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1\documentclass[a4paper]{article}
2\usepackage{graphicx}
3\usepackage{hyperref}
4\usepackage{amsfonts}
5\usepackage{url}      % for URLs and DOIs
6\newcommand{\doi}[1]{\url{http://dx.doi.org/#1}}
7
8%----------title-------------%
9%\title{Inundation Modelling of the December 2004 Indian Ocean Tsunami}
10\title{Benchmarking an Inundation Model using the December 2004 Indian Ocean Tsunami Impact at Patong Beach}
11
12%-------authors-----------
13\author{J.~D. Jakeman\thanks{The Australian National University, Canberra, \textsc{Australia}.
14\protect\url{mailto:john.jakeman@anu.edu.au}}
15\and O.Nielsen\thanks{Geoscience Australia, Canberra, \textsc{Australia}}
16\and R. Mleczko\footnotemark[2]
17\and D. Burbidge\footnotemark[2]
18\and K. VanPutten\footnotemark[2]
19\and S.~G Roberts\footnotemark[1]
20}
21
22%================Start of Document================
23\begin{document}
24\maketitle
25%------Abstract--------------
26\begin{abstract}
27
28\end{abstract}
29
30\tableofcontents
31%================Section===========================
32
33\section{Introduction}
34Tsunami are a potential hazard to coastal communities all over the world. A number of recent large events have increased community and scientific awareness of the need for effective tsunami hazard mitigation. Tsunami modelling is major component of hazard mitigation, which involves detection, forecasting, and emergency preparedness~\cite{synolakis05}. Accurate models can be used to provide information that increases the effectiveness of action undertaken before the event to minimise damage (early warning systems, breakwalls etc.) and protocols put in place to be followed when the flood waters subside.
35
36Several approaches are currently used to model tsunami propagation and inundation. These methods differ in both the formulation used to describe the evolution of the tsunami and the numerical methods used to solve the governing equations. The shallow water wave equations, linearised shallow water wave equations, and Boussinesq-type equations are frequently used to simulate tsunami propagation. The nonlinear nature of these equations, the highly variable nature of the phenomena that they describe and the complex reality of the geometry they operate in necessitate the use of numerical models. These models are typically used to predict quantities such as arrival times, wave speeds and heights and inundation extents which are used to develop efficient hazard mitigation plans. Inaccuracies in model prediction can result in inappropriate evacuation plans and town zoning which may result in loss of life and large financial losses. Consequently tsunami models must undergo sufficient testing to increase scientific and community confidence in the model predictions.
37
38Complete confidence in a model of a physical system frequently in general cannot be established.  One can only hope to state under what conditions the model hypothesis holds true. Specifically the utility of a model can be assessed through a process of validation and verification. Validation assesses the accuracy of the numerical method used to solve the governing equations and verification is used to investigate whether the model adequately represents the physical system. Together these processes can be used to establish the likelihood that that a model is a legitimate hypothesis~\cite{bates01}.
39
40The sources of data used to validate and verify a model can be separated into three main categories; analytical solutions, scale experiments and field measurements. Analytical solutions of the governing equations of a model, if available, provide the best means of validating a numerical hydrodynamic model. However analytical solutions to the governing equations are frequently limited to a small set of idealised examples that do not completely capture the more complex behaviour of `real' events. Scale experiments, typically in the form of wave-tank experiments provide a much more realistic source of data that better captures the complex dynamics of natural tsunami, whilst allowing control of the event and much easier and accurate measurement of the tsunami properties. However comparison of numerical predictions with field data provides the most stringent test of model veracity. The use of field data increases the generality and significance of conclusions made regarding model utility. However the use of field data also significantly increases the uncertainty of the validation experiment that may constrain the ability to make unequivocal statements~\cite{bates01}.
41
42Currently the extent of tsunami related field data is limited. The cost of tsunami monitoring programs and bathymetry and topography surveys prohibits the collection of data in many of the regions in which tsunamis pose greatest threat. The resulting lack of data has limited the number of field data sets available to validate tsunami models, particularly those modelling tsunami inundation. Synolakis et. al~\cite{synolakis07} have developed a set of standards, criteria and procedures for evaluating numerical models of tsunami. They propose three analytical solutions to help identify the validity of a model and  five scale comparisons (wave-tank benchmarks) and two field events to assess model veracity.  The two field data benchmarks are very useful but only capture a small subset of possible tsunami behaviours. The type and size of a tsunami source, propagation extent, and local bathymetry and topography all affect the energy, waveform and subsequent inundation of a tsunami. Consequently additional field data benchmarks that further capture the variability and sensitivity of the real world system would be useful to allow model developers verify their models and subsequently use their models with greater confidence.
