Changeset 7217


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Timestamp:
Jun 18, 2009, 3:45:57 PM (16 years ago)
Author:
ole
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Justified the hideously long lines. This will make it much easier to track
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  • anuga_work/publications/boxing_day_validation_2008/patong_validation.tex

    r7216 r7217  
    1313
    1414%----------title-------------%
    15 \title{Benchmarking Tsunami Models using the December 2004 Indian Ocean Tsunami and its Impact at Patong Beach}
     15\title{Benchmarking Tsunami Models using the December 2004 Indian
     16  Ocean Tsunami and its Impact at Patong Beach}
    1617
    1718%-------authors-----------
    18 \author{J.~D. Jakeman \and O. Nielsen \and K. VanPutten \and D. Burbidge \and R. Mleczko \and N. Horspool}
     19\author{J.~D. Jakeman \and O. Nielsen \and K. VanPutten \and
     20  D. Burbidge \and R. Mleczko \and N. Horspool}
    1921
    2022% to be added when submitted to ocean dynamics
    … …  
    2628%       Geoscience Australia, Canberra, \textsc{Australia}
    2729%}
     30
     31
    2832%================Start of Document================
    2933\begin{document}
    … …  
    3135%------Abstract--------------
    3236\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. 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.
     37In this paper a new benchmark for tsunami model validation is
     38proposed. The benchmark is based upon the 2004 Indian Ocean tsunami,
     39which provides a uniquely large amount of observational data for model
     40comparison. Unlike the small number of existing benchmarks, the
     41proposed test validates all three stages of tsunami evolution -
     42generation, propagation and inundation. Specifically we use geodetic
     43measurements of the Sumatra--Andaman earthquake to validate the
     44tsunami source, altimetry data from the \textsc{jason} satellite to
     45test open ocean propagation, eye-witness accounts to assess near shore
     46propagation and a detailed inundation survey of Patong Bay, Thailand
     47to compare model and observed inundation. Furthermore we utilise this
     48benchmark to further validate the hydrodynamic modelling tool
     49\textsc{anuga} which is used to simulate the tsunami
     50inundation. Important buildings and other structures were incorporated
     51into the underlying computational mesh and shown to have a large
     52influence of inundation extent. Sensitivity analysis also showed that
     53the model predictions are comparatively insensitive to large changes
     54in friction and small perturbations in wave weight at the 100m depth
     55contour.
    3456% to be added when submitted to ocean dynamics
    3557%\keywords{Tsunami \and modelling \and validation and verification \and benchmark}
    … …  
    4062
    4163\section{Introduction}
    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, 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.
    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 a model represents 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 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 
    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 then using it 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 given 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 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}.
    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.
     64Tsunami are a potential hazard to coastal communities all over the
     65world. A number of recent large events have increased community and
     66scientific awareness of the need for effective detection, forecasting,
     67and emergency preparedness. Probabilistic, geological, hydrodynamic,
     68and economic models are required to predict the location and
     69likelihood of an event, the initial sea floor deformation and
     70subsequent propagation and inundation of the tsunami, the
     71effectiveness of hazard mitigation procedures and the economic impact
     72of such measures and the event itself. Here we focus on modelling of
     73the physical processes. For discussion on economic and decision based
     74models refer to~\cite{} and the references therein.
     75
     76Various approaches are currently used to assess the potential impact
     77of tsunami. These methods differ in both the formulation used to
     78describe the evolution of the tsunami and the numerical methods used
     79to solve the governing equations. However any legitimate model must
     80address each of the three distinct stages of tsunami evolution---
     81generation, propagation and inundation. Geological models must be used
     82to provide estimates of initial sea floor and ocean surface
     83deformation. The complexity of these models range from empirical to
     84non-linear three-dimensional mechanical models. The shallow water wave
     85equations, linearised shallow water wave equations, and
     86Boussinesq-type equations are frequently used to simulate tsunami
     87propagation. These models are typically used to predict quantities
     88such as arrival times, wave speeds and heights, and inundation extents
     89which are used to develop efficient hazard mitigation plans.
     90
     91Inaccuracies in model prediction can result in inappropriate
     92evacuation plans and town zoning which may result in loss of life and
     93large financial losses. Consequently tsunami models must undergo
     94sufficient end-to-end testing to increase scientific and community
     95confidence in the model predictions.
     96
     97Complete confidence in a model of a physical system cannot be
     98established.  One can only hope to state under what conditions the
     99model hypothesis holds true. Specifically the utility of a model can
     100be assessed through a process of verification and
     101validation. Verification assesses the accuracy of the numerical method
     102used to solve the governing equations and validation is used to
     103investigate whether the model adequately represents the physical
     104system~\cite{bates01}. Together these processes can be used to
     105establish the likelihood that a model represents a legitimate
     106hypothesis.
     107
     108The sources of data used to validate and verify a model can be
     109separated into three main categories; analytical solutions, scale
     110experiments and field measurements. Analytical solutions of the
     111governing equations of a model, if available, provide the best means
     112of verifying any numerical model. However, analytical solutions are
     113frequently limited to a small set of idealised examples that do not
     114completely capture the more complex behaviour of `real' events. Scale
     115experiments, typically in the form of wave-tank experiments, provide a
     116much more realistic source of data that better captures the complex
     117dynamics of flows such as those generated by tsunami, whilst allowing
     118control of the event and much easier and accurate measurement of the
     119tsunami properties. Comparison of numerical predictions with field
     120data provides the most stringent test. The use of field data increases
     121the generality and significance of conclusions made regarding model
     122utility. On the other hand, it must be noted that the use of field
     123data also significantly increases the uncertainty of the validation
     124experiment that may constrain the ability to make unequivocal
     125statements~\cite{bates01}.
     126
     127Currently, the extent of tsunami related field data is limited. The
     128cost of tsunami monitoring programs, bathymetry and topography surveys
     129prohibits the collection of data in many of the regions in which
     130tsunamis pose greatest threat. The resulting lack of data has limited
     131the number of field data sets available to validate tsunami
     132models. Synolakis et. al~\cite{synolakis07} have developed a set of
     133standards, criteria and procedures for evaluating numerical models of
     134tsunami. They propose three analytical solutions to help identify the
     135validity of a model and five scale comparisons (wave-tank benchmarks)
     136and two field events to assess model veracity.
     137
     138The first field data benchmark introduced by Synolakis compares model
     139results against observed data from the Hokkaido-Nansei-Oki tsunami
     140that occurred around Okushiri Island, Japan on the 12th of July
     1411993. This tsunami provides an example of extreme runup generated from
     142reflections and constructive interference resulting from local
     143topography and bathymetry. The benchmark consists of two tide gauge
     144records and numerous spatially distributed point sites at which
     145modelled maximum runup elevations can be compared. The second
     146benchmark is based upon the Rat Islands Tsunami that occurred off the
     147coast of Alaska on the 17th of November 2003. The Rat island tsunami
     148provides a good test for real-time forecasting models since tsunami
     149was recorded at three tsunameters. The test requires matching the
     150propagation model data with the DART recording to constrain the
     151tsunami source model and then using it to reproduce the tide gauge
     152record at Hilo.
