source: anuga_work/publications/boxing_day_validation_2008/patong_validation.tex @ 7405

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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?)
281FIXME (Jane): Refs for all these.
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).
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 ?) 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.
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 ??
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.
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.
426\caption{Tsunami survey mapping the maximum observed inundation at
427  Patong beach courtesy of the CCOP \protect \cite{szczucinski06}.}
433\subsubsection{Eyewitness Accounts}\label{sec:eyewitness data}
434Eyewitness accounts detailed in~\cite{papadopoulos06}
435report that many people at Patong Beach observed an initial
436retreat (trough or draw down) of
437the shoreline of more than 100 m followed a few minutes later by a
438strong wave (crest). Another less powerful wave arrived another five
439or ten minutes later. Eyewitness statements place the arrival time of
440the first wave between 9:55 am and 10:05 am local time or about 2 hours
441after the source rupture.
442FIXME (Ole): We should add observed arrival time and later relate that to
443the modelled dynamics. Wait for Drew's updated animation.
449\caption{Location of timeseries extracted from the model output.}
458Two videos were sourced\footnote{The footage is
459widely available and can for example be obtained from
461(Comfort Hotel) and
465which include footage of the tsunami in Patong Bay on the day
466of the 2004 Indian Ocean Tsunami. Both videos show an already inundated
467group of buildings. They also show what is to be assumed as the second
468and third waves approaching and further flooding of the buildings and
469street.  The first video is in the very north, filmed from what is
470believed to be the roof of the Novotel Hotel marked ``north'' in Figure
471\ref{fig:gauge_locations}. The second video is in the very south,
472filmed from the second story of a building next door to the Comfort
473Resort near the corner of Ruam Chai St and Thaweewong Road.  This
474location is marked ``south'' in Figure \ref{fig:gauge_locations}.
475Figure~\ref{fig:video_flow} shows stills from this video. Both videos
476were used to estimate flow speeds and inundation depths over time.
484\caption{Four frames from a video where flow rate could be estimated,
485  circle indicates tracked debris, from top left: 0.0 sec, 5.0 s, 7.1
486  s, 7.6 s.}
491Flow rates were estimated using landmarks found in both videos and
492were found to be in the range of 5 to 7 metres per second (+/- 2 m/s)
493in the north and 0.5 to 2 metres per second (+/- 1 m/s) in the south.
494FIXME (Jane): How were these error bounds derived?
495Water depths could also
496be estimated from the videos by the level at which water rose up the
497sides of buildings such as shops. Our estimates are in the order of
4981.5 to 2.0 metres (+/- 0.5 m).
499Fritz ~\cite{fritz06} performed a detailed
500analysis of video frames taken around Banda Aceh and arrived at flow
501speeds in the range of 2 to 5 m/s.
504\subsection{Validation Check-List}
506The data described in this section can be used to construct a
507benchmark to validate all three stages of the evolution of a
508tsunami. In particular we propose that a legitimate tsunami model
509should reproduce the following behaviour:
511 \item reproduce the vertical deformation observed in north-western
512   Sumatra and along the Nicobar--Andaman islands (see
513   Section~\ref{sec:gen_data}),
514 \item reproduce the \textsc{jason} satellite altimetry sea surface
515   anomalies (see Section~\ref{sec:data_jason}),
516 \item reproduce the inundation survey map in Patong city
517   (Figure~\ref{fig:patongescapemap}),
518 \item simulate a leading depression followed by two distinct crests
519   of decreasing magnitude at the beach, and
520 \item predict the water depths and flow speeds, at the locations of
521   the eye-witness videos, that fall within the bounds obtained from
522   the videos.
525Ideally, the model should also be compared to measured timeseries of
526waveheights and velocities but the authors are not aware of the
527availability of such data near Patong Bay.
532\section{Modelling the Event}\label{sec:models}
533Numerous models are currently used to model and predict tsunami
534generation, propagation and run-up~\cite{titov97a,satake95}. Here we
535introduce the three part modelling methodology employed by Geoscience Australia
536to illustrate the utility of the proposed benchmark.
539FIXME (Ole and Jane): Does this need to be so long?
