Semigeostrophic theory on the hemisphere

Abstract

This paper presents the combined isentropic and spherical geostrophic coordinate version of semigeostrophic theory. In order to demonstrate how the theory applies to problems of barotropic-baroclinic instability and Rossby-Haurwitz wave dispersion, we derive the semigeostrophic generalization of the Charney-Stern theorem and compare the semigeostrophic Rossby-Haurwitz wave frequencies with those of Laplace's tidal equations. The agreement between these frequencies is generally better than 0.5%. Thus, the theory apppears to encompass a wide range of meteorological phenomena including both planetary-scale and synoptic-scale waves, along with their finer scale aspects such as fronts and jets. -from Authors