Changeset 6915


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Timestamp:
Apr 28, 2009, 1:00:39 PM (15 years ago)
Author:
jakeman
Message:

John Jakeman: Re-wrote paper according to the last meeting in early april. Still in progress but general structure should no remain fixed

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  • anuga_work/publications/boxing_day_validation_2008/patong_validation.tex

    r6900 r6915  
    44\usepackage{amsfonts}
    55\usepackage{url}      % for URLs and DOIs
    6 \newcommand{\doi}[1]{\url{http://dx.doi.org/#1}}
     6\newcommand{\doi}[1]{\url{http://dx.doComparison of URS model with JASON satellite altimetry. Upper Panel: URS wave heights 120 minutes after the initial earthquake with the JASON satellite track and its observed sea level anomalies overlaid. Note the URS data has not been corrected for the flight path time. Lower Panel: URS wave heights corrected for the time the satellite passed overhead compared to JASON sea level anomaly. The URS model matches the timing and amplitude of the first wave peak and trough but becomes out of phase for later waves, thought to be reflected waves from Aceh Peninsula that are not resolved in the URS model. 
     7i.org/#1}}
    78
    89%----------title-------------%
    … …  
    1718\and D. Burbidge\footnotemark[2]
    1819\and K. VanPutten\footnotemark[2]
    19 \and S.~G Roberts\footnotemark[1]
     20\and N. Horspool\footnotemark[2]
    2021}
    2122
    … …  
    2526%------Abstract--------------
    2627\begin{abstract}
    27 
     28In 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 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 evolution and run rain-induced floods.
    2829\end{abstract}
    2930
    … …  
    3435Tsunami are a potential hazard to coastal communities all over the world. A number of recent large events have increased community and scientific awareness of the need for effective tsunami hazard mitigation. Tsunami modelling is major component of hazard mitigation, which involves detection, forecasting, and emergency preparedness~\cite{synolakis05}. Accurate models can be used to provide information that increases the effectiveness of action undertaken before the event to minimise damage (early warning systems, breakwalls etc.) and protocols put in place to be followed when the flood waters subside.
    3536
    36 Several approaches are currently used to model tsunami propagation and inundation. These methods differ in both the formulation used to describe the evolution of the tsunami and the numerical methods used to solve the governing equations. The shallow water wave equations, linearised shallow water wave equations, and Boussinesq-type equations are frequently used to simulate tsunami propagation. The nonlinear nature of these equations, the highly variable nature of the phenomena that they describe and the complex reality of the geometry they operate in necessitate the use of numerical models. These models are typically used to predict quantities such as arrival times, wave speeds and heights and inundation extents which are used to develop efficient hazard mitigation plans. Inaccuracies in model prediction can result in inappropriate evacuation plans and town zoning which may result in loss of life and large financial losses. Consequently tsunami models must undergo sufficient testing to increase scientific and community confidence in the model predictions.
    37 
    38 Complete confidence in a model of a physical system frequently in general cannot be established.  One can only hope to state under what conditions the model hypothesis holds true. Specifically the utility of a model can be assessed through a process of validation and verification. Validation assesses the accuracy of the numerical method used to solve the governing equations and verification is used to investigate whether the model adequately represents the physical system. Together these processes can be used to establish the likelihood that that a model is a legitimate hypothesis~\cite{bates01}.
    39 
    40 The sources of data used to validate and verify a model can be separated into three main categories; analytical solutions, scale experiments and field measurements. Analytical solutions of the governing equations of a model, if available, provide the best means of validating a numerical hydrodynamic model. However analytical solutions to the governing equations are frequently limited to a small set of idealised examples that do not completely capture the more complex behaviour of `real' events. Scale experiments, typically in the form of wave-tank experiments provide a much more realistic source of data that better captures the complex dynamics of natural tsunami, whilst allowing control of the event and much easier and accurate measurement of the tsunami properties. However comparison of numerical predictions with field data provides the most stringent test of model veracity. The use of field data increases the generality and significance of conclusions made regarding model utility. However the use of field data also significantly increases the uncertainty of the validation experiment that may constrain the ability to make unequivocal statements~\cite{bates01}.
    41 
    42 Currently the extent of tsunami related field data is limited. The cost of tsunami monitoring programs and 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, particularly those modelling tsunami inundation. 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 two field data benchmarks are very useful but only capture a small subset of possible tsunami behaviours. The type and size of a tsunami source, propagation extent, and local bathymetry and topography all affect the energy, waveform and subsequent inundation of a tsunami. Consequently additional field data benchmarks that further capture the variability and sensitivity of the real world system would be useful to allow model developers verify their models and subsequently use their models with greater confidence.
    43 
    44 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 inundation. The benchmark is constructed from data collected around Patong Bay, Thailand immediately following the 2004 Indian Ocean tsunami. This area was chosen because the authors were able to obtain high resolution bathymetry and topography data in this area and an inundation map generated from a survey performed in the aftermath of the tsunami. A description of this data is give in Section~\ref{sec:data}.
    45 
    46 An associated aim of this paper is to illustrate the use of this new benchmark to validate an operational tsunami model called \textsc{anuga} (see Secion~\ref{sec:veri_procedure}). The specific intention is to test the ability of \textsc{anuga} to reproduce the inundation survey of maximum runup. \textsc{Anuga} is a hydrodynamic modelling tool used to simulate the tsunami propagation and run rain-induced floods.
    47 
    48 %================Section===========================
    49 
    50 \section{Event Description}
    51 The devastation caused by the 2004 Samatra-Andaman tsunami has heightened community, scientific and governmental interest in tsunami and in doing so has provided a unique opportunity for further validation of tsunami models. Data sets from seismometers, tide gauges, GPS stations, a few satellite overpasses, subsequent coastal field surveys of run-up and flooding and measurements from ship-based expeditions, have now been made available~\cite{vigny05,amnon05,kawata05,liu05}. A number of studies have utilised this data to calibrate models of the tsunami source\cite{asavanant08,arcas06,grilli07,ioualalen07}. We propose to use this event as an additional field-data benchmark for verification of tsunami models. This event captures certain tsunami behaviours that are not present in the benchmarks proposed by Synolakis et. al~\cite{synolakis07}. FIXME: What kind of behaviours???
    52 
    53 Synolakis detail two field data benchmarks. The first test 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 maximum runup elevations were observed. The second benchmark is based upon the Rat Islands Tsunami that occurred off the coast of Alaska on the 17th of November 2003. Rat island tsunami provides a good test for real-time forecasting models since tsunami was recorded at three tsunameters. The test requires matching the propagation model data with the DART recording to constrain the tsunami source model and using a propagation model to to reproduce the tide gauge record at Hilo.
