Index: /anuga_work/publications/boxing_day_validation_2008/patong_validation.tex
===================================================================
--- /anuga_work/publications/boxing_day_validation_2008/patong_validation.tex	(revision 7216)
+++ /anuga_work/publications/boxing_day_validation_2008/patong_validation.tex	(revision 7217)
@@ -13,8 +13,10 @@
 
 %----------title-------------%
-\title{Benchmarking Tsunami Models using the December 2004 Indian Ocean Tsunami and its Impact at Patong Beach}
+\title{Benchmarking Tsunami Models using the December 2004 Indian
+  Ocean Tsunami and its Impact at Patong Beach}
 
 %-------authors-----------
-\author{J.~D. Jakeman \and O. Nielsen \and K. VanPutten \and D. Burbidge \and R. Mleczko \and N. Horspool}
+\author{J.~D. Jakeman \and O. Nielsen \and K. VanPutten \and
+  D. Burbidge \and R. Mleczko \and N. Horspool}
 
 % to be added when submitted to ocean dynamics
@@ -26,4 +28,6 @@
 %	Geoscience Australia, Canberra, \textsc{Australia}
 %}
+
+
 %================Start of Document================
 \begin{document}
@@ -31,5 +35,23 @@
 %------Abstract--------------
 \begin{abstract}
-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.
+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.
 % to be added when submitted to ocean dynamics
 %\keywords{Tsunami \and modelling \and validation and verification \and benchmark}
@@ -40,35 +62,176 @@
 
 \section{Introduction}
-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.
-
-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. 
-
-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.
-
-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.
-
-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}.
-
-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. 
-
-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.
-
-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}.
-
-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}. 
-
-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. 
+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.
+
+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.
+
+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.
+
+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.
+
+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}.
+
+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.
+
+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.
+
+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}.
+
+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}.
+
+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.
 
 %================Section===========================
 \section{Data}\label{sec:data}
-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}.
-In this section we present the data necessary to implement the proposed benchmark corresponding to each of the three stages of the tsunami's evolution. 
+The 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}.  
+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.
 
 \subsection{Generation}\label{sec:gen_data}
-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.
-
-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}.
-
-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$10 minutes of the earthquake plus the deformation that followed in the days following the earthquake before each particular measurement was actually made (typically of order days). Therefore some of the observations may not contain the purely co-seismic deformation but could include some post-seismic deformation as well~\cite{chlieh07}.
+All tsunami are generated from an initial disturbance of the ocean
+which develops into a low frequency wave that propagates outwards from
+the source. The initial deformation of the water surface is most
+commonly caused by coseismic displacement of the sea floor, but
+submarine mass failures, landslides, volcanoes or asteroids can also
+cause tsunami. In this section we detail the information we used in
+this study to validate models of the sea floor deformation generated
+by the 2004 Sumatra--Andaman earthquake.
+
+The 2004 Sumatra--Andaman tsunami was generated by severe coseismic
+displacement of the sea floor as a result of one of the largest
+earthquakes on record. The mega-thrust earthquake started on the 26
+December 2004 at 0h58'53'' UTC (or just before 8 am local time)
+approximately 70 km offshore North Sumatra
+(\url{http://earthquake.usgs.gov/eqcenter/eqinthenews/2004/usslav}). The
+rupture propagated 1000-1300 km along the Sumatra-Andaman trench to
+the north at a rate of 2.5-3 km.s$^{-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}.
+
+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}.
 
 %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.
@@ -83,20 +246,50 @@
 
 \subsection{Propagation}
-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.
+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.
 
 \subsubsection{Bathymetry Data}
-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.
+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.
 
 The nested bathymetry grid was generated from: 
 \begin{itemize}
-\item A two arc minute grid data set covering the Bay of Bengal, DBDB2, obtained from US Naval Research Labs; 
-\item A 3 second arc grid covering the whole of the Andaman Sea based on Thai Navy charts no 45 and no 362; and 
-\item A one second grid created from the digitised Thai Navy bathymetry chart, no 358. which covers Patong Bay and the immediately adjacent regions.
+\item A two arc minute grid data set covering the Bay of Bengal,
+  DBDB2, obtained from US Naval Research Labs;
+\item A 3 second arc grid covering the whole of the Andaman Sea based
+  on Thai Navy charts no 45 and no 362; and
+\item A one second grid created from the digitised Thai Navy
+  bathymetry chart, no 358. which covers Patong Bay and the
+  immediately adjacent regions.
 \end{itemize}
 
-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}. 
-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.
-
-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. 
+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}.  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.
+
+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.
 
 \begin{figure}[ht]
@@ -109,6 +302,11 @@
 
 \subsubsection{JASON Satellite Altimetry}\label{sec:data_jason}
-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. 
-This data was used to validate the propagation stage in Section \ref{sec:resultsPropagation}.
+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.  This data was
+used to validate the propagation stage in Section
+\ref{sec:resultsPropagation}.
 %DB I suggest we combine with model data to reduce the number of figures. The satellite track is shown in Figure~\ref{fig:satelliteTrack}.
 
