Diffusion and dispersion characterization of a numerical tsunami model

The Method Of Splitting Tsunami numerical model is being developed at the NOAA Center for Tsunami Research for use in the tsunami forecasting system in the United States. The ability to produce fast and accurate forecast of tsunami is critical, and the tradeoff between high speed model runs and numerical errors that are introduced due to finite grid parameters must be evaluated. The details of the underlying numerics of this model are examined in an effort to understand the numerical diffusion and dispersion inherent in finite difference models. Diffusion and dispersion are quantified in a simplified linear case, and extended in a qualitative manner to general cases. This knowledge is valuable in the development of efficient grids that will provide accurate solutions in a tsunami forecasting framework, as well as in choosing free parameters in a manner that allows a fit with theoretical dispersion. A variable space grid scheme that uses numerical dispersion to mimic theoretical dispersion is outlined. Also, areas in parameter space that will result in unrealistic wave fields and thus should be avoided are highlighted.