflections and constructive interference resulting from local topography and bathymetry. The benchmark consists of two tide gauge records and numerous spatially distributed point sites at which modelled maximum runup elevations can be compared. The second benchmark is based upon the Rat Islands Tsunami that occurred off the coast of Alaska on the 17th of November 2003. The Rat island tsunami provides a good test for real-time forecasting models since tsunami was recorded at three tsunameters. The test requires matching the propagation model data with the DART recording to constrain the tsunami source model and using a propagation model to to reproduce the tide gauge record at Hilo. 45 55 46 The evolution of earthquake-generated tsunamis has three distinctive stages: generation, propagation and run-up~\cite{titov97a}. To accurately model the evolution of a tsunami all three stages must be dealt with. In this section we present the data necessary to implement the proposed benchmark corresponding to each of the three stages of the tsunami's evolution. In this paper we develop a field data benchmark to be used in conjunction with the other tests proposed by Synolakis et al.~\cite{synolakis07} to validate and verify tsunami models. Unlike the aforementioned tests, the proposed benchmark allows one to estimate the error in a model prediction for all three distinctive stages of the evolution of a tsunami: generation, propagation and run-up. The benchmark comprises of geodetic measurements of the Sumatra--Andaman earthquake to validate the tsunami source, altimetry data from the JASON satellite to test open ocean propagation, eye-witness accounts to assess near shore propagation and a detailed inundation survey of Patong Bay, Thailand to compare model and observed inundation. A description of this data is give in Section~\ref{sec:data}. 47 48 An associated aim of this paper is to illustrate the use of this new benchmark to validate an operational tsunami model called \textsc{anuga}. A description of \textsc{anuga} is given in Secion~\ref{sec:models} and the validation results are given in Secion~\ref{sec:results}. 56 In this paper we develop a field data benchmark to be used in conjunction with the other tests proposed by Synolakis et al.~\cite{synolakis07} to validate and verify tsunami models. Unlike the aforementioned tests, the proposed benchmark allows evaluation of model structure during all three distinctive stages of the evolution of a tsunami. The benchmark consists of geodetic measurements of the Sumatra--Andaman earthquake which are used to validate the description of the tsunami source, altimetry data from the JASON satellite to test open ocean propagation, eye-witness accounts to assess near shore propagation and a detailed inundation survey of Patong Bay, Thailand to compare model and observed inundation. A description of the data required to construct the benchmark is give in Section~\ref{sec:data}. 57 58 An associated aim of this paper is to illustrate the use of this new benchmark to validate an operational tsunami model called \textsc{anuga} used by Geoscience Australia. A description of \textsc{anuga} is given in Secion~\ref{sec:models} and the validation results are given in Secion~\ref{sec:results}. 59 60 The numerical models used to model tsunami are extremely computationally intensive. Full resolution models of the entire evolution process will often take a number of days to run. Consequently the uncertainty in model predictions is difficult to quantify. However model uncertainty should not be ignored. Section ~\ref{sec:sensitivity} provides a simple sensitivity analysis that can be used to investigate the sensitivity of model predictions to model parameters. 49 61 50 62 %================Section=========================== … … 60 72 All tsunami are generated from an initial disturbance of the ocean which develops into a low frequency wave that propagates outwards from the source. The initial deformation of the water surface is most commonly caused by coseismic displacement of the sea floor, but submarine mass failures, landslides, volcanoes or asteroids can also cause tsunami. In this section we detail the information we used in this study to validate models of the sea floor deformation generated by the 2004 Sumatra--Andaman earthquake. 61 73 62 The 2004 Sumatra--Andaman tsunami was generated by severe coseismic displacement of the sea floor as a result of one of the largest earthquakes on record. The mega-thrust earthquake started on the 26 December 2004 at 0h58'53'' UTC (or just befor 8 am local time) approximately 70 km offshore North Sumatra (\url{http://earthquake.usgs.gov/eqcenter/eqinthenews/2004/usslav}). The rupture propagated 1000-1300 km along the Sumatra-Andaman trench time to the north at a rate of 2.5-3 km.s$^{-1}$ and lasted approximately 8-10 minutes~\cite{ammon05}. Estimates of the moment magnitude of this event range from about 9.1 to 9.3~\cite{chlieh07,stein07}.63 64 The unusually large surface deformation caused by this earthquakes means that there were a range of different geodetic measurements of the surface deformation available. These include field