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Jun 18, 2009, 3:34:41 PM (15 years ago)
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ole
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  • anuga_work/publications/boxing_day_validation_2008/patong_validation.tex

    r7210 r7216  
    1616
    1717%-------authors-----------
    18 \author{J.~D. Jakeman \and O. Nielsen \and R. Mleczko \and D. Burbidge \and K. VanPutten \and N. Horspool}
     18\author{J.~D. Jakeman \and O. Nielsen \and K. VanPutten \and D. Burbidge \and R. Mleczko \and N. Horspool}
    1919
    2020% to be added when submitted to ocean dynamics
    … …  
    3131%------Abstract--------------
    3232\begin{abstract}
    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.
     33In 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. Important buildings and other structures were incorporated into the underlying computational mesh and shown to have a large influence of inundation extent. Sensitivity 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.
    3434% to be added when submitted to ocean dynamics
    3535%\keywords{Tsunami \and modelling \and validation and verification \and benchmark}
    … …  
    4242Tsunami 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.
    4343
    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.
     44Various 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, propagation and inundation. 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.
    4545
    4646Inaccuracies 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.
    4747
    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}.
    51 
    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.
    53 
    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.
    55 
    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}.
     48Complete 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 a model represents a legitimate hypothesis.
     49
     50The 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 flows such as those generated by 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. On the other hand, 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}.
     51
     52Currently, 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.
     53
     54The 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 then using it to reproduce the tide gauge record at Hilo.
     55
     56In 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 given in Section~\ref{sec:data}.
     57
     58An associated aim of this paper is to illustrate the use of this new benchmark to validate an operational tsunami inundation 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}.
    5959
    6060The 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.
    … …  
    6262%================Section===========================
    6363\section{Data}\label{sec:data}
    64 The sheer magnitude of the 2004 Sumatra-Andaman earthquake and the devastation caused by the subsequent tsunami generated much scientific interest. As a result an unusually large amount of post seismic data has been collected and documented. Data sets from seismometers, tide gauges, \textsc{gps} surveys, satellite overpasses, subsequent coastal field surveys of run-up and flooding, and measurements of coseismic displacements and bathymetry from ship-based expeditions, have now been made available.%~\cite{vigny05,amnon05,kawata05,liu05}.
    65 
    66 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.  The final datasets are available on Sourceforge under the ANUGA project (\url{http://sourceforge.net/projects/anuga}). At the time
    67 of writing the direct link is \url{http://tinyurl.com/patong2004-data}.
    68 %
    69 %\url{http://sourceforge.net/project/showfiles.php?group_id=172848&package_id=319323&release_id=677531}.
     64The sheer magnitude of the 2004 Sumatra-Andaman earthquake and the devastation caused by the subsequent tsunami have generated much scientific interest. As a result an unusually large amount of post seismic data has been collected and documented. Data sets from seismometers, tide gauges, \textsc{gps} surveys, satellite overpasses, subsequent coastal field surveys of run-up and flooding, and measurements of coseismic displacements and bathymetry from ship-based expeditions, have now been made available.%~\cite{vigny05,amnon05,kawata05,liu05}.
     65In this section we present the data necessary to implement the proposed benchmark corresponding to each of the three stages of the tsunami's evolution.
    7066
    7167\subsection{Generation}\label{sec:gen_data}
    7268All 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.
    7369
    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}.
     70The 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 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}.
     71
     72The 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 $\sim$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}.
    7773
    7874%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.
    … …  
    8783
    8884\subsection{Propagation}
    89 Once generated a tsunami will propagate outwards from the source until it finally encounters the shallow water bordering coastal regions. This period of the tsunami evolution is referred to as the propagation stage. The height and velocity of the tsunami is dependent on the local bathymetry in the regions through which the wave travels and the size of the initial wave. This section details the bathymetry data needed to model the tsunami propagation and the satellite altimetry transects used here to validate open ocean tsunami models.
     85Once generated a tsunami will propagate outwards from the source until it encounters the shallow water bordering coastal regions. This period of the tsunami evolution is referred to as the propagation stage. The height and velocity of the tsunami is dependent on the local bathymetry in the regions through which the wave travels and the size of the initial wave. This section details the bathymetry data needed to model the tsunami propagation and the satellite altimetry transects used here to validate open ocean tsunami models.
