Changeset 7303


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Timestamp:
Jul 7, 2009, 1:07:44 AM (16 years ago)
Author:
jakeman
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Jakeman: Made minor grammar and spelling changes to validation paper

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anuga_work/publications/boxing_day_validation_2008
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  • anuga_work/publications/boxing_day_validation_2008/patong_validation.tex

    r7255 r7303  
    3737In this paper a new benchmark for tsunami model validation is
    3838proposed. The benchmark is based upon the 2004 Indian Ocean tsunami,
    39 which provides a uniquely large amount of observational data for model
     39which affords a uniquely large amount of observational data for model
    4040comparison. Unlike the small number of existing benchmarks, the
    4141proposed test validates all three stages of tsunami evolution -
    … …  
    5050inundation. Important buildings and other structures were incorporated
    5151into the underlying computational mesh and shown to have a large
    52 influence of inundation extent. Sensitivity analysis also showed that
     52influence on inundation extent. Sensitivity analysis also showed that
    5353the model predictions are comparatively insensitive to large changes
    5454in friction and small perturbations in wave weight at the 100 m depth
    … …  
    7070subsequent propagation and inundation of the tsunami, the
    7171effectiveness of hazard mitigation procedures and the economic impact
    72 of such measures and the event itself. Here we focus on modelling of
     72of such measures and of the event itself. Here we focus on modelling of
    7373the physical processes.
    7474%OLE: I commented this out 23 June 2009 as there was no reference.
    … …  
    8484geodetic and sometimes tsunami data must be used
    8585to provide estimates of initial sea floor and ocean surface
    86 deformation. The complexity of these models range from empirical to
     86deformation. The complexity of these models ranges from empirical to
    8787non-linear three-dimensional mechanical models. The shallow water wave
    8888equations, linearised shallow water wave equations, and
    … …  
    9393
    9494Inaccuracies in model prediction can result in inappropriate
    95 evacuation plans and town zoning which may result in loss of life and
     95evacuation plans and town zoning, which may result in loss of life and
    9696large financial losses. Consequently tsunami models must undergo
    9797sufficient end-to-end testing to increase scientific and community
    … …  
    9999
    100100Complete confidence in a model of a physical system cannot be
    101 established.  One can only hope to state under what conditions the
     101established.  One can only hope to state under what conditions and to what extent the
    102102model hypothesis holds true. Specifically the utility of a model can
    103103be assessed through a process of verification and
    … …  
    110110
    111111The sources of data used to validate and verify a model can be
    112 separated into three main categories; analytical solutions, scale
     112separated into three main categories: analytical solutions, scale
    113113experiments and field measurements. Analytical solutions of the
    114114governing equations of a model, if available, provide the best means
    … …  
    118118experiments, typically in the form of wave-tank experiments, provide a
    119119much more realistic source of data that better captures the complex
    120 dynamics of flows such as those generated by tsunami, whilst allowing
     120dynamics of flows such as those generated by a tsunami, whilst allowing
    121121control of the event and much easier and accurate measurement of the
    122122tsunami properties. Comparison of numerical predictions with field
    … …  
    128128statements~\cite{bates01}.
    129129
    130 Currently, the extent of tsunami related field data is limited. The
     130Currently, the extent of tsunami-related field data is limited. The
    131131cost of tsunami monitoring programs, bathymetry and topography surveys
    132132prohibits the collection of data in many of the regions in which
    … …  
    136136standards, criteria and procedures for evaluating numerical models of
    137137tsunami. They propose three analytical solutions to help identify the
    138 validity of a model and five scale comparisons (wave-tank benchmarks)
     138validity of a model, and five scale comparisons (wave-tank benchmarks)
    139139and two field events to assess model veracity.
    140140
    141 The first field data benchmark introduced by Synolakis compares model
     141The first field data benchmark introduced in \cite{synolakis07} compares model
    142142results against observed data from the Hokkaido-Nansei-Oki tsunami
    143 that occurred around Okushiri Island, Japan on the 12th of July
    144 1993. This tsunami provides an example of extreme runup generated from
     143that occurred around Okushiri Island, Japan on the 12 July
     1441993. This tsunami provides an example of extreme run-up generated from
    145145reflections and constructive interference resulting from local
    146146topography and bathymetry. The benchmark consists of two tide gauge
    147 records and numerous spatially distributed point sites at which
    148 modelled maximum runup elevations can be compared. The second
    149 benchmark is based upon the Rat Islands Tsunami that occurred off the
    150 coast of Alaska on the 17th of November 2003. The Rat island tsunami
    151 provides a good test for real-time forecasting models since tsunami
     147records and numerous spatially-distributed point sites at which
     148modelled maximum run-up elevations can be compared. The second
     149benchmark is based upon the Rat Islands tsunami that occurred off the
     150coast of Alaska on the 17 November 2003. The Rat Island tsunami
     151provides a good test for real-time forecasting models since the tsunami
    152152was recorded at three tsunameters. The test requires matching the
    153153propagation model data with the DART recording to constrain the
    154 tsunami source model and then using it to reproduce the tide gauge
     154tsunami source model, and then using it to reproduce the tide gauge
    155155record at Hilo.
