On the Beta Plane Approximation

Abstract

The beta plane approximation as it is usually derived suffers from the difficulty that it is only valid if the quasi-geostrophic approximation is made. It is not valid for the underlying momentum and continuity equations. The problem in the latter equations is the presence of terms that are of the same order as the beta term but that are not present in the equations for a plane. We show that the difficulty can be overcome by basing the derivation of the beta plane approximation on a suitably chosen spherical coordinate system that is different from the geographical coordinate system.