Suggestions for new tsunami benchmark problems

We believe it would be valuable to develop some new benchmark problems for tsunami modeling that go beyond those included in the current NOAA benchmarks.

Many other communities in computational science have grappled with issues related to the verification and validation of numerical codes and with ways to standardize benchmark problems for comparison of results obtained using different techniques. Some ideas of use in tsunami benchmarking might be found on the following sites:

• SEAM The SEG Advanced Modeling Corporation, which provides benchmarking data sets for seismic imaging.
• more to come...

Some suggested benchmark problems

• The one-dimensional test problems currently included involve exact solutions that are themselves difficult to calculate numerically, e.g. requiring numerical quadrature of Bessel functions. Rather than using limited tests for which such exact solutions are known, it might be preferable to carefully test a 1d numerical model and show that it converges and then use this with very fine grids to generate reference solutions for a wider range of initial conditions. In particular, it would be good to test bathymetry that is more realistic, on the scale of the ocean, continental shelf and beach. [We are working on this.]

• Single wave on a beach, rotated at some angle to the grid in two dimensions. The solution should be a one-dimensional plane wave and the analytic solution can be used for comparison, but this would better test inundation algorithms in two dimensions. Compare the accuracy when the beach is at different angles to the grid. [We are working on this.]

• Radially symmetric problems, such as a radially symmetric ocean with a Gaussian initial perturbation at the center. The waves generated should reach the shore at the same time in all directions, but the shore will be at different angles to the grid in different locations and it will be valuable to compare the accuracy in different locations. The two-dimensional equations can be reformulated as a one-dimensional equation in the radial direction and a very fine grid solution to this problem can be used as a reference solution.

  Some GeoClaw results for a problem of this sort are in the Clawpack distribution: $CLAW/apps/tsunami/bowl-radial.

• Radially symmetric ocean with a shoreline feature at one location along the coast. Compare results obtained when the feature is rotated to different locations. Some tests of this sort are reported in these papers: [awr11], [an11].

• A very simple exact solution is known for water in a parabolic bowl, in which the water surface is linear at all times but the water sloshes around in a circular motion. This would be a good test of wetting and drying as well as conservation.

  The exact solution and some GeoClaw results are in the Clawpack distribution: $CLAW/apps/tsunami/bowl-slosh.

• A 2009 ISEC workshop at Oregon State involved two wave tank experiments that appear to be well documented on their benchmark page. Several sets of model results and presentations are available on the agenda page.

• Standardized test problems related to field data from recent events. Lots of good data is available from the 2004 Sumatra-Andaman event, for example. One specific source model should be specified, along with high resolution bathymetry data for one or more coastal regions where field survey data is available. The ocean bathymetry should also be specified, along with specific outputs for comparison. Comparisons could be done to results obtained on a fine grid with a trusted method, as well as to field data.

  Other possible events: Chile 2010 or Samoa 2009?

• The 11 March 2011 Honshu event will provide many new possibilities since it is being well documented. See our wiki for some available data.