Interactions Between orographically and Thermally Forced Planetary Waves

A comprehensive analysis has been made of the atmospheric planetary wave response to orographic and thermal forcing in midlatitudes using a simple model. Vertical heating profiles with maxima at the surface and in the mid-troposphere are considered. The model is quasi-geostrophic on a beta-plane, and has a constant zonal mean basic-state wind. With these simplifications it is possible to obtain complete analytic solutions, not only for the wave response with and without Ekman pumping, but also for the secondary effects of the waves on the zonal mean flow. The presence of diabatic heating in the waves results in significant non-zero Eliassen-Palm fluxes and violates conditions for non-acceleration of the zonal mean flow, both for propagating and trapped waves. The potential vorticity transport or, alternatively, the Eliassen-Palm flux divergence is shown to be directly related to the vertical heating profile. However, it is the interaction between orographic and thermally forced waves that is mainly responsible for change in the zonal mean flow, and the results therefore strongly depend upon the relative phase of the thermal and orographic forcing. At large heights, remote from the heating it is shown that it is possible to choose an equivalent mountain that would produce the same response in the planetary waves as the thermal forcing. The equivalent mountain height varies inversely as zonal wavenumber. In addition the mid-tropospheric heating profile produces a wave with 4-5 times the amplitude of the wave response to the surface heating profile with the same vertically integrated total heating. Consequently it is mainly in zonal waves 1 and 2 where a mid-tropospheric thermally forced wave can dominate or be comparable to the orographic waves.