43
44In this paper we develop a field data benchmark to be used in conjunction with the other tests proposed by Synolakis et al.~\cite{synolakis07} to validate and verify tsunami inundation. The benchmark is constructed from data collected around Patong Bay, Thailand immediately following the 2004 Indian Ocean tsunami. This area was chosen because the authors were able to obtain high resolution bathymetry and topography data in this area and an inundation map generated from a survey performed in the aftermath of the tsunami. A description of this data is give in Section~\ref{sec:data}.
45
46An associated aim of this paper is to illustrate the use of this new benchmark to validate an operational tsunami model called \textsc{anuga} (see Secion~\ref{sec:veri_procedure}). The specific intention is to test the ability of \textsc{anuga} to reproduce the inundation survey of maximum runup. \textsc{Anuga} is a hydrodynamic modelling tool used to simulate the tsunami propagation and run rain-induced floods.
47
48%================Section===========================
49
50\section{Event Description}
51The devastation caused by the 2004 Samatra-Andaman tsunami has heightened community, scientific and governmental interest in tsunami and in doing so has provided a unique opportunity for further validation of tsunami models. Data sets from seismometers, tide gauges, GPS stations, a few satellite overpasses, subsequent coastal field surveys of run-up and flooding and measurements from ship-based expeditions, have now been made available~\cite{vigny05,amnon05,kawata05,liu05}. A number of studies have utilised this data to calibrate models of the tsunami source\cite{asavanant08,arcas06,grilli07,ioualalen07}. We propose to use this event as an additional field-data benchmark for verification of tsunami models. This event captures certain tsunami behaviours that are not present in the benchmarks proposed by Synolakis et. al~\cite{synolakis07}. FIXME: What kind of behaviours???
52
53Synolakis detail two field data benchmarks. The first test compares model results against observed data from the Hokkaido-Nansei-Oki tsunami that occurred around Okushiri Island, Japan on the 12th of July 1993. This tsunami provides an example of extreme runup generated from reflections and constructive interference resulting from local topography and bathymetry. The benchmark consists of two tide gauge records and numerous spatially distributed point sites at which maximum runup elevations were observed. The second benchmark is based upon the Rat Islands Tsunami that occurred off the coast of Alaska on the 17th of November 2003. Rat island tsunami provides a good test for real-time forecasting models since tsunami was recorded at three tsunameters. The test requires matching the propagation model data with the DART recording to constrain the tsunami source model and using a propagation model to to reproduce the tide gauge record at Hilo.
54
55The 2004 Indian Ocean tsunami was a much larger event than the previous two described (See Section \ref{sec:source}). Consequently the energy of the resulting wave was much larger than the waves generated from the more localised and smaller magnitude aforementioned events. WAS THE WAVELENGTH< VELOCITY (and thus average ocean depth) DIFFERENT FROM THESE TWO EVENTS??? If so state something like. This larger wavelength and energy and simply the different geology of the area produced different a wave signal and different pattern of inundation. Here we focus on the large inundation experienced at Patong Bay on the west coast of Thailand.
56
57\section{Data}\label{sec:data}
58Tsunami models typically require bathymetry and topography data to approximate the local geography, parameterisation of the tsunami source from which appropriate initial conditions can be generated, and certain paramter values such Manning's friction coefficient. Here we discuss the ncessary data needed to implement the proposed benchmark.
59
60\subsection{Bathymetric and topographic data}
61David and Richard:
62
63An unusually large amount of data for the 2004 tsunami, necessary for tsunami verification, is available at Patong Bay and surrounding regions. A number of raw data sets were obtained, analysed and checked for quality and subsequently gridded for easier visualisation and input into the tsunami models. The resulting grid data is relatively coarse in the deeper water and becomes progressively finer as the distance to Patong Bay decreases.
64
65The two minute arc grid data set, DBDB2, was obtained from US Naval Research Labs and used to approximate the bathymetry in the Bay of Bengal. This grid was further interpolated to a 27 second arc grid. In the Andaman Sea the DBDB2 data was replaced with a 3 second grid obtained from NOAA (REF?). Finally, a 1 second grid was used to approximate the bathymetry in Patong Bay and the immediately adjacent regions (FROM WHERE?). This elevation data was created from the digitised Thai Navy bathymetry chart, no 358. A visualisation of the elevation data set used in Patong bay is shown in Figure~\ref{fig:patong_bathymetry}. The continuous topography is an interpolation of known elevation measured at the coloured dots.
