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2% to be added when submitted to ocean dynamics
5%\journalname{Ocean Dynamics}
10\usepackage{url}      % for URLs and DOIs
15\title{Benchmarking Tsunami Models using the December 2004 Indian
16  Ocean Tsunami and its Impact at Patong Bay}
19\author{J.~D. Jakeman \and O. Nielsen \and K. VanPutten \and
20  D. Burbidge \and R. Mleczko \and N. Horspool}
22% to be added when submitted to ocean dynamics
23%\institute{J.~D. Jakeman \at
24%       The Australian National University, Canberra, \textsc{Australia}\
25%       \email{}
26%       \and
27%       O. Nielsen \and R. Mleczko \and D. Burbidge \and K. VanPutten \and N. Horspool \at
28%       Geoscience Australia, Canberra, \textsc{Australia}
32%================Start of Document================
37This paper proposes a new benchmark for tsunami model validation.
38The benchmark is based upon the 2004 Indian Ocean tsunami,
39which affords a uniquely large amount of observational data for events of this kind.
40Unlike the small number of existing benchmarks, the
41proposed test validates all three stages of tsunami evolution -
42generation (FIXME (Jane): really?), propagation and inundation. Specifically we use geodetic
43measurements of the Sumatra--Andaman earthquake to validate the
44tsunami source, altimetry data from the \textsc{jason} satellite to
45test open ocean propagation, eye-witness accounts to assess near shore
46propagation and a detailed inundation survey of Patong city, Thailand
47to compare model and observed inundation. Furthermore we utilise this
48benchmark to further validate the hydrodynamic modelling tool
49\textsc{anuga} which is used to simulate the tsunami
50inundation. Important buildings and other structures were incorporated
51into the underlying computational mesh and shown to have a large
52influence on inundation extent. Sensitivity analysis also showed that
53the model predictions are comparatively insensitive to large changes
54in friction and small perturbations in wave weight at the 100 m depth
56% to be added when submitted to ocean dynamics
57%\keywords{Tsunami \and modelling \and validation and verification \and benchmark}
64Tsunami is a potential hazard to coastal communities all over the
65world. A number of recent large events have increased community and
66scientific awareness of the need for effective detection, forecasting,
67and emergency preparedness. Probabilistic, geophysical and hydrodynamic
68models are required to predict the location and
69likelihood of an event, the initial sea floor deformation and
70subsequent propagation and inundation of the tsunami. Engineering, economic and social vulnerability models can then be used to estimate the
71impact of the event as well as the effectiveness of hazard mitigation
72procedures. In this paper, we focus on modelling of
73the physical processes only.
75Various approaches are currently used to assess the potential tsunami
76inundation of coastal communities.
77These methods differ in both the formulation used to
78describe the evolution of the tsunami and the numerical methods used
79to solve the governing equations. However any legitimate model must
80address each of the three distinct stages of tsunami evolution---
81generation, propagation and inundation. Models combining observed seismic,
82geodetic and sometimes tsunami data must be used
83to provide estimates of initial sea floor and ocean surface
84deformation. The complexity of these models ranges from empirical to
85non-linear three-dimensional mechanical models. The shallow water wave
86equations, linearised shallow water wave equations, and
87Boussinesq-type equations are frequently used to simulate tsunami
88propagation. These models are typically used to predict quantities
89such as arrival times, wave speeds and heights, and inundation extents
90which are used to develop efficient hazard mitigation plans.
92Inaccuracies in model prediction can result in inappropriate
93evacuation plans and town zoning, which may result in loss of life and
94large financial losses. Consequently tsunami models must undergo
95sufficient end-to-end testing to increase scientific and community
96confidence in the model predictions.
98Complete confidence in a model of a physical system cannot be
99established.  One can only hope to state under what conditions and to what extent the
100model hypothesis holds true. Specifically the utility of a model can
101be assessed through a process of verification and
102validation. Verification assesses the accuracy of the numerical method
103used to solve the governing equations and validation is used to
104investigate whether the model adequately represents the physical
105system~\cite{bates01}. Together these processes can be used to
106establish the likelihood that a model represents a legitimate
109The sources of data used to validate and verify a model can be
110separated into three main categories: analytical solutions, scale
111experiments and field measurements. Analytical solutions of the
112governing equations of a model, if available, provide the best means
113of verifying any numerical model. However, analytical solutions are
114frequently limited to a small set of idealised examples that do not
115completely capture the more complex behaviour of `real' events. Scale
116experiments, typically in the form of wave-tank experiments, provide a
117much more realistic source of data that better captures the complex
118dynamics of flows such as those generated by a tsunami, whilst allowing
119control of the event and much easier and accurate measurement of the
120tsunami properties. Comparison of numerical predictions with field
121data provides the most stringent test. The use of field data increases
122the generality and significance of conclusions made regarding model
123utility. On the other hand, it must be noted that the use of field
124data also significantly increases the uncertainty of the validation
125experiment that may constrain the ability to make unequivocal
127FIXME (Jane): Why would that increase the uncertainty?
128FIXME (Phil): references to all of the paragraph above, please
130Currently, the extent of tsunami-related field data is limited. The
131cost of tsunami monitoring programs, bathymetry and topography surveys
132prohibits the collection of data in many of the regions in which
133tsunamis pose greatest threat. The resulting lack of data has limited
134the number of field data sets available to validate tsunami
137Synolakis et al~\cite{synolakis07} have developed a set of
138standards, criteria and procedures for evaluating numerical models of
139tsunami. They propose three analytical solutions to help identify the
140validity of a model, and five scale comparisons (wave-tank benchmarks)
141and two field events to assess model veracity.
143The first field data benchmark introduced in \cite{synolakis07} compares model
144results against observed data from the Hokkaido-Nansei-Oki tsunami
145that occurred around Okushiri Island, Japan on the 12 July
1461993. This tsunami provides an example of extreme run-up generated from
147reflections and constructive interference resulting from local
148topography and bathymetry. The benchmark consists of two tide gauge
149records and numerous spatially-distributed point sites at which
150modelled maximum run-up elevations can be compared. The second
151benchmark is based upon the Rat Islands tsunami that occurred off the
152coast of Alaska on the 17 November 2003. The Rat Island tsunami
153provides a good test for real-time forecasting models since the tsunami
154was recorded at three tsunameters. The test requires matching the
155tsunami propagation model output with the DART recording to constrain the
156tsunami source model, and then using it to reproduce the tide gauge
157record at Hilo, Hawaii.
