source: anuga_work/publications/boxing_day_validation_2008/patong_validation.tex @ 6409

\documentclass[a4paper]{article}
\usepackage{modsim07}
\usepackage{graphicx}
\usepackage{hyperref}

%================Start of Document================
\begin{document}

%----------title-------------
\title{Inundation Modelling of the December 2004 Indian Ocean Tsunami}

%-------authors-----------
\author{J.D.~Jakeman$^1$~~and~~O.~Nielsen$^2$~~and~~R.~Mleczko$^2$~~and~~K.~VanPutten$^2$~~and~~S.G~Roberts$^1$}

%------Affiliation----------
\institute{$^1$The Australian National University, Canberra, Australia \\
$^2$Geoscience Australia, Canberra, Australia\\
Email: \href{mailto:jakeman@maths.anu.edu.au}{john.jakeman@anu.edu.au}}
\keywords{ANUGA, Finite Volume Method, Natural Hazards, Indian Ocean Tsunami, Inundation, Thailand, Phuket, Patong Bay.}

\maketitle

%------Abstract--------------
\begin{abstract}

\end{abstract}
%======================Section 1=================

\section{Introduction}
Tsunami are a potential hazard to coastal communities all over the world. A number of recent large events have increased community and scientific awareness of the need for effective tsunami hazard mitigation. Tsunami modelling is major component of hazard mitigation, which involves detection, forecasting, and emergency preparedness (Synolakis {\it et al.} 2005). 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.

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 commonly accepted descriptions of flow. The complex nature of these equations and the highly variable nature of the phenomena that they describe 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.

Complete 100\% confidence in a model of a physical system cannot be proven. One can only show that the model does not fail under certain conditions. However, 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. %Verification must be used to reduce numerical error before validation is used to assess model structure. In some situations it may be possible to increase the numerical accuracy of a model and produce a worse fit of the observed data. 

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. 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}.

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 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 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}.

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:veri_procedure}.

%=================Section=====================

\section{Indian Ocean tsunami of 24th December 2004}
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 tsunami models. This event captures certain tsunami behaviours that are not present in the benchmarks proposed by Synolakis et. al~\cite{synolakis07}.

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.

%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 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.

\section{Data}\label{sec:data}
Hydrodynamic 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}

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 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.

\subsection{Bathymetric and topographic data}
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 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.

The 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.


\begin{figure}[ht]
\begin{center}
\includegraphics[width=8.0cm,keepaspectratio=true]{patong_bay_data.jpg}
\caption{Is there a new picture with river included???}
\label{fig:patong_bathymetry}
\end{center}
\end{figure}

\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}.

\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)}
\label{fig:chlieh_slip_model}
\end{center}
\end{figure}

\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???

\begin{figure}[ht]
\begin{center}
\includegraphics[width=8.0cm,keepaspectratio=true]{patongescapemap.jpg}
\caption{Map of maximum inundation at Patong bay.}
\label{fig:patongescapemap}
\end{center}
\end{figure}


\section{Verification Procedure}\label{sec:veri_procedure}

%=================Section=====================

\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)\nocite{roberts06}.

\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. 


\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 URS code is also capable of calculating inundation. CAN WE PRODUCE AN INUNDATION MAP OVER THE SAME AREA TO COMPARE WITH ANUGA???

\subsection{Tsunami Inundation}\label{sec:inundation}
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. The computational domain is shown in Figure \ref{fig:computational_domain}
\begin{figure}[ht]
\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???}
\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.

%================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}.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=8.0cm,keepaspectratio=true]{Patong_0_8lowres.jpg}
\caption{Simulated inundation versus observed inundation}
\label{fig:inundationcomparison1cm}
\end{center}
\end{figure}



%================Section=====================

\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 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??


%================Acknowledgement===================
\section{Acknowledgements}
This project was undertaken at Geoscience Australia and the Department of Mathematics, The Australian National University. The authors would like to thank Niran Chaimanee from the CCOP, Thailand for providing the post 2004 tsunami survey data and the elevation data for Patong beach.