66
67\begin{figure}[ht]
68\begin{center}
69\includegraphics[width=8.0cm,keepaspectratio=true]{patong_bay_data.jpg}
70\caption{Visualisation of the elevation data set used in Patong Bay. FIXME: Can we generate a new picture with river included Preferably without the arrows and logo???}
71\label{fig:patong_bathymetry}
72\end{center}
73\end{figure}
74
75The sub-sampling of larger grids was performed by using {\bf resample} a GMT program (\cite{XXX}). The gridding of data was performed using {\bf Intrepid} a commercial geophysical processing package developed by Intrepid Geophysics. The gridding scheme employed the nearest neighbour algorithm followed by and application of minimum curvature akima spline smoothing. Details of the lineage of this dataset is outlined in the Appendix and the final dataset is available at XXXX.
76
77
78FIXME(Richard): Could you please look into these issues and also those in your appendix?
79
80\subsection{Tsunami source}\label{sec:source}
81
82David:
83
84The 2004 Indian Ocean tsunami was generated by severe coseismic displacement of the sea floor as a result of one of the largest earthquakes on record. The M$_w$=9.3 mega-thrust earthquake occurred on the 26 December 2004 at 0h58'53'' UTC approximately 70 km offshore North Sumatra. The disturbance propagated 1200-1300 km along the Sumatra-Andaman trench time at a rate of 2.5-3 km.s$^{-1}$ and lasted approximately 8-10 minutes~\cite{amnon05}.
85
86Many models of this earthquake are available~\cite{chlieh07,XXX}. Some are determined from various geological surveys of the site, others solve an inverse problem which calibrates the source based upon the tsunami wave signal and or runup. The source parameters used to simulate the 2004 Indian Ocean Tsunami were taken from Chlieh~\cite{chlieh07}. This model was created by inversion of the seismic data from GPS measurements and fits both coseismic, tsunami and GPS data in the Andaman Sea well. The resulting sea floor displacement ranges from about - 5.0 to 5.0 metres and is shown in Figure~\ref{fig:chlieh_slip_model}.
87
88\begin{figure}[ht]
89\begin{center}
90\includegraphics[width=5.0cm,keepaspectratio=true]{chlieh_slip_model.png}
91\caption{Location and magnitude of the sea floor displacement associated with the 2004 Indian Ocean tsunami. Source parameters from Chlieh et al.~\cite{chlieh07}}
92\label{fig:chlieh_slip_model}
93\end{center}
94\end{figure}
95
96\subsection{Validation data}
97 Eyewitness accounts detailed in~\cite{papadopoulos06} report that most people at Patong Beach observed an initial retreat of the shoreline of more than 100m followed a few minutes later by a strong wave (crest). Another less powerful wave arrived another five or ten minutes later. Eyewitness statments place the arrival time of the strong wave between 2 hours and 55 inutes to 3 hours and 5 minutes after the source rupture (09:55am to 10:05am local time). After the event (HOw long?) a survey mapped the maximum observed inundation at Patong beach.  The inundation map is shown in Figure~\ref{fig:patongescapemap} and was kindly provided by the Thai Department of Mineral Resources \protect \cite{XXX}.
98
99\begin{figure}[ht]
100\begin{center}
101\includegraphics[width=8.0cm,keepaspectratio=true]{patongescapemap.jpg}
102\caption{Tsunami survey mapping the maximum observed inundation at Patong beach courtesy of the Thai Department of Mineral Resources \protect \cite{XXX}.}
103\label{fig:patongescapemap}
104\end{center}
105\end{figure}
106
107FIXME(Richard): More information deailting construction of this map is needed here. Is more accurate information on arrival times of crests and depression available
108
109%================Section===========================
110\section{Verification Procedure}\label{sec:veri_procedure}
111Intro\\\\
112
113The following observations need to be matched by any numerical tsuanmi model:
114\begin{itemize}
115 \item Simulate a leading depression followed by two distinct crests of decreasing magnitude.
116 \item The arrival time of the first crest should arrive at Patong beach bewtween 2 hours and 55 inutes to 3 hours and 5 minutes after the intial rupture of the source. The subsequent crest arrive five to ten minutes later.
117 \item Simulated inundation in Patong bay should reproduce well the inundation map in Figure~\ref{fig:patongescapemap}.