    54 
    55 The 2004 Indian Ocean tsunami was a much larger event than the previous two described (See Section \ref{sec:source}). Consequently the energy of the resulting wave was much larger than the waves generated from the more localised and smaller magnitude aforementioned events. WAS THE WAVELENGTH< VELOCITY (and thus average ocean depth) DIFFERENT FROM THESE TWO EVENTS??? If so state something like. This larger wavelength and energy and simply the different geology of the area produced different a wave signal and different pattern of inundation. Here we focus on the large inundation experienced at Patong Bay on the west coast of Thailand.
    56 
    57 \section{Data}\label{sec:data}
    58 Tsunami models typically require bathymetry and topography data to approximate the local geography, parameterisation of the tsunami source from which appropriate initial conditions can be generated, and certain paramter values such Manning's friction coefficient. Here we discuss the ncessary data needed to implement the proposed benchmark.
    59 
    60 \subsection{Bathymetric and topographic data}
    61 David and Richard:
    62 
    63 An unusually large amount of data for the 2004 tsunami, necessary for tsunami verification, is available at Patong Bay and surrounding regions. 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.
    64 
    65 The two minute arc grid data set, DBDB2, was obtained from US Naval Research Labs and used to approximate the bathymetry in the Bay of Bengal. This grid was further interpolated to a 27 second arc grid. In the Andaman Sea the DBDB2 data was replaced with a 3 second grid obtained from NOAA (REF?). Finally, a 1 second grid was used to approximate the bathymetry in Patong Bay and the immediately adjacent regions (FROM WHERE?). This elevation data was 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.
     37Several approaches are currently used to model tsunami propagation and inundation. These methods differ in both the formulation used to describe the evolution of the tsunami and the numerical methods used to solve the governing equations. The shallow water wave equations, linearised shallow water wave equations, and Boussinesq-type equations are frequently used to simulate tsunami propagation. The nonlinear nature of these equations, the highly variable nature of the phenomena that they describe and the complex reality of the geometry they operate in, necessitate the use of numerical models. These models are typically used to predict quantities such as arrival times, wave speeds and heights and inundation extents which are used to develop efficient hazard mitigation plans. Inaccuracies in model prediction can result in inappropriate evacuation plans and town zoning which may result in loss of life and large financial losses. Consequently tsunami models must undergo sufficient testing to increase scientific and community confidence in the model predictions.
     38
     39Complete confidence in a model of a physical system frequently in general cannot be established.  One can only hope to state under what conditions the model hypothesis holds true. Specifically the utility of a model can be assessed through a process of verification and validation. Verification assesses the accuracy of the numerical method used to solve the governing equations and validation is used to investigate whether the model adequately represents the physical system~\cite{bates01}. Together these processes can be used to establish the likelihood that that a model is a legitimate hypothesis.
     40
     41The 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 a numerical hydrodynamic model. However analytical solutions to the governing equations are frequently limited to a small set of idealised examples that do not completely capture the more complex behaviour of `real' events. Scale experiments, typically in the form of wave-tank experiments provide a much more realistic source of data that better captures the complex dynamics of natural tsunami, whilst allowing control of the event and much easier and accurate measurement of the tsunami properties. However comparison of numerical predictions with field data provides the most stringent test of model veracity. The use of field data increases the generality and significance of conclusions made regarding model utility. However the use of field data also significantly increases the uncertainty of the validation experiment that may constrain the ability to make unequivocal statements~\cite{bates01}.
     42
     43Currently the extent of tsunami related field data is limited. The cost of tsunami monitoring programs and bathymetry and topography surveys prohibits the collection of data in many of the regions in which tsunamis pose greatest threat. The resulting lack of data has limited the number of field data sets available to validate tsunami models. Synolakis et. al~\cite{synolakis07} have developed a set of standards, criteria and procedures for evaluating numerical models of tsunami. They propose three analytical solutions to help identify the validity of a model and  five scale comparisons (wave-tank benchmarks) and two field events to assess model veracity.
     44
     45The first field data benchmark introduced by Synolakis compares model results against observed data from the Hokkaido-Nansei-Oki tsunami that occurred around Okushiri Island, Japan on the 12th of July 1993. This tsunami provides an example of extreme runup generated from reflections and constructive interference resulting from local topography and bathymetry. The benchmark consists of two tide gauge records and numerous spatially distributed point sites at which modelled maximum runup elevations can be compared. The second benchmark is based upon the Rat Islands Tsunami that occurred off the coast of Alaska on the 17th of November 2003. The Rat island tsunami provides a good test for real-time forecasting models since tsunami was recorded at three tsunameters. The test requires matching the propagation model data with the DART recording to constrain the tsunami source model and using a propagation model to to reproduce the tide gauge record at Hilo.
     46
     47The evolution of earthquake-generated tsunamis has three distinctive stages: generation, propagation and run-up~\cite{titov97a}. To accurately model the evolution of a tsunami all three stages must be dealt with. In this section we present the data necessary to implement the proposed benchmark corresponding to each of the three stages of the tsunami's evolution.  In this paper we develop a field data benchmark to be used in conjunction with the other tests proposed by Synolakis et al.~\cite{synolakis07} to validate and verify tsunami models. Unlike the aforementioned tests the proposed benchmark allows one to estimate the error in a model prediction for all three distinctive stages of the evolution of a tsunami: generation, propagation and run-up. The benchmark comprises of geodetic measurements of the Sumatra--Andaman earthquake to validate the tsunami source, altimetry data from the JASON satellite to test open ocean propagation, eye-witness accounts to assess near shore propagation and a detailed inundation survey of Patong Bay, Thailand to compare model and observed inundation. A description of this data is give in Section~\ref{sec:data}.
     48
     49An associated aim of this paper is to illustrate the use of this new benchmark to validate an operational tsunami model called \textsc{anuga}. A description of \textsc{anuga} is given in Secion~\ref{sec:models} and the validation results are given in Secion~\ref{sec:results}.
     50
     51%================Section===========================
     52\section{Validation Data}\label{sec:data}
     53The shear magnitude of the 2004 Sumatra-Andaman earthquake and the devastation caused by the subsequent tsunami generated much scientific interest. As a result an unusually large amount of post seismic data has been collected and documented. Data sets from seismometers, tide gauges, \textsc{gps} surveys, satellite overpasses, subsequent coastal field surveys of run-up and flooding, and measurements of coseismic displacements and bathymetry from ship-based expeditions, have now been made available.%~\cite{vigny05,amnon05,kawata05,liu05}.
     54
     55The evolution of earthquake-generated tsunamis has three distinctive stages: generation, propagation and run-up~\cite{titov97a}. To accurately model the evolution of a tsunami all three stages must be dealt with. In this section we present the data necessary to implement the proposed benchmark corresponding to each of the three stages of the tsunami's evolution.  The final dataset is available at XXXX.