541There are various approaches to modelling the expected crustal
542deformation from an earthquake. Most approaches model the
543earthquake as a dislocation in a linear elastic medium. Here we use
544the method of Wang et al~\cite{wang03}. One of the main advantages
545of their method is that it allows the dislocation to be located in a
546stratified linear elastic half-space with an arbitrary number of
547layers. Other methods (such as those based on Okada's equations) can
548only model the dislocation in a homogeneous elastic half space, or can
549only include a limited number of layers, and thus cannot model the
550effect of the depth dependence of the elasticity of the
551Earth~\cite{wang03}. The original versions of the codes described here
552are available from \url{}. The
553first program, \textsc{edgrn}, calculates elastic Green's function for
554a set of point sources at a regular set of depths out to a specified
555distance. The equations controlling the deformation are solved by
556using a combination of Hankel's transform and Wang et al's
557implementation of the Thomson-Haskell propagator
558algorithm~\cite{wang03}. Once the Green's functions are calculated
559a slightly modified version of \textsc{edcmp}\footnote{For this study,
560we have made minor modifications
561to \textsc{edcmp} in order for it to provide output in a file format
562compatible with the propagation code in the following section. Otherwise it
563is similar to the original code.} is used to calculate the sea
564floor deformation for a specific subfault. This second code
565discretises the subfault into a set of unit sources and sums the
566elastic Green's functions calculated from \textsc{edgrn} for all the
567unit sources on the fault plane in order to calculate the final static
568deformation caused by a two dimensional dislocation along the
569subfault. This step is possible because of the linearity of the
570governing equations.
572In order to calculate the crustal deformation using these codes
573a model that describes the variation in elastic
574properties with depth and a slip model of the earthquake to describe
575the dislocation is required.
576The elastic parameters used for this study are the
577same as those in Table 2 of Burbidge et al~\cite{burbidge08}. For the slip
578model, there are many possible models for the 2004 Andaman--Sumatran
579earthquake to select from
580~\cite{chlieh07,asavanant08,arcas06,grilli07,ioualalen07}. Some are
581determined from various geological surveys of the site. Others solve
582an inverse problem which calibrates the source based upon the tsunami
583wave signal, the seismic signal and/or even the run-up.
584The source
585parameters used here to simulate the 2004 Indian Ocean tsunami were
586taken from the slip model G-M9.15 of Chlieh
587et al~\cite{chlieh07}. This model was created by inversion of wide
588range of geodetic and seismic data. The slip model consists of 686
58920km x 20km subsegments each with a different slip, strike and dip
590angle. The dip subfaults go from $17.5^0$ in the north and $12^0$ in
591the south. Refer to Chlieh et al~\cite{chlieh07} for a detailed
592discussion of this model and its derivation. Note that the geodetic
593data used in the validation was also included by~\cite{chlieh07} in
594the inversion used to find G-M9.15. Thus the validation is not
595completely independent. However, a reasonable validation would still
596show that the crustal deformation and elastic properties model used
597here is at least as valid as the one used by Chlieh
598et al~\cite{chlieh07} and can reproduce the observations just as
602The \textsc{ursga} model described below was used to simulate the
603propagation of the 2004 Indian Ocean tsunami across the open ocean, based on a
604discrete representation of the initial deformation of the sea floor, as
605described in Section~\ref{sec:modelGeneration}. For the models shown
606here, the uplift is assumed to be instantaneous and creates a wave of
607the same size and amplitude as the co-seismic sea floor deformation.
610\textsc{ursga} is a hydrodynamic code that models the propagation of
611the tsunami in deep water using a finite difference method on a staggered grid.
612It solves the depth integrated linear or nonlinear shallow water equations in
613spherical co-ordinates with friction and Coriolis terms. The code is
614based on Satake~\cite{satake95} with significant modifications made by
615the \textsc{urs} corporation, Thio et al~\cite{thio08} and Geoscience
616Australia, Burbidge et al~\cite{burbidge08}.
617The tsunami was propagated via the nested
618grid system described in Section \ref{sec:propagation data} where
619the coarse grids were used in the open ocean and the finest
620resolution grid was employed in the region closest to Patong bay.
621\textsc{Ursga} is not publicly available.
624The utility of the \textsc{ursga} model decreases with water depth
625unless an intricate sequence of nested grids is employed. In
626comparison \textsc{anuga}, described below, is designed to produce
627robust and accurate predictions of on-shore inundation, but is less
628suitable for earthquake source modelling and large study areas because
629it is based on projected spatial coordinates. Consequently, the
630Geoscience Australia tsunami modelling methodology is based on a
631hybrid approach using models like \textsc{ursga} for tsunami
632propagation up to an offshore depth contour, typically 100 m.
633%Specifically we use the \textsc{ursga} model to simulate the
634%propagation of the 2004 Indian Ocean tsunami in the deep ocean, based
635%on a discrete representation of the initial deformation of the sea
636%floor, described in Section~\ref{sec:modelGeneration}.
