The spectral element method for the shallow water equations on the sphere

The spectral element method is implemented for the shallow water equations in spherical geometry and its performance is compared with other models. This is the first step in evaluating the suitability of spectral elements for climate modeling. The potential advantages and disadvantages of spectral elements over more conventional models used for climate studies are discussed. The method requires that the sphere be tiled with rectangles, for which we make use of the gnomonic projection to map the sphere onto the cube. To measure the performance of the method relative to other models, results are presented from a standard suite of shallow water test cases for the sphere. These results confirm the spectral accuracy of the method. (C) 1997 Academic Press