source: production/onslow_2006/report/modelling_methodology.tex @ 3237

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1Tsunami hazard models have been available for some time. They generally
2work by converting the energy released by a subduction earthquake into
3a vertical displacement of the ocean surface. The resulting wave is
4then propagated across a sometimes vast stretch of ocean using a
5relatively coarse model based on bathymetries with a typical
6resolution of two arc minutes (check this with David).
7The maximal wave height at a fixed contour line near the coastline
8(e.g.\ 50m) is then reported as the hazard to communities ashore.
9Models such as Method of Splitting Tsunamis (MOST) \cite{VT:MOST} and
10``URS model'' \cite{xxx} follow this paradigm.
12To capture the \emph{impact} of a hydrological disaster such as tsunamis on a
13community one must model the details of how waves are reflected and otherwise
14shaped by the local bathymetries as well as the dynamics of the
15runup process onto the topography in question.
16It is well known that local bathymetric and topographic effects are
17critical in determining the severity of a hydrological disaster
18\cite{matsuyama:1999}. To model the
19details of tsunami inundation of a community one must therefore capture what is
20known as non-linear effects and use a much higher resolution for the
21elevation data.
22Linear models typically use data resolutions of the order
23of hundreds of metres, which is sufficient to model long wavelength tsunami waves.
24Non-linear models by contrast require much finer resolution in order to capture
25the complexity associated with the water flow from off to onshore. By contrast, the data
26resolution required is typically of the order of tens of metres.
27The model ANUGA \cite{ON:modsim} is suitable for this type of non-linear
30However, using a non-linear model capable of resolving local bathymetric effects
31and runup using detailed elevation data will require much more computational
32resources than the typical hazard model making it infeasible to use it
33for the entire, end-to-end, modelling.
35We have adopted a hybrid approach whereby we use the output from the 
36hazard model MOST as input to ANUGA at the seaward boundary of its study area.
37In other words, the output of MOST serves as boundary condition for the
38ANUGA model. In this way, we restrict the computationally intensive part only to
39regions where we are interested in the detailed inundation process. 
41Furthermore, to avoid unnecessary computations ANUGA works with an
42unstructured triangular mesh rather than the rectangular grids
43used by e.g.\ MOST. The advantage of an unstructured mesh
44is that different regions can have different resolutions allowing
45computational resources to be directed where they are most needed.
46For example, one might use very high resolution near a community
47or in an estuary, whereas a coarser resolution may be sufficient
48in deeper water where the bathymetric effects are less pronounced.
49Figure \ref{fig:refinedmesh} shows a mesh of variable resolution.
53  \centerline{ \includegraphics[width=100mm, height=75mm]
54             {../report_figures/refined_mesh.jpg}}
56  \caption{Unstructured mesh with variable resolution.}
57  \label{fig:refinedmesh}
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