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1\section{Data}\label{sec:data}
2The sheer magnitude of the 2004 Sumatra-Andaman earthquake and the
3devastation caused by the subsequent tsunami have generated much
4scientific interest. As a result an unusually large amount of post
5seismic data has been collected and documented. Data sets from
6seismometers, tide gauges, \textsc{gps} surveys, satellite overpasses,
7subsequent coastal field surveys of run-up and flooding, and
8measurements of coseismic displacements as well as bathymetry from ship-based
9expeditions, have now been made
10available. %~\cite{vigny05,amnon05,kawata05,liu05}. FIXME (Ole): Refs?  Are the references here inappropriate?
11
12In this section we present the corresponding data necessary to implement
13the proposed benchmark. Here we note that the overwhelming focus of tsunami
14modelling is the prediction of inundation extent. The ``fit'' of observed and
15 modelled runup should have the greatest influence on conclusions regarding
16model validity. In fact for non-physics based models it may not be possible
17 to validate the generation and propagation phases of tsunami evolution.
18However, for physics-based models evaluation of the model during the generation
19 and propagation phases is still useful. If a model is physics-based one
20should ensure that all physics are being modelled accurately. Moreover
21evaluation of all three stages of tsunami evolution can help identify the
22cause of any discrepancies between modelled and observed inundation.
23Consequently in this section we present data not only to facilitate
24validation of inundation but to also aid the assessment of tsunami
25generation and propagation.
26
27\subsection{Generation}\label{sec:gen_data}
28All tsunami are generated from an initial disturbance of the ocean
29which develops into a low frequency wave that propagates outwards from
30the source. The initial deformation of the water surface is most
31commonly caused by coseismic displacement of the sea floor, but
32submarine mass failures, landslides, volcanoes or asteroids can also
33cause tsunami. In this section we detail the information used in
34this study to validate models of the sea floor deformation generated
35by the 2004 Sumatra--Andaman earthquake.
36
37The 2004 Sumatra--Andaman tsunami was generated by a coseismic
38displacement of the sea floor resulting from one of the largest
39earthquakes on record. The mega-thrust earthquake started on the 26
40December 2004 at 0h58'53'' UTC (or just before 8 am local time)
41approximately 70 km offshore of North Sumatra
42(\url{http://earthquake.usgs.gov/eqcenter/eqinthenews/2004/usslav}). The
43rupture propagated 1000-1300 km along the Sumatra-Andaman trench to
44the north at a rate of 2.5-3 km.s$^{-1}$ and lasted approximately 8-10
45minutes~\cite{ammon05}. Estimates of the moment magnitude of this
46event range from about 9.1 to 9.3 $M_w$~\cite{chlieh07,stein07}.
47
48The unusually large surface deformation caused by this earthquake
49means that there were a range of different geodetic measurements of
50the surface deformation available. These include field measurements of
51uplifted or subsided coral heads, continuous or campaign \textsc{GPS}
52measurements and remote sensing measurements of uplift or subsidence
53(see~\cite{chlieh07} and references therein). Here we use the the near-field
54estimates of vertical deformation in northwestern Sumatra and
55the Nicobar-Andaman islands collated by~\cite{chlieh07} to assess whether
56our crustal deformation model of the 2004 Sumatra--Andaman
57earthquake is producing reasonable results. Note that the geodetic
58data used here is a combination of the vertical deformation that
59happened in the $\sim$10 minutes of the earthquake plus the
60deformation that followed in the days following the earthquake before
61each particular measurement was actually made (typically of order
62days). Therefore some of the observations may not contain the purely
63co-seismic deformation but could include some post-seismic deformation
64as well~\cite{chlieh07}.
65
66\subsection{Propagation}
67\label{sec:propagation data}
68Once generated, a tsunami will propagate outwards from the source until
69it encounters the shoreline bordering coastal regions. This period
70of the tsunami evolution is referred to as the propagation stage. The
71height and velocity of the tsunami is dependent on the local
72bathymetry in the regions through which the wave travels and the size
73of the initial wave. This section details the bathymetry data needed
74to model the tsunami propagation and the satellite altimetry transects
75used here to validate open ocean tsunami models.
76
77\subsubsection{Bathymetry Data}\label{sec:bathymetry data}
78The bathymetry data used in this study was derived from the following
79sources:
80\begin{itemize}
81\item a two arc minute grid data set covering the Bay of Bengal,
82  DBDB2, obtained from US Naval Research Labs
83  (\url{http://www7320.nrlssc.navy.mil/DBDB2_WWW});
84\item a 3 second arc grid obtained directly from NOAA covering the
85  whole of the Andaman Sea based on the
86  Smith \& Sandwell 2-minute
87  dataset (\url{http://topex.ucsd.edu/WWW_html/srtm30_plus.html})as well as
88  Thai Navy charts no. 45 and no. 362; and 
89\item a one second grid created from the digitised Thai Navy
90  bathymetry chart, no. 358, which covers Patong Bay and the
91  immediately adjacent regions.
