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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 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
331%DB I suggest we combine with model data to reduce the number of figures. The satellite track is shown in Figure~\ref{fig:satelliteTrack}.
336%\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.}
344%\caption{JASON satellite altimetry seal level anomaly. FIXME: should we include figure here with just JASON altimetry.}
349%FIXME: Can we compare the urs model against the TOPEX-poseidon satellite as well? DB No (we don't have the data currently).
352\label{sec:inundation data}
353FIXME (Ole): Technically propagation covers everything up to
354the coastline and inundation everything on-shore.
355This means that ANUGA covers the final part of the propagation and the inundation part. Should we adopt this distiction throughout the paper?
357Inundation refers to the final stages of the evolution of a tsunami and
358covers the propagation of the tsunami in coastal waters and the
359subsequent run-up onto land. This process is typically the most
360difficult of the three stages to model due to thin layers of water
361flowing rapidly over dry land.  Aside from requiring robust solvers
362which can simulate such complex flow patterns, this part of the
363modelling process also requires high resolution and quality elevation
364data which is often not available. In the case of model validation
365high quality field measurements are also required. For the proposed
366benchmark a high resolution bathymetry (FIXME (Ole): Bathymetry ?) and
367topography data set and a high quality inundation survey map from the
368Coordinating Committee Co-ordinating Committee for Geoscience Programmes
369in East and Southeast Asia (CCOP) (\cite{szczucinski06}) was obtained
370to validate model inundation. See also acknowledgements at the end of this paper.
372In this section we also present eye-witness accounts which can be used
373to qualitatively validate tsunami inundation.
375\subsubsection{Topography Data}
376A one second grid was used to approximate the topography in Patong
377Bay. This elevation data was again created from the digitised Thai
378Navy bathymetry chart, no 358.
379FIXME (Ole): I don't think so. The Navy chart is only offshore.
381 A visualisation of the elevation data
382set used in Patong Bay is shown in
383Figure~\ref{fig:patong_bathymetry}. The continuous topography
384(FIXME(Jane): What is meant by this?) is an
385interpolation of known elevation measured at the coloured dots. FIXME ??
390\caption{3D visualisation of the elevation data set used in Patong Bay showing data points, contours, rivers and roads draped over the final model.}
394FIXME (Jane): legend? Were the contours derived from the final dataset?
395This is not the entire mode, only the bay and the beach.
397\subsubsection{Buildings and Other Structures}
398Human-made buildings and structures can significantly affect tsunami
399inundation. The footprint and number of floors of the
400buildings 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).
401The heights of these
402buildings were estimated assuming that each floor has a height of 3 m and they
403were added to the topographic dataset.
405\subsubsection{Inundation Survey}
406Tsunami run-up is the cause of the largest financial and human
407losses, yet run-up data that can be used to validate model run-up
408predictions is scarce. Of the two field benchmarks proposed
410only the Okushiri benchmark facilitates comparison between
411modelled and observed run-up. One of the major strengths of the
412benchmark proposed here is that modelled run-up can be compared to an
413inundation survey which maps the maximum run-up along an entire coastline
414rather than at a series of discrete sites. The survey map is
415shown in Figure~\ref{fig:patongescapemap} and plots the maximum run-up
416of the 2004 Indian Ocean tsunami in Patong city. Refer to Szczucinski et
417al~\cite{szczucinski06} for further details.
422\caption{Tsunami survey mapping the maximum observed inundation at
423  Patong beach courtesy of the CCOP \protect \cite{szczucinski06}.}
429\subsubsection{Eyewitness Accounts}\label{sec:eyewitness data}
430Eyewitness accounts detailed in~\cite{papadopoulos06}
431report that most people at Patong Beach observed an initial retreat of
432the shoreline of more than 100 m followed a few minutes later, by a
433strong wave (crest). Another less powerful wave arrived another five
434or ten minutes later. Eyewitness statements place the arrival time of
435the strong wave between 2 hours and 55 minutes to 3 hours and 5
436minutes after the source rupture (09:55am to 10:05am local time).
