Changeset 6270


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Feb 4, 2009, 12:18:55 PM (10 years ago)
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jakeman
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updated patong validation paper. An attempt at each section has been made.

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  • anuga_work/publications/boxing_day_validation_2008/patong_validation.tex

    r6240 r6270  
    3636The 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. The solutions provide spatially and temporally distributed values of important observables that can be compared against modelled results. 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 increase the uncertainty of the validation experiment that may constrain the ability to make unequivacol statements~\cite{lane94}.
    3737
    38 Currently the amount 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 and only one of the benchmarks can be used to validate tsunami inundation. The type ans 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.
    39 
    40 In this paper we develop a field data benchmark to be used in conjuction with the other tests proposed by Synolakis et al. to validate and verify tsunami inundation. The benchmark is constructed from data collected around Patong Bay, Thailand during and immeadiately following the 2004 Indian Ocean tsunami tsunami. This area was chosen because the authors were able to obtain unusually high resolution bathymetry and topography data in this area and an extensive 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}.
    41 
    42 An associated aim of this paper is to illustrate the use of this new benchmark to validate a operational tsunami model. The specific intention is to test the ability of ANUGA to reproduce the inundation survey of maximum runup. ANUGA is a hydrodynamic modelling tool used to simulate the tsunami propagation and run rain-induced floods. The components of ANUGA are discussed in Secion\ref{sec:ANUGA}.
     38Currently the amount 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 and only one of the benchmarks can be used to validate tsunami inundation. 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.
     39
     40In this paper we develop a field data benchmark to be used in conjunction with the other tests proposed by Synolakis et al. to validate and verify tsunami inundation. The benchmark is constructed from data collected around Patong Bay, Thailand during and immediately following the 2004 Indian Ocean tsunami tsunami. This area was chosen because the authors were able to obtain unusually high resolution bathymetry and topography data in this area and an extensive 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}.
     41
     42An associated aim of this paper is to illustrate the use of this new benchmark to validate a operational tsunami model. The specific intention is to test the ability of ANUGA to reproduce the inundation survey of maximum runup. ANUGA is a hydrodynamic modelling tool used to simulate the tsunami propagation and run rain-induced floods. The components of ANUGA are discussed in Secion~\ref{sec:veri_procedure}.
    4343
    4444%=================Section=====================
    4545
    4646\section{Indian Ocean tsunami of 24th December 2004}
    47 Although appalling, the devastation caused by the 2004 Indian Ocean 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. Enormous resources have been spent to obtain many measurements of phenomenon pertaining to this event to better understand the destruction that occurred. 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 (Vigny {\it et al.} 2005, Amnon {\it et al.} 2005, Kawata {\it et al.} 2005, and Liu {\it et al.} 2005)\nocite{vigny05,amnon05,kawata05,liu05}. A number of studies have utilised this data to calibrate models of the tsunami source\cite{grilli07} , match tide gauge recordings\cite{}, maximum wave heights~\cite{asavanant08} and runup locations~\cite{ioualalen07}. We propose to use this event as an additional field-data benchmark for verification of tsuanmi models. This event captures certain tsunami behaviours that are not present in the benchmarks proposed by Synolakis et. al~\cite{synolakis07}.
    48 
    49 Synolakis detail two field data banchmarks. The first test compares model results gainst 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 becnhmark is based upon the Rat Islands Tsunami that occured 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 propgation model to to reproduce the tide gauge record at Hilo.
    50 
    51 %The tsunamis used by the two standard benchmarks and the 2004 tsunami are quite different. They all arise from cosiesmic displacement resulting from an earthquake, however they all occur in very different geographical regions. The Hokkaido-Nansei-Oki tsunami was generated by an earthquake with a magnitude of 7.8 and only travelled a small distance before inundating Okishiri Island. The event provides an example of extreme runup genereated from reflections and constructive interference resulting from local topography and bathymetry. In comparison the Rat islands tsunami was generated by an earthquake of the same magnitude but had to travel a much greater distance. The event provides a number of tide gauge recordings that capture the change in wave form as the tsunami evolved.
    52 
    53 The 2004 December tsunami was a much larger event than the previous two described. It was generated by a disturbance, resulting from a M$_w$=9.2-9.3 mega-thrust earthquake, that propagated 1200-1300 km. Consequently the energy of the resulting wave was much larger than the waves generated from the 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 foucs on the larage inundation experienced at Patong bay on the West coast of Thaliand.