92  The gridding of data was performed using {\bf Intrepid}, a commercial
93  geophysical processing package developed by Intrepid Geophysics. The
94  gridding scheme employed the nearest neighbour algorithm followed by
95  an application of minimum curvature akima spline smoothing.
96  See \url{http://www.intrepid-geophysics.com/ig/manuals/english/gridding.pdf} 
97  for details on the Intrepid model. 
98\end{itemize}
99
100These sets were combined via
101interpolation and resampling to produce four nested grids
102which are relatively coarse in the deeper water and
103progressively finer as the distance to
104Patong Beach decreases as shown in Figure~\ref{fig:nested_grids}
105
106The coarsest
107bathymetry was obtained by interpolating the DBDB2 grid to a 27 second
108arc grid. A subsection of this region was then replaced by nine second
109data which was generated by sub-sampling the three second of arc grid from
110NOAA. It is an artificially generated data set which is a subset of the original data.
111
112A subset of the nine second grid was replaced by the three second
113data. Finally, the one second grid was used to approximate the
114bathymetry in Patong Bay and the immediately adjacent regions. Any
115points that deviated from the general trend near the boundary were
116deleted as a quality check.
117
118A one second grid was used to approximate the bathymetry in Patong
119Bay. This elevation data was created from the digitised Thai
120Navy bathymetry chart, no 358. The digitised points and contour lines
121from this chart are shown in Figure~\ref{fig:patong_bathymetry}.
122
123
124The sub-sampling of larger grids was performed by using {\bf resample},
125a Generic Mapping Tools (\textsc{GMT}) program (\cite{wessel98}).
126
127
128\begin{figure}[ht]
129\begin{center}
130\includegraphics[width=\textwidth,keepaspectratio=true]{figures/nested_grids}
131\caption{Nested bathymetry grids.}
132\label{fig:nested_grids}
133\end{center}
134\end{figure}
135
136\subsubsection{JASON Satellite Altimetry}\label{sec:data_jason}
137During the 26 December 2004 event, the \textsc{jason} satellite tracked from
138north to south and over the equator at 02:55 UTC nearly two hours
139after the earthquake \cite{gower05}. The satellite recorded the sea
140level anomaly compared to the average sea level from its previous five
141passes over the same region in the 20-30 days prior. This data was
142used to validate the propagation stage in Section
143\ref{sec:resultsPropagation}.
144
145
146%DB I suggest we combine with model data to reduce the number of figures. The satellite track is shown in Figure~\ref{fig:satelliteTrack}.
147
148\subsection{Inundation}
149\label{sec:inundation data}
150Inundation is the final stage of the evolution of a tsunami and
151refers to the run-up of tsunami onto land. This process is typically the most
152difficult of the three stages to model due to thin layers of water
153flowing rapidly over dry land.  Aside from requiring robust solvers
154which can simulate such complex flow patterns, this part of the
155modelling process also requires high resolution and quality elevation
156data which is often not available. In the case of model validation
157high quality field measurements are also required. For the proposed
158benchmark a high resolution (1 second) topography data set and a
159tsunami inundation survey map from the
160Coordinating Committee Co-ordinating Committee for Geoscience Programmes
161in East and Southeast Asia (CCOP) (\cite{szczucinski06}) was obtained
162to validate model inundation. See also acknowledgements at the end of this paper. In this section we also present eye-witness accounts which can be used
163to qualitatively validate tsunami inundation.
164
165\subsubsection{Topography Data}
166The 1 second onshore topography for Patong Beach provided by the CCOP was
167merged with the nearshore 1 second bathymetry described in Section
168\ref{sec:bathymetry data} to provide a seamless terrain model for the
169bay and community as shown in Figure~\ref{fig:patong_bathymetry}.
170
171
172\begin{figure}[ht]
173\begin{center}
174\includegraphics[width=8.0cm,keepaspectratio=true]{figures/patong_bay_data.jpg}
175\caption{3D visualisation of the elevation data set used in Patong Bay showing data points, contours, rivers and roads draped over the final model.}
176\label{fig:patong_bathymetry}
177\end{center}
178\end{figure}
179FIXME (Jane): legend? Were the contours derived from the final dataset?
180This is not the entire model, only the bay and the beach. RICHARD
181
182\subsubsection{Buildings and Other Structures}
183Human-made buildings and structures can significantly affect tsunami
184inundation. The footprint and number of floors of the
185buildings 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).
186The heights of these
187buildings were estimated assuming that each floor has a height of 3 m and they
188were added to the topographic dataset.
189
190\subsubsection{Inundation Survey}
191Tsunami run-up in built-up areas can be the cause of large financial and human
192losses, yet run-up data that can be used to validate model run-up
193predictions is scarce because such events are relatively infrequent.
194Of the two field benchmarks proposed
195in~\cite{synolakis08},
196only the Okushiri benchmark facilitates comparison between
197modelled and observed run-up. One of the major strengths of the
198benchmark proposed here is that modelled run-up can be compared to an
199inundation survey which maps the maximum run-up along an entire coastline
200rather than at a series of discrete sites. The survey map is
201shown in Figure~\ref{fig:patongescapemap} and plots the maximum run-up
202of the 2004 Indian Ocean tsunami in Patong city. Refer to Szczucinski et
203al~\cite{szczucinski06} for further details.
