Quasi‐geostrophic planetary wave forcing

The problem of stationary planetary wave forcing by orography and longitudinal asymmetry of heating is re‐examined in the light of recent observations and theories of stratospheric motion. It is deduced that the region between 30 and 60km is a sink of planetary wave energy for zonal wavenumbers one and two in winter and that, in contrast to many theoretical descriptions, the transmission of wave energy to these levels is unimpeded. Quasi‐geostrophic theory expressed in spherical polar geometry suggests that in winter, wave energy should be able to propagate freely into the upper stratosphere for the largest scales of motion. Uncertainty in the absorption mechanism is avoided by the use of an energy‐transmitting upper boundary condition at a suitably chosen level and attention is concentrated on the structure of the wave motion below. Features of the January mean contour charts such as the Siberian and Aleutian anticyclones are shown to be consistent with the theory of untrapped, thermally forced motion. Close agreement of the structure of wavenumber one in theoretical solutions with existing observations is obtained for all heights below 30km, vindicating the use of energy‐transmitting boundary conditions. An important consequence of the ability of forced waves to propagate energy into the stratosphere is the poleward transport of heat, which is particularly strong for thermally forced motion near the level of non‐adiabatic heating. These calculations suggest that the contribution of stationary, thermally generated waves to the total poleward transport of heat is a major one in the lower troposphere. Some attempt to describe the monsoonal circulation of the northern hemisphere in summer is made with the inclusion of a stratosphere dominated by easterly mean zonal winds. The presence of a critical layer (where the mean zonal wind vanishes) introduces some interesting problems as regards the ‘realism’ of the linearized solution. Observations in July show that the phases of low wavenumber disturbances tilt rapidly eastwards with height in marked contrast to the westward tilt in winter. Solutions allowing critical‐level absorption are in poor agreement with observation in the troposphere with westward‐sloping phase lines, though the rapid attenuation of all waves in the stratospheric easterlies is well represented.