    156156
    157157In this paper we develop a field data benchmark to be used in
    158158conjunction with the other tests proposed by Synolakis et
    159 al~\cite{synolakis07} to validate and verify tsunami models. Unlike
    160 the aforementioned tests, the proposed benchmark allows evaluation of
    161 model structure during all three distinctive stages of the evolution
    162 of a tsunami. The benchmark consists of geodetic measurements of the
    163 Sumatra--Andaman earthquake which are used to validate the description
     159al~\cite{synolakis07} to validate and verify tsunami models.
     160The benchmark proposed here allows evaluation of
     161model structure during all three distinct stages tsunami evolution.
     162It consists of geodetic measurements of the
     163Sumatra--Andaman earthquake that are used to validate the description
    164164of the tsunami source, altimetry data from the JASON satellite to test
    165165open ocean propagation, eye-witness accounts to assess near shore
    166 propagation and a detailed inundation survey of Patong Bay, Thailand
     166propagation, and a detailed inundation survey of Patong Bay, Thailand
    167167to compare model and observed inundation. A description of the data
    168168required to construct the benchmark is given in
    … …  
    194194measurements of coseismic displacements and bathymetry from ship-based
    195195expeditions, have now been made
    196 available.%~\cite{vigny05,amnon05,kawata05,liu05}. 
    197 In this section we
    198 present the data necessary to implement the proposed benchmark
    199 corresponding to each of the three stages of the tsunami's evolution.
     196available. %~\cite{vigny05,amnon05,kawata05,liu05}. 
     197In this section we present the corresponding data necessary to implement
     198the proposed benchmark for each of the three stages of the tsunami's evolution.
    200199
    201200\subsection{Generation}\label{sec:gen_data}
    … …  
    205204commonly caused by coseismic displacement of the sea floor, but
    206205submarine mass failures, landslides, volcanoes or asteroids can also
    207 cause tsunami. In this section we detail the information we used in
     206cause tsunami. In this section we detail the information used in
    208207this study to validate models of the sea floor deformation generated
    209208by the 2004 Sumatra--Andaman earthquake.
    … …  
    213212earthquakes on record. The mega-thrust earthquake started on the 26
    214213December 2004 at 0h58'53'' UTC (or just before 8 am local time)
    215 approximately 70 km offshore North Sumatra
     214approximately 70 km offshore of North Sumatra
    216215(\url{http://earthquake.usgs.gov/eqcenter/eqinthenews/2004/usslav}). The
    217216rupture propagated 1000-1300 km along the Sumatra-Andaman trench to
    218217the north at a rate of 2.5-3 km.s$^{-1}$ and lasted approximately 8-10
    219218minutes~\cite{ammon05}. Estimates of the moment magnitude of this
    220 event range from about 9.1 to 9.3~\cite{chlieh07,stein07}.
    221 
    222 The unusually large surface deformation caused by this earthquakes
     219event range from about 9.1 to 9.3 $M_w$~\cite{chlieh07,stein07}.
     220
     221The unusually large surface deformation caused by this earthquake
    223222means that there were a range of different geodetic measurements of
    224223the surface deformation available. These include field measurements of
    225224uplifted or subsided coral heads, continuous or campaign \textsc{GPS}
    226225measurements and remote sensing measurements of uplift or subsidence
    227 (see~\cite{chlieh07} and references therein). Here we use the the near
    228 field estimates of vertical deformation in northwestern Sumatra and
     226(see~\cite{chlieh07} and references therein). Here we use the the near-field
     227estimates of vertical deformation in northwestern Sumatra and
    229228the Nicobar-Andaman islands collated by~\cite{chlieh07} to validate
    230229that our crustal deformation model of the 2004 Sumatra--Andaman
    … …  
    249248
    250249\subsection{Propagation}
    251 Once generated a tsunami will propagate outwards from the source until
     250Once generated, a tsunami will propagate outwards from the source until
    252251it encounters the shallow water bordering coastal regions. This period
    253252of the tsunami evolution is referred to as the propagation stage. The
    … …  
    267266The nested bathymetry grid was generated from:
    268267\begin{itemize}
    269 \item A two arc minute grid data set covering the Bay of Bengal,
     268\item a two arc minute grid data set covering the Bay of Bengal,
    270269  DBDB2, obtained from US Naval Research Labs;
    271 \item A 3 second arc grid covering the whole of the Andaman Sea based
    272   on Thai Navy charts no 45 and no 362; and
    273 \item A one second grid created from the digitised Thai Navy
    274   bathymetry chart, no 358. which covers Patong Bay and the
     270\item a 3 second arc grid covering the whole of the Andaman Sea based
     271  on Thai Navy charts no. 45 and no. 362; and
     272\item a one second grid created from the digitised Thai Navy
     273  bathymetry chart, no. 358, which covers Patong Bay and the
    275274  immediately adjacent regions.
