A PV-Based Shallow-Water Model on a Hexagonal–Icosahedral Grid

A new global shallow-water model has been developed. It uses a hexagonal–icosahedral grid, potential vorticity as a prognostic variable, and a conservative, shape-preserving scheme for advection of mass, potential vorticity, and tracers. A semi-implicit time scheme is used so that the maximum time step for stable integrations is limited by the advection speed rather than the gravity wave phase speed. This combination of numerical methods avoids some of the major problems of more traditional numerical methods, such as pole problems, and spurious oscillations and negatives in advected quantities. Sample results from a standard set of test cases are presented to illustrate the model’s performance. In a pure advection test case the model’s advection scheme shows good isotropy and phase-speed properties, but it is a little diffusive. In the remaining test cases the model’s overall accuracy is comparable to that of other gridpoint models for which results are available. Two sources of error are noted. One is the dissipation inherent in the advection scheme, which is estimated to be significantly stronger than the dissipation usually imposed in climate models of comparable resolution. The other is the grid structure, which leads to conspicuous symmetry errors in test cases where the true solution is symmetrical. The symmetry errors appear to arise because the hexagonal grid boxes are not perfectly regular but are somewhat distorted, particularly in certain regions of the grid, leading to larger truncation errors in the advection scheme in those regions.