@@ -132,9 +330,22 @@
 
 \subsection{Inundation}
-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. 
-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. 
-The datasets necessary for reproducing the results of the inundation stage are available on 
-Sourceforge under the ANUGA project (\url{http://sourceforge.net/projects/anuga}). At the time
-of writing the direct link is \url{http://tinyurl.com/patong2004-data}.
+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.  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.  
+
+The datasets necessary for reproducing the results
+of the inundation stage are available on Sourceforge under the ANUGA
+project (\url{http://sourceforge.net/projects/anuga}). At the time of
+writing the direct link is \url{http://tinyurl.com/patong2004-data}.
 %
 %\url{http://sourceforge.net/project/showfiles.php?group_id=172848&package_id=319323&release_id=677531}.
@@ -143,5 +354,10 @@
 
 \subsubsection{Topography Data}
-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.
+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.
 
 \begin{figure}[ht]
@@ -154,18 +370,46 @@
 
 \subsubsection{Buildings and Other Structures}
-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.
+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.
 
 \subsubsection{Inundation Survey}
-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.
+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.
 
 \subsubsection{Eyewitness Accounts}
-FIXME (Ole): I think we should move this to where the results are presented.
-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). 
-
-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
-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
-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
-filmed from a building next door to the Comfort Resort near the corner of Ruam Chai St and FIXME(Ole): XXXX. 
-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. 
+FIXME (Ole): I think we should move this to where the results are
+presented.  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).
+
+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 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
+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
+filmed from a building next door to the Comfort Resort near the corner
+of Ruam Chai St and FIXME(Ole): XXXX.  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.
 
 \begin{figure}[ht]
@@ -175,16 +419,21 @@
 \includegraphics[width=6.0cm,keepaspectratio=true]{flow_rate_south_7_12sec.jpg}
 \includegraphics[width=6.0cm,keepaspectratio=true]{flow_rate_south_7_60sec.jpg}
-\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.}
+\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.}
 \label{fig:video_flow}
 \end{center}
 \end{figure}
 
-Flow rates were estimated using landmarks found in both videos and were found to be in
-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. 
+Flow rates were estimated using landmarks found in both videos and
+were found to be in 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.
 
 \begin{figure}[ht]
 \begin{center}
 \includegraphics[width=8.0cm,keepaspectratio=true]{patongescapemap.jpg}
-\caption{Tsunami survey mapping the maximum observed inundation at Patong beach courtesy of the Thai Department of Mineral Resources \protect \cite{szczucinski06}.}
+\caption{Tsunami survey mapping the maximum observed inundation at
+  Patong beach courtesy of the Thai Department of Mineral Resources
+  \protect \cite{szczucinski06}.}
 \label{fig:patongescapemap}
 \end{center}
@@ -193,41 +442,159 @@
 \subsection{Validation Check-List}
 \label{sec:checkList}
-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:
+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:
 \begin{itemize}
- \item Reproduce the vertical deformation observed in north-western Sumatra and along the Nicobar--Andaman islands, see Section~\ref{sec:gen_data}.
- \item Reproduce the \textsc{jason} satellite altimetry sea surface anomalies, see Section~\ref{sec:data_jason}.
- \item Reproduce the inundation survey map in Patong bay (Figure~\ref{fig:patongescapemap}).
- \item Simulate a leading depression followed by two distinct crests of decreasing magnitude.
- \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.
+ \item Reproduce the vertical deformation observed in north-western
+   Sumatra and along the Nicobar--Andaman islands, see
+   Section~\ref{sec:gen_data}.
+ \item Reproduce the \textsc{jason} satellite altimetry sea surface
+   anomalies, see Section~\ref{sec:data_jason}.
+ \item Reproduce the inundation survey map in Patong bay
+   (Figure~\ref{fig:patongescapemap}).
+ \item Simulate a leading depression followed by two distinct crests
+   of decreasing magnitude.
+ \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.
 \end{itemize}
 
-Ideally, the model should also be compared to measured timeseries of waveheights and velocities 
-but the authors are not aware of the availability of such data.
+Ideally, the model should also be compared to measured timeseries of
+waveheights and velocities but the authors are not aware of the
+availability of such data.
 