    276275\end{itemize}
    … …  
    280279four grids are shown in Figure~\ref{fig:nested_grids}.  The coarsest
    281280bathymetry was obtained by interpolating the DBDB2 grid to a 27 second
    282 arc grid. A subsection of this region was then replaced by 9 second
    283 data which was generated by sub-sampling the 3 second of arc grid from
    284 NOAA. A subset of the 9 second grid was replaced by the 3 second
     281arc grid. A subsection of this region was then replaced by nine second
     282data which was generated by sub-sampling the three second of arc grid from
     283NOAA. A subset of the nine second grid was replaced by the three second
    285284data. Finally, the one second grid was used to approximate the
    286285bathymetry in Patong Bay and the immediately adjacent regions. Any
    … …  
    288287deleted.
    289288
    290 The sub-sampling of larger grids was performed by using {\bf resample}
     289The sub-sampling of larger grids was performed by using {\bf resample},
    291290a Generic Mapping Tools (\textsc{GMT}) program (\cite{wessel98}). The
    292 gridding of data was performed using {\bf Intrepid} a commercial
     291gridding of data was performed using {\bf Intrepid}, a commercial
    293292geophysical processing package developed by Intrepid Geophysics. The
    294293gridding scheme employed the nearest neighbour algorithm followed by
    … …  
    335334
    336335\subsection{Inundation}
    337 Inundation refers to the final stages of the evolution a tsunami and
     336Inundation refers to the final stages of the evolution of a tsunami and
    338337covers the propagation of the tsunami in shallow coastal water and the
    339 subsequent run-up on to land. This process is typically the most
     338subsequent run-up onto land. This process is typically the most
    340339difficult of the three stages to model due to thin layers of water
    341340flowing rapidly over dry land.  Aside from requiring robust solvers
    … …  
    346345benchmark the authors have obtained a high resolution bathymetry and
    347346topography data set and a high quality inundation survey map from the
    348 CCOP in Thailand (\cite{szczucinski06}) which can be used to validate
    349 model inundation. 
     347CCOP in Thailand (\cite{szczucinski06}) to validate model inundation.
    350348
    351349The datasets necessary for reproducing the results
    352 of the inundation stage are available on Sourceforge under the ANUGA
     350of the inundation stage are available on Sourceforge under the \textsc{anuga}
    353351project (\url{http://sourceforge.net/projects/anuga}). At the time of
    354352writing the direct link is \url{http://tinyurl.com/patong2004-data}.
    … …  
    362360Bay. This elevation data was again created from the digitised Thai
    363361Navy bathymetry chart, no 358. A visualisation of the elevation data
    364 set used in Patong bay is shown in
     362set used in Patong Bay is shown in
    365363Figure~\ref{fig:patong_bathymetry}. The continuous topography is an
    366364interpolation of known elevation measured at the coloured dots.
    … …  
    375373
    376374\subsubsection{Buildings and Other Structures}
    377 Human made build and structures can significantly effect tsunami
     375Human-made build and structures can significantly effect tsunami
    378376inundation. The location and size and number of floors of the
    379377buildings in Patong Bay were extracted from a GIS data set provided by
    … …  
    384382\subsubsection{Inundation Survey}
    385383Tsunami run-up is often the cause of the largest financial and human
    386 losses yet run-up data that can be used to validate model runup
    387 predictions is scarce. Of the two field benchmarks proposed by
    388 Synolakis only the Okushiri benchmark facilitates comparison between
     384losses, yet run-up data that can be used to validate model run-up
     385predictions is scarce. Of the two field benchmarks proposed in~\cite{synolakis07},
     386only the Okushiri benchmark facilitates comparison between
    389387modelled and observed run-up. One of the major strengths of the
    390 benchmark proposed here is that modelled runup can be compared to an
    391 inundation survey which maps the maximum run-up along an entire coast
    392 line rather than at a series of discrete sites. The survey map is
     388benchmark proposed here is that modelled run-up can be compared to an
     389inundation survey which maps the maximum run-up along an entire coastline
     390rather than at a series of discrete sites. The survey map is
    393391shown in Figure~\ref{fig:patongescapemap} and plots the maximum run-up
    394 of the 2004 tsunami in Patong bay. Refer to Szczucinski et
     392of the 2004 tsunami in Patong Bay. Refer to Szczucinski et
    395393al~\cite{szczucinski06} for further details.
