Shallow water equations on a spherical geodesic grid

Abstract

A computer model is presented that solves the stream function/velocity potential form of the shallow water equations using a new spherical geodesic grid that covers the sphere more homogeneously and isotropically than latitude-longitude grids. The geometric properties of the grid are considered. Following Masuda. the finite difference methods discretize line integrals to time-step the prognostic equations. Multigrid methods are used to solve the diagnostic equations for the stream function and velocity potential. The model is compared with the Arakawa-Lamb shallow water model and the NCAR spectral transform shallow water model using the suite of seven test cases proposed by Williamson. The model performance characteristics are presented. The test cases show that the evolution of the fields is independent of the relative orientations of the computational grid and the flow pattern. This is particularly true when flow is directed over the pole of the grid. Also, the new model is tested using a Rossby-Haurwitz wave as initial conditions. The initial disturbance breaks down towards lower wavenumbers, but remains symmetric across the equator.