438Two videos were sourced\footnote{The footage is
439widely available and can for example be obtained from
441(Comfort Hotel) and
445which include footage of the tsunami in Patong Bay on the day
446of the 2004 Indian Ocean Tsunami. Both videos show an already inundated
447group of buildings. They also show what is to be assumed as the second
448and third waves approaching and further flooding of the buildings and
449street.  The first video is in the very north, filmed from what is
450believed to be the roof of the Novotel Hotel marked ``north'' in Figure
451\ref{fig:gauge_locations}. The second video is in the very south,
452filmed from the second story of a building next door to the Comfort
453Resort near the corner of Ruam Chai St and Thaweewong Road.  This
454location is marked ``south'' in Figure \ref{fig:gauge_locations}.
455Figure~\ref{fig:video_flow} shows stills from this video. Both videos
456were used to estimate flow speeds and inundation depths over time.
464\caption{Four frames from a video where flow rate could be estimated,
465  circle indicates tracked debris, from top left: 0.0 sec, 5.0 s, 7.1
466  s, 7.6 s.}
471Flow rates were estimated using landmarks found in both videos and
472were found to be in the range of 5 to 7 metres per second (+/- 2 m/s)
473in the north and 0.5 to 2 metres per second (+/- 1 m/s) in the south.
474FIXME (Jane): How were these error bounds derived?
475Water depths could also
476be estimated from the videos by the level at which water rose up the
477sides of buildings such as shops. Our estimates are in the order of
4781.5 to 2.0 metres (+/- 0.5 m).
479Fritz ~\cite{fritz06} performed a detailed
480analysis of video frames taken around Banda Aceh and arrived at flow
481speeds in the range of 2 to 5 m/s.
484\subsection{Validation Check-List}
486The data described in this section can be used to construct a
487benchmark to validate all three stages of the evolution of a
488tsunami. In particular we propose that a legitimate tsunami model
489should reproduce the following behaviour:
491 \item reproduce the vertical deformation observed in north-western
492   Sumatra and along the Nicobar--Andaman islands (see
493   Section~\ref{sec:gen_data}),
494 \item reproduce the \textsc{jason} satellite altimetry sea surface
495   anomalies (see Section~\ref{sec:data_jason}),
496 \item reproduce the inundation survey map in Patong city
497   (Figure~\ref{fig:patongescapemap}),
498 \item simulate a leading depression followed by two distinct crests
499   of decreasing magnitude at the beach, and
500 \item predict the water depths and flow speeds, at the locations of
501   the eye-witness videos, that fall within the bounds obtained from
502   the videos.
505Ideally, the model should also be compared to measured timeseries of
506waveheights and velocities but the authors are not aware of the
507availability of such data near Patong Bay.
512\section{Modelling the Event}\label{sec:models}
513Numerous models are currently used to model and predict tsunami
514generation, propagation and run-up~\cite{titov97a,satake95}. Here we
515introduce the three part modelling methodology employed by Geoscience Australia
516to illustrate the utility of the proposed benchmark.
520There are various approaches to modelling the expected crustal
521deformation from an earthquake. Most approaches model the
522earthquake as a dislocation in a linear elastic medium. Here we use
523the method of Wang et al~\cite{wang03}. One of the main advantages
524of their method is that it allows the dislocation to be located in a
525stratified linear elastic half-space with an arbitrary number of
526layers. Other methods (such as those based on Okada's equations) can
527only model the dislocation in a homogeneous elastic half space, or can
528only include a limited number of layers, and thus cannot model the
529effect of the depth dependence of the elasticity of the
530Earth~\cite{wang03}. The original versions of the codes described here
531are available from \url{}. The
532first program, \textsc{edgrn}, calculates elastic Green's function for
533a set of point sources at a regular set of depths out to a specified
534distance. The equations controlling the deformation are solved by
535using a combination of Hankel's transform and Wang et al's
536implementation of the Thomson-Haskell propagator
537algorithm~\cite{wang03}. Once the Green's functions are calculated
538a slightly modified version of \textsc{edcmp}\footnote{For this study,
539we have made minor modifications
540to \textsc{edcmp} in order for it to provide output in a file format
541compatible with the propagation code in the following section. Otherwise it
542is similar to the original code.} is used to calculate the sea
543floor deformation for a specific subfault. This second code
544discretises the subfault into a set of unit sources and sums the
545elastic Green's functions calculated from \textsc{edgrn} for all the
546unit sources on the fault plane in order to calculate the final static
547deformation caused by a two dimensional dislocation along the
548subfault. This step is possible because of the linearity of the
549governing equations.
