Using Different Formulations of the Transformed Eulerian Mean Equations and Eliassen–Palm Diagnostics in General Circulation Models

Abstract

Transformed Eulerian mean (TEM) equations and Eliassen?Palm (EP) flux diagnostics are presented for the general nonhydrostatic, fully compressible, deep atmosphere formulation of the primitive equations in spherical geometric coordinates. The TEM equations are applied to a general circulation model (GCM) based on these general primitive equations. It is demonstrated that a naive application in this model of the widely used approximations to the EP diagnostics, valid for the hydrostatic primitive equations using log-pressure as a vertical coordinate and presented, for example, by Andrews et al. in 1987 can lead to misleading features in these diagnostics. These features can be of the same order of magnitude as the diagnostics themselves throughout the winter stratosphere. Similar conclusions are found to hold for ?downward control? calculations. The reasons are traced to the change of vertical coordinate from geometric height to log-pressure. Implications for the modeling community, including comparison of model output with that from reanalysis products available only on pressure surfaces, are discussed.