     153
     154In this paper we develop a field data benchmark to be used in
     155conjunction with the other tests proposed by Synolakis et
     156al.~\cite{synolakis07} to validate and verify tsunami models. Unlike
     157the aforementioned tests, the proposed benchmark allows evaluation of
     158model structure during all three distinctive stages of the evolution
     159of a tsunami. The benchmark consists of geodetic measurements of the
     160Sumatra--Andaman earthquake which are used to validate the description
     161of the tsunami source, altimetry data from the JASON satellite to test
     162open ocean propagation, eye-witness accounts to assess near shore
     163propagation and a detailed inundation survey of Patong Bay, Thailand
     164to compare model and observed inundation. A description of the data
     165required to construct the benchmark is given in
     166Section~\ref{sec:data}.
     167
     168An associated aim of this paper is to illustrate the use of this new
     169benchmark to validate an operational tsunami inundation model called
     170\textsc{anuga} used by Geoscience Australia. A description of
     171\textsc{anuga} is given in Secion~\ref{sec:models} and the validation
     172results are given in Secion~\ref{sec:results}.
     173
     174The numerical models used to model tsunami are extremely
     175computationally intensive. Full resolution models of the entire
     176evolution process will often take a number of days to
     177run. Consequently the uncertainty in model predictions is difficult to
     178quantify. However model uncertainty should not be ignored. Section
     179~\ref{sec:sensitivity} provides a simple sensitivity analysis that can
     180be used to investigate the sensitivity of model predictions to model
     181parameters.
    61182
    62183%================Section===========================
    63184\section{Data}\label{sec:data}
    64 The 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}.
    65 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.
     185The sheer magnitude of the 2004 Sumatra-Andaman earthquake and the
     186devastation caused by the subsequent tsunami have generated much
     187scientific interest. As a result an unusually large amount of post
     188seismic data has been collected and documented. Data sets from
     189seismometers, tide gauges, \textsc{gps} surveys, satellite overpasses,
     190subsequent coastal field surveys of run-up and flooding, and
     191measurements of coseismic displacements and bathymetry from ship-based
     192expeditions, have now been made
     193available.%~\cite{vigny05,amnon05,kawata05,liu05}. 
     194In this section we
     195present the data necessary to implement the proposed benchmark
     196corresponding to each of the three stages of the tsunami's evolution.
    66197
    67198\subsection{Generation}\label{sec:gen_data}
    68 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.
    69 
    70 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 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 
    72 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 $\sim$10 minutes of the earthquake plus the deformation that followed in the days following the earthquake before each particular measurement was actually made (typically of order days). Therefore some of the observations may not contain the purely co-seismic deformation but could include some post-seismic deformation as well~\cite{chlieh07}.
     199All tsunami are generated from an initial disturbance of the ocean
     200which develops into a low frequency wave that propagates outwards from
     201the source. The initial deformation of the water surface is most
     202commonly caused by coseismic displacement of the sea floor, but
     203submarine mass failures, landslides, volcanoes or asteroids can also
     204cause tsunami. In this section we detail the information we used in
     205this study to validate models of the sea floor deformation generated
     206by the 2004 Sumatra--Andaman earthquake.
     207
     208The 2004 Sumatra--Andaman tsunami was generated by severe coseismic
     209displacement of the sea floor as a result of one of the largest
     210earthquakes on record. The mega-thrust earthquake started on the 26
     211December 2004 at 0h58'53'' UTC (or just before 8 am local time)
     212approximately 70 km offshore North Sumatra
     213(\url{http://earthquake.usgs.gov/eqcenter/eqinthenews/2004/usslav}). The
     214rupture propagated 1000-1300 km along the Sumatra-Andaman trench to
     215the north at a rate of 2.5-3 km.s$^{-1}$ and lasted approximately 8-10
     216minutes~\cite{ammon05}. Estimates of the moment magnitude of this
     217event range from about 9.1 to 9.3~\cite{chlieh07,stein07}.
     218
     219The unusually large surface deformation caused by this earthquakes
     220means that there were a range of different geodetic measurements of
     221the surface deformation available. These include field measurements of
     222uplifted or subsided coral heads, continuous or campaign \textsc{GPS}
     223measurements and remote sensing measurements of uplift or subsidence
     224(see~\cite{chlieh07} and references therein). Here we use the the near
     225field estimates of vertical deformation in northwestern Sumatra and
     226the Nicobar-Andaman islands collated by~\cite{chlieh07} to validate
     227that our crustal deformation model of the 2004 Sumatra--Andaman
     228earthquake is producing reasonable results. Note that the geodetic
     229data used here is a combination of the vertical deformation that
     230happened in the $\sim$10 minutes of the earthquake plus the
     231deformation that followed in the days following the earthquake before
     232each particular measurement was actually made (typically of order
     233days). Therefore some of the observations may not contain the purely
     234co-seismic deformation but could include some post-seismic deformation
     235as well~\cite{chlieh07}.
    73236
    74237%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.
    … …  
    83246
    84247\subsection{Propagation}
    85 Once 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.
     248Once generated a tsunami will propagate outwards from the source until
     249it encounters the shallow water bordering coastal regions. This period
     250of the tsunami evolution is referred to as the propagation stage. The
     251height and velocity of the tsunami is dependent on the local
     252bathymetry in the regions through which the wave travels and the size
     253of the initial wave. This section details the bathymetry data needed
     254to model the tsunami propagation and the satellite altimetry transects
     255used here to validate open ocean tsunami models.
    86256
    87257\subsubsection{Bathymetry Data}
    88 A number of raw data sets were obtained, analysed and checked for quality and subsequently gridded for easier visualisation and input into the tsunami models. The resulting grid data is relatively coarse in the deeper water and becomes progressively finer as the distance to Patong Bay decreases.
     258A number of raw data sets were obtained, analysed and checked for
     259quality and subsequently gridded for easier visualisation and input
     260into the tsunami models. The resulting grid data is relatively coarse
     261in the deeper water and becomes progressively finer as the distance to
     262Patong Bay decreases.
    89263
    90264The nested bathymetry grid was generated from:
    91265\begin{itemize}
    92 \item A two arc minute grid data set covering the Bay of Bengal, DBDB2, obtained from US Naval Research Labs;
    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
    94 \item A one second grid created from the digitised Thai Navy bathymetry chart, no 358. which covers Patong Bay and the immediately adjacent regions.
     266\item A two arc minute grid data set covering the Bay of Bengal,
     267  DBDB2, obtained from US Naval Research Labs;
     268\item A 3 second arc grid covering the whole of the Andaman Sea based
     269  on Thai Navy charts no 45 and no 362; and
     270\item A one second grid created from the digitised Thai Navy
     271  bathymetry chart, no 358. which covers Patong Bay and the
     272  immediately adjacent regions.
