source: anuga_work/publications/boxing_day_validation_2008/data.tex @ 7463

\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, have now been made
available. %~\cite{vigny05,amnon05,kawata05,liu05}. FIXME (Ole): Refs?  Are the references here inappropriate?

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 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 velocity 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 grid data set covering the Bay of Bengal,
  DBDB2, obtained from US Naval Research Labs 
  (\url{http://www7320.nrlssc.navy.mil/DBDB2_WWW});
\item a 3 second arc grid covering the whole of the Andaman Sea based
  on Thai Navy charts no. 45 and no. 362; and  
  (FIXME (OLE): wait for DB's reply) 
\item a one second grid created from the digitised Thai Navy
  bathymetry chart, no. 358, which covers Patong Bay and the
  immediately adjacent regions.
  The gridding of data was performed using {\bf Intrepid}, a commercial
  geophysical processing package developed by Intrepid Geophysics. The
  gridding scheme employed the nearest neighbour algorithm followed by
  an application of minimum curvature akima spline smoothing. 
  See \url{http://www.intrepid-geophysics.com/ig/manuals/english/gridding.pdf} 
  for details on the Intrepid model.  
\end{itemize}

These sets were combined via 
interpolation and resampling to produce four nested grids 
which are relatively coarse in the deeper water and 
progressively finer as the distance to
Patong Beach decreases as shown in Figure~\ref{fig:nested_grids}.  

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, the one second grid was used to approximate the
bathymetry in Patong Bay and the immediately adjacent regions. Any
points that deviated from the general trend near the boundary were
deleted as a quality check.

A one second grid was used to approximate the bathymetry in Patong
Bay. This elevation data was created from the digitised Thai
Navy bathymetry chart, no 358. The digitised points and contour lines 
from this chart are shown in Figure~\ref{fig:patong_bathymetry}.


The sub-sampling of larger grids was performed by using {\bf resample},
a Generic Mapping Tools (\textsc{GMT}) program (\cite{wessel98}).


\begin{figure}[ht]
\begin{center}
\includegraphics[width=\textwidth,keepaspectratio=true]{figures/nested_grids}
\caption{Nested bathymetry grids.}
\label{fig:nested_grids}
\end{center}
\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 (1 second) topography data set 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. See also acknowledgements at the end of this paper. In this section we also present eye-witness accounts which can be used 
to qualitatively validate tsunami inundation.

\subsubsection{Topography Data}
The 1 second onshore topography for Patong Beach provided by the CCOP was 
merged with the nearshore 1 second bathymetry described in Section 
\ref{sec:bathymetry data} to provide a seamless terrain model for the 
bay and community as shown in Figure~\ref{fig:patong_bathymetry}.


\begin{figure}[ht]
\begin{center}
\includegraphics[width=8.0cm,keepaspectratio=true]{figures/patong_bay_data.jpg}
\caption{3D visualisation of the elevation data set used in Patong Bay showing data points, contours, rivers and roads draped over the final model.}
\label{fig:patong_bathymetry}
\end{center}
\end{figure}
FIXME (Jane): legend? Were the contours derived from the final dataset?
This is not the entire model, only the bay and the beach. RICHARD

\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 a GIS data set which was also provided by the CCOP (see Section \ref{sec:inundation data} for details). 
The heights of these
buildings were estimated assuming that each floor has a height of 3 m and they 
were added to the topographic dataset. 

\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=8.0cm,keepaspectratio=true]{patongescapemap.jpg}
\includegraphics[width=\textwidth,keepaspectratio=true]{figures/post_tsunami_survey.jpg}
\caption{Tsunami survey mapping the maximum observed inundation at
  Patong beach courtesy of the CCOP \protect \cite{szczucinski06}.}
\label{fig:patongescapemap}
\end{center}
\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.
FIXME (Ole): We should add observed arrival time and later relate that to 
the modelled dynamics. Wait for Drew's updated animation.


\begin{figure}[ht]
\begin{center}
%\includegraphics[width=8.0cm,keepaspectratio=true]{gauge_locations.jpg}
\includegraphics[width=\textwidth,keepaspectratio=true]{figures/gauges.jpg}
\caption{Location of timeseries extracted from the model output. FIXME(John):
should we combine the inundation map with the gauages map?}
\label{fig:gauge_locations}
\end{center}
\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 Hotel) 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 Bay on the day
of the 2004 Indian Ocean Tsunami. Both videos show an already inundated
group of buildings. 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}
\caption{Four frames from a video where flow rate could be estimated,
  circle indicates tracked debris, from top left: 0.0 sec, 5.0 s, 7.1
  s, 7.6 s.}
\label{fig:video_flow}
\end{center}
\end{figure}

Flow rates were estimated using landmarks found in both videos and
were found to be in the range of 5 to 7 metres per second (+/- 2 m/s)
in the north and 0.5 to 2 metres per second (+/- 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 metres (+/- 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 reproduce the inundation survey map in Patong city
   (Figure~\ref{fig:patongescapemap}),
 \item simulate a leading depression followed by two distinct crests
   of decreasing magnitude at the beach, and
 \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 reproduce the \textsc{jason} satellite altimetry sea surface
   anomalies (see Section~\ref{sec:data_jason}),
 \item reproduce 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 timeseries of
waveheights and velocities but the authors are not aware of the
availability of such data near Patong Bay.