Changeset 2871


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Timestamp:
May 16, 2006, 11:03:53 AM (18 years ago)
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sexton
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updating smf document

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  • documentation/experimentation/smf.tex

    r2869 r2871  
    5353in inundation modelling}
    5454
    55 Geoscience Australia (GA) is a federal government agency playing a
    56 critical role in enabling government and the community to make
    57 informed decisions about exploration of resources, the management
    58 of the environment, the safety of critical infrastructure and the
    59 resultant wellbeing of all Australians. GA does this by producing
    60 first-class geoscientific information and knowledge.
    61 
    62 The Risk Research Group (RRG) within GA is researching natural and
    63 human-caused hazards to enhance Australia's risk mitigation
    64 capabilities through policy and decision-maker support. The group is
    65 working with other agencies to develop and collect information on
    66 natural disasters, and develop risk models for forecasting the
    67 impact of future hazard events.
    68 
    69 The risks posed by tsunamis is one of the natural hazards areas which
    70 the RRG is investigating. GA can model the propagation of an event
    71 generated by a submarine earthquake
    72 through to inundation ashore. Currently, we are
    73 employing the Method of Splitting Tsunami (MOST) [1] for the event
    74 and subsequent propagation in deep water, and then use ANUGA [2] to
    75 propagate the resultant waves in shallow water and onshore.
    76 
    77 ANUGA has been developed by GA and ANU to solve the nonlinear shallow water
    78 wave equation using the finite volume technique.
    79 An advantage of this technique is that the cell resolution can be changed
    80 according to areas of interest
    81 and that wetting and drying is treated robustly as part of the numerical
    82 scheme. ANUGA is continually being developed and
    83 validated.
     55We work at Geoscience Australia (GA) in the Risk Research Group
     56researching risks posed by a range of natural hazards
     57(http://www.ga.gov.au/urban/projects/risk/index.jsp).
     58Due to recent
     59events, we are investigating the tsunami risk to Australia. To understand
     60impact ashore, we have developed in conjunction
     61with the Australian National University, a hydrodynamic model called
     62ANUGA which uses the finite volume technique, [1].
    8463
    8564A recent tsunami inundation study called for the tsunami source to
    8665be a slump and as such, we implemented the surface elevation
    87 function as described in equation 14 of Watts et al 2005, [3]. The reason
    88 then for our contact is that we have some questions and a request
    89 in regard to this methodology.
     66function as described in Watts et al 2005, [3]. We found this a useful
     67way to incorporate another tsunami-genic event to our understanding
     68of tsunami risk. In trying
     69to implement this function however, we had some questions.
    9070
    9171{\bf Question 1:}   Is there a physical explanation to why the total volume
    9272of the surface elevation function should not be zero?
     73
     74{\bf Question 2:}   Is the substitution of $x_g$ into the elevation function realistic?
    9375
    9476Investigating the long term behaviour of the
     
    9678the slump was added to the system. Further investigation showed that
    9779the depressed volume was greater than the volume displaced above the
    98 water surface with approximately 2-3 \% loss. Figure 2 of [3] shows
    99 surface elevation functions $\eta(x,y)$ for various parameters
    100 which indicate that the total volume is not conserved.
     80water surface with approximately 2-3 \% loss. You can see from
     81Figure 2 of [3] that the
     82surface elevation function $\eta(x,y)$ indicates that
     83the total volume is not conserved.
    10184
    102 Setting the integral of the elevation function to zero will
    103 ensure that volume is conserved. Solving for $\kappa'$ yields the result,
     85However, we can alleviate this issue by finding the appropriate set of parameters which
     86will conserve volume. Setting the integral of the elevation function to zero and
     87solving for $\kappa'$ yields the result,
    10488
    10589$$\kappa' = [
     
    10892]_{x_{\rm min}}^{x_{\rm max}} \ .$$
    10993
    110 \noindent Figure \ref{fig:vol_cons} shows the relationship between
    111 $\kappa'$ and $\Delta x$. It must be noted, that whilst
     94\noindent The relationship between $\kappa'$ and $\Delta x$ is shown in
     95Figure \ref{fig:vol_cons}. It must be noted, that whilst
    11296$\kappa'$ is technically less than 1 for $\Delta x < 5.93$ it is
    113 effectively equal to 1 for those values.
    114 Choosing $\kappa'$ = 0.83, as suggested in [1], will therefore
    115 not guarantee conservation of volumen for any value of $\Delta x$.
     97effectively equal to 1 for those values. From this calculation, it would
     98seem then that there would be no appropriate $\Delta x$ for $\kappa'$ = 0.83
     99(a parameter used in [2]).
    116100
    117 Figure 2 in [3]
    118 could then be reproduced for appropriate values of $\kappa'$ and $\Delta x$ to
     101We've reproduced Figure 2 in [3]
     102for appropriate values of $\kappa'$ and $\Delta x$ to
    119103ensure volume conservation within the system. Using the above
    120104formulation, the values of interest shown in Figure 2 of [3] would
     