    95273\end{itemize}
    96274
    97 The 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}.
    98 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, 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 
    100 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 FIXME(Ole): Need \cite{} here.
     275The final bathymetry data set consists of four nested grids obtained
     276via interpolation and resampling of the aforementioned data sets. The
     277four grids are shown in Figure~\ref{fig:nested_grids}.  The coarsest
     278bathymetry was obtained by interpolating the DBDB2 grid to a 27 second
     279arc grid. A subsection of this region was then replaced by 9 second
     280data which was generated by sub-sampling the 3 second of arc grid from
     281NOAA. A subset of the 9 second grid was replaced by the 3 second
     282data. Finally, the one second grid was used to approximate the
     283bathymetry in Patong Bay and the immediately adjacent regions. Any
     284points that deviated from the general trend near the boundary were
     285deleted.
     286
     287The sub-sampling of larger grids was performed by using {\bf resample}
     288a Generic Mapping Tools (\textsc{GMT}) program (\cite{wessel98}). The
     289gridding of data was performed using {\bf Intrepid} a commercial
     290geophysical processing package developed by Intrepid Geophysics. The
     291gridding scheme employed the nearest neighbour algorithm followed by
     292an application of minimum curvature akima spline smoothing FIXME(Ole):
     293Need \cite{} here.
    101294
    102295\begin{figure}[ht]
    … …  
    109302
    110303\subsubsection{JASON Satellite Altimetry}\label{sec:data_jason}
    111 During 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.
    112 This data was used to validate the propagation stage in Section \ref{sec:resultsPropagation}.
     304During the 26 December 2004 event, the Jason satellite tracked from
     305north to south and over the equator at 02:55 UTC nearly two hours
     306after the earthquake \cite{gower05}. The satellite recorded the sea
     307level anomaly compared to the average sea level from its previous five
     308passes over the same region in the 20-30 days prior.  This data was
     309used to validate the propagation stage in Section
     310\ref{sec:resultsPropagation}.
    113311%DB I suggest we combine with model data to reduce the number of figures. The satellite track is shown in Figure~\ref{fig:satelliteTrack}.
    114312
    … …  
    132330
    133331\subsection{Inundation}
    134 Inundation 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.
    135 Aside 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.
    136 The datasets necessary for reproducing the results of the inundation stage are available on
    137 Sourceforge under the ANUGA project (\url{http://sourceforge.net/projects/anuga}). At the time
    138 of writing the direct link is \url{http://tinyurl.com/patong2004-data}.
     332Inundation refers to the final stages of the evolution a tsunami and
     333covers the propagation of the tsunami in shallow coastal water and the
     334subsequent run-up on to land. This process is typically the most
     335difficult of the three stages to model due to thin layers of water
     336flowing rapidly over dry land.  Aside from requiring robust solvers
     337which can simulate such complex flow patterns, this part of the
     338modelling process also requires high resolution and quality elevation
     339data which is often not available. In the case of model validation
     340high quality field measurements are also required. For the proposed
     341benchmark the authors have obtained a high resolution bathymetry and
     342topography data set and a high quality inundation survey map from the
     343CCOP in Thailand (\cite{szczucinski06}) which can be used to validate
     344model inundation. 
     345
     346The datasets necessary for reproducing the results
     347of the inundation stage are available on Sourceforge under the ANUGA
     348project (\url{http://sourceforge.net/projects/anuga}). At the time of
     349writing the direct link is \url{http://tinyurl.com/patong2004-data}.
    139350%
    140351%\url{http://sourceforge.net/project/showfiles.php?group_id=172848&package_id=319323&release_id=677531}.
    … …  
    143354
    144355\subsubsection{Topography Data}
    145 A one second grid was used to approximate the topography in Patong Bay. This elevation data was again created from the digitised Thai Navy bathymetry chart, no 358. A visualisation of the elevation data set used in Patong bay is shown in Figure~\ref{fig:patong_bathymetry}. The continuous topography is an interpolation of known elevation measured at the coloured dots.
     356A one second grid was used to approximate the topography in Patong
     357Bay. This elevation data was again created from the digitised Thai
     358Navy bathymetry chart, no 358. A visualisation of the elevation data
     359set used in Patong bay is shown in
     360Figure~\ref{fig:patong_bathymetry}. The continuous topography is an
     361interpolation of known elevation measured at the coloured dots.
    146362
    147363\begin{figure}[ht]
    … …  
    154370
    155371\subsubsection{Buildings and Other Structures}
    156 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 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.
     372Human made build and structures can significantly effect tsunami
     373inundation. The location and size and number of floors of the
     374buildings in Patong Bay were extracted from a GIS data set provide by
     375the CCOP in Thailand (\cite{FIXME from RICHARD}). The heights of these
     376buildings were estimated assuming that each floor has a height of 3 m.
    157377
    158378\subsubsection{Inundation Survey}
    159 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 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.
     379Tsunami run-up is often the cause of the largest financial and human
     380losses yet run-up data that can be used to validate model runup
     381predictions is scarce. Of the two field benchmarks proposed by
     382Synolakis only the Okushiri benchmark facilitates comparison between
     383modelled and observed run-up. One of the major strengths of the
     384benchmark proposed here is that modelled runup can be compared to an
     385inundation survey which maps the maximum run-up along an entire coast
     386line rather than at a series of discrete sites. The survey map is
     387shown in Figure~\ref{fig:patongescapemap} and plots the maximum run-up
     388of the 2004 tsunami in Patong bay. Refer to Szczucinski et
     389al~\cite{szczucinski06} for further details.
    160390
    161391\subsubsection{Eyewitness Accounts}
    162 FIXME (Ole): I think we should move this to where the results are presented.
    163 Eyewitness 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 
    165 Two 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
    166 already 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
    167 is 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
    168 filmed from a building next door to the Comfort Resort near the corner of Ruam Chai St and FIXME(Ole): XXXX.
    169 This 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.
     392FIXME (Ole): I think we should move this to where the results are
     393presented.  Eyewitness accounts detailed in~\cite{papadopoulos06}
     394report that most people at Patong Beach observed an initial retreat of
     395the shoreline of more than 100 m followed a few minutes later by a
     396strong wave (crest). Another less powerful wave arrived another five
     397or ten minutes later. Eyewitness statements place the arrival time of
     398the strong wave between 2 hours and 55 minutes to 3 hours and 5
     399minutes after the source rupture (09:55am to 10:05am local time).
     400
     401Two videos were sourced from the internet (FIXME: Where?) which
     402include footage of the tsunami in Patong Bay on the day of the Indian
     403Ocean Tsunami. Both videos show an already inundated group of
     404buildings, they then show what is to be assumed as the second and
     405third waves approaching and further flooding the town. The first video
     406is in the very north filmed from what is believed to be the roof of
     407the Novotel Hotel marked 'North' in Figure
     408\ref{fig:gauge_locations}. The second video is in the very south
     409filmed from a building next door to the Comfort Resort near the corner
     410of Ruam Chai St and FIXME(Ole): XXXX.  This location is marked 'south'
     411in Figure \ref{fig:gauge_locations} and Figure~\ref{fig:video_flow}
     412shows stills from this video. Both videos were used to estimate flow
     413speeds and inundation dephts over time.