551In order to calculate the crustal deformation using these codes
552a model that describes the variation in elastic
553properties with depth and a slip model of the earthquake to describe
554the dislocation is required.
555The elastic parameters used for this study are the
556same as those in Table 2 of Burbidge et al~\cite{burbidge08}. For the slip
557model, there are many possible models for the 2004 Andaman--Sumatran
558earthquake to select from
559~\cite{chlieh07,asavanant08,arcas06,grilli07,ioualalen07}. Some are
560determined from various geological surveys of the site. Others solve
561an inverse problem which calibrates the source based upon the tsunami
562wave signal, the seismic signal and/or even the run-up.
563The source
564parameters used here to simulate the 2004 Indian Ocean tsunami were
565taken from the slip model G-M9.15 of Chlieh
566et al~\cite{chlieh07}. This model was created by inversion of wide
567range of geodetic and seismic data. The slip model consists of 686
56820km x 20km subsegments each with a different slip, strike and dip
569angle. The dip subfaults go from $17.5^0$ in the north and $12^0$ in
570the south. Refer to Chlieh et al~\cite{chlieh07} for a detailed
571discussion of this model and its derivation. Note that the geodetic
572data used in the validation was also included by~\cite{chlieh07} in
573the inversion used to find G-M9.15. Thus the validation is not
574completely independent. However, a reasonable validation would still
575show that the crustal deformation and elastic properties model used
576here is at least as valid as the one used by Chlieh
577et al~\cite{chlieh07} and can reproduce the observations just as
581The \textsc{ursga} model described below was used to simulate the
582propagation of the 2004 Indian Ocean tsunami across the open ocean, based on a
583discrete representation of the initial deformation of the sea floor, as
584described in Section~\ref{sec:modelGeneration}. For the models shown
585here, the uplift is assumed to be instantaneous and creates a wave of
586the same size and amplitude as the co-seismic sea floor deformation.
589\textsc{ursga} is a hydrodynamic code that models the propagation of
590the tsunami in deep water using a finite difference method on a staggered grid.
591It solves the depth integrated linear or nonlinear shallow water equations in
592spherical co-ordinates with friction and Coriolis terms. The code is
593based on Satake~\cite{satake95} with significant modifications made by
594the \textsc{urs} corporation, Thio et al~\cite{thio08} and Geoscience
595Australia, Burbidge et al~\cite{burbidge08}.
596The tsunami was propagated via the nested
597grid system described in Section \ref{sec:propagation data} where
598the coarse grids were used in the open ocean and the finest
599resolution grid was employed in the region closest to Patong bay.
600\textsc{Ursga} is not publicly available.
603The utility of the \textsc{ursga} model decreases with water depth
604unless an intricate sequence of nested grids is employed. In
605comparison \textsc{anuga}, described below, is designed to produce
606robust and accurate predictions of on-shore inundation, but is less
607suitable for earthquake source modelling and large study areas because
608it is based on projected spatial coordinates. Consequently, the
609Geoscience Australia tsunami modelling methodology is based on a
610hybrid approach using models like \textsc{ursga} for tsunami
611propagation up to an offshore depth contour, typically 100 m.
612%Specifically we use the \textsc{ursga} model to simulate the
613%propagation of the 2004 Indian Ocean tsunami in the deep ocean, based
614%on a discrete representation of the initial deformation of the sea
615%floor, described in Section~\ref{sec:modelGeneration}.
616The wave signal and the velocity field is then used as a
617time varying boundary condition for
618the \textsc{anuga} inundation simulation.
619% A description of \textsc{anuga} is the following section.
622\textsc{Anuga} is a Free and Open Source hydrodynamic inundation tool that
623solves the conserved form of the depth-integrated nonlinear shallow
624water wave equations using a Finite-Volume scheme on an
625unstructured triangular mesh.