637The wave signal and the velocity field is then used as a
638time varying boundary condition for
639the \textsc{anuga} inundation simulation.
640% A description of \textsc{anuga} is the following section.
643\textsc{Anuga} is a Free and Open Source hydrodynamic inundation tool that
644solves the conserved form of the depth-integrated nonlinear shallow
645water wave equations using a Finite-Volume scheme on an
646unstructured triangular mesh.
647The scheme, first
648presented by Zoppou and Roberts~\cite{zoppou99}, is a high-resolution
649Godunov-type method that uses the rotational invariance property of
650the shallow water equations to transform the two-dimensional problem
651into local one-dimensional problems. These local Riemann problems are
652then solved using the semi-discrete central-upwind scheme of Kurganov
653et al~\cite{kurganov01} for solving one-dimensional conservation
654equations. The numerical scheme is presented in detail in
655Roberts and Zoppou~\cite{zoppou00,roberts00} and
656Nielsen et al~\cite{nielsen05}. An important capability of the
657finite-volume scheme is that discontinuities in all conserved quantities
658are allowed at every edge in the mesh. This means that the tool is
659well suited to adequately resolving hydraulic jumps, transcritical flows and
660the process of wetting and drying. This means that \textsc{Anuga} 
661is suitable for
662simulating water flow onto a beach or dry land and around structures
663such as buildings. \textsc{Anuga} has been validated against
664%a number of analytical solutions and 
665%FIXME (Ole): Analytical solutions have not been published. Ask Steve.
666the wave tank simulation of the 1993 Okushiri
667Island tsunami~\cite{nielsen05,roberts06}.
668FIXME (Ole): Add reference to Tom Baldock's Dam Break valiadation of ANUGA.
673This section presents a validation of the modelling practice of Geoscience
674Australia against the new proposed benchmarks. The criteria outlined
675in Section~\ref{sec:checkList} are addressed for each of the three stages
676of tsunami evolution.
679The location and magnitude of the sea floor displacement associated
680with the 2004 Sumatra--Andaman tsunami calculated from the G-M9.15
681model of~\cite{chlieh07} is shown in
682Figure~\ref{fig:surface_deformation}. The magnitude of the sea floor
683displacement ranges from about $-3.0$ to $5.0$ metres. The region near
684the fault is predicted to uplift, while that further away from the
685fault subsides. Also shown in Figure~\ref{fig:surface_deformation} are
686the areas that were observed to uplift (arrows pointing up) or subside
687(arrows point down) during and immediately after the earthquake. Most
688of this data comes from uplifted or subsided coral heads. The length of
689the vector increases with the magnitude of the displacement; the length
690corresponding to 1 m of observed motion is shown in the top right
691corner of the figure. As can be seen, the source model detailed in
692Section~\ref{sec:modelGeneration} produces a crustal deformation that
693matches the vertical displacements in the Nicobar-Andaman islands and
694Sumatra very well. Uplifted regions are close to the fault and
695subsided regions are further away. The crosses on
696Figure~\ref{fig:surface_deformation} show estimates of the pivot line
697from the remote sensing data~\cite{chlieh07} and they follow the
698predicted pivot line quite accurately. The average difference between
699the observed motion and the predicted motion (including the pivot line
700points) is only 0.06 m, well below the typical error of the
701observations of between 0.25 and 1.0 m. However, the occasional point
702has quite a large error (over 1 m); for example a couple of
703uplifted/subsided points appear to be on a wrong
704(FIXME (Jane): This is incorrect) side of the predicted
705pivot line~\ref{fig:surface_deformation}. The excellence of the fit is
706not surprising, since the original slip model was chosen
707by~\cite{chlieh07} to fit this (and the seismic data) well.
708This does demonstrate, however, that \textsc{edgrn} and our modified version of
709\textsc{edstat} (FIXME(Jane): This has never been mentioned before)
710can reproduce the correct pattern of vertical
711deformation very well when the slip distribution is well constrained
712and when reasonable values for the elastic properties are used.