    396394
    … …  
    398396Eyewitness accounts detailed in~\cite{papadopoulos06}
    399397report that most people at Patong Beach observed an initial retreat of
    400 the shoreline of more than 100 m followed a few minutes later by a
     398the shoreline of more than 100 m followed a few minutes later, by a
    401399strong wave (crest). Another less powerful wave arrived another five
    402400or ten minutes later. Eyewitness statements place the arrival time of
    … …  
    413411which include footage of the tsunami in Patong Bay on the day
    414412of the Indian Ocean Tsunami. Both videos show an already inundated
    415 group of buildings, they then show what is to be assumed as the second
    416 and third waves approaching and further flooding the buildings and
    417 street.  The first video is in the very north filmed from what is
     413group of buildings. They also show what is to be assumed as the second
     414and third waves approaching and further flooding of the buildings and
     415street.  The first video is in the very north, filmed from what is
    418416believed to be the roof of the Novotel Hotel marked ``north'' in Figure
    419 \ref{fig:gauge_locations}. The second video is in the very south
     417\ref{fig:gauge_locations}. The second video is in the very south,
    420418filmed from the second story of a building next door to the Comfort
    421419Resort near the corner of Ruam Chai St and Thaweewong Road.  This
    422 location is marked ``south'' in Figure \ref{fig:gauge_locations} and
     420location is marked ``south'' in Figure \ref{fig:gauge_locations}.
    423421Figure~\ref{fig:video_flow} shows stills from this video. Both videos
    424422were used to estimate flow speeds and inundation depths over time.
    … …  
    465463should reproduce the following behaviour:
    466464\begin{itemize}
    467  \item Reproduce the vertical deformation observed in north-western
    468    Sumatra and along the Nicobar--Andaman islands, see
    469    Section~\ref{sec:gen_data}.
    470  \item Reproduce the \textsc{jason} satellite altimetry sea surface
    471    anomalies, see Section~\ref{sec:data_jason}.
    472  \item Reproduce the inundation survey map in Patong bay
     465 \item reproduce the vertical deformation observed in north-western
     466   Sumatra and along the Nicobar--Andaman islands (see
     467   Section~\ref{sec:gen_data}).
     468 \item reproduce the \textsc{jason} satellite altimetry sea surface
     469   anomalies (see Section~\ref{sec:data_jason}).
     470 \item reproduce the inundation survey map in Patong bay
    473471   (Figure~\ref{fig:patongescapemap}).
    474  \item Simulate a leading depression followed by two distinct crests
     472 \item simulate a leading depression followed by two distinct crests
    475473   of decreasing magnitude.
    476  \item Predict the water depths and flow speeds, at the locations of
     474 \item predict the water depths and flow speeds, at the locations of
    477475   the eye-witness videos, that fall within the bounds obtained from
    478476   the videos.
    … …  
    489487Numerous models are currently used to model and predict tsunami
    490488generation, propagation and run-up~\cite{titov97a,satake95}. Here we
    491 introduce the modelling methodology employed by Geoscience Australia
    492 to illustrate the utility of the proposed benchmark. Geoscience
    493 Australia's tsunami modelling methodology comprises the three parts;
    494 generation, propagation and inundation
    495 (Sections~\ref{sec:modelGeneration},\ref{sec:modelPropagation} and
    496 \ref{sec:modelInundation} respectively).
     489introduce the three part modelling methodology employed by Geoscience Australia
     490to illustrate the utility of the proposed benchmark.
    497491
    498492\subsection{Generation}\label{sec:modelGeneration}
    … …  
    500494There are various approaches to modelling the expected crustal
    501495deformation from an earthquake at depth. Most approaches model the
    502 earthquake as a dislocation in a linear, elastic medium. Here we use
     496earthquake as a dislocation in a linear elastic medium. Here we use
    503497the method of Wang et al~\cite{wang03}. One of the main advantages
    504498of their method is that it allows the dislocation to be located in a
    … …  
    524518subfault. This step is possible because of the linearity of the
    525519governing equations. For this study, we have made minor modifications
    526 to \textsc{edcmp} in order for it to output in a file format
    527 compatible with the propagation code in the following section but it
    528 is otherwise the similar to the original code.
