source: anuga_work/publications/boxing_day_validation_2008/data.tex @ 7529

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Another stab at the bathymetry section

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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 and high quality topographic data, have now been made
10available. %~\cite{vigny05,amnon05,kawata05,liu05}.
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 extent 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 speed 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 were derived from the following
79sources:
80\begin{itemize}
81\item a two arc minute data grid 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 three arc second data grid obtained directly from NOAA covering the
85  whole of the Andaman Sea based on the
86  Smith \& Sandwell two minute
87  dataset (\url{http://topex.ucsd.edu/WWW_html/srtm30_plus.html}),
88  coastline constrained using SRTM data (\url{http://srtm.csi.cgiar.org})
89  as well as Thai Navy charts no.\ 45 and no.\ 362; and 
90\item Thai Navy chart no.\ 358 providing depth soundings inside Patong Bay.
91\end{itemize}
92
93These data sets were used to produce four nested grids as
94shown in Figure~\ref{fig:nested_grids}.
95The nested approach was chosen to match model resolution requirements
96according to the principle that shallow water flows are more sensitive
97to variations in elevation data than deep water flows. Consequently,
98the elevation data in shallow waters and on-shore need to be resolved
99better than elevation data further off-shore.
100The four nested grids were derived as follows:
101\begin{itemize} 
102  \item \textbf{27~arc second grid} obtained by interpolating the two
103    minute DBDB2 grid. This is the coarsest grid used in the
104    simulations.
105  \item \textbf{9~arc second grid} generated by sub-sampling
106    the three second arc grid from NOAA.
107  \item \textbf{3~arc second grid} formed as a subset of the three second grid
108    from NOAA.
109  \item \textbf{1~arc second grid} created by digitising Thai Navy
110    bathymetry chart no.\ 358 followed by a gridding procedure as
111    described below. This grid is the smallest and
112    covers the Bay area and immediately adjacent regions.
113    The digitised points and contour lines
114    from this chart are shown in Figure~\ref{fig:patong_bathymetry}.
115\end{itemize} 
116   
117The gridding process for the finest grid was performed
118using \textsc{Intrepid}, a commercial geophysical processing
119package developed by Intrepid Geophysics\footnote{See
120  \url{http://www.intrepid-geophysics.com/ig/manuals/english/gridding.pdf}
121  for details on the Intrepid gridding scheme.}. Any points that
122deviated from the general trend near the boundary were deleted
123through a quality control process.  The sub-sampling of larger
124grids was performed by using \textsc{resample}, a Generic Mapping
125Tools (\textsc{GMT}) program \cite{wessel98}.
126
127
128\begin{figure}[ht]
129\begin{center}
130\includegraphics[width=\textwidth,keepaspectratio=true]{figures/nested_grids}
131\end{center}
132
133\caption{Nested elevation grids of the Andaman Sea with
134highest resolution at and around Patong Bay.}
135\label{fig:nested_grids}
136\end{figure}
137
138\subsubsection{JASON Satellite Altimetry}\label{sec:data_jason}
139During the 26 December 2004 event, the \textsc{jason} satellite tracked from
140north to south and over the equator at 02:55~UTC nearly two hours
141after the earthquake \cite{gower05}. The satellite recorded the sea
142level anomaly compared to the average sea level from its previous five
143passes over the same region in the 20-30 days prior. This data was
144used to validate the propagation stage in Section
145\ref{sec:resultsPropagation}.
146
147
148%DB I suggest we combine with model data to reduce the number of figures. The satellite track is shown in Figure~\ref{fig:satelliteTrack}.