204
205\begin{figure}[ht]
206\begin{center}
207\includegraphics[width=\textwidth,keepaspectratio=true]{figures/post_tsunami_survey.jpg}
208\caption{Tsunami survey mapping the maximum observed inundation at
209  Patong beach courtesy of the CCOP \protect \cite{szczucinski06}.}
210\label{fig:patongescapemap}
211\end{center}
212\end{figure}
213
214
215\subsubsection{Eyewitness Accounts}\label{sec:eyewitness data}
216Eyewitness accounts detailed in~\cite{papadopoulos06}
217report that many people at Patong Beach observed an initial
218retreat (trough or draw down) of
219the shoreline of more than 100 m followed a few minutes later by a
220strong wave (crest). Another less powerful wave arrived another five
221or ten minutes later. Eyewitness statements place the arrival time of
222the first wave between 9:55 am and 10:05 am local time or about 2 hours
223after the source rupture.
224
225
226\begin{figure}[ht]
227\begin{center}
228%\includegraphics[width=8.0cm,keepaspectratio=true]{gauge_locations.jpg}
229\includegraphics[width=\textwidth,keepaspectratio=true]{figures/gauges.jpg}
230\caption{Location of timeseries extracted from the model output. FIXME(John):
231should we combine the inundation map with the gauages map?}
232\label{fig:gauge_locations}
233\end{center}
234\end{figure}
235
236Two videos were sourced\footnote{The footage is
237widely available and can, for example, be obtained from
238\url{http://www.archive.org/download/patong_bavarian/patong_bavaria.wmv}
239(Comfort Hotel) and
240\url{http://www.archive.org/download/tsunami_patong_beach/tsunami_patong_beach.wmv}
241(Novotel)}
242%http://wizbangblog.com/content/2005/01/01/wizbang-tsunami.php
243which include footage of the tsunami in Patong Bay on the day
244of the 2004 Indian Ocean Tsunami. Both videos show an already inundated
245group of buildings. They also show what is to be assumed as the second
246and third waves approaching and further flooding of the buildings and
247street.  The first video is in the very north, filmed from what is
248believed to be the roof of the Novotel Hotel marked ``north'' in Figure
249\ref{fig:gauge_locations}. The second video is in the very south,
250filmed from the second story of a building next door to the Comfort
251Resort near the corner of Ruam Chai St and Thaweewong Road.  This
252location is marked ``south'' in Figure \ref{fig:gauge_locations}.
253Figure~\ref{fig:video_flow} shows stills from this video. Both videos
254were used to estimate flow speeds and inundation depths over time.
255
256\begin{figure}[ht]
257\begin{center}
258\includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_0_00sec.jpg}
259\includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_5_04sec.jpg}
260\includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_7_12sec.jpg}
261\includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_7_60sec.jpg}
262\caption{Four frames from a video where flow rate could be estimated,
263  circle indicates tracked debris, from top left: 0.0 sec, 5.0 s, 7.1
264  s, 7.6 s.}
265\label{fig:video_flow}
266\end{center}
267\end{figure}
268
269Flow rates were estimated using landmarks found in both videos and
270were found to be in the range of 5 to 7 metres per second (+/- 2 m/s)
271in the north and 0.5 to 2 metres per second (+/- 1 m/s) in the
272south\footnote{These error bounds were estimated from uncertainty in aligning the debris with building boundaries in the videos.}.
273Water depths could also
274be estimated from the videos by the level at which water rose up the
275sides of buildings such as shops. Our estimates are in the order of
2761.5 to 2.0 metres (+/- 0.5 m estimated error bounds).
277Fritz ~\cite{fritz06} performed a detailed
278analysis of video frames taken around Banda Aceh and arrived at flow
279speeds in the range of 2 to 5 m/s.
280
281
282\subsection{Validation Check-List}
283\label{sec:checkList}
284The data described in this section can be used to construct a
285benchmark to validate tsunami models.
286 In particular we propose that a legitimate tsunami model
287should reproduce the following behaviour:
288\begin{itemize}
289 \item reproduce the inundation survey map in Patong city
290   (Figure~\ref{fig:patongescapemap}),
291 \item simulate a leading depression followed by two distinct crests
292   of decreasing magnitude at the beach, and
293 \item predict the water depths and flow speeds, at the locations of
294   the eye-witness videos, that fall within the bounds obtained from
295   the videos.
296 \item reproduce the \textsc{jason} satellite altimetry sea surface
297   anomalies (see Section~\ref{sec:data_jason}),
298 \item reproduce the vertical deformation observed in north-western
299   Sumatra and along the Nicobar--Andaman islands (see
300   Section~\ref{sec:gen_data}),
301\end{itemize}
302
303Ideally, the model should also be compared to measured timeseries of
304waveheights and velocities but the authors are not aware of the
305availability of such data near Patong Bay.
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