source: production/onslow_2006/report/modelling_methodology.tex @ 3242

Tsunami hazard models have been available for some time. They generally
work by converting the energy released by a subduction earthquake into
a vertical displacement of the ocean surface. The resulting wave is
then propagated across a sometimes vast stretch of ocean using a
relatively coarse model based on bathymetries with a typical
resolution of two arc minutes (check this with David). 
The maximal wave height at a fixed contour line near the coastline
(e.g.\ 50m) is then reported as the hazard to communities ashore. 
Models such as Method of Splitting Tsunamis (MOST) \cite{VT:MOST} and the 
URS Corporation's
Probabilistic Tsunami Hazard Analysis  
\cite{somerville:urs} follow this paradigm.

To capture the \emph{impact} of a hydrological disaster such as tsunamis on a 
community one must model the details of how waves are reflected and otherwise 
shaped by the local bathymetries as well as the dynamics of the 
runup process onto the topography in question.
It is well known that local bathymetric and topographic effects are 
critical in determining the severity of a hydrological disaster 
\cite{matsuyama:1999}. To model the
details of tsunami inundation of a community one must therefore capture what is 
known as non-linear effects and use a much higher resolution for the 
elevation data. 
Linear models typically use data resolutions of the order
of hundreds of metres, which is sufficient to model the tsunami waves
in deeper water where the wavelength is longer. 
Non-linear models however require much finer resolution in order to capture
the complexity associated with the water flow from off to onshore. By contrast, the data
resolution required is typically of the order of tens of metres.
The model ANUGA \cite{ON:modsim} is suitable for this type of non-linear
modelling.
Using a non-linear model capable of resolving local bathymetric effects 
and runup using detailed elevation data will require much more computational 
resources than the typical hazard model making it infeasible to use it 
for the entire, end-to-end, modelling. 

We have adopted a hybrid approach whereby we use the output from the  
hazard model MOST as input to ANUGA at the seaward boundary of its study area. 
In other words, the output of MOST serves as boundary condition for the 
ANUGA model. In this way, we restrict the computationally intensive part only to 
regions where we are interested in the detailed inundation process.  

Furthermore, to avoid unnecessary computations ANUGA works with an 
unstructured triangular mesh rather than the rectangular grids 
used by e.g.\ MOST. The advantage of an unstructured mesh 
is that different regions can have different resolutions allowing 
computational resources to be directed where they are most needed. 
For example, one might use very high resolution near a community 
or in an estuary, whereas a coarser resolution may be sufficient 
in deeper water where the bathymetric effects are less pronounced. 
Figure \ref{fig:refinedmesh} shows a mesh of variable resolution.

\begin{figure}[hbt]

  \centerline{ \includegraphics[width=100mm, height=75mm]
             {../report_figures/refined_mesh.jpg}}

  \caption{Unstructured mesh with variable resolution.}
  \label{fig:refinedmesh}
\end{figure}