The Eulerian form of the Eliassen-Palm flux for quasi-geostrophic motion is generalized to include large-scale eddy forcing of condensation heating. Only the vertical component of the flux has to be modified; it is increased. The Eliassen-Palm theorem still holds, but instead of assuming that the diabatic heating is zero, one assumes that the diabatic heating excluding condensation associated with the large-scale motions is zero. The non-acceleration theorem also still holds, provided one adds the assumption that the Eulerian zonal mean moisture field is stationary. The generalization preserves the relationship between stationary wave energy flux and the Eliassen-Palm flux, but now wave condensation effects are automatically included. In addition, the generalization leads to a function describing the total eddy forcing of the moisture field.
The divergence of the generalized Eliassen-Palm flux is calculated from atmospheric observations and compared with the divergence of the standard flux. The eddy forcing of the zonal mean zonal wind and temperature fields is much stronger when condensation effects are included—for example, in the annual mean it is about two and one half times as strong. The eddy forcing of the moisture field is also calculated. It shows the expected tendency to dry out the subtropics and moisturize middle and high latitudes, but the effect of the meridional eddy flux of moisture is greatly enhanced by the effect of the Ferrel cell induced by the eddy heat fluxes.