\section{Data}\label{sec:data}
The sheer magnitude of the 2004 Sumatra-Andaman earthquake and the
devastation caused by the subsequent tsunami have generated much
scientific interest. As a result an unusually large amount of post
seismic data has been collected and documented. Data sets from
seismometers, tide gauges, \textsc{gps} surveys, satellite overpasses,
subsequent coastal field surveys of run-up and flooding, and
measurements of coseismic displacements as well as bathymetry from ship-based
expeditions and high quality topographic data, have now been made
available. %~\cite{vigny05,amnon05,kawata05,liu05}.

In this section we present the corresponding data necessary to implement 
the proposed benchmark. Here we note that the overwhelming focus of tsunami 
modelling is the prediction of inundation extent. The ``fit'' of observed and
 modelled runup should have the greatest influence on conclusions regarding 
model validity. In fact for non-physics based models it may not be possible
 to validate the generation and propagation phases of tsunami evolution. 
However, for physics-based models evaluation of the model during the generation
 and propagation phases is still useful. If a model is physics-based one 
should ensure that all physics are being modelled accurately. Moreover, 
evaluation of all three stages of tsunami evolution can help identify the 
cause of any discrepancies between modelled and observed inundation. 
Consequently, in this section we present data not only to facilitate 
validation of inundation extent but to also aid the assessment of tsunami 
generation and propagation.

\subsection{Generation}\label{sec:gen_data}
All tsunami are generated from an initial disturbance of the ocean
which develops into a low frequency wave that propagates outwards from
the source. The initial deformation of the water surface is most
commonly caused by coseismic displacement of the sea floor, but
submarine mass failures, landslides, volcanoes or asteroids can also
cause tsunami. In this section we detail the information used in
this study to validate models of the sea floor deformation generated
by the 2004 Sumatra--Andaman earthquake.

The 2004 Sumatra--Andaman tsunami was generated by a coseismic
displacement of the sea floor resulting from one of the largest
earthquakes on record. The mega-thrust earthquake started on the 26
December 2004 at 0h58'53'' UTC (or just before 8 am local time)
approximately 70 km offshore of North Sumatra
(\url{http://earthquake.usgs.gov/eqcenter/eqinthenews/2004/usslav}). The
rupture propagated 1000-1300 km along the Sumatra-Andaman trench to
the north at a rate of 2.5-3 km.s$^{-1}$ and lasted approximately 8-10
minutes~\cite{ammon05}. Estimates of the moment magnitude of this
event range from about 9.1 to 9.3 $M_w$~\cite{chlieh07,stein07}.

The unusually large surface deformation caused by this earthquake
means that there were a range of different geodetic measurements of
the surface deformation available. These include field measurements of
uplifted or subsided coral heads, continuous or campaign \textsc{GPS}
measurements and remote sensing measurements of uplift or subsidence
(see~\cite{chlieh07} and references therein). Here we use the the near-field
estimates of vertical deformation in northwestern Sumatra and
the Nicobar-Andaman islands collated by~\cite{chlieh07} to assess whether
our crustal deformation model of the 2004 Sumatra--Andaman
earthquake is producing reasonable results. Note that the geodetic
data used here is a combination of the vertical deformation that
happened in the $\sim$10 minutes of the earthquake plus the
deformation that followed in the days following the earthquake before
each particular measurement was actually made (typically of order
days). Therefore some of the observations may not contain the purely
co-seismic deformation but could include some post-seismic deformation
as well~\cite{chlieh07}.

\subsection{Propagation}
\label{sec:propagation data}
Once generated, a tsunami will propagate outwards from the source until
it encounters the shoreline bordering coastal regions. This period
of the tsunami evolution is referred to as the propagation stage. The
height and speed of the tsunami is dependent on the local
bathymetry in the regions through which the wave travels and the size
of the initial wave. This section details the bathymetry data needed
to model the tsunami propagation and the satellite altimetry transects
used here to validate open ocean tsunami models.

\subsubsection{Bathymetry Data}\label{sec:bathymetry data}
The bathymetry data used in this study was derived from the following 
sources:
\begin{itemize}
\item a two arc minute data grid covering the Bay of Bengal,
  DBDB2, obtained from US Naval Research Labs 
  (\url{http://www7320.nrlssc.navy.mil/DBDB2_WWW});
\item a three arc second data grid obtained directly from NOAA covering the 
  whole of the Andaman Sea based on the 
  Smith \& Sandwell two minute 
  dataset (\url{http://topex.ucsd.edu/WWW_html/srtm30_plus.html}), 
  coastline constrained using SRTM data (\url{http://srtm.csi.cgiar.org}) 
  as well as Thai Navy charts no.\ 45 and no.\ 362; and  
\item Thai Navy chart no.\ 358 providing water depths in Patong Bay. 
\end{itemize}

These data sets were combined via gridding, interpolation and resampling to produce
four nested grids which are relatively coarse in the deeper water and
progressively finer as the distance to shore Patong Beach decreases as
shown in Figure~\ref{fig:nested_grids}. This progression was chosen
to match model resolution requirements according to the principle that
shallow water flows are more sensitive to variations in elevation data
than deep water flows. Consequently, the elevation data in shallow
waters and on-shore need to be resolved better than elevation data
further off-shore.
  