measurements of uplifted or subsided coral heads, continuous or campaign \textsc{GPS} measur ments and remote sensing measurements of uplift or subsidence (see ~\cite{chlieh07} and references therein). Here we use the the near field estimates of vertical deformation in northwestern Sumatra and the Nicobar-Andaman islands collated by~\cite{chlieh07} to validate that our crustal deformation model of the 2004 Sumatra--Andaman earthquake is producing reasonable results. Note that the geodetic data used here is a combination of the vertical deformation that happened in the ~10 minutes of the earthquake plus the deformation that followed in the days following the earthquake before each particular measurement was actually made (typically of order days). Therefore some of the observations may not contain the purely co-seismic deformation but could include some post-seismic deformation as well~\cite{chlieh07}.74 The 2004 Sumatra--Andaman tsunami was generated by severe coseismic displacement of the sea floor as a result of one of the largest earthquakes on record. The mega-thrust earthquake started on the 26 December 2004 at 0h58'53'' UTC (or just before 8 am local time) approximately 70 km offshore North Sumatra (\url{http://earthquake.usgs.gov/eqcenter/eqinthenews/2004/usslav}). The rupture propagated 1000-1300 km along the Sumatra-Andaman trench time to the north at a rate of 2.5-3 km.s$^{-1}$ and lasted approximately 8-10 minutes~\cite{ammon05}. Estimates of the moment magnitude of this event range from about 9.1 to 9.3~\cite{chlieh07,stein07}. 75 76 The unusually large surface deformation caused by this earthquakes means that there were a range of different geodetic measurements of the surface deformation available. These include field measurements of uplifted or subsided coral heads, continuous or campaign \textsc{GPS} measurements and remote sensing measurements of uplift or subsidence (see ~\cite{chlieh07} and references therein). Here we use the the near field estimates of vertical deformation in northwestern Sumatra and the Nicobar-Andaman islands collated by~\cite{chlieh07} to validate that our crustal deformation model of the 2004 Sumatra--Andaman earthquake is producing reasonable results. Note that the geodetic data used here is a combination of the vertical deformation that happened in the ~10 minutes of the earthquake plus the deformation that followed in the days following the earthquake before each particular measurement was actually made (typically of order days). Therefore some of the observations may not contain the purely co-seismic deformation but could include some post-seismic deformation as well~\cite{chlieh07}. 65 77 66 78 %DAVID: I commented out the figure since we can combine it with the model result without obscuring it. That will keep the number of figures down. … … 93 105 \begin{figure}[ht] 94 106 \begin{center} 95 \includegraphics[width= 8.0cm,keepaspectratio=true]{nested_grids}107 \includegraphics[width=0.75\textwidth,keepaspectratio=true]{nested_grids} 96 108 \caption{Nested grids of elevation data.} 97 109 \label{fig:nested_grids} … … 136 148 137 149 \subsubsection{Buildings and Other Structures} 138 Human made build and structures can significantly effect tsunamni inundation. The location and size and number of floors of the buildings in Patong Bay were extracted from a GIS data set~\cite{}. The heights of these buildings was estimated assuming that each floor was 3m high. 150 Human made build and structures can significantly effect tsunami inundation. The location and size and number of floors of the buildings in Patong Bay were extracted from a GIS data set~\cite{}. The heights of these buildings was estimated assuming that each floor was 3m high. 151 152 \subsubsection{Inundation Survey} 153 Tsunami run-up is often the cause of the largest financial and human losses yet run-up data that can be used to validate model runup predictions is scarce. Of the two field benchmarks proposed by Synolakis only the Okishiri benchmark facilitates comparison between modelled and observed run-up. One of the major strengths of the benchmark proposed here is that modelled runup can be compared to an inundation survey which maps the maximum run-up along an entire coast line rather than at a series of discrete sites. The survey map is shown in Figure~\ref{fig:patongescapemap} and plots the maximum run-up of the 2004 tsunami in Patong bay. Refer to Szczucinski et al~\cite{szczucinski06} for further details. 139 154 140 155 \subsubsection{Eyewitness Accounts} 141 156 Eyewitness accounts detailed in~\cite{papadopoulos06} report that most people at Patong Beach observed an initial retreat of the shoreline of more than 100m followed a few minutes later by a strong wave (crest). Another less powerful wave arrived another five or ten minutes later. Eyewitness statements place the arrival time of the strong wave between 2 hours and 55 minutes to 3 hours and 5 minutes after the source rupture (09:55am to 10:05am local time). 