Implementation of a Hybrid Laplacian Filter in SLOSH to Suppress Numerical Grid Splitting

The Sea Lake and Overland Surges from Hurricanes (SLOSH) model predicts hurricane storm surge. SLOSH performs calculations on an Arakawa B-grid and applies a "del-plus" Laplacian filter on the water surface elevation. The result is a vulnerability to numerical instabilities generated by the discretization of gravity waves on a B-grid, known as checkerboarding. SLOSH has attempted to control checkerboarding by reducing the time step and adjusting the frequency of calls to the filter; however, as SLOSH grids have become more refined, checkerboarding has become more problematic. Atmospheric model developers have ameliorated checkerboarding by introducing a "del-cross" Laplacian filter. Based on the work of Killworth et al. (1991), we have modified SLOSH to use a weighted difference of the del-plus and del-cross Laplacians in a manner consistent with atmospheric models. This allows SLOSH to be run on higher-resolution grids while retaining its computational efficiency, which is crucial to storm surge forecasting.