 
 %================Section===========================
 \section{Modelling the Event}\label{sec:models}
-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).
+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).
 
 \subsection{Generation}\label{sec:modelGeneration}
 
-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.
-
-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.
+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.
+
+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.
 
 \subsection{Propagation}\label{sec:modelPropagation}
-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.
+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.
 
 \subsubsection{URSGA}
-\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. 
+\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.
 
 \subsection{Inundation}\label{sec:modelInundation}
-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. 
-%Specifically we use the \textsc{ursga} model to simulate the propagation of the 2004 Indian Ocean tsunami in the deep ocean, based on a discrete representation of the initial deformation of the sea floor, described in Section~\ref{sec:modelGeneration}. 
-The wave signal is then used as a time varying boundary condition for the \textsc{anuga} inundation simulation.
+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.
+%Specifically we use the \textsc{ursga} model to simulate the
+%propagation of the 2004 Indian Ocean tsunami in the deep ocean, based
+%on a discrete representation of the initial deformation of the sea
+%floor, described in Section~\ref{sec:modelGeneration}.
+The wave signal is then used as a time varying boundary condition for
+the \textsc{anuga} inundation simulation.
 % A description of \textsc{anuga} is the following section.
 
 \subsubsection{ANUGA}
-\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}.
+\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}.
 
 %================Section===========================
@@ -236,5 +603,36 @@
 
 \subsection{Generation}\label{modelGeneration}
-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.
+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.
 
 \begin{figure}[ht]
@@ -242,5 +640,16 @@
 \includegraphics[width=5cm,keepaspectratio=true]{surface_deformation.jpg}
 %\includegraphics[totalheight=0.3\textheight,width=0.8\textwidth]{surface_deformation.jpg}
-\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}.}
+\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}.}
 \label{fig:surface_deformation}
 \end{center}
@@ -249,13 +658,38 @@
 
 \subsection{Propagation}\label{sec:resultsPropagation}
-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$1996 finite difference points. Inside this grid, a nested sequence of grids was used. The grid resolution of the nested grids went from 27 arc seconds in the coarsest grid, down to 9 arc seconds in the second grid, 3 arc seconds in the third grid and finally 1 arc second in the finest grid near Patong. The computational domain is shown in Figure~\ref{fig:computational_domain}.
-
-Figure \ref{fig:jasonComparison} provides a comparison of the \textsc{ursga} predicted sea surface elevation with the JASON satellite altimetry data. The \textsc{ursga} model replicates the amplitude and timing of the first peak and trough well. However, the model does not resolve the double peak of the first wave. Also note that the \textsc{ursga} model prediction of the ocean surface elevation becomes out of phase with the JASON data at 3 to 7 degrees latitude. Chlieh et al~\cite{chlieh07} also observe these misfits and suggest it is caused by a reflected wave from the Aceh Peninsula that is not resolved in the model due to insufficient resolution of the computational mesh and bathymetry data. This is also a limitation of the model presented here, but probably could be improved by nesting grids near Aceh. 
+The deformation results described in Section~\ref{sec:modelGeneration}
+were used to provide a profile of the initial ocean surface
+displacement. This wave was used as an initial condition for
+\textsc{ursga} and was propagated throughout the Bay of Bengal. The
+rectangular computational domain of the largest grid extended from
+90$^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}.
+
+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.
 
 \begin{figure}[ht]
 \begin{center}
 \includegraphics[width=12.0cm,keepaspectratio=true]{jasonComparison.jpg}
-\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. 
-}
+\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.  }
 \label{fig:jasonComparison}
 \end{center}
@@ -263,5 +697,11 @@
 
 \subsection{Inundation}
-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}
+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}
 \begin{figure}[ht]
 \begin{center}
@@ -274,13 +714,55 @@
 \end{figure}
 
-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. 
-
-
-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. 
-
-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
-
-FIXME (Ole): Perhaps rephrase a bit as the 1cm vs 10cm is hard to understand.
-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. 
+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.
+
+
+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.
+
+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
+
+FIXME (Ole): Perhaps rephrase a bit as the 1cm vs 10cm is hard to
+understand.  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.
 
