Stochastic orographic forcing of barotropic β-plane flow

The zonal flow of the atmosphere varies erratically in time, thus providing stochastic sources and sinks of vorticity at the slopes of mountains. The atmospheric response to this stochastic forcing is studied using the linear barotropic vorticity equation for β-plane channel flow. Given the power spectrum of the zonal flow according to observations, the power spectrum of the atmospheric response can be evaluated. First a sinusoidal mountain is prescribed where a rather complete understanding of the resulting power fields can be obtained. Then a circular mountain is exposed to the random variations of the zonal flow and the resulting patterns are found to be in agreement with what one would expect on the basis of the theory of Rossby wave packets in channels. Third the northern hemisphere response is studied and it is concluded that the interaction of the stochastically varying zonal flow with the orography does not strongly contribute to the atmospheric low-frequency variability.