626The scheme, first
627presented by Zoppou and Roberts~\cite{zoppou99}, is a high-resolution
628Godunov-type method that uses the rotational invariance property of
629the shallow water equations to transform the two-dimensional problem
630into local one-dimensional problems. These local Riemann problems are
631then solved using the semi-discrete central-upwind scheme of Kurganov
632et al~\cite{kurganov01} for solving one-dimensional conservation
633equations. The numerical scheme is presented in detail in
634Roberts and Zoppou~\cite{zoppou00,roberts00} and
635Nielsen et al~\cite{nielsen05}. An important capability of the
636finite-volume scheme is that discontinuities in all conserved quantities
637are allowed at every edge in the mesh. This means that the tool is
638well suited to adequately resolving hydraulic jumps, transcritical flows and
639the process of wetting and drying. This means that \textsc{Anuga} 
640is suitable for
641simulating water flow onto a beach or dry land and around structures
642such as buildings. \textsc{Anuga} has been validated against
643%a number of analytical solutions and  FIXME: These have not been published
644the wave tank simulation of the 1993 Okushiri
645Island tsunami~\cite{nielsen05,roberts06}.
646FIXME (Ole): Add reference to Tom Baldock's Dam Break valiadation of ANUGA.
651This section presents a validation of the modelling practice of Geoscience
652Australia against the new proposed benchmarks. The criteria outlined
653in Section~\ref{sec:checkList} are addressed for each of the three stages
654of tsunami evolution.
657The location and magnitude of the sea floor displacement associated
658with the 2004 Sumatra--Andaman tsunami calculated from the G-M9.15
659model of~\cite{chlieh07} is shown in
660Figure~\ref{fig:surface_deformation}. The magnitude of the sea floor
661displacement ranges from about $-3.0$ to $5.0$ metres. The region near
662the fault is predicted to uplift, while that further away from the
663fault subsides. Also shown in Figure~\ref{fig:surface_deformation} are
664the areas that were observed to uplift (arrows pointing up) or subside
665(arrows point down) during and immediately after the earthquake. Most
666of this data comes from uplifted or subsided coral heads. The length of
667the vector increases with the magnitude of the displacement; the length
668corresponding to 1 m of observed motion is shown in the top right
669corner of the figure. As can be seen, the source model detailed in
670Section~\ref{sec:modelGeneration} produces a crustal deformation that
671matches the vertical displacements in the Nicobar-Andaman islands and
672Sumatra very well. Uplifted regions are close to the fault and
673subsided regions are further away. The crosses on
674Figure~\ref{fig:surface_deformation} show estimates of the pivot line
675from the remote sensing data~\cite{chlieh07} and they follow the
676predicted pivot line quite accurately. The average difference between
677the observed motion and the predicted motion (including the pivot line
678points) is only 0.06 m, well below the typical error of the
679observations of between 0.25 and 1.0 m. However, the occasional point
680has quite a large error (over 1 m); for example a couple of
681uplifted/subsided points appear to be on a wrong
682(FIXME (Jane): This is incorrect) side of the predicted
683pivot line~\ref{fig:surface_deformation}. The excellence of the fit is
684not surprising, since the original slip model was chosen
685by~\cite{chlieh07} to fit this (and the seismic data) well.
686This does demonstrate, however, that \textsc{edgrn} and our modified version of
687\textsc{edstat} (FIXME(Jane): This has never been mentioned before)
688can reproduce the correct pattern of vertical
689deformation very well when the slip distribution is well constrained
690and when reasonable values for the elastic properties are used.
696\caption{Location and magnitude of the vertical component of the sea
697  floor displacement associated with the 2004 Indian Ocean tsunami
698  based on the slip model, G-M9.15. The black arrows which point up
699  show areas observed to uplift during and immediately after the
700  earthquake; those pointing down are locations which subsided. The
701  length of the arrow increases with the magnitude of the deformation. The arrow
702  length corresponding to 1 m of deformation is shown in the top right
703  hand corner of the figure. The cross marks show the location of
704  the pivot line (the region between the uplift and subsided region
705  where the uplift is zero) derived from remote sensing
706  (FIXME(Jane): How was that possible?). All the
707  observational data are from the dataset collated
708  by~\cite{chlieh07}.}
714The deformation results described in Section~\ref{sec:modelGeneration}
715were used to provide a profile of the initial ocean surface
716displacement. This wave was used as an initial condition for
717\textsc{ursga} and was propagated throughout the Bay of Bengal. The
718rectangular computational domain of the largest grid extended from
71990$^0$ to 100$^0$ East and 0 to 15$^0$ North and contained
7201335$\times$1996 finite difference points. Inside this grid, a nested
721sequence of grids was used. The grid resolution of the nested grids
722went from 27 arc seconds in the coarsest grid, down to nine arc seconds
723in the second grid, three arc seconds in the third grid and finally one arc
724second in the finest grid near Patong. The computational domain is
725shown in Figure~\ref{fig:computational_domain}.
