source: anuga_work/publications/boxing_day_validation_2008/introduction.tex @ 7522

\section{Introduction}
Tsunami is a potential hazard to coastal communities all over the
world. A number of recent large events have increased community and
scientific awareness of the need for effective detection, forecasting,
and emergency preparedness. Probabilistic, geophysical and hydrodynamic 
models are required to predict the location and
likelihood of an event, the initial sea floor deformation and
subsequent propagation and inundation of the tsunami. Engineering, economic and social vulnerability models can then be used to estimate the
impact of the event as well as the effectiveness of hazard mitigation 
procedures. In this paper, we focus on modelling of
the physical processes only. 

Various approaches are currently used to assess the potential tsunami 
inundation of coastal communities. 
These methods differ in both the formulation used to
describe the evolution of the tsunami and the numerical methods used
to solve the governing equations. The structure of these models ranges 
from data-driven neural networks~\cite{romano09} to
non-linear three-dimensional mechanical models~\cite{zhang08}. 
These models are typically used to predict quantities such as arrival 
times, wave speeds and heights, as well as inundation extents
that can be used to develop efficient hazard mitigation plans. Physics based 
models combine observed seismic, geodetic and sometimes tide gauge data to
 provide estimates of initial sea floor and ocean surface
deformation. The shallow water wave equations~\cite{george06}, 
linearised shallow water wave equations~\cite{liu09}, 
and Boussinesq-type equations~\cite{weiss06} are frequently used to simulate 
tsunami propagation and inundation. 

Inaccuracies in model prediction can result in inappropriate
evacuation plans, town zoning and land use planning, 
which ultimately may result in loss of life and infrastructure. 
Consequently tsunami models must undergo
sufficient end-to-end testing to increase scientific and community
confidence in the model predictions.

Complete confidence in a model of a physical system cannot be
established.  One can only hope to state under what conditions and to 
what extent the
model hypothesis holds true. Specifically, the utility of a model can
be assessed through a process of verification and
validation. Verification assesses the accuracy of the numerical method
used to solve the governing equations and validation is used to
investigate whether the model adequately represents the physical
system~\cite{bates01}. Together these processes can be used to
establish the likelihood that a model represents a legitimate
hypothesis.

The sources of data used to validate and verify a model can be
separated into three main categories: analytical solutions, scale
experiments and field measurements. Analytical solutions, of the
governing equations of a model, if available, provide the best means
of verifying any numerical model. However, analytical solutions are
frequently limited to a small set of idealised examples that do not
completely capture the more complex behaviour of `real' events. Scale
experiments, typically in the form of wave-tank experiments, provide a
much more realistic source of data that better captures the complex
dynamics of flows such as those generated by a tsunami, whilst allowing
control of the event and much easier and accurate measurement of the
tsunami properties. Comparison of numerical predictions with field
data provides the most stringent test. The use of field data increases
the generality and significance of conclusions made regarding model
utility~\cite{bates01}.

Currently, the extent of tsunami-related field data is limited. The
cost of tsunami monitoring programs and the rarity of events as well as 
bathymetry and topography surveys
prohibits the collection of data in many of the regions in which
tsunamis pose the greatest threat. The resulting lack of data has limited
the number of field data sets available to validate tsunami
models. 

Synolakis et al~\cite{synolakis08} have developed a set of
standards, criteria and procedures for evaluating numerical models of
tsunami. They propose a number of analytical solutions to help identify the
validity of a model, and five scale comparisons (wave-tank benchmarks)
and two field events to assess model veracity.

The first field data benchmark introduced in \cite{synolakis08} compares model
results against observed data from the Hokkaido-Nansei-Oki tsunami
that occurred around Okushiri Island, Japan on the 12 July
1993. This tsunami provides an example of extreme run-up generated from
reflections and constructive interference resulting from local
topography and bathymetry. The benchmark consists of two tide gauge
records and numerous spatially-distributed point sites at which
modelled maximum run-up elevations can be compared. The second
benchmark is based upon the Rat Islands tsunami that occurred off the
coast of Alaska on the 17 November 2003. The Rat Island tsunami
provides a good test for real-time forecasting models since the tsunami
was recorded at three tsunameters. The test requires matching the
tsunami propagation model output with the tsunameter recordings to constrain 
the tsunami source model, and then using it to reproduce the tide gauge
record at Hilo, Hawaii. 

In this paper we develop a field data benchmark to be used in
conjunction with the other tests proposed by Synolakis et
al~\cite{synolakis08} to validate and verify tsunami models. 
The benchmark proposed here allows evaluation of
model components during three distinct stages tsunami 
evolution, namely generation, propagation and inundation. 
It consists of geodetic measurements of the
Sumatra--Andaman earthquake that are used to validate the description
of the tsunami source, altimetry data from the \textsc{jason} satellite to test
open ocean propagation, eye-witness accounts to assess near shore
propagation, and a detailed inundation survey of Patong city, Thailand
to compare model and observed inundation. A description of the data
required to construct the benchmark is given in
Section~\ref{sec:data}.

Previous model field evaluations~\cite{watts05,ioualalen07} and 
benchmarks~\cite{synolakis08} have focused on reproducing inundation at 
point sites, which are often sparsely distributed. The stakeholders in 
any tsunami study, such as emergency planners are generally more interested 
in more detailed localised studies of tsunami impacts on populated areas. 
Informed and defensible decisions must be based upon detailed simulations 
that predict local inundation extents. Ideally validation studies should be
 tailored accordingly.

Unlike the existing field benchmarks, the proposed test facilitates
 localised and highly detailed spatially distributed assessment of 
modelled inundation. To the authors knowledge it is also the first benchmark to
assess model inundation influenced by numerous human structures. 
Eye-witness videos have also been considered to allow the qualitative assessment of onshore flow 
patterns.

An associated aim of this paper is to illustrate the use of this new
benchmark to validate the three step modelling methodology employed by 
Geoscience Australia to model tsunami inundation. A description of the model 
components is provided in Section~\ref{sec:models} and the validation
results are given in Section~\ref{sec:results}.

The numerical models used to simulate tsunami impact 
are computationally intensive and high resolution models of the entire
evolution process will often require a number of days to
complete. Consequently, the uncertainty in model predictions is difficult to
quantify as it would require a very large number of simulations. 
However, model uncertainty should not be ignored. Section
~\ref{sec:sensitivity} provides a simple analysis that can
be used to investigate the sensitivity of model predictions to a number 
of key model parameters.