158FIXME (Jane): Are the tsunameters and the DART recordings the same thing?
160In this paper we develop a field data benchmark to be used in
161conjunction with the other tests proposed by Synolakis et
162al~\cite{synolakis07} to validate and verify tsunami models.
163The benchmark proposed here allows evaluation of
164model structure during all three distinct stages tsunami evolution.
165It consists of geodetic measurements of the
166Sumatra--Andaman earthquake that are used to validate the description
167of the tsunami source, altimetry data from the \textsc{jason} satellite to test
168open ocean propagation, eye-witness accounts to assess near shore
169propagation, and a detailed inundation survey of Patong city, Thailand
170to compare model and observed inundation. A description of the data
171required to construct the benchmark is given in
174An associated aim of this paper is to illustrate the use of this new
175benchmark to validate a dedicated inundation model called
176\textsc{anuga} used by Geoscience Australia. A description of
177\textsc{anuga} is given in Section~\ref{sec:models} and the validation
178results are given in Section~\ref{sec:results}.
180The numerical models used to simulate tsunami impact
181are computationally intensive and high resolution models of the entire
182evolution process will often take a number of days to
183run. Consequently, the uncertainty in model predictions is difficult to
184quantify as it would require a very large number of runs.
185However, model uncertainty should not be ignored. Section
186~\ref{sec:sensitivity} provides a simple analysis that can
187be used to investigate the sensitivity of model predictions to model
192The sheer magnitude of the 2004 Sumatra-Andaman earthquake and the
193devastation caused by the subsequent tsunami have generated much
194scientific interest. As a result an unusually large amount of post
195seismic data has been collected and documented. Data sets from
196seismometers, tide gauges, \textsc{gps} surveys, satellite overpasses,
197subsequent coastal field surveys of run-up and flooding, and
198measurements of coseismic displacements as well as bathymetry from ship-based
199expeditions, have now been made
200available. %~\cite{vigny05,amnon05,kawata05,liu05}. FIXME (Ole): Refs? 
202In this section we present the corresponding data necessary to implement
203the proposed benchmark for each of the three stages of the tsunami's evolution.
206All tsunami are generated from an initial disturbance of the ocean
207which develops into a low frequency wave that propagates outwards from
208the source. The initial deformation of the water surface is most
209commonly caused by coseismic displacement of the sea floor, but
210submarine mass failures, landslides, volcanoes or asteroids can also
211cause tsunami. In this section we detail the information used in
212this study to validate models of the sea floor deformation generated
213by the 2004 Sumatra--Andaman earthquake.
215The 2004 Sumatra--Andaman tsunami was generated by a coseismic
216displacement of the sea floor resulting from one of the largest
217earthquakes on record. The mega-thrust earthquake started on the 26
218December 2004 at 0h58'53'' UTC (or just before 8 am local time)
219approximately 70 km offshore of North Sumatra
220(\url{}). The
221rupture propagated 1000-1300 km along the Sumatra-Andaman trench to
222the north at a rate of 2.5-3 km.s$^{-1}$ and lasted approximately 8-10
223minutes~\cite{ammon05}. Estimates of the moment magnitude of this
224event range from about 9.1 to 9.3 $M_w$~\cite{chlieh07,stein07}.
226The unusually large surface deformation caused by this earthquake
227means that there were a range of different geodetic measurements of
228the surface deformation available. These include field measurements of
229uplifted or subsided coral heads, continuous or campaign \textsc{GPS}
230measurements and remote sensing measurements of uplift or subsidence
231(see~\cite{chlieh07} and references therein). Here we use the the near-field
232estimates of vertical deformation in northwestern Sumatra and
233the Nicobar-Andaman islands collated by~\cite{chlieh07} to validate
234that our crustal deformation model of the 2004 Sumatra--Andaman
235earthquake is producing reasonable results. Note that the geodetic
236data used here is a combination of the vertical deformation that
237happened in the $\sim$10 minutes of the earthquake plus the
238deformation that followed in the days following the earthquake before
239each particular measurement was actually made (typically of order
240days). Therefore some of the observations may not contain the purely
241co-seismic deformation but could include some post-seismic deformation
242as well~\cite{chlieh07}.
244%DAVID: I commented out the figure since we can combine it with the model result without obscuring it. That will keep the number of figures down.
249%\caption{Near field geodetic measurements used to validate tsunami generation. FIXME: Insert appropriate figure here}
255\label{sec:propagation data}
256Once generated, a tsunami will propagate outwards from the source until
257it encounters the shallow water bordering coastal regions.
258FIXME (Ole): Need to change this definition. I believe propagation takes place all the way to the shore line and not just up to shallow waters.
260This period
261of the tsunami evolution is referred to as the propagation stage. The
262height and velocity of the tsunami is dependent on the local
263bathymetry in the regions through which the wave travels and the size
264of the initial wave. This section details the bathymetry data needed
265to model the tsunami propagation and the satellite altimetry transects
266used here to validate open ocean tsunami models.
268\subsubsection{Bathymetry Data}
269The bathymetry data used in this study was derived from the following
272\item a two arc minute grid data set covering the Bay of Bengal,
273  DBDB2, obtained from US Naval Research Labs;
274\item a 3 second arc grid covering the whole of the Andaman Sea based
275  on Thai Navy charts no. 45 and no. 362; and
276\item a one second grid created from the digitised Thai Navy
277  bathymetry chart, no. 358, which covers Patong Bay and the
278  immediately adjacent regions.
279  (FIXME (Ole): How was the grid created from these digitised points?) RICHARD
281FIXME (Jane): Refs for all these. RICHARD
283%A number of raw data sets were obtained, analysed and checked for
284%quality and subsequently gridded for easier visualisation and input
285%into the tsunami models.