142 157 143 144 \subsubsection{Inundation Survey} 145 Tsunami run-up is often the cause of the largest financial and human losses yet run-up data that can be used to validate model runup predictions is scarce. Of the two field benchmarks proposed by Synolakis only the Okishiri benchmark facilitates comparison between modelled and observed run-up. One of the major strengths of the benchmark proposed here is that modelled runup can be compared to an inundation survey which maps the maximum run-up along an entire coast line rather than at a series of discrete sites. The survey map is shown in Figure~\ref{fig:patongescapemap} and plots the maximum run-up of the 2004 tsunami in Patong bay. Refer to Szczucinski et al~\cite{szczucinski06} for further details. 158 Two videos were sourced from the internet which include footage of the tsunami in Patong Bay on the day of the Indian Ocean Tsunami. Both videos show an 159 already inundated town, they then show what is to be assumed as the second and third waves approaching and further flooding the town. The first video 160 is in the very north filmed from what is believed to be the roof of the Novotel Hotel. The second video is in the very south 161 filmed from a building next door to the Comort Resort. Figure~\ref{fig:video_flow} shows a video taken near the corner of Ruam Chai St. from which we made our estimates. 162 163 \begin{figure}[ht] 164 \begin{center} 165 \includegraphics[width=6.0cm,keepaspectratio=true]{flow_rate_south_0_00sec.jpg} 166 \includegraphics[width=6.0cm,keepaspectratio=true]{flow_rate_south_5_04sec.jpg} 167 \includegraphics[width=6.0cm,keepaspectratio=true]{flow_rate_south_7_12sec.jpg} 168 \includegraphics[width=6.0cm,keepaspectratio=true]{flow_rate_south_7_60sec.jpg} 169 \caption{four frames from a video where flow rate could be estimated, circle indicates tracked debris, clockwise from top left: 0.0 sec, 5.0 s, 7.1 s, 7.6 s.} 170 \label{fig:video_flow} 171 \end{center} 172 \end{figure} 173 174 Crude flow rates can be estimated with landmarks found in satellite imagery and the use of a GIS and were found to be in 175 the range of 5 to 7 metres per second (+/- 2 m/s) in the north and 0.5 to 2 metres per second (+/- 1 m/s) in the south. 146 176 147 177 \begin{figure}[ht] … … 159 189 \item Reproduce the vertical deformation observed in north-western Sumatra and along the Nicobar--Andaman islands, see Section~\ref{sec:gen_data}. 160 190 \item Reproduce the \textsc{jason} satellite altimetry sea surface anomalies, see Section~\ref{sec:data_jason}. 191 \item Reproduce the inundation survey map in Patong bay (Figure~\ref{fig:patongescapemap}). 161 192 \item Simulate a leading depression followed by two distinct crests of decreasing magnitude. 162 \item Predict the arrival time of the first crest should arrive at Patong beach between 2 hours and 55 minutes to 3 hours and 5 minutes after the initial rupture of the source. The subsequent crest arrive five to ten minutes later. 163 \item Reproduce the inundation survey map in Patong bay (Figure~\ref{fig:patongescapemap}). 193 \item Predict the water depths and flow speeds, at the locations of the eye-witness videos, that fall within the bounds obtained from the videos. 164 194 \end{itemize} 165 195 … … 170 200 \subsection{Generation}\label{sec:modelGeneration} 171 201 172 There are various approaches to modelling the expected crustal deformation from an earthquake at depth. Most approaches model the earthquake as a dislocation in linear, elastic medium. Here we use the method of ~\cite{wang03}. One of the main advantages of their method is that it allows the dislocation to be located in a stratified linear elastic half-space with an arbitary number of layers. Other methods (such as those based on Okada's equations) can only model the dislocation in a homogeneous elastic half space, or can only include a limited number of layers, and thus cannot model the effect of the depth dependence of the elasticity of the Earth~\cite{wang03}. The original versions of the codes described here are available from \url{http://www.iamg.org/CGEditor/index.htm}. The first program, \textsc{EDGRN}, calculates elastic Green's function for a set of point sources at a regular set of depths out to a specified distance. The equations controlling the deformation are solved by using a combination of Hankel's transform and Wang et al's implementation of the Thomson-Haskell propagator algorithm~\cite{wang03}. Once the Green's functions are calculated we use a slightly modified version of \textsc{EDCMP} to calculate the sea floor deformation for a specific subfault. This second code discretises the subfault into a set of unit sources and sums the elastic Green's functions calculated from \textsc{EDGRN} for all the unit sources on the fault plane in order to calculate the final static deformation caused by a two dimensional dislocation along the subfault. This step is possible because of the linearity of the governing equations. For this study, we have made minor modifications to \textsc{EDCMP} in order for it to output in a file format compatible with the propagation code in the following section but it is otherwise the similar to the original code.173 174 In order to calculate the crustal deformation using these codes we thus need to have a model describing the variation in