     56
     57\subsection{Generation}
     58All tsunami are generated from an initial disturbance of the sea surface which develops into a low frequency wave that propagates outwards from the source. The initial deformation of the water surface can be caused by coseismic displacement of the sea floor or submarine mass failure. In this section we detail the information necessary to validate models of tsunami generated by a coseismic displacement of the sea floor by focusing on the generation of the 2004 Sumatra--Andaman tsunami.
     59
     60The 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 M$_w$=9.3 mega-thrust earthquake occurred on the 26 December 2004 at 0h58'53'' UTC approximately 70 km offshore North Sumatra. The disturbance propagated 1200-1300 km along the Sumatra-Andaman trench time at a rate of 2.5-3 km.s$^{-1}$ and lasted approximately 8-10 minutes~\cite{amnon05}.
     61
     62We use near field global positioning surveys (\textsc{gps}) in northwestern Sumatra and the Nicobar-Andaman islands and  continuous and campaign \textsc{gps} measurements from Thailand and Malaysia to verify the \textsc{ursga} model used to generate the tsunami ...
     63
     64FIXME: David and/or Richard could you complete this please
     65
     66\begin{figure}[ht]
     67\begin{center}
     68%\includegraphics[width=8.0cm,keepaspectratio=true]{geodeticMeasurements.jpg}
     69\caption{Near field geodetic measurements used to validate tsunami generation. FIXME: Insert appropriate figure here}
     70\label{fig:geodeticMeasurements}
     71\end{center}
     72\end{figure}
     73
     74\subsection{Propagation}
     75Once generated a tsunami will propagate outwards from the source until it finally encounters the shallow water bordering coastal regions. This period of the tsunami evolution is referred to as the propagation stage. The height and velocity of the tsunami is dependent on the local bathymetry in the regions through which the wave travels. This section details the bathymetry data needed to model the tsunami propagation and \textbf{two} satellite altimetry transects which can be used to validate open ocean tsunami models.
     76
     77\subsubsection{Bathymetry Data}
     78A 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.
     79
     80The nested bathymetry grid was generated from: a two arc minute grid data set covering the Bay of Bengal, DBDB2, obtained from US Naval Research Labs; a 3 second arc grid covering the whole of the Andaman Sea which is based on Thai charts 45 and 362; and a one second grid created from the digitised Thai Navy bathymetry chart, no 358. which covers Patong Bay and the immediately adjacent regions.
     81
     82The final bathymetry data set consits of four nested grids obtained via interpolation and resampling of the aforementioned data sets. The coarsest bathymetry was obtained by interpolating the DBDB2 grid to a 27 second arc grid. A subsection of this region was then replaced by 9 second data which was generated by sub-sampling the 3 second of arc grid from NOAA. A subset of the 9 second grid was replaced by the 3 second data. Finally a one second grid was used to approximate the bathymetry in Patong Bay and the immediately adjacent regions. This elevation data was created from the digitised Thai Navy bathymetry chart, no 358. Any points that deviated from the general trend near the boundary were deleted. See Figure~\ref{fig:nested_grids}.
     83
     84The sub-sampling of larger grids was performed by using {\bf resample} a GMT program (\cite{XXX}). 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 and application of minimum curvature akima spline smoothing.
     85
     86\begin{figure}[ht]
     87\begin{center}
     88\includegraphics[width=8.0cm,keepaspectratio=true]{nested_grids}
     89\caption{Nested grids of elevation data. FIXME: Needs lat longs}
     90\label{fig:nested_grids}
     91\end{center}
     92\end{figure}
     93
     94\subsubsection{JASON Satellite Altimetry}
     95During 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 initial $M_w 9.3$ 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. The satellite track is shown in Figure~\ref{fig:satelliteTrack}.
     96
     97\begin{figure}[ht]
     98\begin{center}
     99%\includegraphics[width=8.0cm,keepaspectratio=true]{sateliteTrack.jpg}
     100\caption{URS wave heights 120 minutes after the initial earthquake with the JASON satellite track and its observed sea level anomalies overlaid. Note the URS data has not been corrected for the flight path time. FIXME: should we just have track and not URS heights.}
     101\label{fig:satelliteTrack}
     102\end{center}
     103\end{figure}
     104
     105\begin{figure}[ht]
     106\begin{center}
     107%\includegraphics[width=8.0cm,keepaspectratio=true]{jasonAltimetry.jpg}
     108\caption{JASON satellite altimetry seal level anomaly. FIXME: should we include figure here with just JASON altimetry.}
     109\label{fig:jasonAltimetry}
     110\end{center}
     111\end{figure}
     112
     113FIXME: Can we compare the urs model against the TOPEX-poseidon satellite as well?
     114
     115\subsection{Inundation}
     116Inundation refers to the final stages of the evolution a tsunami. Specifically the propagation of the tsunami in shallow coastal water and the subsequent run-up on to the shoreline. This process is typically the most difficult of the three stages to model. Aside from requiring robust solvers which can simulate flow over dry land, this part of the modelling process requires high resolution and quality bathymetry data and high quality field measurements, which are often not available. For the proposed benchmark the authors have obtained a high resolution bathymetry and topography data set and a high quality inundation survey map which can be used to validate model inundation. These data sets are described here. In this section we also present eye-witness accounts which can be used to qualitatively validate tsunami inundation.
     117
     118\subsubsection{Topography Data}
     119A 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.
    66120
    67121\begin{figure}[ht]
    68122\begin{center}
    69123\includegraphics[width=8.0cm,keepaspectratio=true]{patong_bay_data.jpg}
    70 \caption{Visualisation of the elevation data set used in Patong Bay. FIXME: Can we generate a new picture with river included Preferably without the arrows and logo???}
     124\caption{Visualisation of the elevation data set used in Patong Bay. FIXME: Can we generate a new picture with river included preferably without the arrows and logo???}
    71125\label{fig:patong_bathymetry}
    72126\end{center}
    73127\end{figure}
    74128
    75 The sub-sampling of larger grids was performed by using {\bf resample} a GMT program (\cite{XXX}). 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 and application of minimum curvature akima spline smoothing. Details of the lineage of this dataset is outlined in the Appendix and the final dataset is available at XXXX.
    76 
    77 
    78 FIXME(Richard): Could you please look into these issues and also those in your appendix?
    79 
    80 \subsection{Tsunami source}\label{sec:source}
    81 
    82 David:
    83 
    84 The 2004 Indian Ocean tsunami was generated by severe coseismic displacement of the sea floor as a result of one of the largest earthquakes on record. The M$_w$=9.3 mega-thrust earthquake occurred on the 26 December 2004 at 0h58'53'' UTC approximately 70 km offshore North Sumatra. The disturbance propagated 1200-1300 km along the Sumatra-Andaman trench time at a rate of 2.5-3 km.s$^{-1}$ and lasted approximately 8-10 minutes~\cite{amnon05}.