287These sets were combined via
288interpolation and resampling to produce four nested grids
289which are relatively coarse in the deeper water and
290progressively finer as the distance to
291Patong Beach decreases as shown in Figure~\ref{fig:nested_grids}
293The coarsest
294bathymetry was obtained by interpolating the DBDB2 grid to a 27 second
295arc grid. A subsection of this region was then replaced by nine second
296data which was generated by sub-sampling the three second of arc grid from
297NOAA (FIXME (Jane): This was not mentioned in the dots above). RICHARD
299A subset of the nine second grid was replaced by the three second
300data. Finally, the one second grid was used to approximate the
301bathymetry in Patong Bay and the immediately adjacent regions. Any
302points that deviated from the general trend near the boundary were
303deleted as a quality check.
305The sub-sampling of larger grids was performed by using {\bf resample},
306a Generic Mapping Tools (\textsc{GMT}) program (\cite{wessel98}). The
307gridding of data was performed using {\bf Intrepid}, a commercial
308geophysical processing package developed by Intrepid Geophysics. The
309gridding scheme employed the nearest neighbour algorithm followed by
310an application of minimum curvature akima spline smoothing.
311See \url{} 
312for details on the Intrepid model.
318\caption{Nested bathymetry grids.}
323\subsubsection{JASON Satellite Altimetry}\label{sec:data_jason}
324During the 26 December 2004 event, the \textsc{jason} satellite tracked from
325north to south and over the equator at 02:55 UTC nearly two hours
326after the earthquake \cite{gower05}. The satellite recorded the sea
327level anomaly compared to the average sea level from its previous five
328passes over the same region in the 20-30 days prior. This data was
329used to validate the propagation stage in Section
331FIXME (Ole): See Phil's second point and email with help from David
334%DB I suggest we combine with model data to reduce the number of figures. The satellite track is shown in Figure~\ref{fig:satelliteTrack}.
339%\caption{URS wave heights 120 minutes after the initial earthquake with the JASON satellite track and its observed sea level anomalies overlaid. Note the URS data has not been corrected for the flight path time. FIXME: should we just have track and not URS heights.}
347%\caption{JASON satellite altimetry seal level anomaly. FIXME: should we include figure here with just JASON altimetry.}
352%FIXME: Can we compare the urs model against the TOPEX-poseidon satellite as well? DB No (we don't have the data currently).
355\label{sec:inundation data}
356FIXME (Ole): Technically propagation covers everything up to
357the coastline and inundation everything on-shore.
358This means that ANUGA covers the final part of the propagation and the inundation part. Should we adopt this distiction throughout the paper?
360Inundation refers to the final stages of the evolution of a tsunami and
361covers the propagation of the tsunami in coastal waters and the
362subsequent run-up onto land. This process is typically the most
363difficult of the three stages to model due to thin layers of water
364flowing rapidly over dry land.  Aside from requiring robust solvers
365which can simulate such complex flow patterns, this part of the
366modelling process also requires high resolution and quality elevation
367data which is often not available. In the case of model validation
368high quality field measurements are also required. For the proposed
369benchmark a high resolution bathymetry (FIXME (Ole): Bathymetry ? - RICHARD) and
370topography data set and a high quality inundation survey map from the
371Coordinating Committee Co-ordinating Committee for Geoscience Programmes
372in East and Southeast Asia (CCOP) (\cite{szczucinski06}) was obtained
373to validate model inundation. See also acknowledgements at the end of this paper.
375In this section we also present eye-witness accounts which can be used
376to qualitatively validate tsunami inundation.
378\subsubsection{Topography Data}
379A one second grid was used to approximate the topography in Patong
380Bay. This elevation data was again created from the digitised Thai
381Navy bathymetry chart, no 358.
382FIXME (Ole): I don't think so. The Navy chart is only offshore. RICHARD
384 A visualisation of the elevation data
385set used in Patong Bay is shown in
386Figure~\ref{fig:patong_bathymetry}. The continuous topography
387(FIXME(Jane): What is meant by this?) is an
388interpolation of known elevation measured at the coloured dots. FIXME RICHARD
393\caption{3D visualisation of the elevation data set used in Patong Bay showing data points, contours, rivers and roads draped over the final model.}
397FIXME (Jane): legend? Were the contours derived from the final dataset?
398This is not the entire model, only the bay and the beach. RICHARD
400\subsubsection{Buildings and Other Structures}
401Human-made buildings and structures can significantly affect tsunami
402inundation. The footprint and number of floors of the
403buildings in Patong Bay were extracted from a GIS data set which was also provided by the CCOP (see Section \ref{sec:inundation data} for details).
404The heights of these
405buildings were estimated assuming that each floor has a height of 3 m and they
406were added to the topographic dataset.
408\subsubsection{Inundation Survey}
409Tsunami run-up in built-up areas can be the cause of large financial and human
410losses, yet run-up data that can be used to validate model run-up
411predictions is scarce because such events are relatively infrequent.
412Of the two field benchmarks proposed
414only the Okushiri benchmark facilitates comparison between
415modelled and observed run-up. One of the major strengths of the
416benchmark proposed here is that modelled run-up can be compared to an
417inundation survey which maps the maximum run-up along an entire coastline
418rather than at a series of discrete sites. The survey map is
419shown in Figure~\ref{fig:patongescapemap} and plots the maximum run-up
420of the 2004 Indian Ocean tsunami in Patong city. Refer to Szczucinski et
421al~\cite{szczucinski06} for further details.
427\caption{Tsunami survey mapping the maximum observed inundation at
428  Patong beach courtesy of the CCOP \protect \cite{szczucinski06}.}
434\subsubsection{Eyewitness Accounts}\label{sec:eyewitness data}
435Eyewitness accounts detailed in~\cite{papadopoulos06}
436report that many people at Patong Beach observed an initial
437retreat (trough or draw down) of
438the shoreline of more than 100 m followed a few minutes later by a
439strong wave (crest). Another less powerful wave arrived another five
440or ten minutes later. Eyewitness statements place the arrival time of
441the first wave between 9:55 am and 10:05 am local time or about 2 hours
442after the source rupture.
443FIXME (Ole): We should add observed arrival time and later relate that to
444the modelled dynamics. Wait for Drew's updated animation.