elastic properties with depth and a slip model of the earthquake to describe the dislocation. The elastic parameters used for this study are the same as those in Table 2 of \cite{burbidge08}. For the slip model, there are many possible models for the 2004 Andaman--Sumatran earthquake to choose from ~\cite{chlieh07,asavanant08,arcas06,grilli07,ioualalen07}. Some are determined from various geological surveys of the site, others solve an inverse problem which calibrates the source based upon the tsunami wave signal, the seismic signal and/or the runup. The source parameters used here to simulate the 2004 Indian Ocean Tsunami were taken from model G-M9.15 from~\cite{chlieh07}. This model was created by inversion of wide range of geodetic and seismic data. The slip model consists of 686 20km x 20km subsegments each with a different slip, strike and dip angle. The dip subfaults go from $17.5^0$ in the north and $12^0$ in the south. Refer to~\cite{chlieh07} for a detailed discussion of this model and its derivation. Note that the geodetic data used in the validation was also included by~\cite{chlieh07} in the inversion used to find G-M9.15, thus the validation is not completely independent. However, a successful validation would still show that the crustal deformation and elastic properties model used here is at least as valid as the one used in~\cite{chlieh07} and can reproduce the observations just as accurately.202 There are various approaches to modelling the expected crustal deformation from an earthquake at depth. Most approaches model the earthquake as a dislocation in linear, elastic medium. Here we use the method of Wang et. al.~\cite{wang03}. One of the main advantages of their method is that it allows the dislocation to be located in a stratified linear elastic half-space with an arbitrary number of layers. Other methods (such as those based on Okada's equations) can only model the dislocation in a homogeneous elastic half space, or can only include a limited number of layers, and thus cannot model the effect of the depth dependence of the elasticity of the Earth~\cite{wang03}. The original versions of the codes described here are available from \url{http://www.iamg.org/CGEditor/index.htm}. The first program, \textsc{edgrn}, calculates elastic Green's function for a set of point sources at a regular set of depths out to a specified distance. The equations controlling the deformation are solved by using a combination of Hankel's transform and Wang et al's implementation of the Thomson-Haskell propagator algorithm~\cite{wang03}. Once the Green's functions are calculated we use a slightly modified version of \textsc{edcmp} to calculate the sea floor deformation for a specific subfault. This second code discretises the subfault into a set of unit sources and sums the elastic Green's functions calculated from \textsc{edgrn} for all the unit sources on the fault plane in order to calculate the final static deformation caused by a two dimensional dislocation along the subfault. This step is possible because of the linearity of the governing equations. For this study, we have made minor modifications to \textsc{edcmp} in order for it to output in a file format compatible with the propagation code in the following section but it is otherwise the similar to the original code. 203 204 In order to calculate the crustal deformation using these codes we thus need to have a model describing the variation in elastic properties with depth and a slip model of the earthquake to describe the dislocation. The elastic parameters used for this study are the same as those in Table 2 of Burbidge~\cite{burbidge08}. For the slip model, there are many possible models for the 2004 Andaman--Sumatran earthquake to choose from ~\cite{chlieh07,asavanant08,arcas06,grilli07,ioualalen07}. Some are determined from various geological surveys of the site, others solve an inverse problem which calibrates the source based upon the tsunami wave signal, the seismic signal and/or the runup. The source parameters used here to simulate the 2004 Indian Ocean tsunami were taken from model G-M9.15 from Chlieh et. al.~\cite{chlieh07}. This model was created by inversion of wide range of geodetic and seismic data. The slip model consists of 686 20km x 20km subsegments each with a different slip, strike and dip angle. The dip subfaults go from $17.5^0$ in the north and $12^0$ in the south. Refer to Chlieh et. al.~\cite{chlieh07} for a detailed discussion of this model and its derivation. Note that the geodetic data used in the validation was also included by~\cite{chlieh07} in the inversion used to find G-M9.15, thus the validation is not completely independent. However, a successful validation would still show that the crustal deformation and elastic properties model used here is at least as valid as the one used by Chlieh et. al.~\cite{chlieh07} and can reproduce the observations just as accurately. 