    54 
    55 \section{Data}
    56 Hydrodynamic simulations require very little data in comparison to models of many other environemental systems. Tsunami models typically only require baythymetry and topography data to approximate the local geography, paramterisation of the tsunami source from which appropriate initial conditions can be generated, and a locally distributed quantity such as manning's friction coefficient to approximate friction. Here we dicuss the bathymetric and topographical data sets and source condition that are necessary to implement the proposed benchmark. Friction is discussed in Section~\ref{sec:}
    57 
    58 The Patong Bay and surrounding region is source to an unusually large amount of data, pertaining to the 2004 tsunami, which is necessary for tsunami verification. The authours obtained a number of raw data sets which were analysed and checked for quality (QCd) and subsequently gridded for easier visualisation and input into tsunami models.
     47Although appalling, the devastation caused by the 2004 Indian Ocean 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. Enormous resources have been spent to obtain many measurements of phenomenon pertaining to this event to better understand the destruction that occurred. 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 (Vigny {\it et al.} 2005, Amnon {\it et al.} 2005, Kawata {\it et al.} 2005, and Liu {\it et al.} 2005)\nocite{vigny05,amnon05,kawata05,liu05}. A number of studies have utilised this data to calibrate models of the tsunami source\cite{grilli07} , match tide gauge recordings\cite{}, maximum wave heights~\cite{asavanant08} and runup locations~\cite{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}.
     48
     49Synolakis 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.
     50
     51%The tsunamis used by the two standard benchmarks and the 2004 tsunami are quite different. They all arise from coseismic displacement resulting from an earthquake, however they all occur in very different geographical regions. The Hokkaido-Nansei-Oki tsunami was generated by an earthquake with a magnitude of 7.8 and only travelled a small distance before inundating Okishiri Island. The event provides an example of extreme runup generated from reflections and constructive interference resulting from local topography and bathymetry. In comparison the Rat islands tsunami was generated by an earthquake of the same magnitude but had to travel a much greater distance. The event provides a number of tide gauge recordings that capture the change in wave form as the tsunami evolved.
     52
     53The 2004 December tsunami was a much larger event than the previous two described. It was generated by a disturbance, resulting from a M$_w$=9.2-9.3 mega-thrust earthquake, that propagated 1200-1300 km. Consequently the energy of the resulting wave was much larger than the waves generated from the 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.
     54
     55\section{Data}\label{sec:data}
     56Hydrodynamic simulations require very little data in comparison to models of many other environmental systems. Tsunami models typically only require baythymetry and topography data to approximate the local geography, parameterisation of the tsunami source from which appropriate initial conditions can be generated, and a locally distributed quantity such as Manning's friction coefficient to approximate friction. Here we discuss the bathymetric and topographical data sets and source condition that are necessary to implement the proposed benchmark. Friction is discussed in Section~\ref{sec:inundation}
     57
     58The Patong Bay and surrounding region is source to an unusually large amount of data, pertaining to the 2004 tsunami, which is necessary for tsunami verification. The authors obtained a number of raw data sets which were analysed and checked for quality (QCd) and subsequently gridded for easier visualisation and input into tsunami models.
    5959
    6060\subsection{Bathymetric and topographic data}
    61 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 we replaced the DBDB2 data with a a 3 second grid obtained from NOAA. Finally a 1 second grid was used to approximate the bathymetry in Patong Bay and the immeadiately adjacent regions. This elevation data was created from the digitised Thai Navy bathymetry chart, no 358. A visualisation of the topography data set used in Patong bay is shown in Figure~\ref{fig:patong_bathymetry}. The continuous topgraphy is an interpolation of the 1 second grid created for this area from the known elevation measured at the coloured dots.
     61The 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 we replaced the DBDB2 data with a a 3 second grid obtained from NOAA. Finally a 1 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. A visualisation of the topography 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.
    6262
    6363The sub-sampling of larger grids was performed by using {\bf resample}  a GMT program. 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.
     
    7272\end{figure}
    7373
    74 \subsection{Tsunami source}
     74\subsection{Tsunami source}\label{sec:source}
    7575The Indian Ocean tsunami of 2004 was generated by severe coseismic displacement of the sea floor as a result of one of the largest earthquakes on record. The M$_w$=9.2-9.3 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 (Amnon {\it et al.} 2005)\nocite{amnon05}.
    7676
    77 Many parameterisations of the 2004 tsunami source are available. Some are determeined from various geolocial surveys of the site, others solve an inverse problem which calibrates the source based upon the tsunami wave signal and or runup. Although possibly producing a closer match between observed and simulated data, the later later is in approporaite for use by this benchmark. The data used to calibrate the model needs to be independent of the validation data. The source parameters used to simulate the 2004 Indian Ocean Tsunami were taken from Chlieh (2007). HOW IS SOURCE PARAMTERISED. FROM GEOGRAPHICAL STUDY OF INVERSE PROBLEM TRYING TO MATCH WAVE SIGNAL. DOES ANYONE HAVE A COPY THEY COULD SEND ME PLEAESE? The resulting sea floor displacement ranges from about - 5.0 to 5.0 metres and is shown in Figure~\ref{fig:chlieh_slip_model}.
