Orographically Forced Planetary Waves in the Northern Hemisphere Winter: Steady State Model with Wave-Coupled Lower Boundary Formulation

Abstract A planetary wave model has been developed in which the orographic forcing at the lower boundary arising from the kinematically induced vertical motion is due to the total flow impinging on the mountains rather than just the zonal mean basic state component of the flow over the mountains used in previous models. Consequently, the effects of the vertical motions produced by the eddies at the lower boundary are included and are found to be as large, if not larger, than the zonal mean component. The model remains linear mathematically, but all the planetary waves become coupled through the lower boundary condition (LBC) and the model wave equations have to be solved for simultaneously. A contrast is drawn between the wave-coupled solutions and the solutions using the traditional lower boundary formulation in which the planetary waves are decoupled. The model is symmetric about the equator and uses the linear balance set of equations on the sphere, with full spherical geometry and spherical harmonic f...