    85 
    86 Many models of this earthquake are available~\cite{chlieh07,XXX}. 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 and or runup. The source parameters used to simulate the 2004 Indian Ocean Tsunami were taken from Chlieh~\cite{chlieh07}. This model was created by inversion of the seismic data from GPS measurements and fits both coseismic, tsunami and GPS data in the Andaman Sea well. The resulting sea floor displacement ranges from about - 5.0 to 5.0 metres and is shown in Figure~\ref{fig:chlieh_slip_model}.
     129\subsubsection{Eyewitness Accounts}
     130Eyewitness accounts detailed in~\cite{papadopoulos06} report that most people at Patong Beach observed an initial retreat of the shoreline of more than 100m followed a few minutes later by a strong wave (crest). Another less powerful wave arrived another five or ten minutes later. Eyewitness statements place the arrival time of the strong wave between 2 hours and 55 minutes to 3 hours and 5 minutes after the source rupture (09:55am to 10:05am local time).
     131
     132\subsubsection{Inundation Survey}
     133Tsunami run-up is often the cause of the largest financial and human losses yet run-up data that can be used to validate model runup predictions is scarce. Of the two field benchmarks proposed by Synolakis only the Okishiri benchmark facilitates comparison between modelled and observed run-up. One of the major strengths of the benchmark proposed here is that modelled runup can be compared to an inundation survey which maps the maximum run-up along an entire coast line rather than at a series of discrete sites. The survey map is shown in Figure~\ref{fig:patongescapemap} and plots the maximum run-up of the 2004 tsunami in Patong bay. Refer to Szczucinski et al~\cite{szczucinski06} for further details.
     134
     135\begin{figure}[ht]
     136\begin{center}
     137\includegraphics[width=8.0cm,keepaspectratio=true]{patongescapemap.jpg}
     138\caption{Tsunami survey mapping the maximum observed inundation at Patong beach courtesy of the Thai Department of Mineral Resources \protect \cite{szczucinski}.}
     139\label{fig:patongescapemap}
     140\end{center}
     141\end{figure}
     142
     143\subsection{Validation Check-List}
     144The 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:
     145\begin{itemize}
     146 \item Reproduce the \textsc{gps} displacement vectors in North-western Sumatra, Thailand and along the Nicobar--Andaman islands (Figure~\ref{fig:geodeticMeasurements})
     147 \item Reproduce the \textsc{jason} \textbf{and TOPEX???} satellite altimetry sea surface anomalies (Figures~\ref{fig:jasonAltimetry} and \ref{fig:topexAltimetry} respectively).
     148 \item Simulate A leading depression followed by two distinct crests of decreasing magnitude.
     149 \item Predict the arrival time of the first crest should arrive at Patong beach between 2 hours and 55 minutes to 3 hours and 5 minutes after the initial rupture of the source. The subsequent crest arrive five to ten minutes later.
     150 \item Reproduce the inundation survey map in Patong bay (Figure~\ref{fig:patongescapemap}).
     151\end{itemize}
     152
     153%================Section===========================
     154\section{Modelling the Event}\label{sec:models}
     155Numerous models are currently used to model and predict tsunami generation, propagation and run-up\cite{titov97,satake95}. Here we introduce the modelling methodology employed by Geoscience Australia to illustrate the utility of the proposed benchmark. Geoscience Australia's tsunami model can again be decomposed into three parts which simulate generation, propagation and inundation (Sections~\ref{modelGeneration},\ref{sec:modelPropagation} and \ref{sec:modelInundation} respectively).
     156
     157\subsection{Generation}\label{sec:modelGeneration}
     158Many models of this earthquake are available~\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 and or runup. The source parameters used to simulate the 2004 Indian Ocean Tsunami were taken from Chlieh~\cite{chlieh07}. This model was created by inversion of various geodetic data including slip distribution and postseismic deformation at sites up to 300km from the epicenter as well as continuous \textsc{gps} measurements of coseismic offset at sites up to and beyond 1100km from the source. The model fault consists of three subsegments with differing strikes and dip angles ranging from $17.5^0$ in the North and $12^0$ in the South. Refer to Chlieh et. al~\cite{chlieh07} for a detailed discussion.
     159
     160\subsection{Propagation}\label{sec:modelPropagation}
     161We use the \textsc{ursga} model to simulate the propagation of the 2004 tsunami in the deep ocean ocean, based on a discrete representation of the initial deformation of the sea floor, described in Section~\ref{sec:modelGeneration}.
     162
     163\subsubsection{URSGA}
     164\textsc{ursga} is a hydrodynamic code that models the propagation of the tsunami in deep water using the finite difference method to solve the depth integrated 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{thio07} and Geoscience Australia~\cite{burbidge07}. 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. FIXME: Check with David.
     165
     166\subsection{Inundation}\label{sec:modelInundation}
     167The utility of the \textsc{ursga} model decreases with water depth unless an intricate sequence of nested grids is employed. In comparison \textsc{anuga} is designed to produce robust and accurate predictions of on-shore inundation in mind, but is less suitable for earthquake source modelling and large study areas. Consequently, the Geoscience Australia tsunami modelling methodology is based on a hybrid approach using models like \textsc{ursga} for tsunami propagation up to a 100m depth contour. Specifically we use the \textsc{ursga} model to simulate the propagation of the 2004 Indian Ocean tsunami in the deep ocean, based on a discrete representation of the initial deformation of the sea floor, described in Section~\ref{sec:modelGeneration}. The wave signal is then used as a time varying boundary condition for the \textsc{anuga} inundation simulation. A description of \textsc{anuga} is the following section.
     168
     169\subsubsection{ANUGA}
     170\textsc{Anuga} is an Open Source hydrodynamic inundation tool that solves the depth integrated nonlinear shallow water wave equations. The scheme used by \textsc{anuga}, first presented by Zoppou and Roberts~\cite{zoppou99}, is a high-resolution Godunov-type method that uses the rotational invariance property of the shallow water equations to transform the two-dimensional problem into local one-dimensional problems. These local Riemann problems are then solved using the semi-discrete central-upwind scheme of Kurganov et al.~\cite{kurganov01} for solving one-dimensional conservation equations. The numerical scheme is presented in detail in Zoppou and Roberts~\cite{zoppou99}, Zoppou and Roberts~\cite{zoppou00}, and Roberts and Zoppou~\cite{roberts00}, Nielsen et al.~\cite{nielsen05}. An important capability of the software is that it can model the process of wetting and drying as water enters and leaves an area. This means that it is suitable for simulating water flow onto a beach or dry land and around structures such as buildings. It is also capable of adequately resolving hydraulic jumps due to the ability of the finite-volume method to handle discontinuities. \textsc{Anuga} has been validated against a number of analytical solutions and the wave tank simulation of the 1993 Okushiri Island tsunami~\cite{roberts06,nielsen05}.