    170414
    171415\begin{figure}[ht]
    … …  
    175419\includegraphics[width=6.0cm,keepaspectratio=true]{flow_rate_south_7_12sec.jpg}
    176420\includegraphics[width=6.0cm,keepaspectratio=true]{flow_rate_south_7_60sec.jpg}
    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.}
     421\caption{Four frames from a video where flow rate could be estimated,
     422  circle indicates tracked debris, from top left: 0.0 sec, 5.0 s, 7.1
     423  s, 7.6 s.}
    178424\label{fig:video_flow}
    179425\end{center}
    180426\end{figure}
    181427
    182 Flow rates were estimated using landmarks found in both videos and were found to be in
    183 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.
     428Flow rates were estimated using landmarks found in both videos and
     429were found to be in the range of 5 to 7 metres per second (+/- 2 m/s)
     430in the north and 0.5 to 2 metres per second (+/- 1 m/s) in the south.
    184431
    185432\begin{figure}[ht]
    186433\begin{center}
    187434\includegraphics[width=8.0cm,keepaspectratio=true]{patongescapemap.jpg}
    188 \caption{Tsunami survey mapping the maximum observed inundation at Patong beach courtesy of the Thai Department of Mineral Resources \protect \cite{szczucinski06}.}
     435\caption{Tsunami survey mapping the maximum observed inundation at
     436  Patong beach courtesy of the Thai Department of Mineral Resources
     437  \protect \cite{szczucinski06}.}
    189438\label{fig:patongescapemap}
    190439\end{center}
    … …  
    193442\subsection{Validation Check-List}
    194443\label{sec:checkList}
    195 The data described in this section can be used to construct a benchmark to validate all three stages of the evolution of a tsunami. In particular we propose that a legitimate tsunami model should reproduce the following behaviour:
     444The data described in this section can be used to construct a
     445benchmark to validate all three stages of the evolution of a
     446tsunami. In particular we propose that a legitimate tsunami model
     447should reproduce the following behaviour:
    196448\begin{itemize}
    197  \item Reproduce the vertical deformation observed in north-western Sumatra and along the Nicobar--Andaman islands, see Section~\ref{sec:gen_data}.
    198  \item Reproduce the \textsc{jason} satellite altimetry sea surface anomalies, see Section~\ref{sec:data_jason}.
    199  \item Reproduce the inundation survey map in Patong bay (Figure~\ref{fig:patongescapemap}).
    200  \item Simulate a leading depression followed by two distinct crests of decreasing magnitude.
    201  \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.
     449 \item Reproduce the vertical deformation observed in north-western
     450   Sumatra and along the Nicobar--Andaman islands, see
     451   Section~\ref{sec:gen_data}.
     452 \item Reproduce the \textsc{jason} satellite altimetry sea surface
     453   anomalies, see Section~\ref{sec:data_jason}.
     454 \item Reproduce the inundation survey map in Patong bay
     455   (Figure~\ref{fig:patongescapemap}).
     456 \item Simulate a leading depression followed by two distinct crests
     457   of decreasing magnitude.
     458 \item Predict the water depths and flow speeds, at the locations of
     459   the eye-witness videos, that fall within the bounds obtained from
     460   the videos.
    202461\end{itemize}
    203462
    204 Ideally, the model should also be compared to measured timeseries of waveheights and velocities
    205 but the authors are not aware of the availability of such data.
     463Ideally, the model should also be compared to measured timeseries of
     464waveheights and velocities but the authors are not aware of the
     465availability of such data.
    206466
    207467
    208468%================Section===========================
    209469\section{Modelling the Event}\label{sec:models}
    210 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 modelling methodology comprises the three parts; generation, propagation and inundation (Sections~\ref{sec:modelGeneration},\ref{sec:modelPropagation} and \ref{sec:modelInundation} respectively).
     470Numerous models are currently used to model and predict tsunami
     471generation, propagation and run-up~\cite{titov97a,satake95}. Here we
     472introduce the modelling methodology employed by Geoscience Australia
     473to illustrate the utility of the proposed benchmark. Geoscience
     474Australia's tsunami modelling methodology comprises the three parts;
     475generation, propagation and inundation
     476(Sections~\ref{sec:modelGeneration},\ref{sec:modelPropagation} and
     477\ref{sec:modelInundation} respectively).
    211478
    212479\subsection{Generation}\label{sec:modelGeneration}
    213480
    214 There 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 
    216 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 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.
     481There are various approaches to modelling the expected crustal
     482deformation from an earthquake at depth. Most approaches model the
     483earthquake as a dislocation in a linear, elastic medium. Here we use
     484the method of Wang et. al.~\cite{wang03}. One of the main advantages
     485of their method is that it allows the dislocation to be located in a
     486stratified linear elastic half-space with an arbitrary number of
     487layers. Other methods (such as those based on Okada's equations) can
     488only model the dislocation in a homogeneous elastic half space, or can
     489only include a limited number of layers, and thus cannot model the
     490effect of the depth dependence of the elasticity of the
     491Earth~\cite{wang03}. The original versions of the codes described here
     492are available from \url{http://www.iamg.org/CGEditor/index.htm}. The
     493first program, \textsc{edgrn}, calculates elastic Green's function for
     494a set of point sources at a regular set of depths out to a specified
     495distance. The equations controlling the deformation are solved by
     496using a combination of Hankel's transform and Wang et al's
     497implementation of the Thomson-Haskell propagator
     498algorithm~\cite{wang03}. Once the Green's functions are calculated we
     499use a slightly modified version of \textsc{edcmp} to calculate the sea
     500floor deformation for a specific subfault. This second code
     501discretises the subfault into a set of unit sources and sums the
     502elastic Green's functions calculated from \textsc{edgrn} for all the
     503unit sources on the fault plane in order to calculate the final static
     504deformation caused by a two dimensional dislocation along the
     505subfault. This step is possible because of the linearity of the
     506governing equations. For this study, we have made minor modifications
     507to \textsc{edcmp} in order for it to output in a file format
     508compatible with the propagation code in the following section but it
     509is otherwise the similar to the original code.