The coarsest bathymetry was obtained by interpolating the DBDB2 grid
to a 27~second arc grid. A subsection of this region was then replaced
by nine second data which was generated by sub-sampling the three
second of arc grid from NOAA. It is an artificially generated data set
which is a subset of the original data.  A subset of the nine second
grid was replaced by the three second data. Finally, a one arc second
grid approximating the bathymetry in Patong Bay and the immediately
adjacent regions was created by digitising Thai Navy bathymetry chart,
no.\ 358. The digitised points and contour lines from this chart are
shown in Figure~\ref{fig:patong_bathymetry}. The gridding was
performed using \textsc{Intrepid}, a commercial geophysical processing
package developed by Intrepid Geophysics\footnote{
See
\url{http://www.intrepid-geophysics.com/ig/manuals/english/gridding.pdf}
for details on the Intrepid gridding scheme.}.
Any points that deviated from the general trend near the boundary were
deleted through a quality control process.
The sub-sampling of larger grids was performed by using \textsc{resample},
a Generic Mapping Tools (\textsc{GMT}) program \cite{wessel98}.


\begin{figure}[ht]
\begin{center}
\includegraphics[width=\textwidth,keepaspectratio=true]{figures/nested_grids}
\end{center}

\caption{Nested elevation grids of the Andaman Sea with 
highest resolution at and around Patong Bay.}
\label{fig:nested_grids}
\end{figure}

\subsubsection{JASON Satellite Altimetry}\label{sec:data_jason}
During the 26 December 2004 event, the \textsc{jason} satellite tracked from
north to south and over the equator at 02:55~UTC nearly two hours
after the earthquake \cite{gower05}. The satellite recorded the sea
level anomaly compared to the average sea level from its previous five
passes over the same region in the 20-30 days prior. This data was
used to validate the propagation stage in Section
\ref{sec:resultsPropagation}.


%DB I suggest we combine with model data to reduce the number of figures. The satellite track is shown in Figure~\ref{fig:satelliteTrack}.

\subsection{Inundation}
\label{sec:inundation data}
Inundation is the final stage of the evolution of a tsunami and refers
to the run-up of tsunami onto land. This process is typically the most
difficult of the three stages to model due to thin layers of water
flowing rapidly over dry land.  Aside from requiring robust solvers
which can simulate such complex flow patterns, this part of the
modelling process also requires high resolution and quality elevation
data which is often not available. In the case of model validation
high quality field measurements are also required. For the proposed
benchmark a high resolution topography data set (in the form of GIS
contour lines) and a tsunami inundation survey map from the
Coordinating Committee Co-ordinating Committee for Geoscience
Programmes in East and Southeast Asia (CCOP) \cite{szczucinski06}
was obtained to validate model inundation. In this section we also present eye-witness
accounts which can be used to qualitatively validate tsunami
inundation.

\subsubsection{Topography Data}
A 1~second grid comprising the onshore topography and the nearshore
bathymetry for Patong Beach was created from the Thai Navy charts
(described in Section \ref{sec:bathymetry data}) and from 1~m and 10~m
elevation contours provided by the CCOP. The 1~second terrain model
for the community is shown in Figure~\ref{fig:patong_bathymetry}.

To provide increased resolution for the surveyed area, 
two 1/3~second grids were created: One for the saddle point covering
Merlin and Tri Trang Beaches (separate survey patch to the left in 
Figure~\ref{fig:patongescapemap})
and one for Patong City and its immediate
shore area (main surveyed area in Figure~\ref{fig:patongescapemap}).
These grids were based on the same data used for 
the 1~second data grid.  The Patong city grid was further modified based on
satellite imagery to include the river and lakes towards the south of
Patong City which were not part of the provided elevation data.  
The depth of the river and lake system was set uniformly to a depth of 1~m.


\begin{figure}[ht]
\begin{center}
\includegraphics[width=8.0cm,keepaspectratio=true]{figures/patong_bay_data.jpg}
\end{center}

\caption{3D view of the elevation data set used for the nearshore propagation and inundation in Patong City showing 
digitised data points and contours as well as rivers and roads 
draped over the data model.}
\label{fig:patong_bathymetry}
\end{figure}


\subsubsection{Buildings and Other Structures}
Human-made buildings and structures can significantly affect tsunami
inundation. The footprint and number of floors of the buildings in
Patong Bay were extracted from the data provided by CCOP.  The heights
of these buildings were estimated assuming that each floor has a
height of 3~m and the resulting profiles were added to the topographic
dataset. The resulting elevation model and its interaction with one of
the tsunami waves can be seen in Figure~\ref{fig:anuga screenshot} in
Section~\ref{sec:inundation results}.