450\caption{Location of timeseries extracted from the model output.}
459Two videos were sourced\footnote{The footage is
460widely available and can for example be obtained from
462(Comfort Hotel) and
466which include footage of the tsunami in Patong Bay on the day
467of the 2004 Indian Ocean Tsunami. Both videos show an already inundated
468group of buildings. They also show what is to be assumed as the second
469and third waves approaching and further flooding of the buildings and
470street.  The first video is in the very north, filmed from what is
471believed to be the roof of the Novotel Hotel marked ``north'' in Figure
472\ref{fig:gauge_locations}. The second video is in the very south,
473filmed from the second story of a building next door to the Comfort
474Resort near the corner of Ruam Chai St and Thaweewong Road.  This
475location is marked ``south'' in Figure \ref{fig:gauge_locations}.
476Figure~\ref{fig:video_flow} shows stills from this video. Both videos
477were used to estimate flow speeds and inundation depths over time.
485\caption{Four frames from a video where flow rate could be estimated,
486  circle indicates tracked debris, from top left: 0.0 sec, 5.0 s, 7.1
487  s, 7.6 s.}
492Flow rates were estimated using landmarks found in both videos and
493were found to be in the range of 5 to 7 metres per second (+/- 2 m/s)
494in the north and 0.5 to 2 metres per second (+/- 1 m/s) in the south.
495FIXME (Jane): How were these error bounds derived? RICHARD
496Water depths could also
497be estimated from the videos by the level at which water rose up the
498sides of buildings such as shops. Our estimates are in the order of
4991.5 to 2.0 metres (+/- 0.5 m).
500Fritz ~\cite{fritz06} performed a detailed
501analysis of video frames taken around Banda Aceh and arrived at flow
502speeds in the range of 2 to 5 m/s.
505\subsection{Validation Check-List}
507The data described in this section can be used to construct a
508benchmark to validate all three stages of the evolution of a
509tsunami. In particular we propose that a legitimate tsunami model
510should reproduce the following behaviour:
512 \item reproduce the vertical deformation observed in north-western
513   Sumatra and along the Nicobar--Andaman islands (see
514   Section~\ref{sec:gen_data}),
515 \item reproduce the \textsc{jason} satellite altimetry sea surface
516   anomalies (see Section~\ref{sec:data_jason}),
517 \item reproduce the inundation survey map in Patong city
518   (Figure~\ref{fig:patongescapemap}),
519 \item simulate a leading depression followed by two distinct crests
520   of decreasing magnitude at the beach, and
521 \item predict the water depths and flow speeds, at the locations of
522   the eye-witness videos, that fall within the bounds obtained from
523   the videos.
526Ideally, the model should also be compared to measured timeseries of
527waveheights and velocities but the authors are not aware of the
528availability of such data near Patong Bay.
533\section{Modelling the Event}\label{sec:models}
534Numerous models are currently used to model and predict tsunami
535generation, propagation and run-up~\cite{titov97a,satake95}. Here we
536introduce the three part modelling methodology employed by Geoscience Australia
537to illustrate the utility of the proposed benchmark.
540FIXME (Ole and Jane): Does this need to be so long?
542There are various approaches to modelling the expected crustal
543deformation from an earthquake. Most approaches model the
544earthquake as a dislocation in a linear elastic medium. Here we use
545the method of Wang et al~\cite{wang03}. One of the main advantages
546of their method is that it allows the dislocation to be located in a
547stratified linear elastic half-space with an arbitrary number of
548layers. Other methods (such as those based on Okada's equations) can
549only model the dislocation in a homogeneous elastic half space, or can
550only include a limited number of layers, and thus cannot model the
551effect of the depth dependence of the elasticity of the
552Earth~\cite{wang03}. The original versions of the codes described here
553are available from \url{}. The
554first program, \textsc{edgrn}, calculates elastic Green's function for
555a set of point sources at a regular set of depths out to a specified
556distance. The equations controlling the deformation are solved by
557using a combination of Hankel's transform and Wang et al's
558implementation of the Thomson-Haskell propagator
559algorithm~\cite{wang03}. Once the Green's functions are calculated
560a slightly modified version of \textsc{edcmp}\footnote{For this study,
561we have made minor modifications
562to \textsc{edcmp} in order for it to provide output in a file format
563compatible with the propagation code in the following section. Otherwise it
564is similar to the original code.} is used to calculate the sea
565floor deformation for a specific subfault. This second code
566discretises the subfault into a set of unit sources and sums the
567elastic Green's functions calculated from \textsc{edgrn} for all the
568unit sources on the fault plane in order to calculate the final static
569deformation caused by a two dimensional dislocation along the
570subfault. This step is possible because of the linearity of the
571governing equations.
573In order to calculate the crustal deformation using these codes
574a model that describes the variation in elastic
575properties with depth and a slip model of the earthquake to describe
576the dislocation is required.
577The elastic parameters used for this study are the
578same as those in Table 2 of Burbidge et al~\cite{burbidge08}. For the slip
579model, there are many possible models for the 2004 Andaman--Sumatran
580earthquake to select from
581~\cite{chlieh07,asavanant08,arcas06,grilli07,ioualalen07}. Some are
582determined from various geological surveys of the site. Others solve
583an inverse problem which calibrates the source based upon the tsunami
584wave signal, the seismic signal and/or even the run-up.
585The source
586parameters used here to simulate the 2004 Indian Ocean tsunami were
587taken from the slip model G-M9.15 of Chlieh
588et al~\cite{chlieh07}. This model was created by inversion of wide
589range of geodetic and seismic data. The slip model consists of 686
59020km x 20km subsegments each with a different slip, strike and dip
591angle. The dip subfaults go from $17.5^0$ in the north and $12^0$ in
592the south. Refer to Chlieh et al~\cite{chlieh07} for a detailed
593discussion of this model and its derivation. Note that the geodetic
594data used in the validation was also included by~\cite{chlieh07} in
595the inversion used to find G-M9.15. Thus the validation is not
596completely independent. However, a reasonable validation would still
597show that the crustal deformation and elastic properties model used
598here is at least as valid as the one used by Chlieh
599et al~\cite{chlieh07} and can reproduce the observations just as
603The \textsc{ursga} model described below was used to simulate the
604propagation of the 2004 Indian Ocean tsunami across the open ocean, based on a
605discrete representation of the initial deformation of the sea floor, as
606described in Section~\ref{sec:modelGeneration}. For the models shown
607here, the uplift is assumed to be instantaneous and creates a wave of
608the same size and amplitude as the co-seismic sea floor deformation.
