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 function representation, truncated to include four zonal modes and up to mode 15 in the meridional direction. There are 11 levels in the vertical with the highest computational level at 5 mb. The model is linearized about a realistic observed January zonal-mean basic state and forced by the Northern Hemisphere orography and a wintertime calculated diabatic heating. In this paper, diabatic heating effects are not included and only the impact of the new LBC is examined in detail. The wave-coupled LBC has significant impact on the forced planetary waves and consequently on the Eliassen-Palm fluxes. The most noticeable responses of the planetary waves at the boundary when the wave-coupled LBC is used are in the vicinity of the Himalayas. The boundary eddies set up perturbation easterlies that locally offset the imposed zonal mean westerlies by forcing the flow to go around the mountains. Thus the wave-coupled LBC allows the total flow at the lower boundary to circumvent the Himalayas, unlike the traditional LBC. The net impact is that the kinematic effects of the Himalayas alone form the basis for a quite realistic Siberian high and Aleutian low, and the resulting East Asian trough is close to the observed position. In contrast, the model with the traditional (wave-decoupled) LBC generates an unrealistic and too strong wave pattern. Consequently, it produces the lower-tropospheric heat flux maximum 15 degrees of latitude too far south and greatly overestimates the strength of the momentum flux near the subtropical tropopause, whereas the wave-coupled solution results in more realistic fluxes, both in amplitude and location. The results show that it is necessary to take account of the fact that the earth's orography is large and cannot be considered as a small perturbation, as in the traditional approach to the LBC.