732\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).}
738Figure \ref{fig:jasonComparison} provides a comparison of the
739\textsc{ursga}-predicted sea surface elevation with the \textsc{jason}
740satellite altimetry data. The \textsc{ursga} model replicates the
741amplitude and timing of the the wave observed at $2.5^0$ South,
742but underestimates the amplitude of the wave further to the south at
743$4^0$ South. In the model, the southern most of these two waves
744appears only as a small bump in the cross section of the model (shown
745in Figure~\ref{fig:jasonComparison}) instead of being a distinct peak
746as can be seen in the satellite data. Also note
747that the \textsc{ursga} model prediction of the ocean surface
748elevation becomes out of phase with the \textsc{jason} 
749data at $3^0$ to $7^0$ North
750latitude. Chlieh et al~\cite{chlieh07} also observed these misfits and
751suggest it is caused by a reflected wave from the Aceh Peninsula that
752is not resolved in the model due to insufficient resolution of the
753computational mesh and bathymetry data. This is also a limitation of
754the model presented here which could be improved by nesting
755grids near Aceh.
760\caption{Comparison of the \textsc{ursga}-predicted surface elevation
761  with the \textsc{jason} satellite altimetry data. The \textsc{ursga} wave
762  heights have been corrected for the time the satellite passed
763  overhead compared to \textsc{jason} sea level anomaly.}
767FIXME (Jane): This graph does not look nice. The legend URS Model should
768be URSGA model.
771After propagating the tsunami in the open ocean using \textsc{ursga},
772the approximated ocean and surface elevation and horisontal flow
773velocities were extracted and used to construct a boundary condition
774for the \textsc{anuga} model. The interface between the \textsc{ursga}
775and \textsc{anuga} models was chosen to roughly follow the 100~m depth
776contour along the west coast of Phuket Island. The computational
777domain is shown in Figure~\ref{fig:computational_domain}.
779The domain was discretised into 386,338 triangles. The resolution of
780the grid was increased in regions inside the bay and on-shore to
781efficiently increase the simulation accuracy for the impact area.
782The grid resolution ranged between a
783maximum triangle area of $1\times 10^5$ m$^2$ near the western ocean
784boundary to $20$ m$^2$ in the small regions surrounding the inundation
785region in Patong Bay. Due to a lack of available data, friction was
786set to a constant throughout the computational domain. For the
787reference simulation, a Manning's coefficient of 0.01 was chosen to
788represent a small resistance to the water flow. See Section
789\ref{sec:friction sensitivity} for details on model sensitivity to
790this parameter.
793The boundary condition at each side of the domain towards the south
794and the north where no information about the incident wave or
795its velocity field is available
796was chosen as a transmissive
797boundary condition, effectively replicating the time dependent wave
798height present just inside the computational domain.
799The velocity field on these boundaries was set
800to zero. Other choices include applying the mean tide value as a
801Dirichlet boundary condition. But experiments as well as the
802result of the verification reported here showed that this approach
803tends to underestimate the tsunami impact due to the tempering of the
804wave near the side boundaries, whereas the transmissive boundary
805condition robustly preserves the wave.
807During the \textsc{anuga} simulation the tide was kept constant at
808$0.80$ m. This value was chosen to correspond to the tidal height
809specified by the Thai Navy tide charts
810(\url{}) at the time the tsunami arrived
811at Patong Bay. Although the tsunami propagated for approximately three
812hours before it reach Patong Bay, the period of time during which the
813wave propagated through the \textsc{anuga} domain is much
814smaller. Consequently the assumption of constant tide height is
817Maximum onshore inundation depth was computed from the model
818throughout the entire Patong Bay region.
819Figure~\ref{fig:inundationcomparison1cm} (left) shows very good
820agreement between the measured and simulated inundation. However
821these results are dependent on the classification used to determine
822whether a region in the numerical simulation was inundated. In
823Figure~\ref{fig:inundationcomparison1cm} (left) a point in the computational
824domain was deemed inundated if at some point in time it was covered by
825at least 1 cm of water. However, the precision of the inundation boundary
826generated by the on-site survey is most likely less than that as it
827was determined by observing water marks and other signs
828left by the receding waters. Consequently the measurement error along
829the inundation boundary of the survey is likely to vary significantly
830and somewhat unpredictably.