     171
     172%================Section===========================
     173\section{Results}\label{sec:results}
     174
     175
     176\subsection{Generation}
     177
     178The resulting sea floor displacement ranges from about $-5.0$ to $5.0$ metres and is shown in Figure~\ref{fig:chlieh_slip_model}.
    87179
    88180\begin{figure}[ht]
    89181\begin{center}
    90182\includegraphics[width=5.0cm,keepaspectratio=true]{chlieh_slip_model.png}
    91 \caption{Location and magnitude of the sea floor displacement associated with the 2004 Indian Ocean tsunami. Source parameters from Chlieh et al.~\cite{chlieh07}}
     183\caption{Location and magnitude of the sea floor displacement associated with the 2004 Indian Ocean tsunami. Source parameters from Chlieh et al.~\cite{chlieh07}. FIXME: add modelled and observed displacement vectors}
    92184\label{fig:chlieh_slip_model}
    93185\end{center}
    94186\end{figure}
    95187
    96 \subsection{Validation data}
    97  Eyewitness accounts detailed in~\cite{papadopoulos06} report that most people at Patong Beach observed an initial retreat of the shoreline of more than 100m followed a few minutes later by a strong wave (crest). Another less powerful wave arrived another five or ten minutes later. Eyewitness statments 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). After the event (HOw long?) a survey mapped the maximum observed inundation at Patong beach.  The inundation map is shown in Figure~\ref{fig:patongescapemap} and was kindly provided by the Thai Department of Mineral Resources \protect \cite{XXX}.
    98  
    99  
    100 %In \cite{papadopoulos06} eyewitness accounts report
    101 %\emph{In Patong beach, most people observed at least two
    102 %waves. It is likely that the leading wave described in both
    103 %Sri Lanka and Maldives was not observed in Patong beach.
    104 %What people said is that the first sea motion was a retreat
    105 %of more than 100 m. A few minutes later the strong wave
    106 %arrived. Then, after another 5 or 10 min. one more wave attacked
    107 %but less violently than the first one. Nearly all the
    108 %interviewed persons reported that the tsunami inundation
    109 %in the Patong beach varied from 150 m to at least 750 m
    110 %(Fig. 16). One eyewitness reported inundation of only 20
    111 %m. As for the arrival time of the strong wave the eyewitnesses
    112 %do not agree. However, most reports concentrated
    113 %around 02:55 to 03:05 (09:55 to 10:05 local) which seems
    114 %to be a reliable description.}
    115 %
    116 %FIXME(Ole): Need discussion of model results in this context.
    117 
    118  
    119 
    120 \begin{figure}[ht]
    121 \begin{center}
    122 \includegraphics[width=8.0cm,keepaspectratio=true]{patongescapemap.jpg}
    123 \caption{Tsunami survey mapping the maximum observed inundation at Patong beach courtesy of the Thai Department of Mineral Resources \protect \cite{XXX}.}
    124 \label{fig:patongescapemap}
    125 \end{center}
    126 \end{figure}
    127 
    128 FIXME(Richard): More information deailting construction of this map is needed here. Is more accurate information on arrival times of crests and depression available
    129 
    130 %================Section===========================
    131 \section{Verification Procedure}\label{sec:veri_procedure}
    132 Intro\\\\
    133 
    134 The following observations need to be matched by any numerical tsuanmi model:
    135 \begin{itemize}
    136  \item Simulate a leading depression followed by two distinct crests of decreasing magnitude.
    137  \item The arrival time of the first crest should arrive at Patong beach bewtween 2 hours and 55 inutes to 3 hours and 5 minutes after the intial rupture of the source. The subsequent crest arrive five to ten minutes later.
    138  \item Simulated inundation in Patong bay should reproduce well the inundation map in Figure~\ref{fig:patongescapemap}.
    139 \end{itemize}
    140 
    141 
    142 \subsection{ANUGA}
    143 \textsc{Anuga} is an Open Source hydrodynamic inundation tool that solves the depth integrated nonlinear shallow water wave equations. The scheme used by \textsc{anuga}, first presented by Zoppou and Roberts~\cite{zoppou99}, is a high-resolution Godunov-type method that uses the rotational invariance property of the shallow water equations to transform the two-dimensional problem into local one-dimensional problems. These local Riemann problems are then solved using the semi-discrete central-upwind scheme of Kurganov et al.~\cite{kurganov01} for solving one-dimensional conservation equations. The numerical scheme is presented in detail in Zoppou and Roberts~\cite{zoppou99}, Zoppou and Roberts~\cite{zoppou00}, and Roberts and Zoppou~\cite{roberts00}, Nielsen et al.~\cite{nielsen05}. An important capability of the software is that it can model the process of wetting and drying as water enters and leaves an area. This means that it is suitable for simulating water flow onto a beach or dry land and around structures such as buildings. It is also capable of adequately resolving hydraulic jumps due to the ability of the finite-volume method to handle discontinuities. \textsc{Anuga} has been validated against a number of analytical solutions and the wave tank simulation of the 1993 Okushiri Island tsunami~\cite{roberts06,nielsen05}.
    144 
    145 \subsection{URSGA}
    146 \textsc{ursga} is a hydrodynamic code that models the propagation of the tsunami in deep water using the finite difference method to solve the depth integrated 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 URS corporation~\cite{thio07} and Geoscience Australia~\cite{burbidge07}. 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. FIXME: Check with David.
    147 
    148 
    149 \subsection{Tsunami Source and Propagation}
    150 The utility of the \textsc{ursga} model decreases with water depth unless an intricate sequence of nested grids is employed. In comparison \textsc{anuga} is designed to produce robust and accurate predictions of on-shore inundation in mind, but is less suitable for earthquake source modelling and large study areas. Consequently, the Geoscience Australia tsunami modelling methodology is based on a hybrid approach using models like \textsc{ursga} for tsunami generation and propagation up to a 100m depth contour. This information then forms a boundary condition for \textsc{anuga} and is propagated on shore to model the inundation. 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:source}. The resulting tsunami was propagated over the entire Bay of Bengal and the wave signal measured along the 100m depth contour offshore Phuket, Thailand. The wave signal is then used as a time varying boundary condition for the \textsc{anuga} inundation simulation.
