source: anuga_work/publications/boxing_day_validation_2008/sensitivity.tex @ 7451

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2\section{Sensitivity Analysis}
4The numerical models used to simulate tsunami impact
5are computationally intensive and high resolution models of the entire
6evolution process will often take a number of days to
7run. Consequently, the uncertainty in model predictions is difficult to
8quantify as it would require a very large number of runs.
9However, model uncertainty should not be ignored. The aim of this section is
10not to provide a detailed investigation of sensitivity but to rather
11illustrate that changes in important parameters of the \textsc{usrga--anuga} 
12model  produce behaviour consistent with the known physics and that
13small changes in these parameters produce bounded variations in the output.
15This section investigates the effect of different values of Manning's
16friction coefficient, changing waveheight at the 100 m depth contour,
17and the presence and absence of buildings in the elevation dataset on
18model maximum inundation.
20The reference model is the one reported in
21Figure~\ref{fig:inundationcomparison1cm} (right) with a friction coefficient of 0.01, buildings included and the boundary condition produced by the
22\textsc{ursga} model.
26\label{sec:friction sensitivity}
27The first sensitivity study investigated the impact of surface roughness on the
28predicted run-up. According to Schoettle~\cite{schoettle2007}
29appropriate values of Manning's coefficient range from 0.007 to 0.03
30for tsunami propagation over a sandy sea floor and the reference model
31uses a value of 0.01.  To investigate sensitivity to this parameter,
32we simulated the maximum onshore inundation using a Manning's
33coefficient of 0.0003 and 0.03. The resulting inundation maps are
34shown in Figure~\ref{fig:sensitivity_friction}
35% and the maximum flow speeds in Figure~\ref{fig:sensitivity_friction_speed}.
36 The figure, along with Table~\ref{table:inundationAreas},
37shows that the on-shore inundation extent decreases with increasing
38friction and that small perturbations in the friction cause bounded
39changes in the output. This is consistent with the conclusions of
40Synolakis~\cite{synolakis05} et al, who state that the long wavelength of
41tsunami tends to mean that friction is less important in
42comparison to the motion of the wave.
45\subsection{Input Wave Height}\label{sec:waveheightSA}
46The effect of the wave height used as input to the inundation model
47\textsc{anuga} was also investigated.
48Figure~\ref{fig:sensitivity_boundary} and  Table~\ref{table:inundationAreas} 
49indicate that the inundation
50severity is directly proportional to the boundary waveheight but small
51perturbations in the input wave height of 10 cm appear to have little
52effect on the final inundated area. Obviously larger perturbations
53will have greater impact. However, wave heights in the open ocean are
54generally well
55predicted by the generation and propagation models such as
56\textsc{ursga} as demonstrated in Section \ref{sec:resultsPropagation} 
57and also in \cite{thomas2009}.
62\subsection{Buildings and Other Structures}
63The presence or absence of physical buildings in the elevation model was also
65Figure~\ref{fig:sensitivity_nobuildings} shows the inundated area
66%and the associated maximum flow speeds
67in the presence and absence of buildings. From
68Table~\ref{table:inundationAreas} it is apparent that densely built-up
69areas act as dissipators greatly reducing the inundated area.
70This result suggest that, when possible the presence of human-made structures
71should be included into the model topography. Furthermore this result also
72indicates that simply matching point sites with much lower resolution meshes
73than used here is an over simplification. Such simulations cannot capture the
74fine detail that so clearly affects inundation.
75%However, flow speeds tend to increase in passages between buildings.
81\caption{$\rho_{in}$ and $\rho_{out}$ of the reference simulation and all sensitivity studies.}
84 & $\rho_{in}$ & $\rho_{out}$ \\ 
86Reference model & 0.79 & 0.20\\ 
87Friction = 0.0003 & 0.83 & 0.26 \\ 
88Friction = 0.03 & 0.67 & 0.09\\ 
89Boundary wave hight minus 10 cm & 0.77 & 0.17 \\
90Boundary wave hight plus 10 cm & 0.82 & 0.22 \\
91No Buildings & 0.94 & 0.44 \\
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