831An inundation threshold of 10 cm therefore was selected for inundation
832extents reported in this paper to reflect
833the more likely accuracy of the survey, and subsequently facilitate a more
834appropriate comparison between the modelled and observed inundation
836Figure~\ref{fig:inundationcomparison1cm} (right) shows the simulated
837inundation using a larger threshold of 10 cm.
840The datasets necessary for reproducing the results
841of the inundation stage are available on Sourceforge under the \textsc{anuga}
842project (\url{}).
843At the time of
844writing the direct link is \url{}.
846The scripts required are part of the \textsc{anuga} distribution also
847available from Sourceforge \url{} under
848the validation section.
850An animation of this simulation is available on the \textsc{anuga} website at \url{} or directly from \url{}.
857\caption{Simulated inundation versus observed inundation using an
858inundation threshold of 1cm (left) and 10cm (right).}
863To quantify the agreement between the observed and simulated inundation we
864introduce the measure
866\rho_{in}=\frac{A(I_m\cap I_o)}{A(I_o)}
868representing the ratio $\rho_{in}$ of the observed
869inundation region $I_o$ captured by the model $I_m$. Another useful
870measure is the fraction of the modelled inundation area that falls
871outside the observed inundation area given by the formula
873\rho_{out}=\frac{A(I_m\setminus (I_m\cap I_o))}{A(I_o)}
875These values for the two aforementioned simulations are given in
876Table~\ref{table:inundationAreas}. High value of both $\rho_{in}$ and $\rho_{out}$ indicate
877that the model overestimates the impact whereas low values of both quantities would indicate
878an underestimation. A high value of $\rho_{in}$ combined with a low value of $\rho_{out}$ 
879indicates a good model prediction of the survey.
881Discrepancies between the survey data and the modelled inundation
882include: unknown distribution of surface roughness, inappropriate
883parameterisation of the source model, effect of humans structures on
884flow, as well as uncertainties in the elevation data, effects of
885erosion and deposition by the tsunami event,
886measurement errors in the GPS survey recordings, and
887missing data in the field survey data itself. The impact of some of
888these sources of uncertainties are is investigated in
891\subsection{Eye-witness accounts}
892Figure \ref{fig:gauge_locations} shows four locations where time
893series have been extracted from the model. The two offshore time series
894are shown in Figure \ref{fig:offshore_timeseries} and the two onshore
895timeseries are shown in Figure \ref{fig:onshore_timeseries}. The
896latter coincide with locations where video footage from the event is
897available as described in Section \ref{sec:eyewitness data}.
902\caption{Location of timeseries extracted from the model output.}
912\caption{Time series obtained from the two offshore gauge locations,
9137C and 10C, shown in Figure \protect \ref{fig:gauge_locations}.}
922\caption{Time series obtained from the two onshore locations, North and South,
923shown in Figure \protect \ref{fig:gauge_locations}.}
929The estimated depths and flow rates given in Section
930\ref{sec:eyewitness data} are shown together with the modelled depths
931and flow rates obtained from the model in Table \ref{tab:depth and
932  flow comparisons}. The minimum depths shown in the model are clearly
933lower than expected and an indication that the tsunami model does not
934predict flow dynamics accurately at this level of detail. However,
935this comparison serves to check that depths and speeds predicted are
936within the range of what is expected.
941  \begin{array}{|l|cc|cc|}
942  \hline
943                 & \multicolumn{2}{|c|}{\mbox{Depth [m]}}
944                 & \multicolumn{2}{c|}{\mbox{Flow [m/s]}} \\ 
945                 & \mbox{Observed} & \mbox{Modelled}
946                 & \mbox{Observed} & \mbox{Modelled} \\ \cline{2-5}                 
947    \mbox{North} & 1.5-2 & 1.4 & 5-7 & 0.1 - 3.3 \\
948    \mbox{South} & 1.5-2 & 1.5 & 0.5-2 & 0.2 - 2.6 \\ \hline
949  \end{array}
951\label{tab:depth and flow comparisons}
953FIXME (Jane): We should perhaps look at average data in area surrounding these points
955%can be estimated with landmarks found in
956%satellite imagery and the use of a GIS and were found to be in the
957%range of 5 to 7 metres per second (+/- 2 m/s) in the north and 0.5 to
958%2 metres per second (+/- 1 m/s) in the south.