%====================Bibliography==============
%\bibliographystyle{thebibliography}
%\bibliography{tsunami07}

\begin{thebibliography}{7}
\bibitem{amnon05}
Ammon, C.J., C. Ji, H. Thio, D. Robinson, Sidao Ni, V. Hjorleifsdottir, H., T. Lay, S. Das, D. Helmberger, G. Ichinose, J. Polet, and D. Wald (2005), Rupture process of the 2004 Sumatra-Andaman earthquake, {\em Science}, {\bf 308}, 1133.
\bibitem{bourgeois99}
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.
\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{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.
\bibitem{gusiakov72}
Gusiakov, V.K. (1972), Static displacement on the surface of an elastic space. Ill-posed problems of mathematical physics and interpretation of geophysical data, {\em Novosibirsk, VC SOAN SSSR},  23-51. In Russian.
\bibitem{jankaew}
Jankaew, K., B. F. Atwater, et al. (2008). Medieval forewarning of the 2004 Indian Ocean tsunami in Thailand, Nature, {\bf 455(7217)}, 1228-1231.
\bibitem{kawata05}
Kawata, T. et XIV alia (2005) Comprehensive analysis of the damage and its impact on coastal zones by the 2004 Indian Ocean tsunami disaster. Technical report, Disaster Prevention Research Institute. http://www.tsunami.civil.tohoku.ac.jp/sumatra2004/\\report.html.
\bibitem{kurganov01}
Kurganov, A., S. Noelle, and G. Petrova (2001), Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations, {\em SIAM Journal of Scientific Computing}, {\bf 23(3)}, 707-740.
\bibitem{lebrun98}
Lebrun, J.F., G.G. Karner, and J.Y. Collot. Fracture zone subduction and reactivation across the Puysegur ridge trench system, southern New Zealand, {\em Journal of Geophysical Research}, {\bf 103}, 7293-7313.
\bibitem{liu05}
Liu P. L.-F., P. Lynett, H. Fernando, B.E. Jaffe, H. Fritz, B. Higman, R. Morton, J. Goff, and C. Synolakis. Observations by the international tsunami survey team in Sri Lanka, {\em Science}, {\bf 308}, 1595.
\bibitem{matsuyama01}
Matsuyama, M. and H. Tanaka (2001) An experimental study of the highest run-up height in the 1993 Okkaido Nansei-Oki earthquake tsunami. In {\em National Tsunami Hazard Mitigation Program Review and International Tsunami Symposium (ITS)}, pages 879-889. U.S. National Tsunami Hazard Mitigation Program.
\bibitem{merrifield05}
Merrifield, M.A., et XXIII alia (2005), Tide gauge observations of the Indian Ocean tsunami, December 26, 2004, {\em Geophysical Research Letters}, {\bf 32}, L09603.
\bibitem{ngdc}
National Geophysical Data Center (NGDC). Indian ocean december 26, 2004: run-ups. http://www.ngdc.noaa.gov/seg/hazard/tsu.shtml
\bibitem{nielsen05}
Nielsen, O.M, S.G Roberts, D. Gray, A. McPherson, and A. Hitchman (2005), Hydrodynamic modelling of coastal inundation. In A. Zerger and R.M. Argent, editors, {\em MODSIM 2005 International Congress on Modelling and Simulation}, pages 518-523. Modelling and Simulation Society of Australia and New Zealand. http://www.mssanz.org.au/modsim05/papers/nielsen.pdf.
\bibitem{roberts06}
Roberts, S.G., O.M. Nielsen, and J.D. Jakeman (2006), Simulation of tsunami and flash flood. Accepted for publication in the refereed proceedings of the International Conference on High Performance Scientific Computing: Modeling, Simulation and Optimization of Complex Processes, March 6-10, 2006, Hanoi Vietnam.
