[7450] | 1 | \section{Data}\label{sec:data} |
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| 2 | The sheer magnitude of the 2004 Sumatra-Andaman earthquake and the |
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| 3 | devastation caused by the subsequent tsunami have generated much |
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| 4 | scientific interest. As a result an unusually large amount of post |
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| 5 | seismic data has been collected and documented. Data sets from |
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| 6 | seismometers, tide gauges, \textsc{gps} surveys, satellite overpasses, |
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| 7 | subsequent coastal field surveys of run-up and flooding, and |
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| 8 | measurements of coseismic displacements as well as bathymetry from ship-based |
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| 9 | expeditions, have now been made |
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[7470] | 10 | available. %~\cite{vigny05,amnon05,kawata05,liu05}. |
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[7450] | 11 | |
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| 12 | In this section we present the corresponding data necessary to implement |
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| 13 | the proposed benchmark. Here we note that the overwhelming focus of tsunami |
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| 14 | modelling is the prediction of inundation extent. The ``fit'' of observed and |
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| 15 | modelled runup should have the greatest influence on conclusions regarding |
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| 16 | model validity. In fact for non-physics based models it may not be possible |
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| 17 | to validate the generation and propagation phases of tsunami evolution. |
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[7451] | 18 | However, for physics-based models evaluation of the model during the generation |
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| 19 | and propagation phases is still useful. If a model is physics-based one |
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[7480] | 20 | should ensure that all physics are being modelled accurately. Moreover, |
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[7451] | 21 | evaluation of all three stages of tsunami evolution can help identify the |
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| 22 | cause of any discrepancies between modelled and observed inundation. |
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[7480] | 23 | Consequently, in this section we present data not only to facilitate |
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[7451] | 24 | validation of inundation but to also aid the assessment of tsunami |
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| 25 | generation and propagation. |
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[7450] | 26 | |
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| 27 | \subsection{Generation}\label{sec:gen_data} |
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| 28 | All tsunami are generated from an initial disturbance of the ocean |
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| 29 | which develops into a low frequency wave that propagates outwards from |
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| 30 | the source. The initial deformation of the water surface is most |
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| 31 | commonly caused by coseismic displacement of the sea floor, but |
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| 32 | submarine mass failures, landslides, volcanoes or asteroids can also |
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| 33 | cause tsunami. In this section we detail the information used in |
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| 34 | this study to validate models of the sea floor deformation generated |
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| 35 | by the 2004 Sumatra--Andaman earthquake. |
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| 36 | |
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| 37 | The 2004 Sumatra--Andaman tsunami was generated by a coseismic |
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| 38 | displacement of the sea floor resulting from one of the largest |
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| 39 | earthquakes on record. The mega-thrust earthquake started on the 26 |
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| 40 | December 2004 at 0h58'53'' UTC (or just before 8 am local time) |
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| 41 | approximately 70 km offshore of North Sumatra |
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| 42 | (\url{http://earthquake.usgs.gov/eqcenter/eqinthenews/2004/usslav}). The |
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| 43 | rupture propagated 1000-1300 km along the Sumatra-Andaman trench to |
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| 44 | the north at a rate of 2.5-3 km.s$^{-1}$ and lasted approximately 8-10 |
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| 45 | minutes~\cite{ammon05}. Estimates of the moment magnitude of this |
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| 46 | event range from about 9.1 to 9.3 $M_w$~\cite{chlieh07,stein07}. |
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| 47 | |
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| 48 | The unusually large surface deformation caused by this earthquake |
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| 49 | means that there were a range of different geodetic measurements of |
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| 50 | the surface deformation available. These include field measurements of |
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| 51 | uplifted or subsided coral heads, continuous or campaign \textsc{GPS} |
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| 52 | measurements and remote sensing measurements of uplift or subsidence |
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| 53 | (see~\cite{chlieh07} and references therein). Here we use the the near-field |
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| 54 | estimates of vertical deformation in northwestern Sumatra and |
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| 55 | the Nicobar-Andaman islands collated by~\cite{chlieh07} to assess whether |
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| 56 | our crustal deformation model of the 2004 Sumatra--Andaman |
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| 57 | earthquake is producing reasonable results. Note that the geodetic |
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| 58 | data used here is a combination of the vertical deformation that |
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| 59 | happened in the $\sim$10 minutes of the earthquake plus the |