718\caption{Location and magnitude of the vertical component of the sea
719  floor displacement associated with the 2004 Indian Ocean tsunami
720  based on the slip model, G-M9.15. The black arrows which point up
721  show areas observed to uplift during and immediately after the
722  earthquake; those pointing down are locations which subsided. The
723  length of the arrow increases with the magnitude of the deformation. The arrow
724  length corresponding to 1 m of deformation is shown in the top right
725  hand corner of the figure. The cross marks show the location of
726  the pivot line (the region between the uplift and subsided region
727  where the uplift is zero) derived from remote sensing
728  (FIXME(Jane): How was that possible?). All the
729  observational data are from the dataset collated
730  by~\cite{chlieh07}.}
736The deformation results described in Section~\ref{sec:modelGeneration}
737were used to provide a profile of the initial ocean surface
738displacement. This wave was used as an initial condition for
739\textsc{ursga} and was propagated throughout the Bay of Bengal. The
740rectangular computational domain of the largest grid extended from
74190$^0$ to 100$^0$ East and 0 to 15$^0$ North and contained
7421335$\times$1996 finite difference points. Inside this grid, a nested
743sequence of grids was used. The grid resolution of the nested grids
744went from 27 arc seconds in the coarsest grid, down to nine arc seconds
745in the second grid, three arc seconds in the third grid and finally one arc
746second in the finest grid near Patong. The computational domain is
747shown in Figure~\ref{fig:computational_domain}.
749FIXME (Ole): I know that a nested ursga model was trialled for the
750end-to-end modelling. However, for the study done here, where models
751were coupled, I didn't think nested grids were used with URSGA -
752and certainly not down to 1 arc second. Can someone shed some light
753on this please?
760\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).}
766Figure \ref{fig:jasonComparison} provides a comparison of the
767\textsc{ursga}-predicted sea surface elevation with the \textsc{jason}
768satellite altimetry data. The \textsc{ursga} model replicates the
769amplitude and timing of the the wave observed at $2.5^0$ South,
770but underestimates the amplitude of the wave further to the south at
771$4^0$ South. In the model, the southern most of these two waves
772appears only as a small bump in the cross section of the model (shown
773in Figure~\ref{fig:jasonComparison}) instead of being a distinct peak
774as can be seen in the satellite data. Also note
775that the \textsc{ursga} model prediction of the ocean surface
776elevation becomes out of phase with the \textsc{jason} 
777data at $3^0$ to $7^0$ North
778latitude. Chlieh et al~\cite{chlieh07} also observed these misfits and
779suggest it is caused by a reflected wave from the Aceh Peninsula that
780is not resolved in the model due to insufficient resolution of the
781computational mesh and bathymetry data. This is also a limitation of
782the model presented here which could be improved by nesting
783grids near Aceh.
788\caption{Comparison of the \textsc{ursga}-predicted surface elevation
789  with the \textsc{jason} satellite altimetry data. The \textsc{ursga} wave
790  heights have been corrected for the time the satellite passed
791  overhead compared to \textsc{jason} sea level anomaly.}
795FIXME (Jane): This graph does not look nice. The legend URS Model should
796be URSGA model.
799After propagating the tsunami in the open ocean using \textsc{ursga},
800the approximated ocean and surface elevation and horisontal flow
801velocities were extracted and used to construct a boundary condition
802for the \textsc{anuga} model. The interface between the \textsc{ursga}
803and \textsc{anuga} models was chosen to roughly follow the 100~m depth
804contour along the west coast of Phuket Island. The computational
805domain is shown in Figure~\ref{fig:computational_domain}.
807The domain was discretised into 386,338 triangles. The resolution of
808the grid was increased in regions inside the bay and on-shore to
809efficiently increase the simulation accuracy for the impact area.
810The grid resolution ranged between a
811maximum triangle area of $1\times 10^5$ m$^2$ 
812(corresponding to approximately 440 m between mesh points)
813near the western ocean
814boundary to $20$ m$^2$ (corresponding to
815approximately 6 m between mesh points)
816in the small regions surrounding the inundation
817region in Patong Bay. The coarse resolution was chosen to be
818commensurate with the model output from the \textsc{ursga} model
819(FIXME - this has to be clearly stated in ursga section)
820while the latter was chosen to match the available resolution of topographic
821data and building data in Patong city.
822Due to a lack of available roughness data, friction was
823set to a constant throughout the computational domain. For the
824reference simulation, a Manning's coefficient of 0.01 was chosen to
825represent a small resistance to the water flow. See Section
826\ref{sec:friction sensitivity} for details on model sensitivity to
827this parameter.
830The boundary condition at each side of the domain towards the south
831and the north where no information about the incident wave or
832its velocity field is available
833was chosen as a transmissive
834boundary condition, effectively replicating the time dependent wave
835height present just inside the computational domain.
