Cartesian Methods for the Shallow Water Equations on a Sphere

A Cartesian method is used in conjunction with the shallow water equations and a spatial discretization based on the Cartesian form of the spherical harmonics. Updates of the momentum equation are accomplished using collocation with spherical harmonics. Computational velocities are expressed in Cartesian coordinates so that no problem with a singularity at the pole is encountered. The geopotential (height) equation is discretized in a similar fashion with a collocation of the divergence term. Error measures and conservation properties of the method are reported for a standard set of test problems. 1 Introduction This report is one of a series of documents concerning the use of numerical methods for global climate modeling. The work reported is sponsored by the CHAMMP initiative of the Department of Energy's Office of Energy Research. CHAMMP is an acronym for Computer Hardware, Advanced Mathematics and Model Physics. Its goal is the development of advanced climate models with considera..