     510
     511In order to calculate the crustal deformation using these codes we
     512thus need to have a model describing the variation in elastic
     513properties with depth and a slip model of the earthquake to describe
     514the dislocation. The elastic parameters used for this study are the
     515same as those in Table 2 of Burbidge~\cite{burbidge08}. For the slip
     516model, there are many possible models for the 2004 Andaman--Sumatran
     517earthquake to choose from
     518~\cite{chlieh07,asavanant08,arcas06,grilli07,ioualalen07}. Some are
     519determined from various geological surveys of the site, others solve
     520an inverse problem which calibrates the source based upon the tsunami
     521wave signal, the seismic signal and/or the runup. The source
     522parameters used here to simulate the 2004 Indian Ocean tsunami were
     523taken from the slip model G-M9.15 from Chlieh
     524et. al.~\cite{chlieh07}. This model was created by inversion of wide
     525range of geodetic and seismic data. The slip model consists of 686
     52620km x 20km subsegments each with a different slip, strike and dip
     527angle. The dip subfaults go from $17.5^0$ in the north and $12^0$ in
     528the south. Refer to Chlieh et. al.~\cite{chlieh07} for a detailed
     529discussion of this model and its derivation. Note that the geodetic
     530data used in the validation was also included by~\cite{chlieh07} in
     531the inversion used to find G-M9.15, thus the validation is not
     532completely independent. However, a successful validation would still
     533show that the crustal deformation and elastic properties model used
     534here is at least as valid as the one used by Chlieh
     535et. al.~\cite{chlieh07} and can reproduce the observations just as
     536accurately.
    217537
    218538\subsection{Propagation}\label{sec:modelPropagation}
    219 We 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.
     539We use the \textsc{ursga} model described below to simulate the
     540propagation of the 2004 tsunami in the deep ocean ocean, based on a
     541discrete representation of the initial deformation of the sea floor,
     542described in Section~\ref{sec:modelGeneration}. For the models shown
     543here, we assume that the uplift is instantaneous and creates a wave of
     544the same size and amplitude as the co-seismic sea floor deformation.
    220545
    221546\subsubsection{URSGA}
    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.
     547\textsc{ursga} is a hydrodynamic code that models the propagation of
     548the tsunami in deep water using a finite difference method to solve
     549the depth integrated linear or nonlinear shallow water equations in
     550spherical co-ordinates with friction and Coriolis terms. The code is
     551based on Satake~\cite{satake95} with significant modifications made by
     552the \textsc{urs} corporation~\cite{thio08} and Geoscience
     553Australia~\cite{burbidge08}. The tsunami is propagated via a staggered
     554grid system. Coarse grids are used in the open ocean and the finest
     555resolution grid is employed in the region of most
     556interest. \textsc{Ursga} is not publicly available.
    223557
    224558\subsection{Inundation}\label{sec:modelInundation}
    225 The 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}.
    227 The wave signal is then used as a time varying boundary condition for the \textsc{anuga} inundation simulation.
     559The utility of the \textsc{ursga} model decreases with water depth
     560unless an intricate sequence of nested grids is employed. In
     561comparison \textsc{anuga}, described below, is designed to produce
     562robust and accurate predictions of on-shore inundation, but is less
     563suitable for earthquake source modelling and large study areas because
     564it is based on projected spatial coordinates. Consequently, the
     565Geoscience Australia tsunami modelling methodology is based on a
     566hybrid approach using models like \textsc{ursga} for tsunami
     567propagation up to a 100 m depth contour.
     568%Specifically we use the \textsc{ursga} model to simulate the
     569%propagation of the 2004 Indian Ocean tsunami in the deep ocean, based
     570%on a discrete representation of the initial deformation of the sea
     571%floor, described in Section~\ref{sec:modelGeneration}.
     572The wave signal is then used as a time varying boundary condition for
     573the \textsc{anuga} inundation simulation.
    228574% A description of \textsc{anuga} is the following section.
    229575
    230576\subsubsection{ANUGA}
    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}.
     577\textsc{Anuga} is an Open Source hydrodynamic inundation tool that
     578solves the conserved form of the depth integrated nonlinear shallow
     579water wave equations. The scheme used by \textsc{anuga}, first
     580presented by Zoppou and Roberts~\cite{zoppou99}, is a high-resolution
     581Godunov-type method that uses the rotational invariance property of
     582the shallow water equations to transform the two-dimensional problem
     583into local one-dimensional problems. These local Riemann problems are
     584then solved using the semi-discrete central-upwind scheme of Kurganov
     585et al.~\cite{kurganov01} for solving one-dimensional conservation
     586equations. The numerical scheme is presented in detail in Zoppou and
     587Roberts~\cite{zoppou99}, Roberts and Zoppou~\cite{roberts00}, and
     588Nielsen et al.~\cite{nielsen05}. An important capability of the
     589software is that it can model the process of wetting and drying as
     590water enters and leaves an area. This means that it is suitable for
     591simulating water flow onto a beach or dry land and around structures
     592such as buildings. It is also capable of adequately resolving
     593hydraulic jumps due to the ability of the finite-volume method to
     594handle discontinuities. The numerical scheme can also handle
     595transitions between sub-critical and super-critical flow regimes
     596seamlessly. \textsc{Anuga} has been validated against a number of
     597analytical solutions and the wave tank simulation of the 1993 Okushiri
     598Island tsunami~\cite{nielsen05,roberts06}.
    232599
    233600%================Section===========================
    … …  
    236603
    237604\subsection{Generation}\label{modelGeneration}
    238 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 0.06 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.
     605The location and magnitude of the sea floor displacement associated
     606with the 2004 Sumatra--Andaman tsunami calculated from the G-M9.15
     607model of~\cite{chlieh07} is shown in
     608Figure~\ref{fig:surface_deformation}. The magnitude of the sea floor
     609displacement ranges from about $-3.0$ to $5.0$ metres. The region near
     610the fault is predicted to uplift, while that further away from the
     611fault subsides. Also shown in Figure~\ref{fig:surface_deformation} are
     612the areas that were observed to uplift (arrows pointing up) or subside
     613(arrows point down) during and immediately after the earthquake. Most
     614of this data comes uplifted or subsided coral heads. The length of
     615vector increases with the magnitude of the displacement, the length
     616corresponding to 1m of observed motion is shown in the top right
     617corner of the figure. As can be seen, the source model detailed in
     618Section~\ref{sec:modelGeneration} produces a crustal deformation that
     619matches the vertical displacements in the Nicobar-Andaman islands and
     620Sumatra very well. Uplifted regions are close to the fault and
     621subsided regions are further away. The crosses on
     622Figure~\ref{fig:surface_deformation} show estimates of the pivot line
     623from the remote sensing data~\cite{chlieh07} and they follow the
     624predicted pivot line quite accurately. The average difference between
     625the observed motion and the predicted motion (including the pivot line
     626points) is only 0.06 m, well below the typical error of the
     627observations of between 0.25 and 1.0 m. However, the occasional point
     628has quite a large error (over 1 m), for example a couple
     629uplifted/subsided points appear to be on a wrong side of the predicted
     630pivot line~\ref{fig:surface_deformation}. The excellence of the fit is
     631not surprising, since the original slip model was chosen
     632by~\cite{chlieh07} to fit this (and the seismic data) well. However,
     633this does demonstrate that \textsc{edgrn} and our modified version of
     634\textsc{edstat} can reproduce the correct pattern of vertical
     635deformation very well when the slip distribution is well constrained
     636and when reasonable values for the elastic properties are used.