     77Many parameterisations of the 2004 tsunami source are available. 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 (2007). This model was created by carefull inversion of the seismic data and fits both coseismic, tsunami and GPS data in the Andaman Sea well. DOES ANYONE HAVE A COPY THEY COULD SEND ME PLEASE? The resulting sea floor displacement ranges from about - 5.0 to 5.0 metres and is shown in Figure~\ref{fig:chlieh_slip_model}.
    7878
    7979\begin{figure}[ht]
     
    9797
    9898
    99 \section{Verification Procedure}
     99\section{Verification Procedure}\label{sec:veri_procedure}
    100100
    101101%=================Section=====================
    102102
    103103\subsection{ANUGA}
    104 ANUGA is an inundation tool that solves the depth integrated shallow water wave equations. The scheme used by ANUGA, first presented by Zoppou and Roberts (1999)\nocite{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 {\it et al.} (2001) \nocite{kurganov01} for solving one-dimensional conservation equations. The numerical scheme is presented in detail in (Zoppou and Roberts 1999, Zoppou and Roberts 2000, and Roberts and Zoppou 2000, Nielsen {\it et al.} 2005) \nocite{zoppou99,zoppou00,roberts00,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.
    105 
    106 
    107 \subsection{Tsunami Souce and Propagation}
    108 We use the URS model to simulate the propagation of the 2004 Indian Ocean tsunami in the deep ocean ocean, based on a discrete representation of the initial deformation of the sea floor, described above.
    109 
    110 The URS code models the propagation of the tsunami in deep water using the finite difference method to solve the non-linear shallow water equations in
    111 spherical co-ordinates with friction and coriolis terms. The code is based on Satake (1995) with significant modifications made by the URS corporation
    112 (Thio et al. 2007) and Geoscience Australia (Burbidge et al. 2007). The tsunami is propagated via a stagered grid system starting with coarser grids
    113 and ending with the finest one. The URS code is also capable of calculating inundation. CAN WE PRODUCE AN INUNDATINO MAP OVER THE SAME AREA TO COMPARE WITH ANUGA???
    114 
    115 The computational domain for the URS simulation, was defined to extend from $...$E to $...$E and from $...$S to $...$S. The bathymetry in this region was estimated using ...
    116 %a 4 arc minute data set developed by the CSIRO specifically for the ocean forecasting system used here. It is based on dbdb2 (NRL), and GEBCO data sets. The tsunami propagation incorporated here was modelled by the Bureau of Meteorology, Australia for six hours using a time step of 5 seconds (4320 time steps in total).
    117 
    118 The output of the URS model was produced for the sole purpose of providing an approximation of the tsunami's size and momentum that can be used to estimate the tsunami run-up. ANUGA could also have been used to model the propagation of the tsunami in the open ocean. The capabilities of the numerical scheme over such a large extent, however, have not been adequately tested. This issue will be addressed in future work.
    119 
    120 \subsection{Tsunami Inundation}
    121 The utility of the URSGA model decreases with water depth unless an intricate sequence of nested grids is employed. On the other hand, while the ANUGA model is less suitable for earth quake source modelling and large study areas, it is designed with detailed on-shore inundation in mind.
    122 Consequently, the Geoscience Australia tsunami modelling methodology is based on a hybrid approach using models like URSGA for tsunami generation and propagation up to a 100m depth contour where the wave is picked up by ANUGA and propagated on shore using the finite-volume method on unstructured triangular meshes.
    123 
    124 In this case the open ocean boundary of the ANUGA study area was chosen to roughly follow the 100m depth contour along the west coast of Phuket Island.
    125 The other boundaries were chosen to maximise the number of locations for which run-up depths were measured, whilst keeping the computational domain `small enough' to avoid excessively large computational time. The computational domain is shown in Figure \ref{fig:computational_domain}
     104ANUGA is an inundation tool that solves the depth integrated shallow water wave equations. The scheme used by ANUGA, first presented by Zoppou and Roberts (1999)\nocite{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 {\it et al.} (2001) \nocite{kurganov01} for solving one-dimensional conservation equations. The numerical scheme is presented in detail in (Zoppou and Roberts 1999, Zoppou and Roberts 2000, and Roberts and Zoppou 2000, Nielsen {\it et al.} 2005) \nocite{zoppou99,zoppou00,roberts00,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. ANUGA has been validated against a number of analytical solutions and the wave tank simulation of the 1993 Okushiri Island tsunami (Roberts {\it et al.} 2006)\nocite{roberts06}.
