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\title{Inundation Modelling from an Earthquake Source}
\date{}

\begin{document}

\maketitle
 \begin{abstract}
The Risk Research Group at Geoscience Australia is playing a role in building 
the capability for the Australian Tsunami Warning System (ATWS). 
The ATWS aims to detect and warn the community
of tsunami-genic events as well as develop community education programs for
preparation of the event. Risk mitigation involves understanding the relative 
risk
of tsunamis to communities so that appropropriate evacuation plans can be 
put in place. 
To develop an understanding of the risk, the Risk Research Group is developing 
decision support tools to assist emergency managers. These tools consist 
of inundation
maps and damage modelling overlaid on aerial photography of the region 
detailing critical
infrastructure. This report deals with the tsunami inundation modelling
and the interaction with the event propagation model, Method of 
Splitting Tsunami (MOST).

  \end{abstract}
  
  \tableofcontents

\section{Introduction}
\label{intro}

To determine tsunami risk, we follow the risk methodology of 
determining the hazard, consequence and
exposure. The tsunami hazard can be generated by
submarine earthquakes and mass failures, as well as volcanoes and asteroid
impacts. Here, we concentrate on submarine earthquakes only. The
Method of Splitting Tsunami (MOST) models the earthquake event and 
propagates the tsunami wave in deep water, \cite{titov:most}. 
GA has used this model to develop 
a preliminary hazard map for Australia which is based
on generating a series of earthquakes along the relevant subduction
zones surrounding Australia. The map details the average wave height
at the 50m contour line and has been used in nominating areas of
detailed inundation modelling by the Fire and Emergency Services Authority
in Western Australia. MOST uses a finite difference technique and is
based on a fixed grid structure. Inputs include bathymetric data, typically
on the order of 100m grid spacing, and details regarding the source, such
as location, size, slip angle, for example.

In determining the 
consequence of the tsunami wave once is reaches the coastline,
we use the software tool ANUGA which solves the shallow water 
wave equation to 
calculate the maximum inundation depth ashore. ANUGA uses the
finite volume technique, \cite{ON:modsim} with the
advantage being that the cell resolution can be changed
according to areas of interest and that wetting and drying
is treated robustly as part of the numerical scheme. 
ANUGA requires a number
of inputs including on and offshore data, 
an initial condition (such as the tidal height), forcing
terms (such as wind) and the boundary condition (such as the form of
the tsunami wave). This report discusses the details of the latter point, 
i.e the interaction between ANUGA and MOST 
focussing on the location at which information is ``best'' 
passed from one model
to the next. 

Drivers for this study surround computational processing time
to develop both {\it tactical} and {\it strategic} decision support tools.
Tactical tools support ``real time'' consequence prediction for 
emergency manager use 
to obtain assessments of tsunami impact and expected 
consequences to guide initial resource deployment. Strategic tools are based
on using estimated recurrence rates of tsunamigenic events (the hazard), 
the modelled 
inundation and associated damage (exposure) 
to present a national tsunami risk map.
On another strategic level,
the precomputed simulations 
and risk maps will comprise a library of scenarios for the Australian Tsunami 
Warning System to assist in mitigation, warning, response and community 
recovery in the event of a tsunami disaster.

\section{The modelling environment}
\label{models}

The purpose of this section is to briefly describe the process of how
ANUGA and MOST interact through the boundary condition. MOST is 
based on a fixed grid and outputs water depth and momentum at
each grid point. For the preliminary hazard map, a 250m (?) grid was used.
By contrast, ANUGA uses an unstructured triangular mesh which therefore
calls for interpolation from the MOST output to the defined boundary. As
MOST is modelling the tsunami wave from its source and is often made
up of a series of waves,
ANUGA needs to account for its time varying nature.
ANUGA deals with a time varying boundary in the following way.


\section{Comparisons}
\label{compare}

This section details a range of comparisons at 
virtual ``gauge'' points located
within the study area, including the boundary. Note, these gauges are 
constructed for computational purposes only and are not physical tide
gauges. The purpose is to ascertain
any relationships between the bathymetric topography and the ``matching'' 
of the ANUGA and MOST outputs. The difficult question is to 
how to define this matching. In this report, we will investigate
the comparison between MOST and ANUGA to determine the point of divergence.
Secondly, we are also interested in the difference in impact ashore
when the boundary is placed at 100m and 50m contour lines.
Section \ref{sec:mostanugaonslow} deals with the first
issue with Section \ref{sec:compare50100onslow} dealing with the second.


Firstly, at what water depth should we place the ANUGA boundary? Where
is the transition from deep water to shallow water? Some have
suggested this can be determined 
by the ratio of the water's depth to the wavelength of the wave. 
In particular,
when the depth of the water, 
$d$, becomes less than one half of the wavelength of the wave, 
$\lambda$
\footnote{http://electron4.phys.utk.edu/141/dec8/December\%208.htm}. 
Wavelengths can often be of the order of 100km which would place the 
transition at 50km! This then aligns with the following NOAA statement, 
"[t]sunami waves are shallow-water waves with long periods and wave lengths."
\footnote{http://www.pmel.noaa.gov/tsunami-hazard/tsunami\_faqs.htm}

Unfortunately, this doesn't help the modelling effort as the study area
is constrained by UTM zones and the computational load. However, the 
former issue
is planned for investigation and the latter is underway through the 
parallelisation of ANUGA.

need some words here about why 100m has been chosen

need some words about the choice of gauge locations. Nick, do they line up
to the grid points used in MOST? 

