The Response of a Simplified GCM to Axisymmetric Forcings: Applicability of the Fluctuation–Dissipation Theorem

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Abstract
Following on their previous work, in which they found the annular modes to be a preferred response of a simplified general circulation model atmosphere to a number of mechanical forcings, the authors now explore the quantitative relationship between forcing and response. In particular, the applicability of the fluctuation-dissipation theorem to this problem is investigated. First, the set of model trials is expanded by including runs in which the applied forcings are thermal rather than mechanical. For thermal forcings confined to the extratropics, "annular mode-like" responses, reminiscent of those found in earlier work, are found, but, as found in previous studies, the response is less like an annular mode when the forcing has significant amplitude in the tropics. Assuming small departures from the control climatology, and making a few further assumptions, the authors derive a theoretical relationship between forcing and response. This relationship is a statement of the fluctuation-dissipation theorem for this problem. The response of the model is found to be qualitatively consistent with the theoretical predictions. However, several aspects of the response diverge quantitatively from the theoretical expectation.