1 | Tsunami hazard models have been available for some time. They generally |
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2 | work by converting the energy released by a subduction earthquake into |
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3 | a vertical displacement of the ocean surface. The resulting wave is |
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4 | then propagated across a sometimes vast stretch of ocean using a |
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5 | relatively coarse model based on bathymetries with a typical |
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6 | resolution of two arc minutes (check this with David). |
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7 | The maximal wave height at a fixed contour line near the coastline |
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8 | (e.g.\ 50m) is then reported as the hazard to communities ashore. |
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9 | Models such as Method of Splitting Tsunamis (MOST) \cite{VT:MOST} and |
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10 | ``URS model'' \cite{xxx} follow this paradigm. |
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11 | |
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12 | To capture the \emph{impact} of a hydrological disaster such as tsunamis on a |
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13 | community one must model the details of how waves are reflected and otherwise |
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14 | shaped by the local bathymetries as well as the dynamics of the |
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15 | runup process onto the topography in question. |
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16 | It is well known that local bathymetric and topographic effects are |
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17 | critical in determining the severity of a hydrological disaster |
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18 | \cite{matsuyama:1999}. To model the |
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19 | details of tsunami inundation of a community one must therefore capture what is |
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20 | known as non-linear effects and use a much higher resolution for the |
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21 | elevation data. |
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22 | Linear models typically use data resolutions of the order |
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23 | of hundreds of metres, which is sufficient to model long wavelength tsunami waves. |
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24 | Non-linear models by contrast require much finer resolution in order to capture |
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25 | the complexity associated with the water flow from off to onshore. By contrast, the data |
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26 | resolution required is typically of the order of tens of metres. |
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27 | The model ANUGA \cite{ON:modsim} is suitable for this type of non-linear |
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28 | modelling. |
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29 | |
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30 | However, using a non-linear model capable of resolving local bathymetric effects |
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31 | and runup using detailed elevation data will require much more computational |
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32 | resources than the typical hazard model making it infeasible to use it |
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33 | for the entire, end-to-end, modelling. |
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34 | |
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35 | We have adopted a hybrid approach whereby we use the output from the |
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36 | hazard model MOST as input to ANUGA at the seaward boundary of its study area. |
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37 | In other words, the output of MOST serves as boundary condition for the |
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38 | ANUGA model. In this way, we restrict the computationally intensive part only to |
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39 | regions where we are interested in the detailed inundation process. |
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40 | |
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41 | Furthermore, to avoid unnecessary computations ANUGA works with an |
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42 | unstructured triangular mesh rather than the rectangular grids |
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43 | used by e.g.\ MOST. The advantage of an unstructured mesh |
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44 | is that different regions can have different resolutions allowing |
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45 | computational resources to be directed where they are most needed. |
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46 | For example, one might use very high resolution near a community |
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47 | or in an estuary, whereas a coarser resolution may be sufficient |
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48 | in deeper water where the bathymetric effects are less pronounced. |
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49 | Figure \ref{fig:refinedmesh} shows a mesh of variable resolution. |
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50 | |
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51 | \begin{figure}[hbt] |
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52 | |
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53 | \centerline{ \includegraphics[width=100mm, height=75mm] |
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54 | {../report_figures/refined_mesh.jpg}} |
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55 | |
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56 | \caption{Unstructured mesh with variable resolution.} |
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57 | \label{fig:refinedmesh} |
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58 | \end{figure} |
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59 | |
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60 | |
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61 | |
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62 | |
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63 | |
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