118\end{itemize}
119
120
121\subsection{ANUGA}
122\textsc{Anuga} is an Open Source hydrodynamic inundation tool that solves the depth integrated nonlinear shallow water wave equations. The scheme used by \textsc{anuga}, first presented by Zoppou and Roberts~\cite{zoppou99}, is a high-resolution Godunov-type method that uses the rotational invariance property of the shallow water equations to transform the two-dimensional problem into local one-dimensional problems. These local Riemann problems are then solved using the semi-discrete central-upwind scheme of Kurganov et al.~\cite{kurganov01} for solving one-dimensional conservation equations. The numerical scheme is presented in detail in Zoppou and Roberts~\cite{zoppou99}, Zoppou and Roberts~\cite{zoppou00}, and Roberts and Zoppou~\cite{roberts00}, Nielsen et al.~\cite{nielsen05}. An important capability of the software is that it can model the process of wetting and drying as water enters and leaves an area. This means that it is suitable for simulating water flow onto a beach or dry land and around structures such as buildings. It is also capable of adequately resolving hydraulic jumps due to the ability of the finite-volume method to handle discontinuities. \textsc{Anuga} has been validated against a number of analytical solutions and the wave tank simulation of the 1993 Okushiri Island tsunami~\cite{roberts06,nielsen05}.
123
124\subsection{URSGA}
125\textsc{ursga} is a hydrodynamic code that models the propagation of the tsunami in deep water using the finite difference method to solve the depth integrated nonlinear shallow water equations in spherical co-ordinates with friction and Coriolis terms. The code is based on Satake~\cite{satake95} with significant modifications made by the URS corporation~\cite{thio07} and Geoscience Australia~\cite{burbidge07}. The tsunami is propagated via a staggered grid system. Coarse grids are used in the open ocean and the finest resolution grid is employed in the region of most interest. \textsc{Ursga} is not publicly available. FIXME: Check with David.
126
127
128\subsection{Tsunami Source and Propagation}
129The utility of the \textsc{ursga} model decreases with water depth unless an intricate sequence of nested grids is employed. In comparison \textsc{anuga} is designed to produce robust and accurate predictions of on-shore inundation in mind, but is less suitable for earthquake source modelling and large study areas. Consequently, the Geoscience Australia tsunami modelling methodology is based on a hybrid approach using models like \textsc{ursga} for tsunami generation and propagation up to a 100m depth contour. This information then forms a boundary condition for \textsc{anuga} and is propagated on shore to model the inundation. Specifically we use the \textsc{ursga} model to simulate the propagation of the 2004 Indian Ocean tsunami in the deep ocean, based on a discrete representation of the initial deformation of the sea floor, described in Section~\ref{sec:source}. The resulting tsunami was propagated over the entire Bay of Bengal and the wave signal measured along the 100m depth contour offshore Phuket, Thailand. The wave signal is then used as a time varying boundary condition for the \textsc{anuga} inundation simulation.
130
131???The \textsc{ursga} code is also capable of calculating inundation. CAN WE PRODUCE AN INUNDATION MAP OVER THE SAME AREA TO COMPARE WITH \textsc{anuga}???
132
133\subsection{Tsunami Inundation}\label{sec:inundation}
134In this case the interface betwen the \textsc{ursga} and \textsc{anuga} models was chosen to roughly follow the 100m depth contour along the west coast of Phuket Island. The computational domain is shown in Figure \ref{fig:computational_domain}
135\begin{figure}[ht]
136\begin{center}
137%\includegraphics[width=5.0cm,keepaspectratio=true]{new_domain.png}
138\includegraphics[width=5.0cm,keepaspectratio=true]{extent_of_ANUGA_model.jpg}
139\caption{Computational domain of the \textsc{anuga} simulation.}
140\label{fig:computational_domain}
141\end{center}
142\end{figure}
143
144The 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??).
145In \cite{schoettle2007} values of Manning's coefficient in the range 0.007 to 0.030 is suggested for tsunami propagation over a sandy sea floor.
146
147The boundary condition at each side of the domain towards the south and the north where no data was available was chosen as a transmissive boundary condition effectively replicating the time dependent wave height present just inside the computational domain. Momentum was set to zero. Other choices include applying the mean tide value as a Dirichlet type boundary condition but experiments as well as the result of the verification reported here showed that this approach tends to under estimate the tsunami impact due to the tempering of the wave near the side boundaries. FIXME(OLE): Should we include Nick's test example?
