The motivation for this research comes from recent work in Atmospheric General Circulation Models (AGCMs) for NWP and climate research. The three-dimensional Primitive Equations used in AGCMs to describe the dynamics of the atmosphere can be decoupled [Lin,1997] into N (number of atmospheric levels) two-dimensional shallow water equations on the sphere. The conservation of mass and vorticity (and thus angular momentum) is key to long term climate simulations. Most current production AGCMs employ orthogonal latitude-longitude grids which suffer from numerical instabilities near the poles due to decreasing spatial intervals. Penta-/hexagonal grids - generated, for example, by properly subdividing a dodecahedron - do not exhibit this deficiency and have certain technical advantages for finite-volume methods.

We present a finite-volume scheme as well as initial numerical simulation results, for the shallow water model on the sphere using penta-/hexagonal grids. The algorithm retains certain aspects of one for latitude-longitude grids [Lin,Rood,1997]. The irregular structure of the new grid, however, presents new challenges, particular for the calculation of energy and geopotential gradients and vorticity fluxes. Radial basis functions are therefore used for the accurate and efficient approximation of these values. The resulting algorithm lends itself well to an implementation on parallel supercomputers.

Rerences:

[Lin,1997] Lin, S.-J., A finite-volume integration method for computing pressure gradient force in general vertical coodinates, Q. J. R. Meteorol. Soc. (1997)No. 123, pp. 1749-1762.

[Lin,Rood,1997] Lin, S.-J., Rood, R.B., An explicit flux-form semi-Lagrangian shallow-water model on the sphere, Q. J. R. Meteorol. Soc. (1997), No. 123, pp. 2477-2498.