    9086
    9187\subsubsection{Bathymetry Data}
    … …  
    9591\begin{itemize}
    9692\item A two arc minute grid data set covering the Bay of Bengal, DBDB2, obtained from US Naval Research Labs;
    97 \item A 3 second arc grid covering the whole of the Andaman Sea which is based on Thai charts 45 and 362; and
     93\item A 3 second arc grid covering the whole of the Andaman Sea based on Thai Navy charts no 45 and no 362; and
    9894\item A one second grid created from the digitised Thai Navy bathymetry chart, no 358. which covers Patong Bay and the immediately adjacent regions.
    9995\end{itemize}
    10096
    101 The final bathymetry data set consits of four nested grids obtained via interpolation and resampling of the aforementioned data sets. The coarsest bathymetry was obtained by interpolating the DBDB2 grid to a 27 second arc grid. A subsection of this region was then replaced by 9 second data which was generated by sub-sampling the 3 second of arc grid from NOAA. A subset of the 9 second grid was replaced by the 3 second data. Finally a one second grid was used to approximate the bathymetry in Patong Bay and the immediately adjacent regions. This elevation data was created from the digitised Thai Navy bathymetry chart, no 358. Any points that deviated from the general trend near the boundary were deleted. See Figure~\ref{fig:nested_grids}.
    102 
    103 The sub-sampling of larger grids was performed by using {\bf resample} a Generic Mapping Tools (\textsc{GMT}) program (\cite{wessel98}). The gridding of data was performed using {\bf Intrepid} a commercial geophysical processing package developed by Intrepid Geophysics. The gridding scheme employed the nearest neighbour algorithm followed by an application of minimum curvature akima spline smoothing.
     97The final bathymetry data set consists of four nested grids obtained via interpolation and resampling of the aforementioned data sets. The four grids are shown in Figure~\ref{fig:nested_grids}.
     98The coarsest bathymetry was obtained by interpolating the DBDB2 grid to a 27 second arc grid. A subsection of this region was then replaced by 9 second data which was generated by sub-sampling the 3 second of arc grid from NOAA. A subset of the 9 second grid was replaced by the 3 second data. Finally, the one second grid was used to approximate the bathymetry in Patong Bay and the immediately adjacent regions. Any points that deviated from the general trend near the boundary were deleted.
     99
     100The sub-sampling of larger grids was performed by using {\bf resample} a Generic Mapping Tools (\textsc{GMT}) program (\cite{wessel98}). The gridding of data was performed using {\bf Intrepid} a commercial geophysical processing package developed by Intrepid Geophysics. The gridding scheme employed the nearest neighbour algorithm followed by an application of minimum curvature akima spline smoothing FIXME(Ole): Need \cite{} here.
    104101
    105102\begin{figure}[ht]
    … …  
    113110\subsubsection{JASON Satellite Altimetry}\label{sec:data_jason}
    114111During the 26 December 2004 event, the Jason satellite tracked from north to south and over the equator at 02:55 UTC nearly two hours after the  earthquake \cite{gower05}. The satellite recorded the sea level anomaly compared to the average sea level from its previous five passes over the same region in the 20-30 days prior.
     112This data was used to validate the propagation stage in Section \ref{sec:resultsPropagation}.
    115113%DB I suggest we combine with model data to reduce the number of figures. The satellite track is shown in Figure~\ref{fig:satelliteTrack}.
    116114
    … …  
    134132
    135133\subsection{Inundation}
    136 Inundation refers to the final stages of the evolution a tsunami. Specifically the propagation of the tsunami in shallow coastal water and the subsequent run-up on to the shoreline. This process is typically the most difficult of the three stages to model. Aside from requiring robust solvers which can simulate flow over dry land, this part of the modelling process requires high resolution and quality bathymetry data and high quality field measurements, which are often not available. For the proposed benchmark the authors have obtained a high resolution bathymetry and topography data set and a high quality inundation survey map which can be used to validate model inundation. These data sets are described here. In this section we also present eye-witness accounts which can be used to qualitatively validate tsunami inundation.
     134Inundation refers to the final stages of the evolution a tsunami and covers the propagation of the tsunami in shallow coastal water and the subsequent run-up on to land. This process is typically the most difficult of the three stages to model due to thin layers of water flowing rapidly over dry land.
