# Changeset 6515

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Timestamp:
Mar 13, 2009, 6:01:53 PM (14 years ago)
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 r6506 (FIXME: CAN WE GET RID OF THIS: 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 one of 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}. 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 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. 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 (FIXME: What?) and only one of the benchmarks can be used to validate tsunami inundation (FIXME: Why?). 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. In 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 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}. %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. The 2004 Indian Ocean tsunami was a much larger event than the previous two described. It was generated by a disturbance, resulting from a M$_w$=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 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. 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. \section{Data}\label{sec:data} \subsection{Tsunami source}\label{sec:source} The 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}. Many 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}. 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 (Amnon {\it et al.} 2005)\nocite{amnon05}. Many models of this earthquake are available FIXME: CITATIONS NEEDED \cite{YYY}. 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) \cite{XXX}. This model was created by 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}. \begin{figure}[ht] \begin{center} \includegraphics[width=8.0cm,keepaspectratio=true]{chlieh_slip_model.png} \caption{Location and magnitude of the sea floor displacement associated with the December 24 2004 tsunami. Source parameters taken from Chlieh {\it et al.} (2007)} \caption{Location and magnitude of the sea floor displacement associated with the 2004 Indian Ocean tsunami. Source parameters from Chlieh {\it et al.} (2007) \cite{XXX}} \label{fig:chlieh_slip_model} \end{center} \subsection{Inundation survey data} The bathymetry data and source parameterisation can be inserted into the tsunami model and run. From the simulation runup and ocean surface elevation can be obtained. We propose that a correct' tsunami model should reproduce the inundation map shown in Figure~\ref{fig:patongescapemap}. Furthermore the model should simulate a leading depression followed by 3??? crests. Is there any eye witness accounts of how many waves arrived a patong??? ... FIXME: This needs to be rephrased. This is about survey data not about bathymetric and source parameters. And it appears that this paragraph really belongs under the next section. The bathymetry data and source parameterisation can be inserted into the tsunami model and run. From the simulation runup and ocean surface elevation can be obtained. We propose that a correct' tsunami model should reproduce the inundation map shown in Figure~\ref{fig:patongescapemap}. Furthermore the model should simulate a leading depression followed by 3??? crests. Is there any eye witness accounts of how many waves arrived a patong??? FIXME: Who will chase this? Richard has the video footage recorded, can you do it? \begin{figure}[ht] \begin{center} \includegraphics[width=8.0cm,keepaspectratio=true]{patongescapemap.jpg} \caption{Map of maximum inundation at Patong bay.} \caption{Tsunami survey mapping the maximum observed inundation at Patong beach courtesy of the Thai Department of Mineral Resources \protect \cite{XXX}.} \label{fig:patongescapemap} \end{center} \subsection{ANUGA} 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. 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 and Nielsen {\it et al.} 2005) \nocite{roberts06,nielsen05}. ANUGA is an Open Source hydrodynamic inundation tool that solves the depth integrated nonlinear 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 and Nielsen {\it et al.} 2005) \nocite{roberts06,nielsen05}. \subsection{URSGA} URSGA 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. 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 (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 staggered grid system starting with coarser grids and ending with the finest one. URSGA is not publicly available. FIXME: Check with David. \subsection{Tsunami Source and Propagation} The 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. The 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 earthquake 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. This information then forms a boundary condition for ANUGA and is propagated on shore to model the inundation. Specifically we use the 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 ANUGA inundation simulation. ???The URS code is also capable of calculating inundation. CAN WE PRODUCE AN INUNDATION MAP OVER THE SAME AREA TO COMPARE WITH ANUGA??? \begin{center} \includegraphics[width=8.0cm,keepaspectratio=true]{new_domain.png} \caption{Computational domain of the ANUGA simulation. CAN WE CREATE A PICTURE LIKE THIS FOR OUR NEW SCENARIO???} \caption{Computational domain of the ANUGA simulation. CAN WE CREATE A PICTURE LIKE THIS FOR OUR NEW SCENARIO??? FIXME: Is this still the case?} \label{fig:computational_domain} \end{center} \end{figure} 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 constant througout the computational domain. A Manning's coefficient of 0.01 was chosen based upon previous numerical experiments conducted by the authors. 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??). %================Section====================== \section{Results} Maximum 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}. 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. 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. FIXME: Take some of this commentary after final runs have been completed. FIXME: Also need a commentary on the dynamics of what is being observed and whether it aligns with eye witness observations. %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}. \begin{figure}[ht] \section{Conclusion} This 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. 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. This 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?? FIXME: Cite more of these and use the proper citation system of LaTeX or even BiBTeX. %====================Bibliography============== Bourgeois, J., C. Petroff, H. Yeh, V. Titov, C. Synolakis, B. Benson, J. Kuroiwa, J. Lander, and E. Norabuena (1999), Geologic setting, field survey and modeling of the Chimbote, northern Peru, tsunami of 21 February 1996, {\em Pure and Applied Geophysics}, {\bf 154(3/4)}, pages 513-540. \bibitem{burbidge} Burbidge, D., P. Cummins, and R. Mleczko (2007), A Probabilistic Tsunami Hazard Assessment for Western Australia, Report to the Fire and Emergency Services Authority of Western Australia. Burbidge, D., P. Cummins, and R. Mleczko (2007), A Probabilistic Tsunami Hazard Assessment for Western Australia, Report to the Fire and Emergency Services Authority of Western Australia. FIXME: Needs to be updated to recent Pageoph reference. \bibitem{chlieh} Chlieh, M., J. P. Avouac, et al. (2007). Coseismic slip and afterslip of the great Mw 9.15 Sumatra-Andaman earthquake of 2004. Bulletin of the Seismological Society of America, {\bf 97(1A) }, S152-S173. \bibitem{greensdale07} Greensdale, D., M . Simanjuntak, D. Burbidge, and J. Chittleborough (2007), A first-generation real-time tsunami forecasting system for the Australian region. BMRC Research Report 126, Bureau of Meteorology Australia. \bibitem{greenslade07} Greenslade, D., M . Simanjuntak, D. Burbidge, and J. Chittleborough (2007), A first-generation real-time tsunami forecasting system for the Australian region. BMRC Research Report 126, Bureau of Meteorology Australia. \bibitem{grilli06} Grilli, S.T., M. Ioualalen, J. Asavanant, F. Shi, J.T Kirby, and P. Watts (2006), Source constraints and model simulation of the December 26, 2004 Indian Ocean tsunami, {\em Journal of Waterways, Port, Ocean and Coastal Engineering}. In press. \section*{Appendix A. Figures and Tables} \subsection (datasets and gridding) \subsection{Datasets and gridding} This 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. FIXME: Is there a standard template for data lineage. \begin{verbatim} E.g. Data Source: 2 min: DBDB 2 9 sec: NOAA 3 sec: aontehusoe Process: ... ... ... \end{verbatim} FIXME: Could we have a map with the nested data sets? Gridded data sets used: The gridding scheme was nearest neighbour followed by minimum curvature akima spline smoothing. \subsection (earthquake source model) \subsection{Earthquake Source Model} FIXME: Is this appendix needed? The earthquake source model of Chlieh was adopted to generate the tsunami simulation. This model was created by carefull inversion of the seismic data and fits both coseismic, tsunami and GPS data in the Andaman Sea well. \subsection (tsunami propagation) \subsection{Tsunami Propagation} FIXME: Is this appendix needed? To to generate and propagate the tsunami the URS code was used. This program solves the shallow water equations using the finite difference method.