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| 60 | deformation that followed in the days following the earthquake before |
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| 61 | each particular measurement was actually made (typically of order |
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| 62 | days). Therefore some of the observations may not contain the purely |
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| 63 | co-seismic deformation but could include some post-seismic deformation |
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| 64 | as well~\cite{chlieh07}. |
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| 65 | |
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| 66 | \subsection{Propagation} |
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| 67 | \label{sec:propagation data} |
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| 68 | Once generated, a tsunami will propagate outwards from the source until |
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| 69 | it encounters the shoreline bordering coastal regions. This period |
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| 70 | of the tsunami evolution is referred to as the propagation stage. The |
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| 71 | height and velocity of the tsunami is dependent on the local |
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| 72 | bathymetry in the regions through which the wave travels and the size |
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| 73 | of the initial wave. This section details the bathymetry data needed |
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| 74 | to model the tsunami propagation and the satellite altimetry transects |
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| 75 | used here to validate open ocean tsunami models. |
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| 76 | |
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[7463] | 77 | \subsubsection{Bathymetry Data}\label{sec:bathymetry data} |
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[7450] | 78 | The bathymetry data used in this study was derived from the following |
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| 79 | sources: |
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| 80 | \begin{itemize} |
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| 81 | \item a two arc minute grid data set covering the Bay of Bengal, |
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[7463] | 82 | DBDB2, obtained from US Naval Research Labs |
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| 83 | (\url{http://www7320.nrlssc.navy.mil/DBDB2_WWW}); |
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[7467] | 84 | \item a 3 second arc grid obtained directly from NOAA covering the |
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| 85 | whole of the Andaman Sea based on the |
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[7468] | 86 | Smith \& Sandwell 2-minute |
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[7473] | 87 | dataset (\url{http://topex.ucsd.edu/WWW_html/srtm30_plus.html}), |
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| 88 | coastline constrained using SRTM data (\url{http://srtm.csi.cgiar.org}) |
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| 89 | as well as Navy charts no.\ 45 and no.\ 362; and |
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[7450] | 90 | \item a one second grid created from the digitised Thai Navy |
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| 91 | bathymetry chart, no. 358, which covers Patong Bay and the |
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[7480] | 92 | immediately adjacent regions. The digitised points and contour lines |
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| 93 | from this chart are shown in Figure~\ref{fig:patong_bathymetry}. |
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| 94 | The gridding of data was performed using \textsc{Intrepid}, a commercial |
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[7463] | 95 | geophysical processing package developed by Intrepid Geophysics. The |
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| 96 | gridding scheme employed the nearest neighbour algorithm followed by |
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| 97 | an application of minimum curvature akima spline smoothing. |
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| 98 | See \url{http://www.intrepid-geophysics.com/ig/manuals/english/gridding.pdf} |
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| 99 | for details on the Intrepid model. |
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[7450] | 100 | \end{itemize} |
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| 101 | |
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| 102 | These sets were combined via |
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| 103 | interpolation and resampling to produce four nested grids |
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| 104 | which are relatively coarse in the deeper water and |
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| 105 | progressively finer as the distance to |
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| 106 | Patong Beach decreases as shown in Figure~\ref{fig:nested_grids}. |
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| 107 | |
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| 108 | The coarsest |
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| 109 | bathymetry was obtained by interpolating the DBDB2 grid to a 27 second |
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| 110 | arc grid. A subsection of this region was then replaced by nine second |
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| 111 | data which was generated by sub-sampling the three second of arc grid from |
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[7463] | 112 | NOAA. It is an artificially generated data set which is a subset of the original data. |
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[7450] | 113 | |
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| 114 | A subset of the nine second grid was replaced by the three second |
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| 115 | data. Finally, the one second grid was used to approximate the |
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[7480] | 116 | bathymetry in Patong Bay. Any |
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[7450] | 117 | points that deviated from the general trend near the boundary were |
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| 118 | deleted as a quality check. |
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| 119 | |
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| 120 | A one second grid was used to approximate the bathymetry in Patong |
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| 121 | Bay. This elevation data was created from the digitised Thai |
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[7480] | 122 | Navy bathymetry chart, no 358. |
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[7450] | 123 | |
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[7463] | 124 | |