611\textsc{ursga} is a hydrodynamic code that models the propagation of
612the tsunami in deep water using a finite difference method on a staggered grid.
613It solves the depth integrated linear or nonlinear shallow water equations in
614spherical co-ordinates with friction and Coriolis terms. The code is
615based on Satake~\cite{satake95} with significant modifications made by
616the \textsc{urs} corporation, Thio et al~\cite{thio08} and Geoscience
617Australia, Burbidge et al~\cite{burbidge08}.
618The tsunami was propagated via the nested
619grid system described in Section \ref{sec:propagation data} where
620the coarse grids were used in the open ocean and the finest
621resolution grid was employed in the region closest to Patong bay.
622\textsc{Ursga} is not publicly available.
625The utility of the \textsc{ursga} model decreases with water depth
626unless an intricate sequence of nested grids is employed. In
627comparison \textsc{anuga}, described below, is designed to produce
628robust and accurate predictions of on-shore inundation, but is less
629suitable for earthquake source modelling and large study areas because
630it is based on projected spatial coordinates. Consequently, the
631Geoscience Australia tsunami modelling methodology is based on a
632hybrid approach using models like \textsc{ursga} for tsunami
633propagation up to an offshore depth contour, typically 100 m.
634%Specifically we use the \textsc{ursga} model to simulate the
635%propagation of the 2004 Indian Ocean tsunami in the deep ocean, based
636%on a discrete representation of the initial deformation of the sea
637%floor, described in Section~\ref{sec:modelGeneration}.
638The wave signal and the velocity field is then used as a
639time varying boundary condition for
640the \textsc{anuga} inundation simulation.
641% A description of \textsc{anuga} is the following section.
644\textsc{Anuga} is a Free and Open Source hydrodynamic inundation tool that
645solves the conserved form of the depth-integrated nonlinear shallow
646water wave equations using a Finite-Volume scheme on an
647unstructured triangular mesh.
648The scheme, first
649presented by Zoppou and Roberts~\cite{zoppou99}, is a high-resolution
650Godunov-type method that uses the rotational invariance property of
651the shallow water equations to transform the two-dimensional problem
652into local one-dimensional problems. These local Riemann problems are
653then solved using the semi-discrete central-upwind scheme of Kurganov
654et al~\cite{kurganov01} for solving one-dimensional conservation
655equations. The numerical scheme is presented in detail in
656Roberts and Zoppou~\cite{zoppou00,roberts00} and
657Nielsen et al~\cite{nielsen05}. An important capability of the
658finite-volume scheme is that discontinuities in all conserved quantities
659are allowed at every edge in the mesh. This means that the tool is
660well suited to adequately resolving hydraulic jumps, transcritical flows and
661the process of wetting and drying. This means that \textsc{Anuga} 
662is suitable for
663simulating water flow onto a beach or dry land and around structures
664such as buildings. \textsc{Anuga} has been validated against
665%a number of analytical solutions and 
666%FIXME (Ole): Analytical solutions have not been published. Ask Steve.
667the wave tank simulation of the 1993 Okushiri
668Island tsunami~\cite{nielsen05,roberts06}.
669FIXME (Ole): Add reference to Tom Baldock's Dam Break valiadation of ANUGA.
674This section presents a validation of the modelling practice of Geoscience
675Australia against the new proposed benchmarks. The criteria outlined
676in Section~\ref{sec:checkList} are addressed for each of the three stages
677of tsunami evolution.
680The location and magnitude of the sea floor displacement associated
681with the 2004 Sumatra--Andaman tsunami calculated from the G-M9.15
682model of~\cite{chlieh07} is shown in
683Figure~\ref{fig:surface_deformation}. The magnitude of the sea floor
684displacement ranges from about $-3.0$ to $5.0$ metres. The region near
685the fault is predicted to uplift, while that further away from the
686fault subsides. Also shown in Figure~\ref{fig:surface_deformation} are
687the areas that were observed to uplift (arrows pointing up) or subside
688(arrows point down) during and immediately after the earthquake. Most
689of this data comes from uplifted or subsided coral heads. The length of
690the vector increases with the magnitude of the displacement; the length
691corresponding to 1 m of observed motion is shown in the top right
692corner of the figure. As can be seen, the source model detailed in
693Section~\ref{sec:modelGeneration} produces a crustal deformation that
694matches the vertical displacements in the Nicobar-Andaman islands and
695Sumatra very well. Uplifted regions are close to the fault and
696subsided regions are further away. The crosses on
697Figure~\ref{fig:surface_deformation} show estimates of the pivot line
698from the remote sensing data~\cite{chlieh07} and they follow the
699predicted pivot line quite accurately. The average difference between
700the observed motion and the predicted motion (including the pivot line
701points) is only 0.06 m, well below the typical error of the
702observations of between 0.25 and 1.0 m. However, the occasional point
703has quite a large error (over 1 m); for example a couple of
704uplifted/subsided points appear to be on a wrong
705(FIXME (Jane): This is incorrect) side of the predicted
706pivot line~\ref{fig:surface_deformation}. The excellence of the fit is
707not surprising, since the original slip model was chosen
708by~\cite{chlieh07} to fit this (and the seismic data) well.
709This does demonstrate, however, that \textsc{edgrn} and our modified version of
710\textsc{edstat} (FIXME(Jane): This has never been mentioned before)
711can reproduce the correct pattern of vertical
712deformation very well when the slip distribution is well constrained
713and when reasonable values for the elastic properties are used.