175 205 176 206 \subsection{Propagation}\label{sec:modelPropagation} … … 191 221 192 222 \subsection{Generation}\label{modelGeneration} 193 The location and magnitude of the sea floor displacement associated with the 2004 Sumatra--Andaman tsunami calculated from the G-M9.15 model of~\cite{chlieh07} is shown in Figure~\ref{fig:surface_deformation}. The magnitude of the sea floor displacement ranges from about $-3.0$ to $5.0$ metres. The region near the fault is predicted to uplift, while that further away from the fault subsides. Also shown in Figure~\ref{fig:surface_deformation} are the areas that were observed to uplift (arrows pointing up) or subside (arrows point down) during and immediately after the earthquake. Most of this data comes uplifted or subsided coral heads. The length of vector increases with the magni utude of the displacement, the length corresponding to 1m of observed motion is shown in the top right corner of the figure. As can be seen, the source model detailed in Section~\ref{sec:modelGeneration} produces a crustal deformation that matches the vertical displacements in the Nicobar-Andaman islands and Sumatra very well. Uplifted regions are close to the fault and subsided regions are further away. The crosses on Figure~\ref{fig:surface_deformation} show estimates of the pivot line from the remote sensing data~\cite{chlieh07} and they follow the predicted pivgot line quite accurately. The average difference between the observed motion and the predicted motion (including the pivot line points) is only 0.06m, well below the typical error of the observations of between 0.25 and 1.0m. However, the occasional point has quite a large error (over 1m), for example a couple uplifted/subsided points appear to be on a wrong side of the predicted pivot line~\ref{fig:surface_deformation}. These points are rare, most fit the predicted vertical motion very well. The excellence of the fit is not surprising, since the original slip model was chosen by~\cite{chlieh07} to fit this (and the seismic data) well. However, this does demonstrate that \textsc{edgrn} and our modified version of \textsc{edstat} can reproduce the correct pattern of vertical deformation very well when the slip distribution is well constrained and when reasonable values for the elastic properties are used.223 The location and magnitude of the sea floor displacement associated with the 2004 Sumatra--Andaman tsunami calculated from the G-M9.15 model of~\cite{chlieh07} is shown in Figure~\ref{fig:surface_deformation}. The magnitude of the sea floor displacement ranges from about $-3.0$ to $5.0$ metres. The region near the fault is predicted to uplift, while that further away from the fault subsides. Also shown in Figure~\ref{fig:surface_deformation} are the areas that were observed to uplift (arrows pointing up) or subside (arrows point down) during and immediately after the earthquake. Most of this data comes uplifted or subsided coral heads. The length of vector increases with the magnitude of the displacement, the length corresponding to 1m of observed motion is shown in the top right corner of the figure. As can be seen, the source model detailed in Section~\ref{sec:modelGeneration} produces a crustal deformation that matches the vertical displacements in the Nicobar-Andaman islands and Sumatra very well. Uplifted regions are close to the fault and subsided regions are further away. The crosses on Figure~\ref{fig:surface_deformation} show estimates of the pivot line from the remote sensing data~\cite{chlieh07} and they follow the predicted pivot line quite accurately. The average difference between the observed motion and the predicted motion (including the pivot line points) is only 0.06m, well below the typical error of the observations of between 0.25 and 1.0m. However, the occasional point has quite a large error (over 1m), for example a couple uplifted/subsided points appear to be on a wrong side of the predicted pivot line~\ref{fig:surface_deformation}. These points are rare, most fit the predicted vertical motion very well. The excellence of the fit is not surprising, since the original slip model was chosen by~\cite{chlieh07} to fit this (and the seismic data) well. However, this does demonstrate that \textsc{edgrn} and our modified version of \textsc{edstat} can reproduce the correct pattern of vertical deformation very well when the slip distribution is well constrained and when reasonable values for the elastic properties are used. 194 224 195 225 \begin{figure}[ht] … … 203 233 204 234 \subsection{Propagation} 205 The deformation results described in Section~\ref{sec:modelGeneration} w as then used to provide an profile of the initial ocean surface displacement. This wave was used as an initial condition for \textsc{ursga} and was propagated the tsunami throughtout the Bay of Bengal. The rectangular computational domain of the largest grid extended from 90$^0$ to 100$^0$East and 0 to 15$^0$North and contained 1335$\times$1996 finite difference points. Inside this grid, a nested sequence of grids was used. The grid resolution of the nested grids went from 27 arc seconds in the coarsest grid, down to 9 arc seconds in the second grid, 3 arc seconds in the thrid grid and finally 1 arc second in the finest grid near Patong. The computational domain is shown in Figure\ref{fig:computational_domain}.235 The deformation results described in Section~\ref{sec:modelGeneration} were used to provide an profile of the initial ocean surface displacement. This wave was used as an initial condition for \textsc{ursga} and was propagated the tsunami throughtout the Bay of Bengal. The rectangular computational domain of the largest grid extended from 90$^0$ to 100$^0$East and 0 to 15$^0$North and contained 1335$\times$1996 finite difference points. Inside this grid, a nested sequence of grids was used. The grid resolution of the nested grids went from 27 arc seconds in the coarsest grid, down to 9 arc seconds in the second grid, 3 arc seconds in the third grid and finally 1 arc second in the finest grid near Patong. The computational domain is shown in Figure\ref{fig:computational_domain}. 