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1\section{Introduction}
2Tsunami is a potential hazard to coastal communities all over the
3world. A number of recent large events have increased community and
4scientific awareness of the need for effective detection, forecasting,
5and emergency preparedness. Probabilistic, geophysical and hydrodynamic
6models are required to predict the location and
7likelihood of an event, the initial sea floor deformation and
8subsequent propagation and inundation of the tsunami. Engineering, economic and social vulnerability models can then be used to estimate the
9impact of the event as well as the effectiveness of hazard mitigation
10procedures. In this paper, we focus on modelling of
11the physical processes only.
12
13Various approaches are currently used to assess the potential tsunami
14inundation of coastal communities.
15These methods differ in both the formulation used to
16describe the evolution of the tsunami and the numerical methods used
17to solve the governing equations. The structure of these models ranges
18from data-driven neural networks~\cite{romano09} to
19non-linear three-dimensional mechanical models~\cite{zhang08}.
20These models are typically used to predict quantities such as arrival
21times, wave speeds and heights, as well as inundation extents
22which can be used to develop efficient hazard mitigation plans. Physics based
23models combine observed seismic, geodetic and sometimes tsunami data to
24 provide estimates of initial sea floor and ocean surface
25deformation. The shallow water wave equations~\cite{george06},
26linearised shallow water wave equations~\cite{liu09},
27and Boussinesq-type equations~\cite{weiss06} are frequently used to simulate
28tsunami propagation and inundation.
29
30Inaccuracies in model prediction can result in inappropriate
31evacuation plans and town zoning, which may result in loss of life and
32large financial losses. Consequently tsunami models must undergo
33sufficient end-to-end testing to increase scientific and community
34confidence in the model predictions.
35
36Complete confidence in a model of a physical system cannot be
37established.  One can only hope to state under what conditions and to
38what extent the
39model hypothesis holds true. Specifically, the utility of a model can
40be assessed through a process of verification and
41validation. Verification assesses the accuracy of the numerical method
42used to solve the governing equations and validation is used to
43investigate whether the model adequately represents the physical
44system~\cite{bates01}. Together these processes can be used to
45establish the likelihood that a model represents a legitimate
46hypothesis.
47
48The sources of data used to validate and verify a model can be
49separated into three main categories: analytical solutions, scale
50experiments and field measurements. Analytical solutions, of the
51governing equations of a model, if available, provide the best means
52of verifying any numerical model. However, analytical solutions are
53frequently limited to a small set of idealised examples that do not
54completely capture the more complex behaviour of `real' events. Scale
55experiments, typically in the form of wave-tank experiments, provide a
56much more realistic source of data that better captures the complex
57dynamics of flows such as those generated by a tsunami, whilst allowing
58control of the event and much easier and accurate measurement of the
59tsunami properties. Comparison of numerical predictions with field
60data provides the most stringent test. The use of field data increases
61the generality and significance of conclusions made regarding model
62utility~\cite{bates01}.
63
64Currently, the extent of tsunami-related field data is limited. The
65cost of tsunami monitoring programs, bathymetry and topography surveys
66prohibits the collection of data in many of the regions in which
67tsunamis pose greatest threat. The resulting lack of data has limited
68the number of field data sets available to validate tsunami
69models.
70
71Synolakis et al~\cite{synolakis08} have developed a set of
72standards, criteria and procedures for evaluating numerical models of
73tsunami. They propose a number of analytical solutions to help identify the
74validity of a model, and five scale comparisons (wave-tank benchmarks)
75and two field events to assess model veracity.
76
77The first field data benchmark introduced in \cite{synolakis08} compares model
78results against observed data from the Hokkaido-Nansei-Oki tsunami
79that occurred around Okushiri Island, Japan on the 12 July
801993. This tsunami provides an example of extreme run-up generated from
81reflections and constructive interference resulting from local
82topography and bathymetry. The benchmark consists of two tide gauge
83records and numerous spatially-distributed point sites at which
84modelled maximum run-up elevations can be compared. The second
85benchmark is based upon the Rat Islands tsunami that occurred off the
86coast of Alaska on the 17 November 2003. The Rat Island tsunami
87provides a good test for real-time forecasting models since the tsunami
88was recorded at three tsunameters. The test requires matching the
89tsunami propagation model output with the tsunameter recordings to constrain
90the tsunami source model, and then using it to reproduce the tide gauge
91record at Hilo, Hawaii.
92
93In this paper we develop a field data benchmark to be used in
94conjunction with the other tests proposed by Synolakis et
95al~\cite{synolakis08} to validate and verify tsunami models.
96The benchmark proposed here allows evaluation of
97model structure during all three distinct stages tsunami evolution.
98It consists of geodetic measurements of the
99Sumatra--Andaman earthquake that are used to validate the description
100of the tsunami source, altimetry data from the \textsc{jason} satellite to test
101open ocean propagation, eye-witness accounts to assess near shore
102propagation, and a detailed inundation survey of Patong city, Thailand
103to compare model and observed inundation. A description of the data
104required to construct the benchmark is given in
105Section~\ref{sec:data}.
106
107Previous model field evaluations~\cite{watts05,ioualalen07} and
108benchmarks~\cite{synolakis08} have focused on reproducing inundation at
109point sites, which are often sparsely distributed. The stakeholders in
110any tsunami study, such as emergency planners are generally more interested
111in more detailed localised studies of tsunami impacts on populated areas.
112Informed and defensible decisions must be based upon detailed simulations
113that predict local inundation extents. Ideally validation studies should be
114 tailored accordingly.
115
116Unlike the existing field benchmarks the proposed test facilitates
117 localised and highly detailed spatially distributed assessment of
118modelled inundation. To the authors knowledge it is also the first benchmark to
119assess model inundation influenced by numerous human structures.
120Eye-witness videos have also been considered to allow the qualitative assessment of onshore flow
121patterns.
122
123An associated aim of this paper is to illustrate the use of this new
124benchmark to validate the three step modelling methodology employed by
125Geoscience Australia to model tsunami inundation. A description of the model
126components is provided in Section~\ref{sec:models} and the validation
127results are given in Section~\ref{sec:results}.
128
129The numerical models used to simulate tsunami impact
130are computationally intensive and high resolution models of the entire
131evolution process will often take a number of days to
132run. Consequently, the uncertainty in model predictions is difficult to
133quantify as it would require a very large number of runs.
134However, model uncertainty should not be ignored. Section
135~\ref{sec:sensitivity} provides a simple analysis that can
136be used to investigate the sensitivity of model predictions to a number
137of model parameters.
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