719\caption{Location and magnitude of the vertical component of the sea
720  floor displacement associated with the 2004 Indian Ocean tsunami
721  based on the slip model, G-M9.15. The black arrows which point up
722  show areas observed to uplift during and immediately after the
723  earthquake; those pointing down are locations which subsided. The
724  length of the arrow increases with the magnitude of the deformation. The arrow
725  length corresponding to 1 m of deformation is shown in the top right
726  hand corner of the figure. The cross marks show the location of
727  the pivot line (the region between the uplift and subsided region
728  where the uplift is zero) derived from remote sensing
729  (FIXME(Jane): How was that possible?). All the
730  observational data are from the dataset collated
731  by~\cite{chlieh07}.}
737The deformation results described in Section~\ref{sec:modelGeneration}
738were used to provide a profile of the initial ocean surface
739displacement. This wave was used as an initial condition for
740\textsc{ursga} and was propagated throughout the Bay of Bengal. The
741rectangular computational domain of the largest grid extended from
74290$^0$ to 100$^0$ East and 0 to 15$^0$ North and contained
7431335$\times$1996 finite difference points. Inside this grid, a nested
744sequence of grids was used. The grid resolution of the nested grids
745went from 27 arc seconds in the coarsest grid, down to nine arc seconds
746in the second grid, three arc seconds in the third grid and finally one arc
747second in the finest grid near Patong. The computational domain is
748shown in Figure~\ref{fig:computational_domain}.
750FIXME (Ole): I know that a nested ursga model was trialled for the
751end-to-end modelling. However, for the study done here, where models
752were coupled, I didn't think nested grids were used with URSGA -
753and certainly not down to 1 arc second. Can someone shed some light
754on this please? RICHARD
759\caption{Computational domain of the \textsc{ursga} simulation (inset: white and black squares and main: black square) and the \textsc{anuga} simulation (main and inset: red polygon).}
765Figure \ref{fig:jasonComparison} provides a comparison of the
766\textsc{ursga}-predicted sea surface elevation with the \textsc{jason}
767satellite altimetry data. The \textsc{ursga} model replicates the
768amplitude and timing of the the wave observed at $2.5^0$ South,
769but underestimates the amplitude of the wave further to the south at
770$4^0$ South. In the model, the southern most of these two waves
771appears only as a small bump in the cross section of the model (shown
772in Figure~\ref{fig:jasonComparison}) instead of being a distinct peak
773as can be seen in the satellite data. Also note
774that the \textsc{ursga} model prediction of the ocean surface
775elevation becomes out of phase with the \textsc{jason} 
776data at $3^0$ to $7^0$ North
777latitude. Chlieh et al~\cite{chlieh07} also observed these misfits and
778suggest it is caused by a reflected wave from the Aceh Peninsula that
779is not resolved in the model due to insufficient resolution of the
780computational mesh and bathymetry data. This is also a limitation of
781the model presented here which could be improved by nesting
782grids near Aceh.
787\caption{Comparison of the \textsc{ursga}-predicted surface elevation
788  with the \textsc{jason} satellite altimetry data. The \textsc{ursga} wave
789  heights have been corrected for the time the satellite passed
790  overhead compared to \textsc{jason} sea level anomaly.}
794FIXME (Jane): This graph does not look nice. The legend URS Model should
795be URSGA model.
798After propagating the tsunami in the open ocean using \textsc{ursga},
799the approximated ocean and surface elevation and horisontal flow
800velocities were extracted and used to construct a boundary condition
801for the \textsc{anuga} model. The interface between the \textsc{ursga}
802and \textsc{anuga} models was chosen to roughly follow the 100~m depth
803contour along the west coast of Phuket Island. The computational
804domain is shown in Figure~\ref{fig:computational_domain}.
806The domain was discretised into 386,338 triangles. The resolution of
807the grid was increased in regions inside the bay and on-shore to
808efficiently increase the simulation accuracy for the impact area.
809The grid resolution ranged between a
810maximum triangle area of $1\times 10^5$ m$^2$ 
811(corresponding to approximately 440 m between mesh points)
812near the western ocean
813boundary to $20$ m$^2$ (corresponding to
814approximately 6 m between mesh points)
815in the small regions surrounding the inundation
816region in Patong Bay. The coarse resolution was chosen to be
817commensurate with the model output from the \textsc{ursga} model
818(FIXME - this has to be clearly stated in ursga section) RICHARD
819while the latter was chosen to match the available resolution of topographic
820data and building data in Patong city.
821Due to a lack of available roughness data, friction was
822set to a constant throughout the computational domain. For the
823reference simulation, a Manning's coefficient of 0.01 was chosen to
824represent a small resistance to the water flow. See Section
825\ref{sec:friction sensitivity} for details on model sensitivity to
826this parameter.
829The boundary condition at each side of the domain towards the south
830and the north where no information about the incident wave or
831its velocity field is available
832was chosen as a transmissive
833boundary condition, effectively replicating the time dependent wave
834height present just inside the computational domain.
835The velocity field on these boundaries was set
836to zero. Other choices include applying the mean tide value as a
837Dirichlet boundary condition. But experiments as well as the
838result of the verification reported here showed that this approach
839tends to underestimate the tsunami impact due to the tempering of the
840wave near the side boundaries, whereas the transmissive boundary
841condition robustly preserves the wave.
843During the \textsc{anuga} simulation the tide was kept constant at
844$0.80$ m. This value was chosen to correspond to the tidal height
845specified by the Thai Navy tide charts
846(\url{}) at the time the tsunami arrived
847at Patong Bay. Although the tsunami propagated for approximately three
848hours before it reach Patong Bay, the period of time during which the
849wave propagated through the \textsc{anuga} domain is much
850smaller. Consequently the assumption of constant tide height is
853Maximum onshore inundation depth was computed from the model
854throughout the entire Patong Bay region and used to generate
855a measure of the inundated area.
856Figure~\ref{fig:inundationcomparison1cm} (left) shows very good
857agreement between the measured and simulated inundation. However
858these results are dependent on the classification used to determine
859whether a region in the numerical simulation was inundated. In
860Figure~\ref{fig:inundationcomparison1cm} (left) a point in the computational
861domain was deemed inundated if at some point in time it was covered by
862at least 1 cm of water. However, the precision of the inundation boundary
863generated by the on-site survey is most likely less than that as it
864was determined by observing water marks and other signs
865left by the receding waters. Consequently the measurement error along
866the inundation boundary of the survey is likely to vary significantly
867and somewhat unpredictably.
868An inundation threshold of 10 cm therefore was selected for inundation
869extents reported in this paper to reflect
870the more likely accuracy of the survey, and subsequently facilitate a more
871appropriate comparison between the modelled and observed inundation
873Figure~\ref{fig:inundationcomparison1cm} (right) shows the simulated
874inundation using a larger threshold of 10 cm.