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[7480] | 125 | The sub-sampling of larger grids was performed by using \textsc{resample}, |
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[7463] | 126 | a Generic Mapping Tools (\textsc{GMT}) program (\cite{wessel98}). |
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[7450] | 127 | |
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| 128 | |
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| 129 | \begin{figure}[ht] |
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| 130 | \begin{center} |
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| 131 | \includegraphics[width=\textwidth,keepaspectratio=true]{figures/nested_grids} |
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[7480] | 132 | \end{center} |
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| 133 | |
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[7450] | 134 | \caption{Nested bathymetry grids.} |
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| 135 | \label{fig:nested_grids} |
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| 136 | \end{figure} |
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| 137 | |
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| 138 | \subsubsection{JASON Satellite Altimetry}\label{sec:data_jason} |
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| 139 | During the 26 December 2004 event, the \textsc{jason} satellite tracked from |
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| 140 | north to south and over the equator at 02:55 UTC nearly two hours |
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| 141 | after the earthquake \cite{gower05}. The satellite recorded the sea |
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| 142 | level anomaly compared to the average sea level from its previous five |
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| 143 | passes over the same region in the 20-30 days prior. This data was |
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| 144 | used to validate the propagation stage in Section |
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| 145 | \ref{sec:resultsPropagation}. |
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| 146 | |
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| 147 | |
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| 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}. |
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| 149 | |
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| 150 | \subsection{Inundation} |
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| 151 | \label{sec:inundation data} |
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[7480] | 152 | Inundation is the final stage of the evolution of a tsunami and refers |
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| 153 | to the run-up of tsunami onto land. This process is typically the most |
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[7450] | 154 | difficult of the three stages to model due to thin layers of water |
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| 155 | flowing rapidly over dry land. Aside from requiring robust solvers |
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| 156 | which can simulate such complex flow patterns, this part of the |
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| 157 | modelling process also requires high resolution and quality elevation |
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| 158 | data which is often not available. In the case of model validation |
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| 159 | high quality field measurements are also required. For the proposed |
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[7480] | 160 | benchmark a high resolution topography data set (in the form of GIS |
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| 161 | contour lines) and a tsunami inundation survey map from the |
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| 162 | Coordinating Committee Co-ordinating Committee for Geoscience |
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| 163 | Programmes in East and Southeast Asia (CCOP) (\cite{szczucinski06}) |
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| 164 | was obtained to validate model inundation. See also acknowledgements |
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| 165 | at the end of this paper. In this section we also present eye-witness |
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| 166 | accounts which can be used to qualitatively validate tsunami |
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| 167 | inundation. |
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[7450] | 168 | |
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| 169 | \subsubsection{Topography Data} |
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[7480] | 170 | A 1 second grid comprising the onshore topography and the nearshore |
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| 171 | bathymetry for Patong Beach was created from the Navy charts |
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| 172 | (described in Section \ref{sec:bathymetry data}) and from 1 m and 10 m |
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| 173 | elevation contours provided by the CCOP (see Section |
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| 174 | \ref{sec:inundation data} for details). The 1 second terrain model |
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| 175 | for the and community as shown in Figure~\ref{fig:patong_bathymetry}. |
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[7450] | 176 | |
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[7480] | 177 | Two 1/3 second grids were created: One for the saddle point covering |
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| 178 | Merlin and Tri Trang Beaches and one for Patong City and its immediate |
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| 179 | shore area. These grids were based on the same data used for the 1 |
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| 180 | second data grid. The Patong city grid was further modified based on |
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| 181 | satellite imagery to include the river and lakes towards the south of |
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| 182 | Patong City which were not part of the provided elevation data. |
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| 183 | The depth of the river and lake system was set uniformly to a depth of 1 m. |
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[7450] | 184 | |
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[7473] | 185 | |
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[7450] | 186 | \begin{figure}[ht] |
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| 187 | \begin{center} |
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| 188 | \includegraphics[width=8.0cm,keepaspectratio=true]{figures/patong_bay_data.jpg} |
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[7480] | 189 | \end{center} |
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| 190 | |