 An 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}.
@@ -297,20 +779,36 @@
 \end{figure}
 
-To quantify the agreement between observed and simulated inundation we introduce the measure
+To quantify the agreement between observed and simulated inundation we
+introduce the measure
 \begin{equation}
 A(I_{in})=\frac{A(I_m\cap I_o)}{A(I_o)}
 \end{equation}
-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
+representing the ratio $A(I_{in})$ 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
 \begin{equation}
 A(I_{out})=\frac{A(I_m\setminus (I_m\cap I_o))}{A(I_o)}
 \end{equation}
-These values for the two aforementioned simulations are given in Table~\ref{table:inundationAreas}
-FIXME (Ole): The left hand side of these equations are not areas - consider another symbol.
-
-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}
+These values for the two aforementioned simulations are given in
+Table~\ref{table:inundationAreas} FIXME (Ole): The left hand side of
+these equations are not areas - consider another symbol.
+
+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}
 
 \subsection{Eye-witness accounts}
-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
-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.
+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 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.
 
 \begin{figure}[ht]
@@ -341,9 +839,20 @@
 \end{figure}
 
-FIXME(Ole): This is a repetition of an earlier section. I'll look at that soon.
-Crude flow rates can be estimated with landmarks found in satellite imagery and the use of a GIS and were found to be in
-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
-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
-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.
+FIXME(Ole): This is a repetition of an earlier section. I'll look at
+that soon.  
+Crude flow rates can be estimated with landmarks found in
+satellite imagery and the use of a GIS and were found to be in 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
+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
+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.
 
 
@@ -353,16 +862,40 @@
 \section{Sensitivity Analysis}
 \label{sec:sensitivity}
-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.
+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.
 
 %========================Friction==========================%
 \subsection{Friction}
 \label{sec:friction sensitivity}
-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. 
-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.
+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.  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.
 
 %========================Wave-Height==========================%
 \subsection{Input Wave Height}\label{sec:waveheightSA}
-The effect of the wave-height used as input to the inundation model \textsc{anuga} was also investigated.  
-Figure~\ref{fig:sensitivity_boundary} indicates that the inundation severity is directly proportional to the boundary waveheight but small perturbations in the input wave-height of 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.
+The effect of the wave-height used as input to the inundation model
+\textsc{anuga} was also investigated.
+Figure~\ref{fig:sensitivity_boundary} indicates that the inundation
+severity is directly proportional to the boundary waveheight but small
+perturbations in the input wave-height of 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.
 
 
@@ -370,5 +903,11 @@
 %========================Buildings==========================%
 \subsection{Buildings and Other Structures}
-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}.
+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}.
 
 \begin{table}
@@ -394,14 +933,45 @@
 
 \section{Conclusion}
-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}. 
-
-This study also shows that the tsunami impact modelling methodology adopted is sane and able to predict inundation extents with reasonable accuracy.
-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. 
-
-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.
+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}.
+
+This study also shows that the tsunami impact modelling methodology
+adopted is sane and able to predict inundation extents with reasonable
+accuracy.  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.
+
+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.
 
 %================Acknowledgement===================
 \section*{Acknowledgements}
-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.
+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.
 
 \section{Appendix}
@@ -411,6 +981,12 @@
 \includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_minus10}
 \includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_plus10}
-\caption{Model results with wave height at ANUGA boundary artificially modified 
-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.}
+\caption{Model results with wave height at ANUGA boundary artificially
+  modified 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.}
 \label{fig:sensitivity_boundary}
 \end{center}
@@ -432,9 +1008,11 @@
 \includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_reference}
 \includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_nobuildings}
-\caption{This figure shows the effect of having buildings as part of the 
-elevation data set.
-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.
-As expected, the absence of buildings will increase the inundation extent 
-beyond what was surveyed.}
+\caption{This figure shows the effect of having buildings as part of
+  the elevation data set.  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.  As expected, the absence of
+  buildings will increase the inundation extent beyond what was
+  surveyed.}
 \label{fig:sensitivity_nobuildings}
 \end{center}
@@ -446,5 +1024,6 @@
 \includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_reference_speed}
 \includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_nobuildings_speed}
-\caption{The maximal flow speeds for the same model parameterisations found in Figure \protect \ref{fig:sensitivity_nobuildings}.}
+\caption{The maximal flow speeds for the same model parameterisations
+  found in Figure \protect \ref{fig:sensitivity_nobuildings}.}
 \label{fig:sensitivity_nobuildings_speed}
 \end{center}
@@ -456,7 +1035,14 @@
 \includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_f0003}
 \includegraphics[width=3.5cm,keepaspectratio=true]{sensitivity_f03}
-\caption{Model results for different values of Manning's friction coefficient.
-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 
-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.}
+\caption{Model results for different values of Manning's friction
+  coefficient. 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 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.}
 \label{fig:sensitivity_friction}
 \end{center}