     135Aside from requiring robust solvers which can simulate such complex flow patterns, this part of the modelling process also requires high resolution and quality elevation data which is often not available. In the case of model validation high quality field measurements are also required. For the proposed benchmark the authors have obtained a high resolution bathymetry and topography data set and a high quality inundation survey map from the CCOP in Thailand (\cite{szczucinski06}) which can be used to validate model inundation.
     136The datasets necessary for reproducing the results of the inundation stage are available on
     137Sourceforge under the ANUGA project (\url{http://sourceforge.net/projects/anuga}). At the time
     138of writing the direct link is \url{http://tinyurl.com/patong2004-data}.
     139%
     140%\url{http://sourceforge.net/project/showfiles.php?group_id=172848&package_id=319323&release_id=677531}.
     141
     142In this section we also present eye-witness accounts which can be used to qualitatively validate tsunami inundation.
    137143
    138144\subsubsection{Topography Data}
    … …  
    148154
    149155\subsubsection{Buildings and Other Structures}
    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.
     156Human 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 provide by the CCOP in Thailand (\cite{FIXME from RICHARD}). The heights of these buildings were estimated assuming that each floor has a height of 3 m.
    151157
    152158\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.
     159Tsunami 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 Okushiri 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.
    154160
    155161\subsubsection{Eyewitness Accounts}
    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).
    157 
    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.
     162FIXME (Ole): I think we should move this to where the results are presented.
     163Eyewitness accounts detailed in~\cite{papadopoulos06} report that most people at Patong Beach observed an initial retreat of the shoreline of more than 100 m 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).
     164
     165Two videos were sourced from the internet (FIXME: Where?) which include footage of the tsunami in Patong Bay on the day of the Indian Ocean Tsunami. Both videos show an
     166already inundated group of buildings, they then show what is to be assumed as the second and third waves approaching and further flooding the town. The first video
     167is in the very north filmed from what is believed to be the roof of the Novotel Hotel marked 'North' in Figure \ref{fig:gauge_locations}. The second video is in the very south
     168filmed from a building next door to the Comfort Resort near the corner of Ruam Chai St and FIXME(Ole): XXXX.
     169This location is marked 'south' in Figure \ref{fig:gauge_locations} and Figure~\ref{fig:video_flow} shows stills from this video. Both videos were used to estimate flow speeds and inundation dephts over time.
    162170
    163171\begin{figure}[ht]
    … …  
    167175\includegraphics[width=6.0cm,keepaspectratio=true]{flow_rate_south_7_12sec.jpg}
    168176\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.}
     177\caption{Four frames from a video where flow rate could be estimated, circle indicates tracked debris, from top left: 0.0 sec, 5.0 s, 7.1 s, 7.6 s.}
    170178\label{fig:video_flow}
    171179\end{center}
    172180\end{figure}
    173181
    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
     182Flow rates were estimated using landmarks found in both videos and were found to be in
    175183the 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.
    176184
    … …  
    194202\end{itemize}
    195203
     204Ideally, the model should also be compared to measured timeseries of waveheights and velocities
     205but the authors are not aware of the availability of such data.
     206
     207
    196208%================Section===========================
    197209\section{Modelling the Event}\label{sec:models}
    198 Numerous models are currently used to model and predict tsunami generation, propagation and run-up\cite{titov97a,satake95}. Here we introduce the modelling methodology employed by Geoscience Australia to illustrate the utility of the proposed benchmark. Geoscience Australia's tsunami model can again be decomposed into three parts which simulate generation, propagation and inundation (Sections~\ref{sec:modelGeneration},\ref{sec:modelPropagation} and \ref{sec:modelInundation} respectively).
     210Numerous models are currently used to model and predict tsunami generation, propagation and run-up~\cite{titov97a,satake95}. Here we introduce the modelling methodology employed by Geoscience Australia to illustrate the utility of the proposed benchmark. Geoscience Australia's tsunami modelling methodology comprises the three parts; generation, propagation and inundation (Sections~\ref{sec:modelGeneration},\ref{sec:modelPropagation} and \ref{sec:modelInundation} respectively).
    199211
    200212\subsection{Generation}\label{sec:modelGeneration}
    201213
    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.
     214There are various approaches to modelling the expected crustal deformation from an earthquake at depth. Most approaches model the earthquake as a dislocation in a 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.
     215
     216In 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 the slip 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.