\bibitem{roberts00}
Roberts, S.G. and C. Zoppou (2000), Robust and efficent solution of the 2d shallow water wave equation with domains containg dry beds, {\em The ANZIAM Journal}, {\bf 42(E)}, C1260-C1282.
\bibitem{satake95}
Satake, K. (1995). Linear and nonlinear computations of the 1992 Nicaragua earthquake tsunami. Pure and Applied Geophysics, {\bf 144(3)}, 455-470.
\bibitem{synolakis05}
Synolakis, C., E. Okal, and E. Bernard (2005), The megatsunami of December 26 2004, {\em The Bridge, National Academy of Engineering Publications}, {\bf 35(2)}, 36-35.
\bibitem{titov05}
Titov, V.V., F. Gonz\'{a}lez E. Bernard, M. Eble, H. Mofjeld, J. Newman, and A. Venturato (2005), Real-time tsunami forecasting: Challenges and solutions, {\em Natural Hazards}, {\bf 35}, 41-58.
\bibitem{titov95}
Titov, V.V. and C. Synolakis (1995), Modeling of breaking and nonbreaking long wave evolution and run-up using VTCS-2, {\em Journal of Waterways, Port, Ocean and Coastal Engineering}, {\bf 121(6)}, 308-316.
\bibitem{titov97a}
Titov, V.V. and F.I. Gonzalez (1997), Implementation and testing of the method of splitting tsunami (MOST) model, {\em NOAA Technical Memorandum}.
\bibitem{titov01}
Titov, V.V., F.I. Gonzalez, H.O. Mofjeld, and J.C. Newman (2001), Project SIFT (short-term inundation forecasting for tsunamis), In {\em ITS Proceedings}.
\bibitem{gica08}
Gica, E., M. Spillane, V.V. Titov, C.D. Chamberlin, and J.C. Newman (2008): Development of the forecast propagation database for NOAA's Short-term Inundation Forecast for Tsunamis (SIFT). NOAA Tech. Memo. {\bf OAR PMEL-139}, 89 pp.
\bibitem{titov97b}
Titov, V.V. and C.E. Synolakis (1997), Extreme inundation flows during the hokkaido Nansei-Oki tsunami, {\em Geophysical Research Letters}, {\bf 24(11)}, 1315-1318.
\bibitem{tsuji95}
Tsuji, T., S. Matsutomi, F. Imamura, and C.E. Synolakis (1995), Field survey of the east Java earthquake and tsunami, {\em Pure and Applied Geophysics}, {\bf 144(3/4)}, 839-855.
\bibitem{vigny05}
Vigny, C., W.J.F. Simons, S. Abu, R. Bamphenyu, N. C. Satirapod, C. Subarya Choosakul, A. Socquet, K. Omar, H.Z. Abidin, and B.A.C. Ambrosius (2005), Insight into the 2004 Sumatra-Andaman earthquake from GPS measurements in southeast Asia, {\em Nature}, {\bf 436}, 201-206.
\bibitem{wang95}
Wang, R., F. L. Martin, et al. (2003). Computation of deformation induced by earthquakes in a multi-layered elastic crust - FORTRAN program EDGRN/EDCMP. Computers and Geosciences, {\bf 29}, 195-207.
\bibitem{yeh94}
Yeh, H., V.V Titov, V. Gusiakov, E. Pelinovsky, V. Khramushin, and V. Kaistrenko (1994), The 1994 Shikotan earthquake tsunami, {\em  Pure and Applied Geophysics}, {\bf 144(3/4)}, 569-593.
\bibitem{zoppou99}
Zoppou, C., and S.G Roberts (1999), Catastrophic collapse of water supply reserviours in urban areas, {\em Journal of Hydraulic Engineering}, {\bf 125(7)}, 686-695.
\bibitem{zoppou00}
Zoppou, C. and S.G Roberts (2000), Numerical solution of the two-dimensional unsteady dam break, {\em Applied Mathematical Modelling}, {\bf 24}, 457-475.
\end{thebibliography}