877The datasets necessary for reproducing the results
878of the inundation stage are available on Sourceforge under the \textsc{anuga}
879project (\url{}).
880At the time of
881writing the direct link is \url{}.
883The scripts required are part of the \textsc{anuga} distribution also
884available from Sourceforge \url{} under
885the validation section.
887An animation of this simulation is available on the \textsc{anuga} website at \url{} or directly from \url{}.
895\caption{Simulated inundation versus observed inundation using an
896inundation threshold of 1cm (left) and 10cm (right).}
901To quantify the agreement between the observed and simulated inundation we
902introduce the measure
904\rho_{in}=\frac{A(I_m\cap I_o)}{A(I_o)}
906representing the ratio $\rho_{in}$ of the observed
907inundation region $I_o$ captured by the model $I_m$. Another useful
908measure is the fraction of the modelled inundation area that falls
909outside the observed inundation area given by the formula
911\rho_{out}=\frac{A(I_m\setminus (I_m\cap I_o))}{A(I_o)}
913These values for the two aforementioned simulations are given in
914Table~\ref{table:inundationAreas}. High value of both $\rho_{in}$ and $\rho_{out}$ indicate
915that the model overestimates the impact whereas low values of both quantities would indicate
916an underestimation. A high value of $\rho_{in}$ combined with a low value of $\rho_{out}$ 
917indicates a good model prediction of the survey.
919Discrepancies between the survey data and the modelled inundation
920include: unknown distribution of surface roughness, inappropriate
921parameterisation of the source model, effect of humans structures on
922flow, as well as uncertainties in the elevation data, effects of
923erosion and deposition by the tsunami event,
924measurement errors in the GPS survey recordings, and
925missing data in the field survey data itself. The impact of some of
926these sources of uncertainties are is investigated in
929\subsection{Eye-witness accounts}
930Figure \ref{fig:gauge_locations} shows four locations where time
931series have been extracted from the model. The two offshore time series
932are shown in Figure \ref{fig:offshore_timeseries} and the two onshore
933timeseries are shown in Figure \ref{fig:onshore_timeseries}. The
934latter coincide with locations where video footage from the event is
935available as described in Section \ref{sec:eyewitness data}.
941\caption{Time series obtained from the two offshore gauge locations,
9427C and 10C, shown in Figure \protect \ref{fig:gauge_locations}.}
951\caption{Time series obtained from the two onshore locations, North and South,
952shown in Figure \protect \ref{fig:gauge_locations}.}
958The estimated depths and flow rates given in Section
959\ref{sec:eyewitness data} are shown together with the modelled depths
960and flow rates obtained from the model in
961Table \ref{tab:depth and flow comparisons}.
962The predicted maximum depths and speeds are all of the same order
963of what was observed. However, unlike the real event,
964the model estimates complete withdrawal of the water between waves at the
965chosen locations and shows that the model must be used with caution at this
966level of detail.
967Nonetheless, this comparison serves to check that depths and speeds
968predicted are within the range of what is expected.
973  \begin{array}{|l|cc|cc|}
974  \hline
975                 & \multicolumn{2}{|c|}{\mbox{Depth [m]}}
976                 & \multicolumn{2}{c|}{\mbox{Flow [m/s]}} \\ 
977                 & \mbox{Observed} & \mbox{Modelled}
978                 & \mbox{Observed} & \mbox{Modelled} \\ \cline{2-5}                 
979    \mbox{North} & 1.5-2 & 1.4 & 5-7 & 0.1 - 3.3 \\
980    \mbox{South} & 1.5-2 & 1.5 & 0.5-2 & 0.2 - 2.6 \\ \hline
981  \end{array}
983\label{tab:depth and flow comparisons}
985FIXME (Jane): We should perhaps look at average data in area surrounding these points
987%can be estimated with landmarks found in
988%satellite imagery and the use of a GIS and were found to be in the
989%range of 5 to 7 metres per second (+/- 2 m/s) in the north and 0.5 to
990%2 metres per second (+/- 1 m/s) in the south.
992Given the uncertainties in both model and observations, there is agreement
993between the values obtained from the videos and the simulations.
995% Our modelled flow rates show
996%maximum values in the order of 0.2 to 2.6 m/s in the south and 0.1 to
997%3.3 m/s for the north as shown in the figures. Water depths could also
998%be estimated from the videos by the level at which water rose up the
999%sides of buildings such as shops. Our estimates are in the order of
1000%1.5 to 2.0 metres (+/- 0.5 m). This is in the same range as our
1001%modelled maximum depths of 1.4 m in the north and 1.5 m in the south
1002%as seen in the figure.
1009\section{Sensitivity Analysis}
1011This section investigates the effect of different values of Manning's
1012friction coefficient, changing waveheight at the 100 m depth contour,
1013and the presence and absence of buildings in the elevation dataset on
1014model maximum inundation. The reference model is the one reported in
1015Figure~\ref{fig:inundationcomparison1cm} (right) with a friction coefficient of 0.01,
1016buildings included and the boundary condition produced by the
1017\textsc{ursga} model.
1021\label{sec:friction sensitivity}
1022The first sensitivity study investigated the impact of surface roughness on the
1023predicted run-up. According to Schoettle~\cite{schoettle2007}
1024appropriate values of Manning's coefficient range from 0.007 to 0.03
1025for tsunami propagation over a sandy sea floor and the reference model
1026uses a value of 0.01.  To investigate sensitivity to this parameter,
1027we simulated the maximum onshore inundation using a Manning's
1028coefficient of 0.0003 and 0.03. The resulting inundation maps are
1029shown in Figure~\ref{fig:sensitivity_friction} and the maximum flow
1030speeds in Figure~\ref{fig:sensitivity_friction_speed}. These figures
1031show that the on-shore inundation extent decreases with increasing
1032friction and that small perturbations in the friction cause bounded
1033changes in the output. This is consistent with the conclusions of
1034Synolakis~\cite{synolakis05} et al, who state that the long wavelength of
1035tsunami tends to mean that friction is less important in
1036comparison to the motion of the wave.
1039\subsection{Input Wave Height}\label{sec:waveheightSA}
1040The effect of the wave height used as input to the inundation model
1041\textsc{anuga} was also investigated.