    140124\end{figure}
    141125
    142 The next question is then how this alteration affects the impact onshore?
    143 It is of course expected to increase the inundation depth
    144 due to the increased volume of water which can
    145 be propagated ashore. In one investigation, we saw little
    146 change to the inundation extent, but some significant increases in
    147 maximum inundation depth in some locations.
     126For our particular test case, changing the surface elevation function
     127in this way increases the inundation depth ashore by a factor greater than
     128the water loss.
    148129
    149 {\bf Question 2:}   Is the substitution of $x_g$ into the elevation function realistic?
    150 
    151 Watts et al [3] provide additional information on the value of
    152 $\Delta x$; $x_0 - \Delta x \approx x_g$, where $x_g$ is formulated
     130Our next question is whether it was appropriate to substitute
     131the formulation for $x_g$ into the surface elevation function using
     132$x_0 - \Delta x \approx x_g$.
     133($x_g$ is formulated
    153134as $x_g = d/\tan \theta + T/ \sin \theta$ (described as a gauge
    154 located above the SMF initial submergence location in [4]). Here $d$
    155 represents the depth at where the SMF is situated, $T$ the thickness
    156 and $\theta$ the slope of the bed. As a result, $\kappa'$ can be
    157 recast as
     135located above the SMF initial submergence location in [4]).)
     136In this
     137way, $\kappa'$ as described above would not
     138be dependent on $\Delta x$;
    158139
    159140$$\kappa'  \approx {\rm erf} ( \frac{x - x_0}{\sqrt\lambda_0} ) /
     
    161142- x_g}{\sqrt \lambda_0 } )$$
    162143
    163 \noindent thereby eliminating $\Delta x$ from the surface elevation
    164 function, $\eta(x,y)$.
    165144
    166145We are continuing to seek out validation data sets to improve the
     
    168147the model against the Benchmark Problem #2 – Tsunami Run-up
    169148onto a complex 3-dimensional beach, as provided to the 3rd
    170 International Workshop on Long Wave Run-up in 2004, see [2].
    171 We note in [5] your proposal for others to employ the benchmark
     149International Workshop on Long Wave Run-up in 2004, see [1].
     150We note in [4] your proposal for others to employ the benchmark
    172151cases described there for experimental or numerical work.
    173152Your model has been compared with the laboratory experiments in 2003 [5] and
     
    181160\parindent 0pt
    182161
    183 We look forward to your response regarding the questions and the request.
     162We look forward to your response.
    184163
    185164Yours sincerely,
     
    191170{\bf References}
    192171
    193 [1]
    194 Titov, V.V., and F.I. Gonzalez (1997), Implementation and testing of
    195 the Method of Splitting Tsunami (MOST) model, NOAA Technical Memorandum
    196 ERL PMEL-112.
    197 
    198 [2] Nielsen, O., S. Robers, D. Gray, A. McPherson, and A. Hitchman (2005)
     172[1] Nielsen, O., S. Robers, D. Gray, A. McPherson, and A. Hitchman (2005)
    199173Hydrodynamic modelling of coastal inundation, MODSIM 2005 International
    200174Congress on Modelling and Simulation. Modelling and Simulation Society
     
    202176http://www.msanz.org.au/modsim05/papers/nielsen.pdf (CHECK THIS!!)
    203177
    204 [3] Watts, P., Grilli, S.T., Tappin, D.R. and Fryer, G.J. (2005),
     178[2] Watts, P., Grilli, S.T., Tappin, D.R. and Fryer, G.J. (2005),
    205179Tsunami generation by submarine mass failure Part II: Predictive
    206180equations and case studies, Journal of Waterway, Port, Coastal, and
    207181Ocean Engineering, 131, 298 - 310.
    208182
    209 [4] Grilli, S.T. and Watts, P. (2005), Tsunami generation by
     183[3] Grilli, S.T. and Watts, P. (2005), Tsunami generation by
    210184submarine mass failure Part I: Modeling, experimental validation,
    211185and sensitivity analyses, Journal of Waterway, Port, Coastal, and
    212186Ocean Engineering, 131, 283 - 297.
    213187
    214 [5] Watts, P., Imamura, F. and Grilli, S. (2000)
    215 Comparting Model Simulations of three Benchmark Tsunami Generation,
     188[4] Watts, P., Imamura, F. and Grilli, S. (2000)
     189Comparting Model Simulations of Three Benchmark Tsunami Generation,
    216190Science of Tsunami Hazards, 18, 2, 107-123.
    217191
    218 [6] Enet, F., Grilli, S.T. and Watts, P. (2003), Laboratory Experiments for
     192[5] Enet, F., Grilli, S.T. and Watts, P. (2003), Laboratory Experiments for
    219193Tsunamis Generated by Underwater Landslides: Comparison with Numerical Modeling,
    220194Proceedings of the Thirteenth (2003) International Offshore and
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