206 236 207 237 Figure \ref{fig:jasonComparison} provides a comparison of the \textsc{ursga} predicted surface elevation with the JASON satellite altimetry data. The \textsc{ursga} model replicates the amplitude and timing of the first peak and trough well. However the model does not resolve the double peak of the first wave. Also note that the \textsc{ursga} model prediction of the ocean surface elevation becomes out of phase with the JASON data at 3 to 7 degrees latitude. Chlieh et al~\cite{chlieh07} also observe these misfits and suggest it is caused by a reflected wave from the Aceh Peninsula that is not resolved in the model due to insufficient resolution of the computational mesh and bathymetry data. This is also a limitation of the model presented here, but probably could be improved by nesting grids near Aceh. … … 235 265 During the \textsc{anuga} simulation the tide was kept constant at $0.80$m. This value was chosen to correspond to the tidal height specified by the Thai Navy tide charts (\url{http://www.navy.mi.th/hydro/}) at the time the tsunami arrived at Patong Bay. Although the tsunami propagated for approximately 3 hours before it reach Patong Bay, the period of time during which the wave propagated through the \textsc{anuga} domain is much smaller. Consequently the assumption of constant tide height is reasonable 236 266 237 FIXME(John): Need a commentary on the dynamics of what is being observed and whether it aligns with eye witness observations.238 Both the URS model and the \textsc{anuga} inundation model shows that the event comprises a train of waves some with preceding drawdown effects Add details of waveform with a graph from URL and a gauge from \textsc{anuga} and discuss. This will come from the work of Kristy (plots of water depth and speed at two locations on beach and one of shore) and Richard (approximating water depth and wave speeds from videos).239 240 267 Maximum onshore inundation elevation was simulated throughout the entire Patong Bay region. Figure~\ref{fig:inundationcomparison1cm} shows very good agreement between the measured and simulated inundation. The \textsc{anuga} simulation determines a region to be inundated if at some point in time it was covered by at least 1cm of water. This precision in field measurements is impossible to obtain. The inundation boundary is determined by observing water marks and other signs left by the receding waters. The precision of the observed inundation map is, most likely, at least an order of magnitude worse than the \textsc{anuga} simulation. The simulated inundation based upon a 10cm threshold is shown in Figure~\ref{fig:inundationcomparison1cm}. An inundation threshold of 10cm was selected for all future simulations to reflect the likely accuracy of the survey and subsequently facilitate a more appropriate comparison between the modelled and observed inundation area. 241 268 … … 243 270 244 271 %\url{https://datamining.anu.edu.au/anuga/attachment/wiki/AnugaPublications/patong_2004_indian_ocean_tsunami_ANUGA_animation.mov}. 245 246 247 248 272 249 273 \begin{figure}[ht] … … 268 292 Additional causes of the discrepancies between the survey data and the modelled inundated include: unknown distribution of surface roughness, inappropriate parameterisation of the source model, effect of humans structures on flow, as well as uncertainties in the elevation data, effects of erosion and deposition by the tsunami event, measurement errors, and missing data in the field survey data itself. The impact of some of these sources of uncertainties are is investigated in Section~\ref{sec:sensitivity} 269 293 270 271 \section{Dynamic behaviour of the tsunami} 272 294 \subsection{Eye-witness accounts} 273 295 Figure \ref{fig:gauge_locations} shows four locations where time series have been extracted from the model. The two offshore timeseries are shown in Figure \ref{fig:offshore_timeseries} and 274 296 the two onshore timeseries are shown in Figure \ref{fig:onshore_timeseries}. The latter coincide with locations where video footage from the event is available. … … 301 323 \end{figure} 302 324 303 \subsubsection{Video Evidence}304 Two videos were sourced from the internet which include footage of the tsunami in Patong Bay on the day of the Indian Ocean Tsunami. Both videos show an305 already inundated town, they then show what is to be assumed as the second and third waves approaching and further