Resonant Planetary Waves in a Spherical Atmosphere

Abstract

A global model of planetary wave propagation in a spherical atmosphere is used to examine the spectrum of free or resonant planetary waves of the solstitial stratosphere. These free modes are located by forcing the model with a weak periodic vertical velocity along the lower boundary and looking for a resonant response in wave amplitude. The modes correspond to the natural traveling oscillations in the earth's atmosphere, of which the 5-day wave is the best known example. The 15-day wave observed by Madden (1978) and others is found to be such a resonant mode. We find that the strong stratospheric winds cause the 15-day wave to become baroclinic by trapping the wave between the earth's surface and the strong winds at the stratopause. The strong winds effectively reduce the atmospheric damping which greatly reduces the amplitude of barotropic waves with periods >10 days. The computed meridional structure of the 15-day wave is in reasonable agreement with Madden's (1978) observations at extratropical latitudes. Our results indicate that a mode resembling the H? Hough function represents the principal resonant component. Other resonances at periods longer than 15 days for zonal harmonies 1, 2 and 3 are shown, and these modes are also baroclinic. At very long periods (50?100 days) broad resonant peaks are observed for all three zonal harmonics. These peaks indicate that the structure of stationary planetary waves is very sensitive to changes in the mean zonal wind (frequency changes in this model) as has been noted by other authors.