148
149%================Section===========================
150\section{Results}
151Maximum 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.
152
153An 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.
154
155
156FIXME: Take some of this commentary after final runs have been completed.
157FIXME: Also need a commentary on the dynamics of what is being observed and whether it aligns with eye witness observations.
158%The \textsc{anuga} simulation determines a region to be inundated if at some point in time it was covered by at least 1cm of water. This precision in field measurements is impossible to obtain. The inundation boundary is determined by observing water marks and other signs left by the receeding waters. The precision of the observed inundation map is, most likely, at least an order of magnitude worse than the \textsc{anuga} simulation. The simulated inundation based upon a 10cm threshold is shown in Figure~\ref{fig:inundationcomparison10cm}.
159
160Both the URS model and the \textsc{anuga} inundation model shows that the event comprises a train of waves some with preciding drawdown effects (ADD details of waveform with a graph from URL and a gauge from \textsc{anuga} and discuss).
161
162\begin{figure}[ht]
163\begin{center}
164\includegraphics[width=10.0cm,keepaspectratio=true]{Depth_small_transmissive_d0.jpg}
165\caption{Simulated inundation versus observed inundation}
166\label{fig:inundationcomparison1cm}
167\end{center}
168\end{figure}
169
170
171
172%================Section===========================
173
174\section{Conclusion}
175This 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.
176
177This paper also illustrates the effectiveness of the proposed new benchmark. The benchmark is used to test the veracity of the hydrodynamic \textsc{anuga} designed spcefically to model on-shore inundation. Very good agreement is obtained between the observed and simulated runup. The \textsc{ursga} tsunami package was also tested. Much worse results were obtained??
178
179
180%================Acknowledgement===================
181\section*{Acknowledgements}
182This 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.
183
184%====================Bibliography==================
185\bibliographystyle{plain}
186\bibliography{tsunami07}
187
188%===============Appendicies========================
189
190\section*{Appendix A. Figures and Tables}
191\label{sec:appendix}
192\subsection*{Datasets and gridding}
193
194This 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.
195
196
197FIXME: Is there a standard template for data lineage.
198
199\begin{verbatim} 
200E.g.
201Data Source:
2022 min: DBDB 2
2039 sec: NOAA
2043 sec: aontehusoe
205
206
207Process:
208  ...
209  ...
210  ...
211\end{verbatim} 
212 
213FIXME: Could we have a map with the nested data sets?
214
215
216
217
218
219Gridded data sets used:
220
221DBDB2 2 minute of arc grid from the US Naval Research Labs.
222This grid was also interpolated to 27 sec of arc and used in a nested grid scheme.
223
224Indian Ocean 27 sec of arc grid created by:
225Interpolating the DBDB2 2 minute of arc grid.
226In the region where the 9 sec grid sits the data was cut out and replaced by the 9 sec data.
227Any points that deviated from the general trend near the boundary were deleted.
228The data was then re-gridded.
229
230Andaman Sea 9 sec of arc grid created by:
231Sub-sampling the 3 sec of arc grid from NOAA.
232In the region where the 3 sec grid sits the data was cut out and replaced by the 3 sec data.
233Any points that deviated from the general trend near the boundary were deleted.
234The data was then re-gridded.
235
236Thailand off-shore 3 sec of arc grid created by:
237cropping 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.
238This grid was obtained from NOAA.
239In the region where the 1 sec grid sits the data was cut out and replaced by the 1 sec data.
240Any points that deviated from the general trend near the boundary were deleted.
241The data was then re-gridded.
242
243Patong Bay 1 second of arc grid created from:
244elevation data contained in a GIS of Patong Bay supplied by Niran Chaimanee, Geo-environment Sector Manager, CCOP T/S, Bangkok.
245Digitised Thai Navy bathymetry chart no 358.
246
247The sub-sampling of larger grids was performed by using {\bf resample}  a GMT program.
248The gridding of data was performed using {\bf Intrepid} a commercial geophysical processing package developed by Intrepid Geophysics.
249The gridding scheme was nearest neighbour followed by minimum curvature akima spline smoothing. See Figure~\ref{fig:nested_grids}.
250
251\begin{figure}[ht]
252\begin{center}
253\includegraphics[width=8.0cm,keepaspectratio=true]{nested_grids}
254\caption{Nested grids of elevation data.}
255\label{fig:nested_grids}
256\end{center}
257\end{figure}
258
259
260
261\subsection*{Earthquake Source Model}
262FIXME: Is this appendix needed?