149
150\subsection{Inundation}
151\label{sec:inundation data}
152Inundation is the final stage of the evolution of a tsunami and refers
153to the run-up of tsunami onto land. This process is typically the most
154difficult of the three stages to model due to thin layers of water
155flowing rapidly over dry land.  Aside from requiring robust solvers
156which can simulate such complex flow patterns, this part of the
157modelling process also requires high resolution and quality elevation
158data which is often not available. In the case of model validation
159high quality field measurements are also required. For the proposed
160benchmark a high resolution topography data set (in the form of GIS
161contour lines) and a tsunami inundation survey map from the
162Coordinating Committee Co-ordinating Committee for Geoscience
163Programmes in East and Southeast Asia (CCOP) \cite{szczucinski06}
164was obtained to validate model inundation. In this section we also present eye-witness
165accounts which can be used to qualitatively validate tsunami
166inundation.
167
168\subsubsection{Topography Data}
169A 1~second grid comprising the onshore topography and the nearshore
170bathymetry for Patong Beach was created from the Thai Navy charts
171(described in Section \ref{sec:bathymetry data}) and from 1~m and 10~m
172elevation contours provided by the CCOP. The 1~second terrain model
173for the community is shown in Figure~\ref{fig:patong_bathymetry}.
174
175To provide increased resolution for the surveyed area,
176two 1/3~second grids were created: One for the saddle point covering
177Merlin and Tri Trang Beaches (separate survey patch to the left in
178Figure~\ref{fig:patongescapemap})
179and one for Patong City and its immediate
180shore area (main surveyed area in Figure~\ref{fig:patongescapemap}).
181These grids were based on the same data used for
182the 1~second data grid.  The Patong city grid was further modified based on
183satellite imagery to include the river and lakes towards the south of
184Patong City which were not part of the provided elevation data. 
185The depth of the river and lake system was set uniformly to a depth of 1~m.
186
187
188\begin{figure}[ht]
189\begin{center}
190\includegraphics[width=8.0cm,keepaspectratio=true]{figures/patong_bay_data.jpg}
191\end{center}
192
193\caption{3D view of the elevation data set used for the nearshore propagation and inundation in Patong City showing
194digitised data points and contours as well as rivers and roads
195draped over the data model.}
196\label{fig:patong_bathymetry}
197\end{figure}
198
199
200\subsubsection{Buildings and Other Structures}
201Human-made buildings and structures can significantly affect tsunami
202inundation. The footprint and number of floors of the buildings in
203Patong Bay were extracted from the data provided by CCOP.  The heights
204of these buildings were estimated assuming that each floor has a
205height of 3~m and the resulting profiles were added to the topographic
206dataset. The resulting elevation model and its interaction with one of
207the tsunami waves can be seen in Figure~\ref{fig:anuga screenshot} in
208Section~\ref{sec:inundation results}.
209
210
211\subsubsection{Inundation Survey}
212Tsunami run-up in built-up areas can be the cause of large financial and human
213losses, yet run-up data that can be used to validate model run-up
214predictions is scarce because such events are relatively infrequent.
215Of the two field benchmarks proposed
216in~\cite{synolakis08},
217only the Okushiri benchmark facilitates comparison between
218modelled and observed run-up. One of the major strengths of the
219benchmark proposed here is that modelled run-up can be compared to an
220inundation survey which maps the maximum run-up along an entire coastline
221rather than at a series of discrete sites. The survey map is
222shown in Figure~\ref{fig:patongescapemap} and plots the maximum run-up
223of the 2004 Indian Ocean tsunami in Patong city. Refer to Szczucinski et
224al~\cite{szczucinski06} for further details.
225
226\begin{figure}[ht]
227\begin{center}
228\includegraphics[width=\textwidth,keepaspectratio=true]{figures/post_tsunami_survey.jpg}
229\end{center}
230
231\caption{Tsunami survey mapping the maximum observed inundation at
232  Patong City courtesy of the CCOP \protect \cite{szczucinski06}.}
233\label{fig:patongescapemap}
234\end{figure}
235
236
237\subsubsection{Eyewitness Accounts}\label{sec:eyewitness data}
238Eyewitness accounts detailed in~\cite{papadopoulos06}
239report that many people at Patong Beach observed an initial
240retreat (trough or draw down) of
241the shoreline of more than 100~m followed a few minutes later by a
242strong wave (crest). Another less powerful wave arrived another five
243or ten minutes later. Eyewitness statements place the arrival time of
244the first wave between 9:55~am and 10:05~am local time or about 2~hours
245after the source rupture.