    239637
    240638\begin{figure}[ht]
    … …  
    242640\includegraphics[width=5cm,keepaspectratio=true]{surface_deformation.jpg}
    243641%\includegraphics[totalheight=0.3\textheight,width=0.8\textwidth]{surface_deformation.jpg}
    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}.}
     642\caption{Location and magnitude of the vertical component of the sea
     643  floor displacement associated with the 2004 Indian Ocean tsunami
     644  based on the slip model, G-M9.15. The black arrows which point up
     645  show areas observed to uplift during and immediately after the
     646  earthquake, those point down are locations which subsided. The
     647  length of increases with the magnitude of the deformation. The arrow
     648  length corresponding to 1 m of deformation is shown in the top right
     649  hand corner of the figure. The crosses marks show the location of
     650  the pivot line (the region between the uplift and subsided region
     651  where the uplift is zero) derived from remote sensing. All the
     652  observational data come from the dataset collated
     653  by~\cite{chlieh07}.}
    245654\label{fig:surface_deformation}
    246655\end{center}
    … …  
    249658
    250659\subsection{Propagation}\label{sec:resultsPropagation}
    251 The 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$1996 finite difference points. Inside this grid, a nested sequence of grids was used. The grid resolution of the nested grids went from 27 arc seconds in the coarsest grid, down to 9 arc seconds in the second grid, 3 arc seconds in the third grid and finally 1 arc second in the finest grid near Patong. The computational domain is shown in Figure~\ref{fig:computational_domain}.
    252 
    253 Figure \ref{fig:jasonComparison} provides a comparison of the \textsc{ursga} predicted sea surface elevation with the JASON satellite altimetry data. The \textsc{ursga} model replicates the amplitude and timing of the first peak and trough well. However, the model does not resolve the double peak of the first wave. Also note that the \textsc{ursga} model prediction of the ocean surface elevation becomes out of phase with the JASON data at 3 to 7 degrees latitude. Chlieh et al~\cite{chlieh07} also observe these misfits and suggest it is caused by a reflected wave from the Aceh Peninsula that is not resolved in the model due to insufficient resolution of the computational mesh and bathymetry data. This is also a limitation of the model presented here, but probably could be improved by nesting grids near Aceh.
     660The deformation results described in Section~\ref{sec:modelGeneration}
     661were used to provide a profile of the initial ocean surface
     662displacement. This wave was used as an initial condition for
     663\textsc{ursga} and was propagated throughout the Bay of Bengal. The
     664rectangular computational domain of the largest grid extended from
     66590$^0$ to 100$^0$ East and 0 to 15$^0$ North and contained
     6661335$\times$1996 finite difference points. Inside this grid, a nested
     667sequence of grids was used. The grid resolution of the nested grids
     668went from 27 arc seconds in the coarsest grid, down to 9 arc seconds
     669in the second grid, 3 arc seconds in the third grid and finally 1 arc
     670second in the finest grid near Patong. The computational domain is
     671shown in Figure~\ref{fig:computational_domain}.
     672
     673Figure \ref{fig:jasonComparison} provides a comparison of the
     674\textsc{ursga} predicted sea surface elevation with the JASON
     675satellite altimetry data. The \textsc{ursga} model replicates the
     676amplitude and timing of the first peak and trough well. However, the
     677model does not resolve the double peak of the first wave. Also note
     678that the \textsc{ursga} model prediction of the ocean surface
     679elevation becomes out of phase with the JASON data at 3 to 7 degrees
     680latitude. Chlieh et al~\cite{chlieh07} also observe these misfits and
     681suggest it is caused by a reflected wave from the Aceh Peninsula that
     682is not resolved in the model due to insufficient resolution of the
     683computational mesh and bathymetry data. This is also a limitation of
     684the model presented here, but probably could be improved by nesting
     685grids near Aceh.
    254686
    255687\begin{figure}[ht]
    256688\begin{center}
    257689\includegraphics[width=12.0cm,keepaspectratio=true]{jasonComparison.jpg}
    258 \caption{Comparison of the \textsc{ursga} predicted surface elevation with the JASON satellite altimetry data. The \textsc{ursga} wave heights have been corrected for the time the satellite passed overhead compared to JASON sea level anomaly.
    259 }
     690\caption{Comparison of the \textsc{ursga} predicted surface elevation
     691  with the JASON satellite altimetry data. The \textsc{ursga} wave
     692  heights have been corrected for the time the satellite passed
     693  overhead compared to JASON sea level anomaly.  }
    260694\label{fig:jasonComparison}
    261695\end{center}
    … …  
    263697
    264698\subsection{Inundation}
    265 After 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}
     699After propagating the tsunami in the open ocean using \textsc{ursga}
     700the approximated ocean and surface elevation and horisontal flow
     701velocities were extracted and used to construct a boundary condition
     702for the \textsc{anuga} model. The interface betwen the \textsc{ursga}
     703and \textsc{anuga} models was chosen to roughly follow the 100 m depth
     704contour along the west coast of Phuket Island. The computational
     705domain is shown in Figure \ref{fig:computational_domain}
    266706\begin{figure}[ht]
    267707\begin{center}
    … …  
    274714\end{figure}
    275715
    276 The 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 
    279 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 whereas the transmissive boundary condition robustly preserves the wave.
    280 
    281 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
    282 
    283 FIXME (Ole): Perhaps rephrase a bit as the 1cm vs 10cm is hard to understand.
    284 Maximum 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.
     716The domain was discretised into 386,338 triangles. The resolution of
     717the grid was increased in certain regions to efficiently increase the
     718accuracy of the simulation. The grid resolution ranged between a
     719maximum triangle area of $1\times 10^5$ m$^2$ near the Western ocean
     720boundary to $20$ m$^2$ in the small regions surrounding the inundation
     721region in Patong Bay. Due to a lack of available data, friction was
     722set to a constant throughout the computational domain. For the
     723reference simulation a Manning's coefficient of 0.01 was chosen to
     724represent a small resistance to the water flow. See Section
     725\ref{sec:friction sensitivity} for details on model sensitivity to
     726this parameter.
     727
     728
     729The boundary condition at each side of the domain towards the south
     730and the north where no data was available was chosen as a transmissive
     731boundary condition effectively replicating the time dependent wave
     732height present just inside the computational domain. Momentum was set
     733to zero. Other choices include applying the mean tide value as a
     734Dirichlet type boundary condition but experiments as well as the
     735result of the verification reported here showed that this approach
     736tends to under estimate the tsunami impact due to the tempering of the
     737wave near the side boundaries whereas the transmissive boundary
     738condition robustly preserves the wave.
