Some Effects of the Upper Boundary Condition and Vertical Resolution on Modeling Forced Stationary Planetary Waves

Abstract

Some consequences of applying the boundary condition dp/dt=0 at p=0 in a linearized middle-latitude ?-plane model of forced stationary planetary waves are investigated. The perturbations, which are assumed to be quasi-geostrophic and subject to Newtonian cooling, are superimposed on an isothermal basic state having a realistic vertical profile of the mean zonal wind. Computations of the wave structures are made using finite differences in the vertical with various resolutions. They are compared with those obtained in a model which uses a radiation condition at its upper boundary. The influence of the mean zonal wind distribution is investigated by using vertical profiles which are representative of winter, spring and fall. In general, the results show that insufficient resolution in the stratosphere can lead to a spurious energy reflection at the upper boundary and to a wave structure which is completely in error.