    205217
    206218\subsection{Propagation}\label{sec:modelPropagation}
    207 We use the \textsc{ursga} model to simulate the propagation of the 2004 tsunami in the deep ocean ocean, based on a discrete representation of the initial deformation of the sea floor, described in Section~\ref{sec:modelGeneration}. For the models shown here, we assume that the uplift is instantaneous and creates a wave of the same size and amplitude as the co-seismic sea floor deformation.
     219We use the \textsc{ursga} model described below to simulate the propagation of the 2004 tsunami in the deep ocean ocean, based on a discrete representation of the initial deformation of the sea floor, described in Section~\ref{sec:modelGeneration}. For the models shown here, we assume that the uplift is instantaneous and creates a wave of the same size and amplitude as the co-seismic sea floor deformation.
    208220
    209221\subsubsection{URSGA}
    210 \textsc{ursga} is a hydrodynamic code that models the propagation of the tsunami in deep water using the finite difference method to solve the depth integrated linear or nonlinear shallow water equations in spherical co-ordinates with friction and Coriolis terms. The code is based on Satake~\cite{satake95} with significant modifications made by the \textsc{urs} corporation~\cite{thio08} and Geoscience Australia~\cite{burbidge08}. The tsunami is propagated via a staggered grid system. Coarse grids are used in the open ocean and the finest resolution grid is employed in the region of most interest. \textsc{Ursga} is not publicly available.
     222\textsc{ursga} is a hydrodynamic code that models the propagation of the tsunami in deep water using a finite difference method to solve the depth integrated linear or nonlinear shallow water equations in spherical co-ordinates with friction and Coriolis terms. The code is based on Satake~\cite{satake95} with significant modifications made by the \textsc{urs} corporation~\cite{thio08} and Geoscience Australia~\cite{burbidge08}. The tsunami is propagated via a staggered grid system. Coarse grids are used in the open ocean and the finest resolution grid is employed in the region of most interest. \textsc{Ursga} is not publicly available.
    211223
    212224\subsection{Inundation}\label{sec:modelInundation}
    213 The utility of the \textsc{ursga} model decreases with water depth unless an intricate sequence of nested grids is employed. In comparison \textsc{anuga} is designed to produce robust and accurate predictions of on-shore inundation in mind, but is less suitable for earthquake source modelling and large study areas. Consequently, the Geoscience Australia tsunami modelling methodology is based on a hybrid approach using models like \textsc{ursga} for tsunami propagation up to a 100m depth contour. Specifically we use the \textsc{ursga} model to simulate the propagation of the 2004 Indian Ocean tsunami in the deep ocean, based on a discrete representation of the initial deformation of the sea floor, described in Section~\ref{sec:modelGeneration}. The wave signal is then used as a time varying boundary condition for the \textsc{anuga} inundation simulation. A description of \textsc{anuga} is the following section.
     225The utility of the \textsc{ursga} model decreases with water depth unless an intricate sequence of nested grids is employed. In comparison \textsc{anuga}, described below, is designed to produce robust and accurate predictions of on-shore inundation, but is less suitable for earthquake source modelling and large study areas because it is based on projected spatial coordinates. Consequently, the Geoscience Australia tsunami modelling methodology is based on a hybrid approach using models like \textsc{ursga} for tsunami propagation up to a 100 m depth contour.
     226%Specifically we use the \textsc{ursga} model to simulate the propagation of the 2004 Indian Ocean tsunami in the deep ocean, based on a discrete representation of the initial deformation of the sea floor, described in Section~\ref{sec:modelGeneration}.
     227The wave signal is then used as a time varying boundary condition for the \textsc{anuga} inundation simulation.
     228% A description of \textsc{anuga} is the following section.