     520to \textsc{edcmp} in order for it to provide output in a file format
     521compatible with the propagation code in the following section. Otherwise it
     522is similar to the original code.
    529523
    530524In order to calculate the crustal deformation using these codes we
    531 thus need to have a model describing the variation in elastic
     525need a model that describes the variation in elastic
    532526properties with depth and a slip model of the earthquake to describe
    533527the dislocation. The elastic parameters used for this study are the
    534528same as those in Table 2 of Burbidge~\cite{burbidge08}. For the slip
    535529model, there are many possible models for the 2004 Andaman--Sumatran
    536 earthquake to choose from
     530earthquake to select from
    537531~\cite{chlieh07,asavanant08,arcas06,grilli07,ioualalen07}. Some are
    538 determined from various geological surveys of the site, others solve
     532determined from various geological surveys of the site. Others solve
    539533an inverse problem which calibrates the source based upon the tsunami
    540 wave signal, the seismic signal and/or the runup. The source
     534wave signal, the seismic signal and/or the run-up. The source
    541535parameters used here to simulate the 2004 Indian Ocean tsunami were
    542 taken from the slip model G-M9.15 from Chlieh
     536taken from the slip model G-M9.15 of Chlieh
    543537et al~\cite{chlieh07}. This model was created by inversion of wide
    544538range of geodetic and seismic data. The slip model consists of 686
    … …  
    548542discussion of this model and its derivation. Note that the geodetic
    549543data used in the validation was also included by~\cite{chlieh07} in
    550 the inversion used to find G-M9.15, thus the validation is not
    551 completely independent. However, a successful validation would still
     544the inversion used to find G-M9.15. Thus the validation is not
     545completely independent. However, a reasonable validation would still
    552546show that the crustal deformation and elastic properties model used
    553547here is at least as valid as the one used by Chlieh
    … …  
    558552We use the \textsc{ursga} model described below to simulate the
    559553propagation of the 2004 tsunami in the deep ocean ocean, based on a
    560 discrete representation of the initial deformation of the sea floor,
     554discrete representation of the initial deformation of the sea floor, as
    561555described in Section~\ref{sec:modelGeneration}. For the models shown
    562556here, we assume that the uplift is instantaneous and creates a wave of
    … …  
    565559\subsubsection{URSGA}
    566560\textsc{ursga} is a hydrodynamic code that models the propagation of
    567 the tsunami in deep water using a finite difference method on a staggered grid
    568 to solve
    569 the depth integrated linear or nonlinear shallow water equations in
     561the tsunami in deep water using a finite difference method on a staggered grid.
     562It solves the depth integrated linear or nonlinear shallow water equations in
    570563spherical co-ordinates with friction and Coriolis terms. The code is
    571564based on Satake~\cite{satake95} with significant modifications made by
    … …  
    596589\subsubsection{ANUGA}
    597590\textsc{Anuga} is an Open Source hydrodynamic inundation tool that
    598 solves the conserved form of the depth integrated nonlinear shallow
     591solves the conserved form of the depth-integrated nonlinear shallow
    599592water wave equations. The scheme used by \textsc{anuga}, first
    600593presented by Zoppou and Roberts~\cite{zoppou99}, is a high-resolution
    … …  
    620613%================Section===========================
    621614\section{Results}\label{sec:results}
    622 This section presents a validation of the modelling practice of Geoscience Australia against the new proposed benchmarks. The criteria outlined in Section~\ref{sec:checkList} are addressed for each three stages of tsunami evolution.
     615This section presents a validation of the modelling practice of Geoscience
     616Australia against the new proposed benchmarks. The criteria outlined
     617in Section~\ref{sec:checkList} are addressed for each of the three stages
     618of tsunami evolution.
    623619
    624620\subsection{Generation}\label{modelGeneration}
    … …  
    632628the areas that were observed to uplift (arrows pointing up) or subside
    633629(arrows point down) during and immediately after the earthquake. Most
    634 of this data comes uplifted or subsided coral heads. The length of
    635 vector increases with the magnitude of the displacement, the length
     630of this data comes from uplifted or subsided coral heads. The length of
     631vector increases with the magnitude of the displacement; the length
    636632corresponding to 1 m of observed motion is shown in the top right
    637633corner of the figure. As can be seen, the source model detailed in
    … …  
    646642points) is only 0.06 m, well below the typical error of the
    647643observations of between 0.25 and 1.0 m. However, the occasional point
    648 has quite a large error (over 1 m), for example a couple
     644has quite a large error (over 1 m); for example a couple
    649645uplifted/subsided points appear to be on a wrong side of the predicted
    650646pivot line~\ref{fig:surface_deformation}. The excellence of the fit is
    651647not surprising, since the original slip model was chosen
    652 by~\cite{chlieh07} to fit this (and the seismic data) well. However,
    653 this does demonstrate that \textsc{edgrn} and our modified version of
     648by~\cite{chlieh07} to fit this (and the seismic data) well.
