A Formulation of Three Dimensional Wave Activity Flux Describing Wave Propagation on the Mass-Weighted Isentropic Time Mean Equation

Abstract

The Transformed Eulerian-Mean (TEM) equations derived by D. G. Andrews and M. E. McIntyre are powerful tools for diagnosing the meridional circulation and wave-mean interaction in the troposphere and/or middle atmosphere. However, the TEM equations cannot properly treat the lower boundary and unstable waves. The Mass-weighted Isentropic zonal Mean (MIM) equations derived by T. Iwasaki are the equations that overcome those problems and are recently used for analyzing polar cold air outbreak. On the other hand, the MIM equations have not been extended to three dimensions (3D), especially for wave activity flux, although the TEM equations have been extended by several studies. The present study formulates the 3D wave activity flux describing wave propagation in the mass-weighted isentropic time mean equations. A dispersion relation for inertia-gravity waves and Rossby waves on those equations is also derived and used to relate the 3D wave activity flux to the group velocity. Finally, we use the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-analysis (ERA-Interim) data and report the comparison result of 3D wave activity fluxes between TEM and mass-weighted isentropic time mean equations.