\subsection{Onslow case study}

\subsubsection{MOST and ANUGA comparison - 100m contour}
\label{sec:mostanugaonslow}

Before considering any comparison, we will investigate how the maximum
amplitude varies as the tsunami wave reaches the shore. The theory
says that the amplitude will grow and the velocity decrease to zero.

have a plot here that has the bed elevation on the x-axis and the 
maximum amplitude on the y-axis

have a plot here that has the bed elevation on the x-axis and the 
maximum amplitude on the y-axis

We want to compare MOST and ANUGA all the way to the shore - as
close as practical anyway. It is important to note here
that MOST and ANUGA are using different bathymetry data sets, with MOST
typically using a much coarser grid than ANUGA. We interpolate
both MOST and ANUGA output onto the defined point locations. Due to the
fact that ANUGA is utilising a finer resolution bathymetry set, 
we will expect to see richer detail in the ANUGA output. 

\input{comparison_onslow}

The table should show us where it is appropriate to place
the boundary.

\begin{table}
\label{table:mostanugacomparisononslow}
\caption{Comparison in output between ANUGA boundary at 100m 
MOST output.}
\centering
\begin{tabular}{|l|l|l|}\hline
Point location & MOST & ANUGA \\ \hline
& some sort of measure of fit - eg max/min amplitude&   \\ \hline
\end{tabular}
\end{table}

or perhaps ditch the table and repeat the graphs above
with both ANUGA and MOST

\subsubsection{ANUGA comparison - 50m and 100m contour}
\label{sec:compare50100onslow}

The following shows the time series for the point locations
described in Table \ref{table:locationsonslow}.
It is evident from the model output when the boundary is placed 
at the 50m contour does not pick up the
detail which is evident in the output for the 100m contour. This 
is due to the fact that the output
for the 100m contour has been propagated by ANUGA which is more effective
in modelling the propagation in shallow water. 
It seems that the maximum amplitudes are
effectively matched for most of the locations chosen; 
see for example the output for the Ocean polygon 1 and 2 locations.

\input{50100MOSTcomparison_onslow}

It is more instructive in this case to compare differences in
inundation depths and extent ashore as the boundary location is changed.
Table \ref{table:anugacomparisononslow} lists inundation depths
for locations within the internal polygon with the finest resolution.

\begin{table}
\label{table:anugacomparisononslow}
\caption{Comparison in inundation depth at select locations when ANUGA boundary 
is at the 50m and 100m contour.}
\centering
\begin{tabular}{|l|l|l|}\hline
Point location & Boundary at 50m contour & Boundary at 100m contour \\ \hline
&  &   \\ \hline
\end{tabular}
\end{table}

\begin{figure}
\caption{Map showing inundation extent for 50m and 100m contour line.}
\label{fig:extentcomparisononslow}
\end{figure}

\subsection{Pt Hedland case study}

\subsubsection{MOST and ANUGA comparison - 100m contour}
\label{mostanugapthedland}

\begin{table}
\label{table:mostanugacomparisonpthedland}
\caption{Comparison in output between ANUGA boundary at 100m 
MOST output.}
\centering
\begin{tabular}{|l|l|l|}\hline
Point location & MOST & ANUGA \\ \hline
& some sort of measure of fit &   \\ \hline
\end{tabular}
\end{table}

\subsubsection{ANUGA comparison - 50m and 100m contour}
\label{compare50100pthedland}

%\input{comparison_pt_hedland}

\begin{table}
\label{table:anugacomparisonpthedland}
\caption{Comparison in inundation depth at select location when ANUGA boundary 
is at the 50m and 100m contour.}
\centering
\begin{tabular}{|l|l|l|}\hline
Point location & Boundary at 50m contour & Boundary at 100m contour \\ \hline
&  &   \\ \hline
\end{tabular}
\end{table}

\begin{figure}
\caption{Map showing inundation extent for 50m and 100m contour line.}
\label{fig:extentcomparisonpthedland}
\end{figure}

\section{Summary}
\label{summary}

\begin{thebibliography}{99}

\bibitem{titov:most} Titov, V.V., and F.I. Gonzalez (1997), Implementation 
and testing of
the Method of Splitting Tsunami (MOST) model, NOAA Technical Memorandum
ERL PMEL-112.

\bibitem{ON:modsim} Nielsen, O., S. Robers, D. Gray, A. McPherson, and 
A. Hitchman (2005)
Hydrodynamic modelling of coastal inundation, MODSIM 2005 International
Congress on Modelling and Simulation. Modelling and Simulation Society 
of Australian and New Zealand, 518-523, \newline URL: 
http://www.mssanz.org.au/modsim05/papers/nielsen.pdf


\end{thebibliography}

\end{document}
