An analytic study of the Charney problem on the sphere

An analytic study of the Charney (1947) problem is presented, in which a shortwave approximation and a two-scale assumption are adopted to derive approximate solutions for the problem. The solutions contain a second-order turning point whose location is important in determining the properties of baroclinic unstable waves. This turning point is located at the maximum of the meridional temperature gradient. The solutions indicate a close relation between baroclinic instability on the sphere and on a Beta-plane. The solutions have some limitations and are not valid for long waves. It is suggested that the solutions have implications for parameterizations of eddy fluxes in climate modeling.