Comparison of Horizontal Difference Schemes for the Shallow Water Equations on a Sphere

The accuracy of horizontal difference schemes used in the hydrodynamics parts of General Circulation Models are compared by means of numerical experiments for the shallow water equations on a sphere. As expected, the phase lag of moving waves decreases as the order of accuracy of a scheme increases or as the grid resolution increases. Overall, Takano and Wurtele's partial fourth order energy and potential enstrophy conserving sdheme on the C grid is most accurate. It is clearly superior to the other schemes for the Rossby-Huarwitz wave number 6 initial conditions for coarse grid resolution.