%===============Appendicis

\section*{Appendix A. Figures and Tables}

\subsection (datasets and gridding)

Gridded data sets used:

DBDB2 2 minute of arc grid from the US Naval Research Labs.
This grid was also interpolated to 27 sec of arc and used in a nested grid scheme.

Indian Ocean 27 sec of arc grid created by:
Interpolating the DBDB2 2 minute of arc grid.
In the region where the 9 sec grid sits the data was cut out and replaced by the 9 sec data.
Any points that deviated from the general trend near the boundary were deleted.
The data was then re-gridded.

Andaman Sea 9 sec of arc grid created by:
Sub-sampling the 3 sec of arc grid from NOAA.
In the region where the 3 sec grid sits the data was cut out and replaced by the 3 sec data.
Any points that deviated from the general trend near the boundary were deleted.
The data was then re-gridded.

Thailand off-shore 3 sec of arc grid created by:
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.
This grid was obtained from NOAA.
In the region where the 1 sec grid sits the data was cut out and replaced by the 1 sec data.
Any points that deviated from the general trend near the boundary were deleted.
The data was then re-gridded.

Patong Bay 1 second of arc grid created from:
elevation data contained in a GIS of Patong Bay supplied by Niran Chaimanee, Geo-environment Sector Manager, CCOP T/S, Bangkok.
Digitised Thai Navy bathymetry chart no 358.

The 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 was nearest neighbour followed by minimum curvature akima spline smoothing.

\subsection (earthquake source model)

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)

To to generate and propagate the tsunami the URS code was used. This program solves the shallow water equations using the finite difference method.
It can also be used in a nexted grid scheme and does on-shore inundation.

%%%%%%%%%%%%%%%%%%%%%%%

\end{document}


Main source of uncertainty arises from inaccuracies in initial condition (source), inaccurate bathymetry data, to a lesser extent friction

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. 

Expressions:
sufficient verification/falsification of model
Confidently utilise a model

Predictive valdiation of only one aspect of model evaluation. Need to assess model explanation.

Conservation of mass
convergence

spatial and temporal discretisation errors, round off errors due to limited numerical precision

analytical benchmarking:
ensuring equations are solved accurately
single wave on a beach
Solitary wave on composite beach
subaerial landslide on simple beach

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.

scale comparisions (laboratory benchmarking):
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
Single wave on a simple beacj
Solitary wave on composite beach
Conical island
Monai Valley
Landslide

includes comparisons with validation data sets generated by other models of higher dimensionality and resolution.

Often flow geometries are simplified


Field benchmarking:
Most important verification process
Hydrodynamic inversion to predict the source is an ill posed problem
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
17 November 2003 Rat Islands Tsunami

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.

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.

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.

verfication need to assess point data, spatially distributed data and bulk (lumped) data.

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.


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

Notes:
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.



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 DART recording to constrain the tsunami source model. The inundation model is to reproduce the tide gauge record at Hilo.

Patong Bay benchamark provides spatially distributed field data for comparison. 

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. 

DO I SAY WE HAVE MUX @ FILES DESCRIBING SHAPE OF WAVE YES. MAKES CONSISTENT

Notes:  * Model source developed independently of inundation data.
        * Patong region was chosen because high resolution inundation map and bathymetry and topography data was available there

Geoscience Australia, in an open collaboration with the Mathematical Sciences Institute, The Australian National University, is developing a software application, 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 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.

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

article={ioualalen07,
title={Modeling the 26 December 2004 Indian Ocean tsunami: Case study of impact in Thailand},
author=-{Ioualalen, M. and Asavanant, J. and  Kaewbanjak, N. and Grilli, S.~T. and Kirby, J.~T. and Watts, P.},
year={2007},
journal ={ J. Geophys. Res.},
volume={112},
doi={http://dx.doi.org/10.1029/2006JC003850}
}

article={hirata06
title={The 2004 Indian Ocean tsunami: Tsunami source model from satellite altimetry},
author={Hirata, K. and Satake, K. and Tanioka, Y. and  Kuragano, T. and Hasegawa, Y. and   Hayashi, Y. and Hamada, N.},
journal={Earth, Planets and Space}
year={2006},
volume={58},
number={2},
pages={195--201}
}

@InBook{asavanant08,
ALTauthor = {Asavanant, J. and  Ioualalen, M. and Kaewbanjak, N. and Grilli, S.~T. and Watts, P. and Kirby, J.~T. and Shi, F.},
ALTeditor = {},
title = {Modeling, Simulation and Optimization of Complex Processes},
chapter = {Numerical Simulation of the December 26, 2004: Indian Ocean Tsunami },
publisher = {   Springer Berlin Heidelberg},
year = {2008},
pages = {59--68},
}

@article{grilli07,
author = {St\'{e}phan T. Grilli and Mansour Ioualalen and Jack Asavanant and Fengyan Shi and James T. Kirby and Philip Watts},
title = {Source Constraints and Model Simulation of the December 26, 2004, Indian Ocean Tsunami},
publisher = {ASCE},
year = {2007},
journal = {Journal of Waterway, Port, Coastal, and Ocean Engineering},
volume = {133},
number = {6},
pages = {414-428},
url = {http://link.aip.org/link/?QWW/133/414/1},
doi = {10.1061/(ASCE)0733-950X(2007)133:6(414)}
}