     649This does demonstrate, however, that \textsc{edgrn} and our modified version of
    654650\textsc{edstat} can reproduce the correct pattern of vertical
    655651deformation very well when the slip distribution is well constrained
    … …  
    664660  based on the slip model, G-M9.15. The black arrows which point up
    665661  show areas observed to uplift during and immediately after the
    666   earthquake, those point down are locations which subsided. The
    667   length of increases with the magnitude of the deformation. The arrow
     662  earthquake; those pointing down are locations which subsided. The
     663  length of the arrow increases with the magnitude of the deformation. The arrow
    668664  length corresponding to 1 m of deformation is shown in the top right
    669   hand corner of the figure. The crosses marks show the location of
     665  hand corner of the figure. The cross marks show the location of
    670666  the pivot line (the region between the uplift and subsided region
    671667  where the uplift is zero) derived from remote sensing. All the
    672   observational data come from the dataset collated
     668  observational data are from the dataset collated
    673669  by~\cite{chlieh07}.}
    674670\label{fig:surface_deformation}
    … …  
    6856811335$\times$1996 finite difference points. Inside this grid, a nested
    686682sequence of grids was used. The grid resolution of the nested grids
    687 went from 27 arc seconds in the coarsest grid, down to 9 arc seconds
    688 in the second grid, 3 arc seconds in the third grid and finally 1 arc
     683went from 27 arc seconds in the coarsest grid, down to nine arc seconds
     684in the second grid, three arc seconds in the third grid and finally one arc
    689685second in the finest grid near Patong. The computational domain is
    690686shown in Figure~\ref{fig:computational_domain}.
    691687
    692688Figure \ref{fig:jasonComparison} provides a comparison of the
    693 \textsc{ursga} predicted sea surface elevation with the JASON
     689\textsc{ursga}-predicted sea surface elevation with the JASON
    694690satellite altimetry data. The \textsc{ursga} model replicates the
    695 amplitude and timing of the the wave observed at 2.5 degrees South,
     691amplitude and timing of the the wave observed at $2.5^0$ South,
    696692but underestimates the amplitude of the wave further to the south at
    697 4 degrees South. In the model, the southern most of these two waves
    698 appears only as a small bump in the cross section of the model shown
    699 in Figure~\ref{fig:jasonComparison} instead of being a distinct peak
     693$4^0$ South. In the model, the southern most of these two waves
     694appears only as a small bump in the cross section of the model (shown
     695in Figure~\ref{fig:jasonComparison}) instead of being a distinct peak
    700696as can be seen in the satellite data. Also note
    701697that the \textsc{ursga} model prediction of the ocean surface
    702 elevation becomes out of phase with the JASON data at 3 to 7 degrees
    703 latitude. Chlieh et al~\cite{chlieh07} also observe these misfits and
     698elevation becomes out of phase with the JASON data at $3^0$ to $7^0$ North
     699latitude. Chlieh et al~\cite{chlieh07} also observed these misfits and
    704700suggest it is caused by a reflected wave from the Aceh Peninsula that
    705701is not resolved in the model due to insufficient resolution of the
    … …  
    711707\begin{center}
    712708\includegraphics[width=12.0cm,keepaspectratio=true]{jasonComparison.jpg}
    713 \caption{Comparison of the \textsc{ursga} predicted surface elevation
     709\caption{Comparison of the \textsc{ursga}-predicted surface elevation
    714710  with the JASON satellite altimetry data. The \textsc{ursga} wave
    715711  heights have been corrected for the time the satellite passed
    … …  
    720716
    721717\subsection{Inundation}
    722 After propagating the tsunami in the open ocean using \textsc{ursga}
     718After propagating the tsunami in the open ocean using \textsc{ursga},
    723719the approximated ocean and surface elevation and horisontal flow
    724720velocities were extracted and used to construct a boundary condition
    … …  
    752748The boundary condition at each side of the domain towards the south
    753749and the north where no data was available was chosen as a transmissive
    754 boundary condition effectively replicating the time dependent wave
     750boundary condition, effectively replicating the time dependent wave
    755751height present just inside the computational domain. Momentum was set
    756752to zero. Other choices include applying the mean tide value as a
    757 Dirichlet type boundary condition but experiments as well as the
     753Dirichlet type boundary condition. But experiments as well as the
    758754result of the verification reported here showed that this approach
    759 tends to under estimate the tsunami impact due to the tempering of the
    760 wave near the side boundaries whereas the transmissive boundary
     755tends to underestimate the tsunami impact due to the tempering of the
     756wave near the side boundaries, whereas the transmissive boundary
    761757condition robustly preserves the wave.