960Given the uncertainties in both model and observations, there is agreement
961between the values obtained from the videos and the simulations.
963% Our modelled flow rates show
964%maximum values in the order of 0.2 to 2.6 m/s in the south and 0.1 to
965%3.3 m/s for the north as shown in the figures. Water depths could also
966%be estimated from the videos by the level at which water rose up the
967%sides of buildings such as shops. Our estimates are in the order of
968%1.5 to 2.0 metres (+/- 0.5 m). This is in the same range as our
969%modelled maximum depths of 1.4 m in the north and 1.5 m in the south
970%as seen in the figure.
977\section{Sensitivity Analysis}
979This section investigates the effect of different values of Manning's
980friction coefficient, changing waveheight at the 100 m depth contour,
981and the presence and absence of buildings in the elevation dataset on
982model maximum inundation. The reference model is the one reported in
983Figure~\ref{fig:inundationcomparison1cm} (right) with a friction coefficient of 0.01,
984buildings included and the boundary condition produced by the
985\textsc{ursga} model.
989\label{sec:friction sensitivity}
990The first sensitivity study investigated the impact of surface roughness on the
991predicted run-up. According to Schoettle~\cite{schoettle2007}
992appropriate values of Manning's coefficient range from 0.007 to 0.03
993for tsunami propagation over a sandy sea floor and the reference model
994uses a value of 0.01.  To investigate sensitivity to this parameter,
995we simulated the maximum onshore inundation using a Manning's
996coefficient of 0.0003 and 0.03. The resulting inundation maps are
997shown in Figure~\ref{fig:sensitivity_friction} and the maximum flow
998speeds in Figure~\ref{fig:sensitivity_friction_speed}. These figures
999show that the on-shore inundation extent decreases with increasing
1000friction and that small perturbations in the friction cause bounded
1001changes in the output. This is consistent with the conclusions of
1002Synolakis~\cite{synolakis05} et al, who state that the long wavelength of
1003tsunami tends to mean that friction is less important in
1004comparison to the motion of the wave.
1007\subsection{Input Wave Height}\label{sec:waveheightSA}
1008The effect of the wave height used as input to the inundation model
1009\textsc{anuga} was also investigated.
1010Figure~\ref{fig:sensitivity_boundary} indicates that the inundation
1011severity is directly proportional to the boundary waveheight but small
1012perturbations in the input wave height of 10 cm appear to have little
1013effect on the final inundated area. Obviously larger perturbations
1014will have greater impact. However, wave heights in the open ocean are
1015generally well
1016predicted by the generation and propagation models such as
1017\textsc{ursga} as demonstrated in Section \ref{sec:resultsPropagation} 
1018and also in \cite{thomas2009}.
1023\subsection{Buildings and Other Structures}
1024The presence or absence of physical buildings in the elevation model was also
1027shows the inundated area and the associated maximum flow speeds
1028in the presence and absence of buildings. It
1029is apparent that densely built-up areas act as
1030dissipators greatly reducing the inundated area. However, flow speeds
1031tend to increase in passages between buildings.
