Abstract
The method to integrate the vorticity equation with the use of surface spherical harmonics has several advantages over the conventional method that uses the grid points. Namely,1) no relaxation is required to solve the poisson equation,2) we are not worried by the troubles accompanying the boundaries,3) it has no such malignant truncation error as can be seen in the grid point method, which was already pointed out by Phillips,4) square velocity and square vorticity are conserved. So, several points are explained here for preparations for the actual integration of barotropic equation.
First, selection rules of interaction coefficients to determine the combinations of disturbances which contribute to the variation of a certain disturbance and the method to calculate them are investigated. And the method how to expand the meteorological elements into the series of surface spherical harmonics, the individual points necessary for the actual integration are also presented, with one example.