    762758
    … …  
    785781the inundation boundary of the survey is likely to vary significantly
    786782and somewhat unpredictably.
    787 Consequently, an inundation threshold of 10 cm was selected for inundation
     783An inundation threshold of 10 cm therefore was selected for inundation
    788784extents reported in this paper to reflect
    789 the more likely accuracy of the survey and subsequently facilitate a more
     785the more likely accuracy of the survey, and subsequently facilitate a more
    790786appropriate comparison between the modelled and observed inundation
    791787area.
    … …  
    794790
    795791
    796 An animation of this simulation is available on the ANUGA website at \url{https://datamining.anu.edu.au/anuga} or directly from \url{http://tinyurl.com/patong2004}.
     792An animation of this simulation is available on the \textsc{anuga} website at \url{https://datamining.anu.edu.au/anuga} or directly from \url{http://tinyurl.com/patong2004}.
    797793
    798794%\url{https://datamining.anu.edu.au/anuga/attachment/wiki/AnugaPublications/patong_2004_indian_ocean_tsunami_ANUGA_animation.mov}.
    … …  
    808804\end{figure}
    809805
    810 To quantify the agreement between observed and simulated inundation we
     806To quantify the agreement between the observed and simulated inundation we
    811807introduce the measure
    812808\begin{equation}
    813809\rho_{in}=\frac{A(I_m\cap I_o)}{A(I_o)}
    814810\end{equation}
    815 representing the ratio $\rho_{in}$ of observed
     811representing the ratio $\rho_{in}$ of the observed
    816812inundation region $I_o$ captured by the model $I_m$. Another useful
    817813measure is the fraction of the modelled inundation area that falls
    … …  
    821817\end{equation}
    822818These values for the two aforementioned simulations are given in
    823 Table~\ref{table:inundationAreas}. High value of both $\rho_{in}$ and $\rho_{out}$ indicates
     819Table~\ref{table:inundationAreas}. High value of both $\rho_{in}$ and $\rho_{out}$ indicate
    824820that the model overestimates the impact whereas low values of both quantities would indicate
    825821an underestimation. A high value of $\rho_{in}$ combined with a low value of $\rho_{out}$
    826822indicates a good model prediction of the survey.
    827823
    828 Discrepancies between the survey data and the modelled inundated
     824Discrepancies between the survey data and the modelled inundation
    829825include: unknown distribution of surface roughness, inappropriate
    830826parameterisation of the source model, effect of humans structures on
    … …  
    837833\subsection{Eye-witness accounts}
    838834Figure \ref{fig:gauge_locations} shows four locations where time
    839 series have been extracted from the model. The two offshore timeseries
     835series have been extracted from the model. The two offshore time series
    840836are shown in Figure \ref{fig:offshore_timeseries} and the two onshore
    841837timeseries are shown in Figure \ref{fig:onshore_timeseries}. The
    … …  
    856852\includegraphics[width=10.0cm,keepaspectratio=true]{gauge_bay_depth.jpg}
    857853\includegraphics[width=10.0cm,keepaspectratio=true]{gauge_bay_speed.jpg}
    858 \caption{Timeseries obtained from the two offshore locations shown in Figure \protect \ref{fig:gauge_locations}.}
     854\caption{Time series obtained from the two offshore locations shown in Figure \protect \ref{fig:gauge_locations}.}
    859855\end{center}
    860856\label{fig:offshore_timeseries}
    … …  
    865861\includegraphics[width=10.0cm,keepaspectratio=true]{gauges_hotels_depths.jpg}
    866862\includegraphics[width=10.0cm,keepaspectratio=true]{gauges_hotels_speed.jpg}
    867 \caption{Timeseries obtained from the two onshore locations shown in Figure \protect \ref{fig:gauge_locations}.}
     863\caption{Time series obtained from the two onshore locations shown in Figure \protect \ref{fig:gauge_locations}.}
    868864\end{center}
    869865\label{fig:onshore_timeseries}
    … …  
    924920and the presence and absence of buildings in the elevation dataset on
    925921model maximum inundation. The reference model is the one reported in
    926 Figure~\ref{fig:inundationcomparison1cm} (right) with friction = 0.01,
     922Figure~\ref{fig:inundationcomparison1cm} (right) with a friction coefficient of 0.01,
    927923buildings included and the boundary condition produced by the URSGA model.