    151 
    152 ???The \textsc{ursga} code is also capable of calculating inundation. CAN WE PRODUCE AN INUNDATION MAP OVER THE SAME AREA TO COMPARE WITH \textsc{anuga}???
    153 
    154 \subsection{Tsunami Inundation}\label{sec:inundation}
     188\subsection{Propagation}
     189Figure \ref{fig:jasonComparison} provides a comparison of the \textsc{ursga} prediceted 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. The generation model presented in Section~\ref{sec:modelGeneration} simulates a single uplift displacement, howver the observed double peak may have been generated by superposition of the initial waves from the rupture of two fault sections \cite{harig08}.
     190
     191Also 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{chileh07} also observe this misfit 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.
     192
     193\begin{figure}[ht]
     194\begin{center}
     195\includegraphics[width=12.0cm,keepaspectratio=true]{jasonComparison.jpg}
     196\caption{Comparison of the \textsc{ursga} prediceted 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.
     197}
     198\label{fig:jasonComparison}
     199\end{center}
     200\end{figure}
     201
     202\subsection{Inundation}
    155203In this case the interface betwen the \textsc{ursga} and \textsc{anuga} models was chosen to roughly follow the 100m depth contour along the west coast of Phuket Island. The computational domain is shown in Figure \ref{fig:computational_domain}
    156204\begin{figure}[ht]
    157205\begin{center}
    158 %\includegraphics[width=5.0cm,keepaspectratio=true]{new_domain.png}
    159206\includegraphics[width=5.0cm,keepaspectratio=true]{extent_of_ANUGA_model.jpg}
    160 \caption{Computational domain of the \textsc{anuga} simulation.}
     207\caption{Computational domain of the \textsc{anuga} simulation. FIXME: Add lat longs}
    161208\label{fig:computational_domain}
    162209\end{center}
    163210\end{figure}
    164211
    165 The domain was discretised into approximately ...,000 triangles. The resolution of the grid was increased in certain regions to efficiently increase the accuracy of the simulation. The grid resolution ranged between a maximum triangle area of $...\times 10^5$ m$^2$ near the Western ocean boundary to $...$ 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 througout the computational domain. A Manning's coefficient of 0.01 was chosen based upon previous numerical experiments conducted by the authors (FIXME: Citation Tom Baldock?? Or Duncan??).
    166 In \cite{schoettle2007} values of Manning's coefficient in the range 0.007 to 0.030 is suggested for tsunami propagation over a sandy sea floor.
    167 
    168 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. FIXME(OLE): Should we include Nick's test example?
    169 
    170 %================Section===========================
    171 \section{Results}
    172 \label{sec:results}
    173 Maximum onshore inundation elevation was simulated throughout the entire Patong Bay region. Figure~\ref{fig:inundationcomparison1cm} shows very good agreement between the measured and simulated inundation. Discrepencies between the survey data and the modelled inundated area are apparant and would be due to a number of issues: These include uncertainties in the elevation data, simplifications in the models involved, effects of erosion and deposition by the tsunami event, unknown distribution of surface roughness, as well as measurement errors and missing data in the field survey data itself.
    174 
    175 An inundation threshold of 10cm was selected in the model to reflect the likely accurracy of the survey in order to better compare the modelled inundation area to the field survey.
    176 
    177 
    178 FIXME: Take some of this commentary after final runs have been completed.
    179 FIXME: Also need a commentary on the dynamics of what is being observed and whether it aligns with eye witness observations.
    180 %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 receeding 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:inundationcomparison10cm}.
    181 
    182 Both the URS model and the \textsc{anuga} inundation model shows that the event comprises a train of waves some with preciding drawdown effects (ADD details of waveform with a graph from URL and a gauge from \textsc{anuga} and discuss).
     212The domain was discretised into approximately ...,000 triangles. The resolution of the grid was increased in certain regions to efficiently increase the accuracy of the simulation. The grid resolution ranged between a maximum triangle area of $...\times 10^5$ m$^2$ near the Western ocean boundary to $...$ 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 based upon previous numerical experiments conducted by the authors (FIXME: Citation Tom Baldock?? Or Duncan??).
     213
     214The 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.
     215
     216FIXME: Need a commentary on the dynamics of what is being observed and whether it aligns with eye witness observations.
     217Both the URS model and the \textsc{anuga} inundation model shows that the event comprises a train of waves some with preceding drawdown effects (ADD details of waveform with a graph from URL and a gauge from \textsc{anuga} and discuss).
     218
     219Maximum onshore inundation elevation was simulated throughout the entire Patong Bay region. Figure~\ref{fig:inundationcomparison1cm} shows very good agreement between the measured and simulated inundation. The \textsc{anuga} simulation determines a region to be inundated if at some point in time it was covered by at least 1cm of water. This precision in field measurements is impossible to obtain. The inundation boundary is determined by observing water marks and other signs left by the receding waters. The precision of the observed inundation map is, most likely, at least an order of magnitude worse than the \textsc{anuga} simulation. The simulated inundation based upon a 10cm threshold is shown in Figure~\ref{fig:inundationcomparison10cm}. An inundation threshold of 10cm was selected for all future simulations to reflect the likely accuracy of the survey and subsequently faciliate a more appropriate comparison between the modelled and observed inundation area.
    183220
    184221\begin{figure}[ht]
    185222\begin{center}
    186223\includegraphics[width=10.0cm,keepaspectratio=true]{Depth_small_transmissive_d0.jpg}
    187 \caption{Simulated inundation versus observed inundation}
     224\caption{Simulated inundation versus observed inundation using an inundation threshold of 1cm}
    188225\label{fig:inundationcomparison1cm}
    189226\end{center}
    190227\end{figure}
    191228
    192 
    193 
     229\begin{figure}[ht]
     230\begin{center}
     231\includegraphics[width=10.0cm,keepaspectratio=true]{Depth_small_transmissive_d0.jpg}
     232\caption{Simulated inundation versus observed inundation using an inundation threshold of 10cm}
     233\label{fig:inundationcomparison10cm}
     234\end{center}
     235\end{figure}
     236
     237Here we introudce the measure
     238\begin{equation}
     239\mathcal{A}_{in}=\frac{A_m\cap A_o}{A_o}
     240\end{equation}
     241to quantify the fraction of the obesrved inundation area $A_o$ captured by the model $A_m$. Another useful measure is the fraction of the modelled inundation area that falls outside the observed inundation area given by the formula
     242\begin{equation}
     243\mathcal{A}_{out}=\frac{A_m\setminus (A_m\cap A_o)}{A_o}
     244\end{equation}
     245These values for the two aformentioned simulations are given in Table~\ref{table:inundationAreas}
     246\begin{center}
     247% use packages: array
     248\begin{tabular}{|c|c|c|}\label{table:inundationAreas}
     249 & × & × \\
     250\hline\hline
     251× & × & \\
     252× & × & \\
     253\hline
     254\end{tabular}
     255\end{center}
     256
     257Additional causes of the discrepancies between the survey data and the modelled inundated include: unknown distribution of surface roughness, inappropriate paramterisation 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 invetigated in Section~\ref{sec:sensitivity}
    194258
    195259%================Section===========================
    196260\section{Sensitivities of inundation model}
    197 
     261\label{sec:sensitivity}
    198262This section shows how model results vary as a result of changing the waveheight at the ANUGA boundary where it was coupled with the URSGA model
    199263(Figures \ref{fig:sensitivity_boundary} and
    … …  
    215279FIXME(Ole): It would be nice if we could be a little more quantitative - e.g. along the lines of the MISG study that John and Jane participated in. Thoughts anyone?