    214229
    215230\subsubsection{ANUGA}
    216 \textsc{Anuga} is an Open Source hydrodynamic inundation tool that solves the depth integrated nonlinear shallow water wave equations. The scheme used by \textsc{anuga}, first presented by Zoppou and Roberts~\cite{zoppou99}, is a high-resolution Godunov-type method that uses the rotational invariance property of the shallow water equations to transform the two-dimensional problem into local one-dimensional problems. These local Riemann problems are then solved using the semi-discrete central-upwind scheme of Kurganov et al.~\cite{kurganov01} for solving one-dimensional conservation equations. The numerical scheme is presented in detail in Zoppou and Roberts~\cite{zoppou99}, Zoppou and Roberts~\cite{zoppou00}, and Roberts and Zoppou~\cite{roberts00}, Nielsen et al.~\cite{nielsen05}. An important capability of the software is that it can model the process of wetting and drying as water enters and leaves an area. This means that it is suitable for simulating water flow onto a beach or dry land and around structures such as buildings. It is also capable of adequately resolving hydraulic jumps due to the ability of the finite-volume method to handle discontinuities. \textsc{Anuga} has been validated against a number of analytical solutions and the wave tank simulation of the 1993 Okushiri Island tsunami~\cite{roberts06,nielsen05}.
     231\textsc{Anuga} is an Open Source hydrodynamic inundation tool that solves the conserved form of the depth integrated nonlinear shallow water wave equations. The scheme used by \textsc{anuga}, first presented by Zoppou and Roberts~\cite{zoppou99}, is a high-resolution Godunov-type method that uses the rotational invariance property of the shallow water equations to transform the two-dimensional problem into local one-dimensional problems. These local Riemann problems are then solved using the semi-discrete central-upwind scheme of Kurganov et al.~\cite{kurganov01} for solving one-dimensional conservation equations. The numerical scheme is presented in detail in Zoppou and Roberts~\cite{zoppou99}, Roberts and Zoppou~\cite{roberts00}, and Nielsen et al.~\cite{nielsen05}. An important capability of the software is that it can model the process of wetting and drying as water enters and leaves an area. This means that it is suitable for simulating water flow onto a beach or dry land and around structures such as buildings. It is also capable of adequately resolving hydraulic jumps due to the ability of the finite-volume method to handle discontinuities. The numerical scheme can also handle transitions between sub-critical and super-critical flow regimes seamlessly. \textsc{Anuga} has been validated against a number of analytical solutions and the wave tank simulation of the 1993 Okushiri Island tsunami~\cite{nielsen05,roberts06}.
    217232
    218233%================Section===========================
    219234\section{Results}\label{sec:results}
    220 This section presents validates the modelling practice of Geoscience Australia against the new proposed benchmarks. The criteria outlined in Section\ref{sec:checkList} are addressed for each three stages of tsunami evolution.
     235This section presents a validation of the modelling practice of Geoscience Australia against the new proposed benchmarks. The criteria outlined in Section~\ref{sec:checkList} are addressed for each three stages of tsunami evolution.
    221236
    222237\subsection{Generation}\label{modelGeneration}
    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.
     238The 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 0.06 m, well below the typical error of the observations of between 0.25 and 1.0 m. However, the occasional point has quite a large error (over 1 m), for example a couple uplifted/subsided points appear to be on a wrong side of the predicted pivot line~\ref{fig:surface_deformation}. 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.
    224239
    225240\begin{figure}[ht]
    … …  
    227242\includegraphics[width=5cm,keepaspectratio=true]{surface_deformation.jpg}
    228243%\includegraphics[totalheight=0.3\textheight,width=0.8\textwidth]{surface_deformation.jpg}
    229 \caption{Location and magnitude of the vertical component of the sea floor displacement associated with the 2004 Indian Ocean tsunami based on the slip model, G-M9.15. The black arrows which point up show areas observed to uplift during and immediately after the earthquake, those point down are locations which subsided. The length of increases with the magnitude of the deformation. The arrow length corresponding to 1m of deformation is shown in the top right hand corner of the figure. The crosses marks show the location of the pivot line (the region between the uplift and subsided region where the uplift is zero) derived from remote sensing. All the observational data come from the dataset collated by~\cite{chlieh07}.}
     244\caption{Location and magnitude of the vertical component of the sea floor displacement associated with the 2004 Indian Ocean tsunami based on the slip model, G-M9.15. The black arrows which point up show areas observed to uplift during and immediately after the earthquake, those point down are locations which subsided. The length of increases with the magnitude of the deformation. The arrow length corresponding to 1 m of deformation is shown in the top right hand corner of the figure. The crosses marks show the location of the pivot line (the region between the uplift and subsided region where the uplift is zero) derived from remote sensing. All the observational data come from the dataset collated by~\cite{chlieh07}.}
    230245\label{fig:surface_deformation}
    231246\end{center}
    232247\end{figure}
    233248
    234 \subsection{Propagation}
    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$1996 finite difference points. Inside this grid, a nested sequence of grids was used. The grid resolution of the nested grids went from 27 arc seconds in the coarsest grid, down to 9 arc seconds in the second grid, 3 arc seconds in the third grid and finally 1 arc second in the finest grid near Patong. The computational domain is shown in Figure\ref{fig:computational_domain}.