    928924
    … …  
    935931for tsunami propagation over a sandy sea floor and the reference model
    936932uses a value of 0.01.  To investigate sensitivity to this parameter,
    937 we simulated the maximum onshore inundation using the a Manning's
     933we simulated the maximum onshore inundation using a Manning's
    938934coefficient of 0.0003 and 0.03. The resulting inundation maps are
    939935shown in Figure~\ref{fig:sensitivity_friction} and the maximum flow
    … …  
    942938friction and that small perturbations in the friction cause bounded
    943939changes in the output. This is consistent with the conclusions of
    944 Synolakis~\cite{synolakis05} who states that the long wavelength of
    945 tsunami tends to mean that the friction is less important in
     940Synolakis~\cite{synolakis05} et al, who state that the long wavelength of
     941tsunami tends to mean that friction is less important in
    946942comparison to the motion of the wave.
    947943
    948944%========================Wave-Height==========================%
    949945\subsection{Input Wave Height}\label{sec:waveheightSA}
    950 The effect of the wave-height used as input to the inundation model
     946The effect of the wave height used as input to the inundation model
    951947\textsc{anuga} was also investigated.
    952948Figure~\ref{fig:sensitivity_boundary} indicates that the inundation
    953949severity is directly proportional to the boundary waveheight but small
    954 perturbations in the input wave-height of 10 cm appear to have little
     950perturbations in the input wave height of 10 cm appear to have little
    955951effect on the final on-shore run-up. Obviously larger perturbations
    956952will have greater impact. However, this value is generally well
    … …  
    966962shows the maximum run-up and associated flow speeds in the presence and absence of buildings. It
    967963is apparent that the inundation is much more severe when the presence
    968 of man made structures and buildings are ignored.
     964of human made structures and buildings are ignored.
    969965
    970966\begin{table}
    … …  
    992988This paper proposes an additional field data benchmark for the
    993989verification of tsunami inundation models. Currently, there is a
    994 scarcity of appropriate validation datasets due to a lack of well
    995 documented historical tsunami impacts. The benchmark proposed here
     990scarcity of appropriate validation datasets due to a lack of well-documented
     991historical tsunami impacts. The benchmark proposed here
    996992utilises the uniquely large amount of observational data for model
    997993comparison obtained during, and immediately following, the
    998 Sumatra--Andaman tsunami of 26th December 2004. Unlike the small
     994Sumatra--Andaman tsunami of 26 December 2004. Unlike the small
    999995number of existing benchmarks, the proposed test validates all three
    1000996stages of tsunami evolution - generation, propagation and
    1001997inundation. In an attempt to provide higher visibility and easier
    1002 accessibility for tsunami benchmark problems the data used to
     998accessibility for tsunami benchmark problems, the data used to
    1003999construct the proposed benchmark is documented and freely available at
    10041000\url{http://tinyurl.com/patong2004-data}.
    … …  
    10151011
    10161012A simple sensitivity analysis was performed to assess the influence of
    1017 small changes in friction, wave-height at the 100 m depth contour and
     1013small changes in friction, wave height at the 100 m depth contour and
    10181014the presence of buildings and other structures on the model
    10191015predictions. The presence of buildings has the greatest influence on
    10201016the simulated inundation extent. The value of friction and small
    1021 perturbations in the waveheight at the ANUGA boundary have
     1017perturbations in the waveheight at the \textsc{anuga} boundary have
    10221018comparatively little effect on the model results.
    10231019
    … …  
    10581054\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_minus10cm_depth}
    10591055\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_plus10cm_depth}
    1060 \caption{Model results with wave height at ANUGA boundary artificially
    1061   modified to asses sensitivities. The reference inundation extent is shown in Figure
     1056\caption{Model results with wave height at \textsc{anuga} boundary artificially
     1057  modified to assess sensitivities. The reference inundation extent is shown in Figure
    10621058  \protect \ref{fig:reference_model} (left).  The left and right images
    1063   show the inundation results if the wave at the ANUGA boundary
     1059  show the inundation results if the wave at the \textsc{anuga} boundary
    10641060  is reduced or increased by 10cm respectively. The inundation
    10651061  severity varies in proportion to the boundary waveheight, but the
    … …  
    11051101\includegraphics[width=6cm,keepaspectratio=true]{sensitivity_f0_03_depth}
    11061102\caption{Model results for different values of Manning's friction
    1107   coefficient shown to asses sensitivities. The reference inundation extent for a
     1103  coefficient shown to assess sensitivities. The reference inundation extent for a
    11081104  friction value of 0.01 is shown in Figure
    11091105  \protect \ref{fig:reference_model} (left).  The left and right images

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