    216280
    217  
    218 
    219 
    220281\begin{figure}[ht]
    221282\begin{center}
    … …  
    308369
    309370\section{Conclusion}
    310 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. This new benchmark involves the comparison of model predictions of onshore inundation in Patong Bay, Phuket Thailand caused by the 2004 Indian Ocean tsunami. Specifically a field survey mapping of observed inundation is used as a spatially distributed test of model performance. Although two other field data benchmarks exist (FIXME: WHICH?), this proposed benchmark provides a novel investigation of the dynamics of extreme tsunami events not before tested. The benchmark could be further improved with the inclusion of local tide gauge data, against which wave signal could be compared, however, to the authors knowledge no such data exist for this event.
    311 
    312 This paper also illustrates the effectiveness of the proposed new benchmark. The benchmark is used to test the veracity of the hydrodynamic \textsc{anuga} designed spcefically to model on-shore inundation. Very good agreement is obtained between the observed and simulated runup. The \textsc{ursga} tsunami package was also tested. Much worse results were obtained??
    313 
     371This 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.
    314372
    315373%================Acknowledgement===================
    … …  
    317375This 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.
    318376
    319 %===============Appendicies========================
     377%===============Appendices========================
    320378
    321379\section*{Appendix A. Figures and Tables}
    … …  
    325383This section outlines the origins and processes by which the elevation data was created. In general high resolution data sets were embedded into coarser data sets to match the modelled areas of interest.
    326384
    327 
    328 FIXME: Is there a standard template for data lineage.
    329 
    330 \begin{verbatim}
    331 E.g.
    332 Data Source:
    333 2 min: DBDB 2
    334 9 sec: NOAA
    335 3 sec: aontehusoe
    336 
    337 
    338 Process:
    339   ...
    340   ...
    341   ...
    342 \end{verbatim}
    343  
    344 FIXME: Could we have a map with the nested data sets?
    345 
    346 
    347 
    348 
    349 
    350 Gridded data sets used:
    351 
    352 DBDB2 2 minute of arc grid from the US Naval Research Labs.
    353 This grid was also interpolated to 27 sec of arc and used in a nested grid scheme.
    354 
    355 Indian Ocean 27 sec of arc grid created by:
    356 Interpolating the DBDB2 2 minute of arc grid.
    357 In the region where the 9 sec grid sits the data was cut out and replaced by the 9 sec data.
    358 Any points that deviated from the general trend near the boundary were deleted.
    359 The data was then re-gridded.
    360 
    361 Andaman Sea 9 sec of arc grid created by:
    362 Sub-sampling the 3 sec of arc grid from NOAA.
    363 In the region where the 3 sec grid sits the data was cut out and replaced by the 3 sec data.
    364 Any points that deviated from the general trend near the boundary were deleted.
    365 The data was then re-gridded.
    366 
    367 Thailand off-shore 3 sec of arc grid created by:
    368 cropping a much larger 3 sec of arc grid covering the whole of the Andaman Sea which itself was based on Thai charts 45 and 362.
    369 This grid was obtained from NOAA.
    370 In the region where the 1 sec grid sits the data was cut out and replaced by the 1 sec data.
    371 Any points that deviated from the general trend near the boundary were deleted.
    372 The data was then re-gridded.
    373 
    374 Patong Bay 1 second of arc grid created from:
    375 elevation data contained in a GIS of Patong Bay supplied by Niran Chaimanee, Geo-environment Sector Manager, CCOP T/S, Bangkok.
    376 Digitised Thai Navy bathymetry chart no 358.
    377 
    378 The sub-sampling of larger grids was performed by using {\bf resample}  a GMT program.
    379 The gridding of data was performed using {\bf Intrepid} a commercial geophysical processing package developed by Intrepid Geophysics.
    380 The gridding scheme was nearest neighbour followed by minimum curvature akima spline smoothing. See Figure~\ref{fig:nested_grids}.
    381 
    382 \begin{figure}[ht]
    383 \begin{center}
    384 \includegraphics[width=8.0cm,keepaspectratio=true]{nested_grids}
    385 \caption{Nested grids of elevation data.}
    386 \label{fig:nested_grids}
    387 \end{center}
    388 \end{figure}
    389 
    390 
    391 
    392 \subsection*{Earthquake Source Model}
    393 FIXME: Is this appendix needed?
    394 
    395 The earthquake source model of Chlieh was adopted to generate the tsunami simulation. This model was created by carefull inversion of the seismic
    396 data and fits both coseismic, tsunami and GPS data in the Andaman Sea well.
    397 
    398 \subsection*{Tsunami Propagation}
    399 FIXME: Is this appendix needed?
    400 
    401 To to generate and propagate the tsunami the URS code was used. This program solves the shallow water equations using the finite difference method.
    402 It can also be used in a nexted grid scheme and does on-shore inundation.
    403 
    404 
    405 
    406385%====================Bibliography==================
    407386\bibliographystyle{plain}
    408387\bibliography{tsunami07}
    409 
    410 
    411388\end{document}
    412389
    … …  
    418395Main source of uncertainty arises from inaccuracies in initial condition (source), inaccurate bathymetry data, to a lesser extent friction
    419396
    420 single experiment can refute model but cannot validate it. Need as many tests as possible to be confident in rpediction. Question arises. How mnay should we do. With finite experiments more weight should be given to a particular experiment if the range of the inout function and the material properties are both broad so that the universal character of the model is tested.
    421 
    422 Expressions:
    423 sufficient verification/falsification of model
    424 Confidently utilise a model
    425 
    426 Predictive valdiation of only one aspect of model evaluation. Need to assess model explanation.
    427 
    428 Conservation of mass
    429 convergence
    430 
    431 spatial and temporal discretisation errors, round off errors due to limited numerical precision
    432 
    433 analytical benchmarking:
    434 ensuring equations are solved accurately
    435 single wave on a beach
    436 Solitary wave on composite beach
    437 subaerial landslide on simple beach
    438 
    439 Analytical solutions only represent idealised and simplfied events that do not fully capture the complexity of 'real' flows. Provide temporally and spatially distributed data that field data can rearely match.
