A New Formulation of the Spectral Energy Budget of the Atmosphere, with Application to Two High-Resolution General Circulation Models

A new formulation of the spectral energy budget of kinetic and available potential energies of the atmosphere is derived, with spherical harmonics as base functions. Compared to previous formulations, there are three main improvements: (i) the topography is taken into account, (ii) the exact three-dimensional advection terms are considered, and (iii) the vertical flux is separated from the energy transfer between different spherical harmonics. Using this formulation, results from two different high-resolution GCMs are analyzed: the Atmospheric GCM for the Earth Simulator (AFES) T639L24 and the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecast System (IFS) T1279L91. The spectral fluxes show that the AFES, which reproduces quite realistic horizontal spectra with a k(-5/3) inertial range at the mesoscales, simulates a strong downscale energy cascade. In contrast, neither the k(-5/3) vertically integrated spectra nor the downscale energy cascade are produced by the ECMWF IFS.