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[7470] | 191 | \caption{3D visualisation of the elevation data set used for the nearshore propagation and and inundation in Patong Bay showing |
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| 192 | digitised data points and contours as well as rivers and roads |
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| 193 | draped over the data model.} |
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[7450] | 194 | \label{fig:patong_bathymetry} |
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| 195 | \end{figure} |
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| 196 | |
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[7470] | 197 | |
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[7450] | 198 | \subsubsection{Buildings and Other Structures} |
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| 199 | Human-made buildings and structures can significantly affect tsunami |
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| 200 | inundation. The footprint and number of floors of the |
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[7480] | 201 | buildings in Patong Bay were extracted from the data provided by CCOP. |
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[7450] | 202 | The heights of these |
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| 203 | buildings were estimated assuming that each floor has a height of 3 m and they |
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| 204 | were added to the topographic dataset. |
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| 205 | |
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[7473] | 206 | |
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[7450] | 207 | \subsubsection{Inundation Survey} |
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| 208 | Tsunami run-up in built-up areas can be the cause of large financial and human |
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| 209 | losses, yet run-up data that can be used to validate model run-up |
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| 210 | predictions is scarce because such events are relatively infrequent. |
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| 211 | Of the two field benchmarks proposed |
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| 212 | in~\cite{synolakis08}, |
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| 213 | only the Okushiri benchmark facilitates comparison between |
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| 214 | modelled and observed run-up. One of the major strengths of the |
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| 215 | benchmark proposed here is that modelled run-up can be compared to an |
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| 216 | inundation survey which maps the maximum run-up along an entire coastline |
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| 217 | rather than at a series of discrete sites. The survey map is |
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| 218 | shown in Figure~\ref{fig:patongescapemap} and plots the maximum run-up |
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| 219 | of the 2004 Indian Ocean tsunami in Patong city. Refer to Szczucinski et |
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| 220 | al~\cite{szczucinski06} for further details. |
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| 221 | |
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| 222 | \begin{figure}[ht] |
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| 223 | \begin{center} |
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| 224 | \includegraphics[width=\textwidth,keepaspectratio=true]{figures/post_tsunami_survey.jpg} |
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[7480] | 225 | \end{center} |
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| 226 | |
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[7450] | 227 | \caption{Tsunami survey mapping the maximum observed inundation at |
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| 228 | Patong beach courtesy of the CCOP \protect \cite{szczucinski06}.} |
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| 229 | \label{fig:patongescapemap} |
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| 230 | \end{figure} |
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| 231 | |
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| 232 | |
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| 233 | \subsubsection{Eyewitness Accounts}\label{sec:eyewitness data} |
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| 234 | Eyewitness accounts detailed in~\cite{papadopoulos06} |
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| 235 | report that many people at Patong Beach observed an initial |
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| 236 | retreat (trough or draw down) of |
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| 237 | the shoreline of more than 100 m followed a few minutes later by a |
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| 238 | strong wave (crest). Another less powerful wave arrived another five |
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| 239 | or ten minutes later. Eyewitness statements place the arrival time of |
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| 240 | the first wave between 9:55 am and 10:05 am local time or about 2 hours |
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| 241 | after the source rupture. |
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| 242 | |
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| 243 | |
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| 244 | \begin{figure}[ht] |
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| 245 | \begin{center} |
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| 246 | \includegraphics[width=\textwidth,keepaspectratio=true]{figures/gauges.jpg} |
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[7480] | 247 | \end{center} |
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| 248 | |
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[7470] | 249 | \caption{Location of timeseries extracted from the model output.} |
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[7450] | 250 | \label{fig:gauge_locations} |
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| 251 | \end{figure} |
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| 252 | |
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| 253 | Two videos were sourced\footnote{The footage is |
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| 254 | widely available and can, for example, be obtained from |
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| 255 | \url{http://www.archive.org/download/patong_bavarian/patong_bavaria.wmv} |
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| 256 | (Comfort Hotel) and |
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| 257 | \url{http://www.archive.org/download/tsunami_patong_beach/tsunami_patong_beach.wmv} |
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| 258 | (Novotel)} |
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| 259 | %http://wizbangblog.com/content/2005/01/01/wizbang-tsunami.php |