1037\caption{$\rho_{in}$ and $\rho_{out}$ of the reference simulation and all sensitivity studies.}
1040 & $\rho_{in}$ & $\rho_{out}$ \\ 
1042Reference model & 0.79 & 0.20\\ 
1043Friction = 0.0003 & 0.83 & 0.26 \\ 
1044Friction = 0.03 & 0.67 & 0.09\\ 
1045Boundary wave hight minus 10 cm & 0.77 & 0.17 \\
1046Boundary wave hight plus 10 cm & 0.82 & 0.22 \\
1047No Buildings & 0.94 & 0.44 \\
1056This paper proposes an additional field data benchmark for the
1057verification of tsunami inundation models. Currently, there is a
1058scarcity of appropriate validation datasets due to a lack of well-documented
1059historical tsunami impacts. The benchmark proposed here
1060utilises the uniquely large amount of observational data for model
1061comparison obtained during, and immediately following, the
1062Sumatra--Andaman tsunami of 26 December 2004. Unlike the small
1063number of existing benchmarks, the proposed test validates all three
1064stages of tsunami evolution - generation, propagation and
1065inundation. In an attempt to provide higher visibility and easier
1066accessibility for tsunami benchmark problems, the data used to
1067construct the proposed benchmark is documented and freely available at
1070This study also shows that the tsunami impact modelling methodology
1071adopted is credible and able to predict inundation extents with reasonable
1072accuracy.  An associated aim of this paper was to further validate the
1073hydrodynamic modelling tool \textsc{anuga} which is used to simulate
1074the tsunami inundation. Model predictions
1075matched well the geodetic measurements of the Sumatra--Andaman earthquake,
1076altimetry data from the \textsc{jason}, eye-witness accounts of wave
1077front arrival times and flow speeds and a detailed inundation survey
1078of Patong Bay, Thailand.
1080A simple sensitivity analysis was performed to assess the influence of
1081small changes in friction, wave height at the 100 m depth contour and
1082the presence of buildings and other structures on the model
1083predictions. Of these three, the presence of buildings was shown to
1084have the greatest influence on
1085the simulated inundation extent. The value of friction and small
1086perturbations in the waveheight at the \textsc{anuga} boundary have
1087comparatively little effect on the model results.
1091This project was undertaken at Geoscience Australia and the Department
1092of Mathematics, The Australian National University. The authors would
1093like to thank Niran Chaimanee from the CCOP for providing
1094the post 2004 tsunami survey data, building footprints, aerial
1095photography and the elevation data for Patong city, Prapasri Asawakun
1096from the Suranaree University of Technology and Parida Kuneepong for
1097supporting this work; and Drew Whitehouse from the Australian National
1098University for preparing the animation of the simulated impact.
1103This appendix present the images used to assess the model sensitivities described in
1110\caption{Results from reference model as reported in Section \protect \ref{sec:results},
1111  i.e.\ including buildings and a friction value of 0.01. The seaward boundary condition is as
1112  provided by the \textsc{ursga} model. The left image shows the maximum
1113  modelled depth while the right hand image shows the maximum modelled
1114  flow velocities.}
1125\caption{Model results with wave height at \textsc{anuga} boundary artificially
1126  modified to assess sensitivities. The reference inundation extent is shown in Figure
1127  \protect \ref{fig:reference_model} (left).  The left and right images
1128  show the inundation results if the wave at the \textsc{anuga} boundary
1129  is reduced or increased by 10 cm respectively. The inundation
1130  severity varies in proportion to the boundary waveheight, but the
1131  model results are only slightly sensitive to this parameter for the
1132  range of values tested.}
1136FIXME (Jane): How and why was the +/- 10 cm chosen?
1143\caption{The maximal flow speeds for the same model parameterisations
1144  found in Figure \protect \ref{fig:sensitivity_boundary}. The
1145  reference flow speeds are shown in Figure \protect
1146  \ref{fig:reference_model} (right).}
1155\caption{Model results show the effect of buildings in
1156  the elevation data set.
1157  The left hand image shows the maximum inundation depth results for
1158  a model entirely without buildings.  As expected, the absence of
1159  buildings will increase the inundation extent beyond what was
1160  surveyed. The right hand image shows the corresponding flow speeds in the absence of buildings. 
1161  The reference results are as shown in Figure
1162  \protect \ref{fig:reference_model}.}
1172\caption{Model results for different values of Manning's friction
1173  coefficient shown to assess sensitivities. The reference inundation extent for a
1174  friction value of 0.01 is shown in Figure
1175  \protect \ref{fig:reference_model} (left).  The left and right images
1176  show the inundation results for friction values of 0.0003 and
1177  0.03 respectively. The inundation extent increases for the lower
1178  friction value while the higher slows the flow and decreases the
1179  inundation extent. Ideally, friction should vary across the entire
1180  domain depending on terrain and vegetation, but this is beyond the
1181  scope of this study.}
1190\caption{The maximal flow speeds for the same model parameterisations
1191  found in Figure \protect \ref{fig:sensitivity_friction}. The
1192  reference flow speeds are shown in Figure \protect
1193  \ref{fig:reference_model} (right).}
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