    440 
    441 scale comparisions (laboratory benchmarking):
    442 Scale differences are not belived to be important. scale experiments generally do not have same bootom firction characteristics as real scenario but has not proven to be a problem. The long wavelngth of tsunami tends to mean that the friction is less important in comparison to the motion of the wave
    443 Single wave on a simple beacj
     397scale comparisons (laboratory benchmarking):
     398Scale differences are not believed to be important. scale experiments generally do not have same bootom friction characteristics as real scenario but has not proven to be a problem. The long wavelength of tsunami tends to mean that the friction is less important in comparison to the motion of the wave
     399Single wave on a simple beach
    444400Solitary wave on composite beach
    445401Conical island
    … …  
    447403Landslide
    448404
    449 includes comparisons with validation data sets generated by other models of higher dimensionality and resolution.
    450 
    451 Often flow geometries are simplified
    452 
    453 
    454405Field benchmarking:
    455406Most important verification process
    456407Hydrodynamic inversion to predict the source is an ill posed problem
    457 12 July 1993 Hokkaido-Nansei-Oki tsunami around Okushiri Island Japan exreme runup height of 31.7m was found at the tip of a narrow gulley with the small cove at Monai
     40812 July 1993 Hokkaido-Nansei-Oki tsunami around Okushiri Island Japan extreme runup height of 31.7m was found at the tip of a narrow gully with the small cove at Monai
    45840917 November 2003 Rat Islands Tsunami
    459410
    460 Construction of more than one model can reveal biases in a single model. Two types of comparisons 1 between those that are comceptually simailar and those that re different. In former case interested in how choice of numerical solver and discretisation effects results and the later can help determine the level of physical processs representation necessary to represent an observed data set.
    461 
    462 Movinf to field data increases the gnereality and siginificance of svientifice evidence obatined. However we also significantly incerase the uncertainty of the validation experioment that may constrain the ability to make unequivacol statments. E.g. in bathymetry source condition friction.
    463 
    464 Calibratino of the model is often used to compensate for uncertainty in the model inputs. Calibartion results in a further loss of experimental control as a unique solution may not exist.
    465 
    466 verfication need to assess point data, spatially distributed data and bulk (lumped) data.
    467 
    468 Synolakis et. al~\cite{synolakis07} detail two field events that have been previoulsy used to validate tsunami models, the Hokkaido-Nansei-Oki tsunami that occured around Okushiri Island, Japan on 2nd of July 1993 and the Rat Islands Tsunami that inundated the occured off the coast of Alaska on the 17th of November 2003.
    469 
    470 
    471 inundation map only useful if mesh and topography resolution fine enough hard to measure what the model predicts how deep does inundation need to be for it to be visible during a field study
    472 
    473 Notes:
    474 Okushiri provides an example of extreme runup genereated from reflections and constructive interference resulting from local topography and bathymetry. Numerous point sites at which runup elevations were observed are available.  The highest runup of 31.7 m in a valley north of Monai needs to be approximated with the numerical model. In addition, two tide gage records at Iwanai and Esashi need to be estimated.
    475 
    476 
    477 
    478 Rat Island tsuanmi provides a good test for real-time forecasting models since tsnumai was recorded at three tsunameters. The test requires matching the propagation model data with the recordings to constrain the tsunami source model. The inundation model is to reproduce the tide gauge record at Hilo.
    479 
    480 Patong Bay benchmark provides spatially distributed field data for comparison.
    481 
    482 single experiment can refute model but cannot validate it. Need as many tests as possible to be confident in prediction. Question arises. How mnay should we do.
    483 
    484 DO I SAY WE HAVE MUX @ FILES DESCRIBING SHAPE OF WAVE YES. MAKES CONSISTENT
    485 
    486 Notes:  * Model source developed independently of inundation data.
    487         * Patong region was chosen because high resolution inundation map and bathymetry and topography data was available there
    488 
    489 Geoscience Australia, in an open collaboration with the Mathematical Sciences Institute, The Australian National University, is developing a software application, \textsc{anuga}, to model the hydrodynamics of tsunamis, floods and storm surges. The open source software implements a finite volume central-upwind Godunov method to solve the non-linear depth-averaged shallow water wave equations. This paper investigates the veracity of \textsc{anuga}  when used to model tsunami inundation.  A particular aim was to make use of the comparatively large amount of observed data corresponding to the Indian ocean tsunmai event of December 2004, to provide a conditional assessment of the computational model's performance. Specifically a comparison is made between an inundation map, constructed from observed data, against modelled maximum inundation. This comparison shows that there is very good agreement between the simulated and observed values. The sensitivity of model results to the resolution of bathymetry data used in the model was also investigated. It was found that the performance of the model could be drastically improved by using finer bathymetric data which better captures local topographic features. The effects of two different source models was also explored.
    490 
    491 different even types submarine mass failure generate larger events because of proximity more directional wave generation even if data is available it is hard to access
    492 
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    562 
    563 
    564 
     411Construction of more than one model can reveal biases in a single model. Two types of comparisons 1 between those that are conceptually similar and those that re different. In former case interested in how choice of numerical solver and discretisation effects results and the later can help determine the level of physical process representation necessary to represent an observed data set.
     412
     413Moving to field data increases the generality and significance of scientific evidence obtained. However we also significantly increase the uncertainty of the validation experiment that may constrain the ability to make unequivacol statements. E.g. in bathymetry source condition friction.
     414
     415The two field data benchmarks are very useful but only capture a small subset of possible tsunami behaviours and do not assess all three stages of tsunami evolution (generation,propagation and inundation) together. The type and size of a tsunami source, propagation extent, and local bathymetry and topography all affect the energy, waveform and subsequent inundation of a tsunami. Consequently additional field data benchmarks, such as the one proposed here, that further capture the variability and sensitivity of the real world system would be useful to allow model developers verify their models and subsequently use their models with greater confidence.
     416
     417To investigate the impact of these uncertainties a number of sensitivity studies were performed. The first study investigated the impact of surface roughness on the predicted run-up. According to Schoellte~\cite{schoettle2007} appropariate values of Manning's coefficient range from 0.007 to 0.030 for tsunami propagation over a sandy sea floor.  Consequently we simulated the maximum onshore inundation using the a manning's coefficient of 0.0003 and 0.03. The resulting runup is shown in Figures~\ref{fig:inundation0.0003} and \ref{inundation0.03}, respectively.
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