836The velocity field on these boundaries was set
837to zero. Other choices include applying the mean tide value as a
838Dirichlet boundary condition. But experiments as well as the
839result of the verification reported here showed that this approach
840tends to underestimate the tsunami impact due to the tempering of the
841wave near the side boundaries, whereas the transmissive boundary
842condition robustly preserves the wave.
844During the \textsc{anuga} simulation the tide was kept constant at
845$0.80$ m. This value was chosen to correspond to the tidal height
846specified by the Thai Navy tide charts
847(\url{}) at the time the tsunami arrived
848at Patong Bay. Although the tsunami propagated for approximately three
849hours before it reach Patong Bay, the period of time during which the
850wave propagated through the \textsc{anuga} domain is much
851smaller. Consequently the assumption of constant tide height is
854Maximum onshore inundation depth was computed from the model
855throughout the entire Patong Bay region and used to generate
856a measure of the inundated area.
857Figure~\ref{fig:inundationcomparison1cm} (left) shows very good
858agreement between the measured and simulated inundation. However
859these results are dependent on the classification used to determine
860whether a region in the numerical simulation was inundated. In
861Figure~\ref{fig:inundationcomparison1cm} (left) a point in the computational
862domain was deemed inundated if at some point in time it was covered by
863at least 1 cm of water. However, the precision of the inundation boundary
864generated by the on-site survey is most likely less than that as it
865was determined by observing water marks and other signs
866left by the receding waters. Consequently the measurement error along
867the inundation boundary of the survey is likely to vary significantly
868and somewhat unpredictably.
869An inundation threshold of 10 cm therefore was selected for inundation
870extents reported in this paper to reflect
871the more likely accuracy of the survey, and subsequently facilitate a more
872appropriate comparison between the modelled and observed inundation
874Figure~\ref{fig:inundationcomparison1cm} (right) shows the simulated
875inundation using a larger threshold of 10 cm.
878The datasets necessary for reproducing the results
879of the inundation stage are available on Sourceforge under the \textsc{anuga}
880project (\url{}).
881At the time of
882writing the direct link is \url{}.
884The scripts required are part of the \textsc{anuga} distribution also
885available from Sourceforge \url{} under
886the validation section.
888An 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 sensitivities described in
1142\caption{Results from reference model as reported in Section \protect \ref{sec:results},
1143  i.e.\ including buildings and a friction value of 0.01. The seaward boundary condition is as
1144  provided by the \textsc{ursga} model. The left image shows the maximum
1145  modelled depth while the right hand image shows the maximum modelled
1146  flow velocities.}
1157\caption{Model results with wave height at \textsc{anuga} boundary artificially
1158  modified to assess sensitivities. The reference inundation extent is shown in Figure
1159  \protect \ref{fig:reference_model} (left).  The left and right images
1160  show the inundation results if the wave at the \textsc{anuga} boundary
1161  is reduced or increased by 10 cm respectively. The inundation
1162  severity varies in proportion to the boundary waveheight, but the
1163  model results are only slightly sensitive to this parameter for the
1164  range of values tested.}
1168FIXME (Jane): How and why was the +/- 10 cm chosen?
1175\caption{The maximal flow speeds for the same model parameterisations
1176  found in Figure \protect \ref{fig:sensitivity_boundary}. The
1177  reference flow speeds are shown in Figure \protect
1178  \ref{fig:reference_model} (right).}
1187\caption{Model results show the effect of buildings in
1188  the elevation data set.
1189  The left hand image shows the maximum inundation depth results for
1190  a model entirely without buildings.  As expected, the absence of
1191  buildings will increase the inundation extent beyond what was
1192  surveyed. The right hand image shows the corresponding flow speeds in the absence of buildings. 
1193  The reference results are as shown in Figure
1194  \protect \ref{fig:reference_model}.}
1205\caption{Model results for different values of Manning's friction
1206  coefficient shown to assess sensitivities. The reference inundation extent for a
1207  friction value of 0.01 is shown in Figure
1208  \protect \ref{fig:reference_model} (left).  The left and right images
1209  show the inundation results for friction values of 0.0003 and
1210  0.03 respectively. The inundation extent increases for the lower
1211  friction value while the higher slows the flow and decreases the
1212  inundation extent. Ideally, friction should vary across the entire
1213  domain depending on terrain and vegetation, but this is beyond the
1214  scope of this study.}
1223\caption{The maximal flow speeds for the same model parameterisations
1224  found in Figure \protect \ref{fig:sensitivity_friction}. The
1225  reference flow speeds are shown in Figure \protect
1226  \ref{fig:reference_model} (right).}
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