     105
     106\subsection{URSGA}
     107URSGA is a hydrodynamic code that models the propagation of the tsunami in deep water using the finite difference method to solve the non-linear shallow water equations in spherical co-ordinates with friction and Coriolis terms. The code is based on Satake (1995) with significant modifications made by the URS corporation (Thio et al. 2007) and Geoscience Australia (Burbidge et al. 2007). The tsunami is propagated via a stagered grid system starting with coarser grids and ending with the finest one.
     108
     109
     110\subsection{Tsunami Source and Propagation}
     111The utility of the URSGA model decreases with water depth unless an intricate sequence of nested grids is employed. In comparison ANUGA is designed to produce robust and accurate predictions of on-shore inundation in mind, but is less suitable for earth quake source modelling and large study areas. Consequently, the Geoscience Australia tsunami modelling methodology is based on a hybrid approach using models like URSGA for tsunami generation and propagation up to a 100m depth contour where the wave is picked up by ANUGA and propagated on shore. Specifically we use the URSGA model to simulate the propagation of the 2004 Indian Ocean tsunami in the deep ocean 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 contour offshore of Phuket, Thailand. The wave signal is then used as a time varying boundary condition for the ANUGA inundation simulation.
     112
     113???The URS code is also capable of calculating inundation. CAN WE PRODUCE AN INUNDATION MAP OVER THE SAME AREA TO COMPARE WITH ANUGA???
     114
     115\subsection{Tsunami Inundation}\label{sec:inundation}
     116In this case the open ocean boundary of the ANUGA study area 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}
    126117\begin{figure}[ht]
    127118\begin{center}
    128119\includegraphics[width=8.0cm,keepaspectratio=true]{new_domain.png}
    129 \caption{Computational Domain. CAN WE CREATE A PICTURE LIKE THIS FOR OUR NEW SCENARIO}
     120\caption{Computational domain of the ANUGA simulation. CAN WE CREATE A PICTURE LIKE THIS FOR OUR NEW SCENARIO???}
    130121\label{fig:computational_domain}
    131122\end{center}
    132123\end{figure}
    133124
    134 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 run-up points and tide gauges. The triangle size around islands and obstacles which "significantly affect" the tsunami was also reduced. The authors used their discretion to determine what obstacles significantly affect the wave through an iterative process.
    135 
     125The 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 constant througout the computational domain. A Manning's coefficient of 0.01 was chosen based upon previous numerical experiments conducted by the authors.
    136126
    137127%================Section======================
    138128\section{Results}
     129Maximum on-shore 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 discrepencies between the two inundation regions may be a result of the large measurement error in the field survey data. The 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 ANUGA simulation. The simulated inundation based upon a 10cm threshold is shown in Figure~\ref{fig:inundationcomparison10cm}.
     130
    139131\begin{figure}[ht]
    140132\begin{center}
    141133\includegraphics[width=8.0cm,keepaspectratio=true]{Patong_0_8lowres.jpg}
    142134\caption{Simulated inundation versus observed inundation}
    143 \label{fig:inundationcomparison}
    144 \end{center}
    145 \end{figure}
     135\label{fig:inundationcomparison1cm}
     136\end{center}
     137\end{figure}
     138
     139
    146140
    147141%================Section=====================
    148142
    149 \section{Discussion and Conclusions}
    150 We have simulated the inundation of the tsunami of a small irregular region of the west Thailand coast surrounding Phuket using the inundation tool ANUGA. The tsunami size and position at the boundaries of this region were estimated using the MOST model which was used to simulate the generation and propagation of the tsunami in the deep ocean. Specifically the parameterisation of Greensdale {\it et al.} (2007) \nocite{greensdale07} was used to describe the tsunami source and the subsequent wave elevation and momentum required by the inundation simulation were interpolated from the MOST simulation at each time step.
     143\section{Conclusion}
     144This paper proposes an additional field data benchmark for the verification of tsunami inundation models. Currently the number of appropriate tests are limited due to a lack of tsunami data. The new benchmark involves the comparison of model predictions of on-shore inundation in Patong Bay, Phuket Thailand caused by the mega tsunami of December 26th 2004. Specifically a field survey mapping observed inundation is used as a spatially distributed test of model performance. Although two other field data benchmarks exists, the 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 exists.
     145
     146This paper also illustrates the effectiveness of the proposed new benchmark. The benchmark is used to test the veracity of the hydrodynamic ANUGA designed spcefically to model on-shore inundation. Very good agreement is obtained between the observed and simulated runup. The URSGA tsunami package was also tested. Much worse results were obtained??
    151147
    152148
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