     739
     740During the \textsc{anuga} simulation the tide was kept constant at
     741$0.80$ m. This value was chosen to correspond to the tidal height
     742specified by the Thai Navy tide charts
     743(\url{http://www.navy.mi.th/hydro/}) at the time the tsunami arrived
     744at Patong Bay. Although the tsunami propagated for approximately 3
     745hours before it reach Patong Bay, the period of time during which the
     746wave propagated through the \textsc{anuga} domain is much
     747smaller. Consequently the assumption of constant tide height is
     748reasonable
     749
     750FIXME (Ole): Perhaps rephrase a bit as the 1cm vs 10cm is hard to
     751understand.  Maximum onshore inundation elevation was computed from
     752the model throughout the entire Patong Bay
     753region. Figure~\ref{fig:inundationcomparison1cm} shows very good
     754agreement between the measured and simulated inundation. The
     755\textsc{anuga} simulation determines a region to be inundated if at
     756some point in time it was covered by at least 1cm of water. This
     757precision in field measurements is impossible to obtain. The
     758inundation boundary is determined by observing water marks and other
     759signs left by the receding waters. The precision of the observed
     760inundation map is, most likely, at least an order of magnitude worse
     761than the \textsc{anuga} simulation. The simulated inundation based
     762upon a 10cm threshold is shown in
     763Figure~\ref{fig:inundationcomparison1cm}. An inundation threshold of
     76410cm was selected for all future simulations to reflect the likely
     765accuracy of the survey and subsequently facilitate a more appropriate
     766comparison between the modelled and observed inundation area.
    285767
    286768An 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}.
    … …  
    297779\end{figure}
    298780
    299 To quantify the agreement between observed and simulated inundation we introduce the measure
     781To quantify the agreement between observed and simulated inundation we
     782introduce the measure
    300783\begin{equation}
    301784A(I_{in})=\frac{A(I_m\cap I_o)}{A(I_o)}
    302785\end{equation}
    303 to quantify the fraction of the area $A(I_{in})$ of observed inundation region $I_o$ captured by the model $I_m$. Another useful measure is the fraction of the modelled inundation area that falls outside the observed inundation area given by the formula
     786representing the ratio $A(I_{in})$ of observed
     787inundation region $I_o$ captured by the model $I_m$. Another useful
     788measure is the fraction of the modelled inundation area that falls
     789outside the observed inundation area given by the formula
    304790\begin{equation}
    305791A(I_{out})=\frac{A(I_m\setminus (I_m\cap I_o))}{A(I_o)}
    306792\end{equation}
    307 These values for the two aforementioned simulations are given in Table~\ref{table:inundationAreas}
    308 FIXME (Ole): The left hand side of these equations are not areas - consider another symbol.
    309 
    310 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}
     793These values for the two aforementioned simulations are given in
     794Table~\ref{table:inundationAreas} FIXME (Ole): The left hand side of
     795these equations are not areas - consider another symbol.
     796
     797Discrepancies between the survey data and the modelled inundated
     798include: unknown distribution of surface roughness, inappropriate
     799parameterisation of the source model, effect of humans structures on
     800flow, as well as uncertainties in the elevation data, effects of
     801erosion and deposition by the tsunami event, measurement errors, and
     802missing data in the field survey data itself. The impact of some of
     803these sources of uncertainties are is investigated in
     804Section~\ref{sec:sensitivity}
    311805
    312806\subsection{Eye-witness accounts}
    313 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
    314 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.
     807Figure \ref{fig:gauge_locations} shows four locations where time
     808series have been extracted from the model. The two offshore timeseries
     809are shown in Figure \ref{fig:offshore_timeseries} and the two onshore
     810timeseries are shown in Figure \ref{fig:onshore_timeseries}. The
     811latter coincide with locations where video footage from the event is
     812available.
    315813
    316814\begin{figure}[ht]
    … …  
    341839\end{figure}
    342840
    343 FIXME(Ole): This is a repetition of an earlier section. I'll look at that soon.
    344 Crude flow rates can be estimated with landmarks found in satellite imagery and the use of a GIS and were found to be in
    345 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
    346 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
    347 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.
     841FIXME(Ole): This is a repetition of an earlier section. I'll look at
     842that soon. 
     843Crude flow rates can be estimated with landmarks found in
     844satellite imagery and the use of a GIS and were found to be in the
     845range of 5 to 7 metres per second (+/- 2 m/s) in the north and 0.5 to
     8462 metres per second (+/- 1 m/s) in the south. This is in agreement
     847with results from our simulations. Our modelled flow rates show
     848maximum values in the order of 0.2 to 2.6 m/s in the south and 0.1 to
     8493.3 m/s for the north as shown in the figures. Water depths could also
     850be estimated from the videos by the level at which water rose up the
     851sides of buildings such as shops. Our estimates are in the order of
     8521.5 to 2.0 metres (+/- 0.5 m). This is in the same range as our
     853modelled maximum depths of 1.4 m in the north and 1.5 m in the south
     854as seen in the figure. Fritz ~\cite{fritz06} performed a detailed
     855analysis of video frames taken around Banda Aceh and arrived at flow
     856speeds in the range of 2 to 5 m/s.
    348857
    349858
    … …  
    353862\section{Sensitivity Analysis}
    354863\label{sec:sensitivity}
    355 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.
     864This section investigates the effect of different values of Manning's
     865friction coefficient, changing waveheight at the 100m depth contour,
     866and the presence and absence of buildings in the elevation dataset on
     867model maximum inundation.
    356868
    357869%========================Friction==========================%
    358870\subsection{Friction}
    359871\label{sec:friction sensitivity}
    360 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 and the reference model uses a value of 0.01.
    361 To 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.
     872The first study investigated the impact of surface roughness on the
     873predicted run-up. According to Schoettle~\cite{schoettle2007}
     874appropriate values of Manning's coefficient range from 0.007 to 0.030
     875for tsunami propagation over a sandy sea floor and the reference model
     876uses a value of 0.01.  To investigate sensitivity to this parameter,
     877we simulated the maximum onshore inundation using the a Manning's
     878coefficient of 0.0003 and 0.03. The resulting inundation maps are
     879shown in Figure~\ref{fig:sensitivity_friction} and the maximum flow
     880speeds in Figure~\ref{fig:sensitivity_friction_speed}. These figures
     881show that the on-shore inundation extent decreases with increasing
     882friction and that small perturbations in the friction cause bounded
     883changes in the output. This is consistent with the conclusions of
     884Synolakis~\cite{synolakis05} who states that the long wavelength of
     885tsunami tends to mean that the friction is less important in
     886comparison to the motion of the wave.
    362887
    363888%========================Wave-Height==========================%
    364889\subsection{Input Wave Height}\label{sec:waveheightSA}
    365 The effect of the wave-height used as input to the inundation model \textsc{anuga} was also investigated. 
    366 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 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.
     890The effect of the wave-height used as input to the inundation model
     891\textsc{anuga} was also investigated.
     892Figure~\ref{fig:sensitivity_boundary} indicates that the inundation
     893severity is directly proportional to the boundary waveheight but small
     894perturbations in the input wave-height of 10 cm appear to have little
     895effect on the final on-shore run-up. Obviously larger perturbations
     896will have greater impact. However, this value is generally well
     897predicted by the generation and propagation models such as
     898\textsc{ursga}. See e.g. \cite{FIXME} Toshi Baba's validation study at
     899Kuril islands.