    236 
    237 Figure \ref{fig:jasonComparison} provides a comparison of the \textsc{ursga} predicted surface elevation with the JASON satellite altimetry data. The \textsc{ursga} model replicates the amplitude and timing of the first peak and trough well. However the model does not resolve the double peak of the first wave. Also note that the \textsc{ursga} model prediction of the ocean surface elevation becomes out of phase with the JASON data at 3 to 7 degrees latitude. Chlieh et al~\cite{chlieh07} also observe these misfits and suggest it is caused by a reflected wave from the Aceh Peninsula that is not resolved in the model due to insufficient resolution of the computational mesh and bathymetry data. This is also a limitation of the model presented here, but probably could be improved by nesting grids near Aceh.
     249
     250\subsection{Propagation}\label{sec:resultsPropagation}
     251The deformation results described in Section~\ref{sec:modelGeneration} were used to provide a profile of the initial ocean surface displacement. This wave was used as an initial condition for \textsc{ursga} and was propagated throughout the Bay of Bengal. The rectangular computational domain of the largest grid extended from 90$^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}.
     252
     253Figure \ref{fig:jasonComparison} provides a comparison of the \textsc{ursga} predicted sea 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.
    238254
    239255\begin{figure}[ht]
    … …  
    247263
    248264\subsection{Inundation}
    249 After propagating the tsunami in the open ocean using \textsc{ursga} the approximated ocean and surface elevation and tsunami velocities were extracted and used to construct a boundary condition for the \textsc{anuga} model. The interface betwen the \textsc{ursga} and \textsc{anuga} models was chosen to roughly follow the 100m depth contour along the west coast of Phuket Island. The computational domain is shown in Figure \ref{fig:computational_domain}
     265After propagating the tsunami in the open ocean using \textsc{ursga} the approximated ocean and surface elevation and horisontal flow velocities were extracted and used to construct a boundary condition for the \textsc{anuga} model. The interface betwen the \textsc{ursga} and \textsc{anuga} models was chosen to roughly follow the 100 m depth contour along the west coast of Phuket Island. The computational domain is shown in Figure \ref{fig:computational_domain}
    250266\begin{figure}[ht]
    251267\begin{center}
    … …  
    258274\end{figure}
    259275
    260 The domain was discretised into approximately 350,000 triangles. The resolution of the grid was increased in certain regions to efficiently increase the accuracy of the simulation. The grid resolution ranged between a maximum triangle area of $1\times 10^5$ m$^2$ near the Western ocean boundary to $3$ m$^2$ in the small regions surrounding the inundation region in Patong Bay. Due to a lack of available data, friction was set to a constant throughout the computational domain. For the reference simulation a Manning's coefficient of 0.01 was chosen to represent a small resistance to the water flow. See Section \ref{sec:friction sensitivity} for details on model sensitivity to this parameter.
    261 
    262 
    263 The boundary condition at each side of the domain towards the south and the north where no data was available was chosen as a transmissive boundary condition effectively replicating the time dependent wave height present just inside the computational domain. Momentum was set to zero. Other choices include applying the mean tide value as a Dirichlet type boundary condition but experiments as well as the result of the verification reported here showed that this approach tends to under estimate the tsunami impact due to the tempering of the wave near the side boundaries.
    264 
    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
    266 
    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.
     276The domain was discretised into 386,338 triangles. The resolution of the grid was increased in certain regions to efficiently increase the accuracy of the simulation. The grid resolution ranged between a maximum triangle area of $1\times 10^5$ m$^2$ near the Western ocean boundary to $20$ m$^2$ in the small regions surrounding the inundation region in Patong Bay. Due to a lack of available data, friction was set to a constant throughout the computational domain. For the reference simulation a Manning's coefficient of 0.01 was chosen to represent a small resistance to the water flow. See Section \ref{sec:friction sensitivity} for details on model sensitivity to this parameter.
