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It is well-known that when Rossby waves are stationary in the belt of mid-latitude westerlies, resonance conditions occur allowing the atmospheric response to external perturbations to be greatly enhanced. The concept lies at the heart of the interaction of planetary flows with topographic mountain chains. In contrast, early studies of the atmospheric response to thermal forcing, focussed on the off resonance response. Now available, many GCM studies dealing with the atmospheric response to prescribed SST have revealed a great variety of responses, the difficulty of extracting the signal at planetary scale being compounded by the overwhelming activity of transient eddies at the synoptic scale. Given the long lasting influence of large scale SST anomalies, climate predictability may be expected to improve if one can identify feedbacks between the large scale climate anomalies and the SST distribution. We propose a simple theory that explores the physics of this atmospheric response to SST and may suggest ways to analyze data from the more complex GCM. We neglect all interactions between the transient eddies and the large scale waves that would go beyond Fickian mixing laws although there is evidence that the transient eddies by themselves take part in the maintenance of the low frequency variability. Because the observed perturbations are small, a linear theory is appropriate. Using a 2-level model of the atmosphere, a resonance condition occurs when the Rossby waves are stationary against the vertically averaged mean zonal flow. The resonance is sharp when eddy dissipation through surface friction is small. In a small wavenumber window controlled by the vertical structure of the mean flow, the response is equivalent barotropic and baroclinic elsewhere. Only in this window is the familiar response of high SLP downstream of warm SST recovered. For certain combination of thermal damping and surface drag, the atmospheric response is amplified to produce a positive feedback on the SST. When the atmospheric model is coupled to a one and a half level ocean model with a zonally periodic geometry appropriate to the Southern Oceans, a linear instability appears. The application of this process of thermal resonance to the Antarctic circumpolar wave is discussed. We find that under realistic values of the mean state, an unstable coupled wave emerges in a narrow wavenumber window which coincides with the near resonance conditions found previously in the atmospheric model. This instability provides a powerful scale selective mechanism for the perturbations. The thermal forcing is primarily responsible for amplification of the SST while the powerful Antarctic circumpolar current is primarily responsible for advecting the anomalies around the globe and setting the period. |
