Integration of the barotropic vorticity equation on a spherical geodesic grid
Williamson, David L.
- Publisher: Co-Action Publishing
A quasi-homogeneous net of points over a sphere for numerical integration is defined. The grid consists of almost equal-area, equilateral spherical triangles covering the sphere. Finite difference approximations for a nondivergent, barotropic model expressed in terms of a streamfunction are proposed for an arbitrary triangular grid. These differences are applied to the spherical geodesic grid. The model is integrated for 12-day periods using analytic initial conditions of wave number six and four. The numerical solution with these special initial conditions follows the analytic solution quite closely, the only difference being a small phase error. Small truncation errors are noticeable in the square of the streamfunction averaged over latitude bands.DOI: 10.1111/j.2153-3490.1968.tb00406.x