INTEGRATION OF THE NONDIVERGENT BAROTROPIC VORTICITY EQUATION WITH AN ICOSAHEDRAL-HEXAGONAL GRID FOR THE SPHERE

Abstract

A finite difference scheme is developed for numerical integration of the nondivergent barotropic vorticity equation with an icosahedral-hexagonal grid covering the sphere. The grid is made by dividing the 20 triangular faces of an icosahedron into smaller triangles, the vertices of which are the grid points. Each grid point is surrounded by six neighboring points, except the 12 vertices of the icosahedron which are surrounded by five points. The difference scheme for the advection of vorticity exactly conserves total vorticity, total square vorticity, and total kinetic energy. A numerical test is made, with a stationary Neamtan wave as the initial condition, by integrating over 8 days with 1-hr. time steps and a grid of 1002 points for the sphere. There is practically no distortion of the waves over the 8 days, but there is a phase displacement error of about 1° of long. per day toward the west.