The Generalization of Semigeostrophic Theory to the β-Plane

Abstract

We develop here the isentropic?geostrophic coordinate version of semigeostrophic theory on a midlatitude ?-plane. This approach results in a simple mathematical form in which the horizontal ageostrophic velocities are implicit and the entire dynamics reduces to a predictive equation for the potential pseudodensity and an invertibility relation. Linearized versions of the theory lead to a generalized Charney?Stern theorem for combined barotropic?baroclinic instability and to Rossby wave solutions with a meridional structure different from that in quasi-geostrophic theory.