263
264The earthquake source model of Chlieh was adopted to generate the tsunami simulation. This model was created by carefull inversion of the seismic
265data and fits both coseismic, tsunami and GPS data in the Andaman Sea well.
266
267\subsection*{Tsunami Propagation}
268FIXME: Is this appendix needed?
269
270To to generate and propagate the tsunami the URS code was used. This program solves the shallow water equations using the finite difference method.
271It can also be used in a nexted grid scheme and does on-shore inundation.
272
273%%%%%%%%%%%%%%%%%%%%%%%
274
275\end{document}
276
277
278Main source of uncertainty arises from inaccuracies in initial condition (source), inaccurate bathymetry data, to a lesser extent friction
279
280single 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.
281
282Expressions:
283sufficient verification/falsification of model
284Confidently utilise a model
285
286Predictive valdiation of only one aspect of model evaluation. Need to assess model explanation.
287
288Conservation of mass
289convergence
290
291spatial and temporal discretisation errors, round off errors due to limited numerical precision
292
293analytical benchmarking:
294ensuring equations are solved accurately
295single wave on a beach
296Solitary wave on composite beach
297subaerial landslide on simple beach
298
299Analytical 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.
300
301scale comparisions (laboratory benchmarking):
302Scale 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
303Single wave on a simple beacj
304Solitary wave on composite beach
305Conical island
306Monai Valley
307Landslide
308
309includes comparisons with validation data sets generated by other models of higher dimensionality and resolution.
310
311Often flow geometries are simplified
312
313
314Field benchmarking:
315Most important verification process
316Hydrodynamic inversion to predict the source is an ill posed problem
31712 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
31817 November 2003 Rat Islands Tsunami
319
320Construction 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.
321
322Movinf 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.
323
324Calibratino 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.
325
326verfication need to assess point data, spatially distributed data and bulk (lumped) data.
327
328Synolakis 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.
329
330
331inundation 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
332
333Notes:
334Okushiri 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.
335
336
337
338Rat Island tsuanmi provides a good test for real-time forecasting models since tsnumai was recorded at three tsunameters. The test requires matching the propagation model data with the recordings to constrain the tsunami source model. The inundation model is to reproduce the tide gauge record at Hilo.
339
340Patong Bay benchmark provides spatially distributed field data for comparison.
341
342single 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.
343
344DO I SAY WE HAVE MUX @ FILES DESCRIBING SHAPE OF WAVE YES. MAKES CONSISTENT
345
346Notes:  * Model source developed independently of inundation data.
347        * Patong region was chosen because high resolution inundation map and bathymetry and topography data was available there
348
349Geoscience Australia, in an open collaboration with the Mathematical Sciences Institute, The Australian National University, is developing a software application, \textsc{anuga}, to model the hydrodynamics of tsunamis, floods and storm surges. The open source software implements a finite volume central-upwind Godunov method to solve the non-linear depth-averaged shallow water wave equations. This paper investigates the veracity of \textsc{anuga}  when used to model tsunami inundation.  A particular aim was to make use of the comparatively large amount of observed data corresponding to the Indian ocean tsunmai event of December 2004, to provide a conditional assessment of the computational model's performance. Specifically a comparison is made between an inundation map, constructed from observed data, against modelled maximum inundation. This comparison shows that there is very good agreement between the simulated and observed values. The sensitivity of model results to the resolution of bathymetry data used in the model was also investigated. It was found that the performance of the model could be drastically improved by using finer bathymetric data which better captures local topographic features. The effects of two different source models was also explored.
350
351different 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
352
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422
423In \cite{papadopoulos06} eyewitness accounts report
424\emph{In Patong beach, most people observed at least two
425waves. It is likely that the leading wave described in both
426Sri Lanka and Maldives was not observed in Patong beach.
427What people said is that the first sea motion was a retreat
428of more than 100 m. A few minutes later the strong wave
429arrived. Then, after another 5 or 10 min. one more wave attacked
430but less violently than the first one. Nearly all the
431interviewed persons reported that the tsunami inundation
432in the Patong beach varied from 150 m to at least 750 m
433(Fig. 16). One eyewitness reported inundation of only 20
434m. As for the arrival time of the strong wave the eyewitnesses
435do not agree. However, most reports concentrated
436around 02:55 to 03:05 (09:55 to 10:05 local) which seems
437to be a reliable description.}
438
439FIXME(Ole): Need discussion of model results in this context.
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