     277
     278
     279The boundary condition at each side of the domain towards the south and the north where no data was available was chosen as a transmissive boundary condition effectively replicating the time dependent wave height present just inside the computational domain. Momentum was set to zero. Other choices include applying the mean tide value as a Dirichlet type boundary condition but experiments as well as the result of the verification reported here showed that this approach tends to under estimate the tsunami impact due to the tempering of the wave near the side boundaries whereas the transmissive boundary condition robustly preserves the wave.
     280
     281During 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
     282
     283FIXME (Ole): Perhaps rephrase a bit as the 1cm vs 10cm is hard to understand.
     284Maximum onshore inundation elevation was computed from the model 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.
    268285
    269286An animation of this simulation is available on the ANUGA website at \url{https://datamining.anu.edu.au/anuga} or directly from \url{http://tinyurl.com/patong2004}.
    … …  
    280297\end{figure}
    281298
    282 Here we introduce the measure
     299To quantify the agreement between observed and simulated inundation we introduce the measure
    283300\begin{equation}
    284301A(I_{in})=\frac{A(I_m\cap I_o)}{A(I_o)}
    … …  
    289306\end{equation}
    290307These values for the two aforementioned simulations are given in Table~\ref{table:inundationAreas}
    291 
    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}
     308FIXME (Ole): The left hand side of these equations are not areas - consider another symbol.
     309
     310Discrepancies 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}
    293311
    294312\subsection{Eye-witness accounts}
    … …  
    323341\end{figure}
    324342
     343FIXME(Ole): This is a repetition of an earlier section. I'll look at that soon.
    325344Crude flow rates can be estimated with landmarks found in satellite imagery and the use of a GIS and were found to be in
    326345the 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
    … …  
    339358\subsection{Friction}
    340359\label{sec:friction sensitivity}
    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
    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.
     360The 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 and the reference model uses a value of 0.01.
     361To investigate sensitivity to this parameter, we simulated the maximum onshore inundation using the a Manning's coefficient of 0.0003 and 0.03. The resulting inundation maps are shown in Figure~\ref{fig:sensitivity_friction} and  the maximum flow speeds in Figure~\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.
    343362
    344363%========================Wave-Height==========================%
    345364\subsection{Input Wave Height}\label{sec:waveheightSA}
    346 The effect of the wave-height used as input to the inundation model \textsc{anuga} was also investigated.  Figure\ref{fig:sensitivity_boundary} indicates that the inundation severity is directly proportional to the boundary waveheight but small perturbations in the input wave-height of 10cm seem to have little effect on the final on-shore run-up. Obviously larger perturbations will have greater impact, however unlike the uncertainty in the friction, the range of uncertainty in the propagation wave-height is hard to estimate.
     365The effect of the wave-height used as input to the inundation model \textsc{anuga} was also investigated. 
     366Figure~\ref{fig:sensitivity_boundary} indicates that the inundation severity is directly proportional to the boundary waveheight but small perturbations in the input wave-height of 10 cm appear to have little effect on the final on-shore run-up. Obviously larger perturbations will have greater impact. However, this value is generally well predicted by the generation and propagation models such as \textsc{ursga}. See e.g. \cite{FIXME} Toshi Baba's validation study at Kuril islands.
    347367
    348368
    … …  
    350370%========================Buildings==========================%
    351371\subsection{Buildings and Other Structures}
    352 The presence of buildings has the greatest influence on the maximum on-shore inundation extent. Figure \ref{fig:sensitivity_nobuildings} and shows the maximum run-up in the presence and absence of buildings. It is apparent that the inundation is much more severe when the presence of man made structures and buildings are ignored. Maximal flow speeds for these two model parameterisations are shown in Figure~\ref{fig:sensitivity_nobuildings_speed}.
     372The presence of buildings has the greatest influence on the maximum on-shore inundation extent. Figure~\ref{fig:sensitivity_nobuildings} shows the maximum run-up in the presence and absence of buildings. It is apparent that the inundation is much more severe when the presence of man made structures and buildings are ignored. Maximal flow speeds for these two model parameterisations are shown in Figure~\ref{fig:sensitivity_nobuildings_speed}.
    353373
    354374\begin{table}
    … …  
    376396This 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}.
    377397
     398This study also shows that the tsunami impact modelling methodology adopted is sane and able to predict inundation extents with reasonable accuracy.
    378399An 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.
    379400
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