246
247
248\begin{figure}[ht]
249\begin{center}
250\includegraphics[width=\textwidth,keepaspectratio=true]{figures/gauges.jpg}
251\end{center}
252
253\caption{Location of time series extracted from the model output.}
254\label{fig:gauge_locations}
255\end{figure}
256
257Two videos were sourced\footnote{The footage is
258widely available and can, for example, be obtained from
259\url{http://www.archive.org/download/patong_bavarian/patong_bavaria.wmv}
260(Comfort Resort) and
261\url{http://www.archive.org/download/tsunami_patong_beach/tsunami_patong_beach.wmv}
262(Novotel).}
263%http://wizbangblog.com/content/2005/01/01/wizbang-tsunami.php
264which include footage of the tsunami in Patong City on the day
265of the 2004 Indian Ocean tsunami. Both videos show an already inundated
266street. They also show what is to be assumed as the second
267and third waves approaching and further flooding of the buildings and
268street. The first video is in the very north, filmed from what is
269believed to be the roof of the Novotel Hotel marked ``north'' in Figure
270\ref{fig:gauge_locations}. The second video is in the very south,
271filmed from the second story of a building next door to the Comfort
272Resort near the corner of Ruam Chai St and Thaweewong Road.  This
273location is marked ``south'' in Figure \ref{fig:gauge_locations}.
274Figure~\ref{fig:video_flow} shows stills from this video. Both videos
275were used to estimate flow speeds and inundation depths over time.
276
277\begin{figure}[ht]
278\begin{center}
279\includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_0_00sec.jpg}
280\includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_5_04sec.jpg}
281\includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_7_12sec.jpg}
282\includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_7_60sec.jpg}
283\end{center}
284
285\caption{Four frames from a video where flow rate could be estimated,
286  circle indicates tracked debris, from top left: 0.0 s, 5.0 s, 7.1
287  s, 7.6 s.}
288\label{fig:video_flow}
289\end{figure}
290
291Flow rates were estimated using landmarks found in both videos and
292were found to be in the range of 5 to 7 m/s ($\pm$2 m/s)
293in the north and 0.5 to 2 m/s ($\pm$1 m/s) in the
294south\footnote{These error bounds were estimated from uncertainty in aligning the debris with building boundaries in the videos.}.
295Water depths could also
296be estimated from the videos by the level at which water rose up the
297sides of buildings such as shops. Our estimates are in the order of
2981.5 to 2.0 m ($\pm$0.5 m estimated error bounds).
299Fritz~\cite{fritz06} performed a detailed
300analysis of video frames taken around Banda Aceh and arrived at flow
301speeds in the range of 2 to 5 m/s.
302
303
304\subsection{Validation Check-List}
305\label{sec:checkList}
306The data described in this section can be used to construct a
307benchmark to validate tsunami models.
308 In particular we propose that a legitimate tsunami model
309should reproduce the following behaviour:
310\begin{itemize}
311 \item the inundation survey map in Patong city
312   (Figure~\ref{fig:patongescapemap}),
313 \item a leading depression followed by two distinct crests
314   of decreasing magnitude at the beach,
315 \item predict the water depths and flow speeds, at the locations of
316   the eye-witness videos, that fall within the bounds obtained from
317   the videos,
318 \item the \textsc{jason} satellite altimetry sea surface
319   anomalies (see Section~\ref{sec:data_jason}), and
320 \item the vertical deformation observed in north-western
321   Sumatra and along the Nicobar--Andaman islands (see
322   Section~\ref{sec:gen_data}).
323\end{itemize}
324
325Ideally, the model should also be compared to measured time series of
326wave heights and flow speeds but the authors are not aware of the
327availability of such data near Patong Bay.
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