1042Figure~\ref{fig:sensitivity_boundary} indicates that the inundation
1043severity is directly proportional to the boundary waveheight but small
1044perturbations in the input wave height of 10 cm appear to have little
1045effect on the final inundated area. Obviously larger perturbations
1046will have greater impact. However, wave heights in the open ocean are
1047generally well
1048predicted by the generation and propagation models such as
1049\textsc{ursga} as demonstrated in Section \ref{sec:resultsPropagation} 
1050and also in \cite{thomas2009}.
1055\subsection{Buildings and Other Structures}
1056The presence or absence of physical buildings in the elevation model was also
1059shows the inundated area and the associated maximum flow speeds
1060in the presence and absence of buildings. It
1061is apparent that densely built-up areas act as
1062dissipators greatly reducing the inundated area. However, flow speeds
1063tend to increase in passages between buildings.
1069\caption{$\rho_{in}$ and $\rho_{out}$ of the reference simulation and all sensitivity studies.}
1072 & $\rho_{in}$ & $\rho_{out}$ \\ 
1074Reference model & 0.79 & 0.20\\ 
1075Friction = 0.0003 & 0.83 & 0.26 \\ 
1076Friction = 0.03 & 0.67 & 0.09\\ 
1077Boundary wave hight minus 10 cm & 0.77 & 0.17 \\
1078Boundary wave hight plus 10 cm & 0.82 & 0.22 \\
1079No Buildings & 0.94 & 0.44 \\
1088This paper proposes an additional field data benchmark for the
1089verification of tsunami inundation models. Currently, there is a
1090scarcity of appropriate validation datasets due to a lack of well-documented
1091historical tsunami impacts. The benchmark proposed here
1092utilises the uniquely large amount of observational data for model
1093comparison obtained during, and immediately following, the
1094Sumatra--Andaman tsunami of 26 December 2004. Unlike the small
1095number of existing benchmarks, the proposed test validates all three
1096stages of tsunami evolution - generation, propagation and
1097inundation. In an attempt to provide higher visibility and easier
1098accessibility for tsunami benchmark problems, the data used to
1099construct the proposed benchmark is documented and freely available at
1102This study also shows that the tsunami impact modelling methodology
1103adopted is credible and able to predict inundation extents with reasonable
1104accuracy.  An associated aim of this paper was to further validate the
1105hydrodynamic modelling tool \textsc{anuga} which is used to simulate
1106the tsunami inundation. Model predictions
1107matched well the geodetic measurements of the Sumatra--Andaman earthquake,
1108altimetry data from the \textsc{jason}, eye-witness accounts of wave
1109front arrival times and flow speeds and a detailed inundation survey
1110of Patong Bay, Thailand.
1112A simple sensitivity analysis was performed to assess the influence of
1113small changes in friction, wave height at the 100 m depth contour and
1114the presence of buildings and other structures on the model
1115predictions. Of these three, the presence of buildings was shown to
1116have the greatest influence on
1117the simulated inundation extent. The value of friction and small
1118perturbations in the waveheight at the \textsc{anuga} boundary have
1119comparatively little effect on the model results.
1123This project was undertaken at Geoscience Australia and the Department
1124of Mathematics, The Australian National University. The authors would
1125like to thank Niran Chaimanee from the CCOP for providing
1126the post 2004 tsunami survey data, building footprints, aerial
1127photography and the elevation data for Patong city, Prapasri Asawakun
1128from the Suranaree University of Technology and Parida Kuneepong for
1129supporting this work; and Drew Whitehouse from the Australian National
1130University for preparing the animation of the simulated impact.
1135This appendix present the images used to assess the model
1136sensitivities described in
1144\caption{Results from reference model as reported in Section
1145\protect \ref{sec:results},
1146  i.e.\ including buildings and a friction value of 0.01.
1147  The seaward boundary condition is as
1148  provided by the \textsc{ursga} model. The left image shows the maximum
1149  modelled depth while the right hand image shows the maximum modelled
1150  flow velocities.}
1162\caption{Model results with wave height at \textsc{anuga} boundary artificially
1163  modified to assess sensitivities.
1164  The reference inundation extent is shown in Figure
1165  \protect \ref{fig:reference_model} (left).  The left and right images
1166  show the inundation results if the wave at the \textsc{anuga} boundary
1167  is reduced or increased by 10 cm respectively. The inundation
1168  severity varies in proportion to the boundary waveheight, but the
1169  model results are only slightly sensitive to this parameter for the
1170  range of values tested.}
1174FIXME (Jane): How and why was the +/- 10 cm chosen?
1181\caption{The maximal flow speeds for the same model parameterisations
1182  found in Figure \protect \ref{fig:sensitivity_boundary}. The
1183  reference flow speeds are shown in Figure \protect
1184  \ref{fig:reference_model} (right).}
1194\caption{Model results show the effect of buildings in
1195  the elevation data set.
1196  The left hand image shows the inundation extent as modelled in the reference
1197  model (Figure \protect \ref{fig:reference_model}.})
1198  which includes buildings in the elevation data. The right hand image
1199  shows the result for a bare-earth model i.e. entirely without buildings. 
1200  As expected, the absence of
1201  buildings will increase the inundation extent beyond what was
1202  surveyed.
1204  % FIXME (Ole): Include speed picture elsewhere
1205  %The right hand image shows the corresponding flow speeds in the absence of buildings. 
1206  %The reference results are as shown in Figure
1207  %\protect \ref{fig:reference_model}.}
1218\caption{Model results for different values of Manning's friction
1219  coefficient shown to assess sensitivities.
1220  The reference inundation extent for a
1221  friction value of 0.01 is shown in Figure
1222  \protect \ref{fig:reference_model} (left).  The left and right images
1223  show the inundation results for friction values of 0.0003 and
1224  0.03 respectively. The inundation extent increases for the lower
1225  friction value while the higher slows the flow and decreases the
1226  inundation extent. Ideally, friction should vary across the entire
1227  domain depending on terrain and vegetation, but this is beyond the
1228  scope of this study.}
1237\caption{The maximal flow speeds for the same model parameterisations
1238  found in Figure \protect \ref{fig:sensitivity_friction}. The
1239  reference flow speeds are shown in Figure \protect
1240  \ref{fig:reference_model} (right).}
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