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| 260 | which include footage of the tsunami in Patong Bay on the day |
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| 261 | of the 2004 Indian Ocean Tsunami. Both videos show an already inundated |
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| 262 | group of buildings. They also show what is to be assumed as the second |
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| 263 | and third waves approaching and further flooding of the buildings and |
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| 264 | street. The first video is in the very north, filmed from what is |
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| 265 | believed to be the roof of the Novotel Hotel marked ``north'' in Figure |
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| 266 | \ref{fig:gauge_locations}. The second video is in the very south, |
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| 267 | filmed from the second story of a building next door to the Comfort |
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| 268 | Resort near the corner of Ruam Chai St and Thaweewong Road. This |
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| 269 | location is marked ``south'' in Figure \ref{fig:gauge_locations}. |
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| 270 | Figure~\ref{fig:video_flow} shows stills from this video. Both videos |
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| 271 | were used to estimate flow speeds and inundation depths over time. |
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| 272 | |
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| 273 | \begin{figure}[ht] |
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| 274 | \begin{center} |
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| 275 | \includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_0_00sec.jpg} |
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| 276 | \includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_5_04sec.jpg} |
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| 277 | \includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_7_12sec.jpg} |
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| 278 | \includegraphics[width=5.0cm,keepaspectratio=true]{figures/flow_rate_south_7_60sec.jpg} |
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[7480] | 279 | \end{center} |
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| 280 | |
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[7450] | 281 | \caption{Four frames from a video where flow rate could be estimated, |
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[7480] | 282 | circle indicates tracked debris, from top left: 0.0 s, 5.0 s, 7.1 |
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[7450] | 283 | s, 7.6 s.} |
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| 284 | \label{fig:video_flow} |
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| 285 | \end{figure} |
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| 286 | |
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| 287 | Flow rates were estimated using landmarks found in both videos and |
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[7480] | 288 | were found to be in the range of 5 to 7 m/s ($\pm$2 m/s) |
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| 289 | in the north and 0.5 to 2 m/s ($\pm$1 m/s) in the |
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[7463] | 290 | south\footnote{These error bounds were estimated from uncertainty in aligning the debris with building boundaries in the videos.}. |
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[7450] | 291 | Water depths could also |
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| 292 | be estimated from the videos by the level at which water rose up the |
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| 293 | sides of buildings such as shops. Our estimates are in the order of |
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[7480] | 294 | 1.5 to 2.0 m ($\pm$0.5 m estimated error bounds). |
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| 295 | Fritz~\cite{fritz06} performed a detailed |
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[7450] | 296 | analysis of video frames taken around Banda Aceh and arrived at flow |
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| 297 | speeds in the range of 2 to 5 m/s. |
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| 298 | |
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| 299 | |
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| 300 | \subsection{Validation Check-List} |
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| 301 | \label{sec:checkList} |
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| 302 | The data described in this section can be used to construct a |
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| 303 | benchmark to validate tsunami models. |
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| 304 | In particular we propose that a legitimate tsunami model |
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| 305 | should reproduce the following behaviour: |
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| 306 | \begin{itemize} |
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| 307 | \item reproduce the inundation survey map in Patong city |
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| 308 | (Figure~\ref{fig:patongescapemap}), |
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| 309 | \item simulate a leading depression followed by two distinct crests |
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| 310 | of decreasing magnitude at the beach, and |
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| 311 | \item predict the water depths and flow speeds, at the locations of |
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| 312 | the eye-witness videos, that fall within the bounds obtained from |
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| 313 | the videos. |
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[7451] | 314 | \item reproduce the \textsc{jason} satellite altimetry sea surface |
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| 315 | anomalies (see Section~\ref{sec:data_jason}), |
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[7450] | 316 | \item reproduce the vertical deformation observed in north-western |
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| 317 | Sumatra and along the Nicobar--Andaman islands (see |
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| 318 | Section~\ref{sec:gen_data}), |
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| 319 | \end{itemize} |
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| 320 | |
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| 321 | Ideally, the model should also be compared to measured timeseries of |
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| 322 | waveheights and velocities but the authors are not aware of the |
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| 323 | availability of such data near Patong Bay. |
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