    367900
    368901
    … …  
    370903%========================Buildings==========================%
    371904\subsection{Buildings and Other Structures}
    372 The 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}.
     905The presence of buildings has the greatest influence on the maximum
     906on-shore inundation extent. Figure~\ref{fig:sensitivity_nobuildings}
     907shows the maximum run-up in the presence and absence of buildings. It
     908is apparent that the inundation is much more severe when the presence
     909of man made structures and buildings are ignored. Maximal flow speeds
     910for these two model parameterisations are shown in
     911Figure~\ref{fig:sensitivity_nobuildings_speed}.
    373912
    374913\begin{table}
    … …  
    394933
    395934\section{Conclusion}
    396 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}.
    397 
    398 This study also shows that the tsunami impact modelling methodology adopted is sane and able to predict inundation extents with reasonable accuracy.
    399 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.
    400 
    401 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.
     935This paper proposes an additional field data benchmark for the
     936verification of tsunami inundation models. Currently, there is a
     937scarcity of appropriate validation datasets due to a lack of well
     938documented historical tsunami impacts. The benchmark proposed here
     939utilises the uniquely large amount of observational data for model
     940comparison obtained during, and immediately following, the
     941Sumatra--Andaman tsunami of 26th December 2004. Unlike the small
     942number of existing benchmarks, the proposed test validates all three
     943stages of tsunami evolution - generation, propagation and
     944inundation. In an attempt to provide higher visability and easier
     945accessibility for tsunami benchmark problems the data used to
     946construct the proposed benchmark is documented and freely available at
     947\url{http://tinyurl.com/patong2004-data}.
     948
     949This study also shows that the tsunami impact modelling methodology
     950adopted is sane and able to predict inundation extents with reasonable
     951accuracy.  An associated aim of this paper was to further validate the
     952hydrodynamic modelling tool \textsc{anuga} which is used to simulate
     953the tsunami inundation and run rain-induced floods. Model predictions
     954matched well geodetic measurements of the Sumatra--Andaman earthquake,
     955altimetry data from the \textsc{jason}, eye-witness accounts of wave
     956front arrival times and flow speeds and a detailed inundation survey
     957of Patong Bay, Thailand.
     958
     959A simple sensitivity analysis was performed to assess the influence of
     960small changes in friction, wave-height at the 100m depth contour and
     961the presence of buildings and other structures on the model
     962predictions. The presence of buildings has the greatest influence on
     963the simulated inundation extent. The value of friction and small
     964perturbations in the waveheight at the ANUGA boundary have
     965comparatively little effect on the model results.
    402966
    403967%================Acknowledgement===================
    404968\section*{Acknowledgements}
    405 This project was undertaken at Geoscience Australia and the Department of Mathematics, The Australian National University. The authors would like to thank Niran Chaimanee from the CCOP, Thailand for providing the post 2004 tsunami survey data and the elevation data for Patong beach, Prapasri Asawakun from the Suranaree University of Technology and Parida Kuneepong for supporting this work; and Drew Whitehouse from the Australian National University for preparing the animation.
     969This project was undertaken at Geoscience Australia and the Department
     970of Mathematics, The Australian National University. The authors would
     971like to thank Niran Chaimanee from the CCOP, Thailand for providing
     972the post 2004 tsunami survey data and the elevation data for Patong
     973beach, Prapasri Asawakun from the Suranaree University of Technology
     974and Parida Kuneepong for supporting this work; and Drew Whitehouse
     975from the Australian National University for preparing the animation.
    406976
    407977\section{Appendix}
    … …  
    411981\includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_minus10}
    412982\includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_plus10}
    413 \caption{Model results with wave height at ANUGA boundary artificially modified
    414 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.}
     983\caption{Model results with wave height at ANUGA boundary artificially
     984  modified to asses sensitivities. The first image is the reference
     985  inundation extent as reported in Section \protect \ref{sec:results}
     986  while the second and third show the inundation results if the wave
     987  at the ANUGA boundary is reduced or increased by 10cm
     988  respectively. The inundation severity varies in proportion to the
     989  boundary waveheight, but the model results are only slightly
     990  sensitive to this parameter for the range of values tested.}
    415991\label{fig:sensitivity_boundary}
    416992\end{center}
    … …  
    4321008\includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_reference}
    4331009\includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_nobuildings}
    434 \caption{This figure shows the effect of having buildings as part of the
    435 elevation data set.
    436 The first image is the reference inundation extent as reported in Section \protect \ref{sec:results} where buildings were included. The second shows the inundation results for a model entirely without buildings.
    437 As expected, the absence of buildings will increase the inundation extent
    438 beyond what was surveyed.}
     1010\caption{This figure shows the effect of having buildings as part of
     1011  the elevation data set.  The first image is the reference inundation
     1012  extent as reported in Section \protect \ref{sec:results} where
     1013  buildings were included. The second shows the inundation results for
     1014  a model entirely without buildings.  As expected, the absence of
     1015  buildings will increase the inundation extent beyond what was
     1016  surveyed.}
    4391017\label{fig:sensitivity_nobuildings}
    4401018\end{center}
    … …  
    4461024\includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_reference_speed}
    4471025\includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_nobuildings_speed}
    448 \caption{The maximal flow speeds for the same model parameterisations found in Figure \protect \ref{fig:sensitivity_nobuildings}.}
     1026\caption{The maximal flow speeds for the same model parameterisations
     1027  found in Figure \protect \ref{fig:sensitivity_nobuildings}.}
    4491028\label{fig:sensitivity_nobuildings_speed}
    4501029\end{center}
    … …  
    4561035\includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_f0003}
    4571036\includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_f03}
    458 \caption{Model results for different values of Manning's friction coefficient.
    459 The first image is the reference inundation extent as reported in Section \protect \ref{sec:results} where the friction value $0.01$ was used across the
    460 entire domain while the second and third show the inundation results for friction values of 0.0003 and 0.03 respectively. The inundation extent increases for the lower friction value while the higher slows the flow and decreases the inundation extent. Ideally, friction should vary across the entire domain depending on terrain and vegetation, but this is beyond the scope of this study.}
     1037\caption{Model results for different values of Manning's friction
     1038  coefficient. The first image is the reference inundation extent as
     1039  reported in Section \protect \ref{sec:results} where the friction
     1040  value $0.01$ was used across the entire domain while the second and
     1041  third show the inundation results for friction values of 0.0003 and
     1042  0.03 respectively. The inundation extent increases for the lower
     1043  friction value while the higher slows the flow and decreases the
     1044  inundation extent. Ideally, friction should vary across the entire
     1045  domain depending on terrain and vegetation, but this is beyond the
     1046  scope of this study.}
    4611047\label{fig:sensitivity_friction}
    4621048\end{center}
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