THE GENERALIZATION OF SEMIGEOSTROPHIC THEORY TO THE BETA-PLANE

We develop here the isentropic-geostrophic coordinate version of semigeostrophic theory on a midlatitude β-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. -Authors