flooding the town. The first video306 is in the very north filmed from what is believed to be the roof of the Novotel Hotel. The second video is in the very south307 filmed from a building next door to the Comort Resort. Figure 11 shows a video taken near the corner of Ruam Chai St. from which we made our estimates.308 309 310 \begin{figure}[ht]311 \begin{center}312 \includegraphics[width=6.0cm,keepaspectratio=true]{flow_rate_south_0_00sec.jpg}313 \includegraphics[width=6.0cm,keepaspectratio=true]{flow_rate_south_5_04sec.jpg}314 \includegraphics[width=6.0cm,keepaspectratio=true]{flow_rate_south_7_12sec.jpg}315 \includegraphics[width=6.0cm,keepaspectratio=true]{flow_rate_south_7_60sec.jpg}316 \caption{four frames from a video where flow rate could be estimated, circle indicates tracked debris, clockwise from top left: 0.0 sec, 5.0 s, 7.1 s, 7.6 s.}317 \label{fig:video_flow}318 \end{center}319 \end{figure}320 321 322 325 Crude flow rates can be estimated with landmarks found in satellite imagery and the use of a GIS and were found to be in 323 326 the range of 5 to 7 metres per second (+/- 2 m/s) in the north and 0.5 to 2 metres per second (+/- 1 m/s) in the south. This is in agreement 324 327 with results from our simulations. Our modelled flow rates show maximum values in the order of 0.2 to 2.6 m/s in the south and 0.1 to 325 3.3 m/s for the north as shown in the figures. Water depths could also be estimated from the videos by the level at which water rose up the sides of buildings such as shops. Our estimates are in the order of 1.5 to 2.0 metres (+/- 0.5 m). This is in the same range as our modelled maximum depths of 1.4 m in the north and 1.5 m in the south as seen in the figure. Fritz ~\cite{fritz06} did a detailed analysis of video frames taken around Banda Aceh and arrived at flow speeds in the range of 2 to 5 m/s. 328 3.3 m/s for the north as shown in the figures. Water depths could also be estimated from the videos by the level at which water rose up the sides of buildings such as shops. Our estimates are in the order of 1.5 to 2.0 metres (+/- 0.5 m). This is in the same range as our modelled maximum depths of 1.4 m in the north and 1.5 m in the south as seen in the figure. Fritz ~\cite{fritz06} performed a detailed analysis of video frames taken around Banda Aceh and arrived at flow speeds in the range of 2 to 5 m/s. 329 326 330 327 331 … … 330 334 \section{Sensitivity Analysis} 331 335 \label{sec:sensitivity} 332 This section shows how model maximum inundation varies with: different values of Manning's friction coefficient; changing waveheight at the ANUGA boundary (where it was coupled with the URSGA model); and finally the presence and absence of buildings in the elevation dataset.336 This section investigates the effect of different values of Manning's friction coefficient, changing waveheight at the 100m depth contour, and the presence and absence of buildings in the elevation dataset on model maximum inundation. 333 337 334 338 %========================Friction==========================% … … 336 340 \label{sec:friction sensitivity} 337 341 The first study investigated the impact of surface roughness on the predicted run-up. According to Schoettle~\cite{schoettle2007} appropriate values of Manning's coefficient range from 0.007 to 0.030 for tsunami propagation over a sandy sea floor. Consequently we simulated the maximum onshore inundation using the a Manning's coefficient of 0.0003 and 0.03. The resulting run-up is shown in Figures 338 \ref{fig:sensitivity_friction} and the maximum flow speeds\ref{fig:sensitivity_friction_speed}. These figure rs show that the on-shoerinundation extent decreases with increasing friction and that small perturbations in the friction cause bounded changes in the output. This is consistent with the conclusions of Synolakis~\cite{synolakis05} who states that the long wavelength of tsunami tends to mean that the friction is less important in comparison to the motion of the wave.342 \ref{fig:sensitivity_friction} and the maximum flow speeds\ref{fig:sensitivity_friction_speed}. These figures show that the on-shore inundation extent decreases with increasing friction and that small perturbations in the friction cause bounded changes in the output. This is consistent with the conclusions of Synolakis~\cite{synolakis05} who states that the long wavelength of tsunami tends to mean that the friction is less important in comparison to the motion of the wave. 339 343 340 344 %========================Wave-Height==========================% … … 370 374 371 375 \section{Conclusion} 372 This paper proposes an additional field data benchmark for the verification of tsunami inundation models. Currently, there is a scarcity of appropriate validation datasets due to a lack of well documented historical tsunami impacts. FIXME(John): Complete... 373 374 From the sensitivity studies it appears that the presence or absence of buildings is the most important parameter followed by the right choice of friction whereas a small perturbation in the waveheight at the ANUGA boundary has comparatively little effect on the model results. 