\subsubsection{Inundation Survey}
Tsunami run-up in built-up areas can be the cause of large financial and human
losses, yet run-up data that can be used to validate model run-up
predictions is scarce because such events are relatively infrequent. 
Of the two field benchmarks proposed 
in~\cite{synolakis08},
only the Okushiri benchmark facilitates comparison between
modelled and observed run-up. One of the major strengths of the
benchmark proposed here is that modelled run-up can be compared to an
inundation survey which maps the maximum run-up along an entire coastline
rather than at a series of discrete sites. The survey map is
shown in Figure~\ref{fig:patongescapemap} and plots the maximum run-up
of the 2004 Indian Ocean tsunami in Patong city. Refer to Szczucinski et
al~\cite{szczucinski06} for further details.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=\textwidth,keepaspectratio=true]{figures/post_tsunami_survey.jpg}
\end{center}

\caption{Tsunami survey mapping the maximum observed inundation at
  Patong City courtesy of the CCOP \protect \cite{szczucinski06}.}
\label{fig:patongescapemap}
\end{figure}


\subsubsection{Eyewitness Accounts}\label{sec:eyewitness data}
Eyewitness accounts detailed in~\cite{papadopoulos06}
report that many people at Patong Beach observed an initial 
retreat (trough or draw down) of
the shoreline of more than 100~m followed a few minutes later by a
strong wave (crest). Another less powerful wave arrived another five
or ten minutes later. Eyewitness statements place the arrival time of
the first wave between 9:55~am and 10:05~am local time or about 2~hours 
after the source rupture.


\begin{figure}[ht]
\begin{center}
\includegraphics[width=\textwidth,keepaspectratio=true]{figures/gauges.jpg}
\end{center}

\caption{Location of time series extracted from the model output.}
\label{fig:gauge_locations}
\end{figure}

Two videos were sourced\footnote{The footage is 
widely available and can, for example, be obtained from 
\url{http://www.archive.org/download/patong_bavarian/patong_bavaria.wmv}
(Comfort Resort) and
\url{http://www.archive.org/download/tsunami_patong_beach/tsunami_patong_beach.wmv}
(Novotel).}
%http://wizbangblog.com/content/2005/01/01/wizbang-tsunami.php
which include footage of the tsunami in Patong City on the day
of the 2004 Indian Ocean tsunami. Both videos show an already inundated
street. They also show what is to be assumed as the second
and third waves approaching and further flooding of the buildings and
street. The first video is in the very north, filmed from what is
believed to be the roof of the Novotel Hotel marked ``north'' in Figure
\ref{fig:gauge_locations}. The second video is in the very south,
filmed from the second story of a building next door to the Comfort
Resort near the corner of Ruam Chai St and Thaweewong Road.  This
location is marked ``south'' in Figure \ref{fig:gauge_locations}. 
Figure~\ref{fig:video_flow} shows stills from this video. Both videos
were used to estimate flow speeds and inundation depths over time.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_0_00sec.jpg}
\includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_5_04sec.jpg}
\includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_7_12sec.jpg}
\includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_7_60sec.jpg}
\end{center}

\caption{Four frames from a video where flow rate could be estimated,
  circle indicates tracked debris, from top left: 0.0 s, 5.0 s, 7.1
  s, 7.6 s.}
\label{fig:video_flow}
\end{figure}

Flow rates were estimated using landmarks found in both videos and
were found to be in the range of 5 to 7 m/s ($\pm$2 m/s)
in the north and 0.5 to 2 m/s ($\pm$1 m/s) in the 
south\footnote{These error bounds were estimated from uncertainty in aligning the debris with building boundaries in the videos.}.
Water depths could also
be estimated from the videos by the level at which water rose up the
sides of buildings such as shops. Our estimates are in the order of
1.5 to 2.0 m ($\pm$0.5 m estimated error bounds). 
Fritz~\cite{fritz06} performed a detailed
analysis of video frames taken around Banda Aceh and arrived at flow
speeds in the range of 2 to 5 m/s.


\subsection{Validation Check-List}
\label{sec:checkList}
The data described in this section can be used to construct a
benchmark to validate tsunami models.
 In particular we propose that a legitimate tsunami model
should reproduce the following behaviour:
\begin{itemize}
 \item the inundation survey map in Patong city
   (Figure~\ref{fig:patongescapemap}),
 \item a leading depression followed by two distinct crests
   of decreasing magnitude at the beach,
 \item predict the water depths and flow speeds, at the locations of
   the eye-witness videos, that fall within the bounds obtained from
   the videos,
 \item the \textsc{jason} satellite altimetry sea surface
   anomalies (see Section~\ref{sec:data_jason}), and
 \item the vertical deformation observed in north-western
   Sumatra and along the Nicobar--Andaman islands (see
   Section~\ref{sec:gen_data}).
\end{itemize}

Ideally, the model should also be compared to measured time series of
wave heights and flow speeds but the authors are not aware of the
availability of such data near Patong Bay.