376 This paper proposes an additional field data benchmark for the verification of tsunami inundation models. Currently, there is a scarcity of appropriate validation datasets due to a lack of well documented historical tsunami impacts. The benchmark proposed here utilises the uniquely large amount of observational data for model comparison obtained during, and immediately following, the Sumatra--Andaman tsunami of 26th December 2004. Unlike the small number of existing benchmarks, the proposed test validates all three stages of tsunami evolution - generation, propagation and inundation. In an attempt to provide higher visability and easier accessibility for tsunami benchmark problems the data used to construct the proposed benchmark is documented and freely available at \url{http://tinyurl.com/patong2004-data}. 377 378 An associated aim of this paper was to further validate the hydrodynamic modelling tool \textsc{anuga} which is used to simulate the tsunami inundation and run rain-induced floods. Model predictions matched well geodetic measurements of the Sumatra--Andaman earthquake, altimetry data from the \textsc{jason}, eye-witness accounts of wave front arrival times and flow speeds and a detailed inundation survey of Patong Bay, Thailand. 379 380 A simple sensitivity analysis was performed to assess the influence of small changes in friction, wave-height at the 100m depth contour and the presence of buildings and other structures on the model predictions. The presence of buildings has the greatest influence on the simulated inundation extent. The value of friction and small perturbations in the waveheight at the ANUGA boundary have comparatively little effect on the model results. 375 381 376 382 %================Acknowledgement=================== … … 384 390 \includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_minus10} 385 391 \includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_plus10} 386 \caption{Model results with wav height at ANUGA boundary artificially modified392 \caption{Model results with wave height at ANUGA boundary artificially modified 387 393 to asses sensitivities. The first image is the reference inundation extent as reported in Section \protect \ref{sec:results} while the second and third show the inundation results if the wave at the ANUGA boundary is reduced or increased by 10cm respectively. The inundation severity varies in proportion to the boundary waveheight, but the model results are only slightly sensitive to this parameter for the range of values tested.} 388 394 \label{fig:sensitivity_boundary} … … 449 455 450 456 %====================Bibliography================== 451 \bibliographystyle{ plain}457 \bibliographystyle{spmpsci} 452 458 \bibliography{tsunami07} 453 459 \end{document} 454 455 456 ===================457 NOTES TO BE REMOVED458 459 Main source of uncertainty arises from inaccuracies in initial condition (source), inaccurate bathymetry data, to a lesser extent friction460 461 scale comparisons (laboratory benchmarking):462 Scale differences are not believed to be important. scale experiments generally do not have same bootom friction characteristics as real scenario but has not proven to be a problem. The long wavelength of tsunami tends to mean that the friction is less important in comparison to the motion of the wave463 Single wave on a simple beach464 Solitary wave on composite beach465 Conical island466 Monai Valley467 Landslide468 469 Field benchmarking:470 Most important verification process471 Hydrodynamic inversion to predict the source is an ill posed problem472 12 July 1993 Hokkaido-Nansei-Oki tsunami around Okushiri Island Japan extreme runup height of 31.7m was found at the tip of a narrow gully with the small cove at Monai473 17 November 2003 Rat Islands Tsunami474 475 Construction of more than one model can reveal biases in a single model. Two types of comparisons 1 between those that are conceptually similar and those that re different. In former case interested in how choice of numerical solver and discretisation effects results and the later can help determine the level of physical process representation necessary to represent an observed data set.476 477 Moving to field data increases the generality and significance of scientific evidence obtained. However we also significantly increase the uncertainty of the validation experiment that may constrain the ability to make unequivacol statements. E.g. in bathymetry source condition friction.478 479 The two field data benchmarks are very useful but only capture a small subset of possible tsunami behaviours and do not assess all three stages of tsunami evolution (generation,propagation and inundation) together. The type and size of a tsunami source, propagation extent, and local bathymetry and topography all affect the energy, waveform and subsequent inundation of a tsunami. Consequently additional field data benchmarks, such as the one proposed here, that further capture the variability and sensitivity of the real world system would be useful to allow model developers verify their models and subsequently use their models with greater confidence.
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