Climate Response Using a Three-Dimensional Operator Based on the Fluctuation–Dissipation Theorem

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Abstract
The fluctuation–dissipation theorem (FDT) states that for systems with certain properties it is possible to generate a linear operator that gives the response of the system to weak external forcing simply by using covariances and lag-covariances of fluctuations of the undisturbed system. This paper points out that the theorem can be shown to hold for systems with properties very close to the properties of the earth’s atmosphere. As a test of the theorem’s applicability to the atmosphere, a three-dimensional operator for steady responses to external forcing is constructed for data from an atmospheric general circulation model (AGCM). The response of this operator is then compared to the response of the AGCM for various heating functions. In most cases, the FDT-based operator gives three-dimensional responses that are very similar in structure and amplitude to the corresponding GCM responses. The operator is also able to give accurate estimates for the inverse problem in which one derives the forci... Abstract The fluctuation–dissipation theorem (FDT) states that for systems with certain properties it is possible to generate a linear operator that gives the response of the system to weak external forcing simply by using covariances and lag-covariances of fluctuations of the undisturbed system. This paper points out that the theorem can be shown to hold for systems with properties very close to the properties of the earth’s atmosphere. As a test of the theorem’s applicability to the atmosphere, a three-dimensional operator for steady responses to external forcing is constructed for data from an atmospheric general circulation model (AGCM). The response of this operator is then compared to the response of the AGCM for various heating functions. In most cases, the FDT-based operator gives three-dimensional responses that are very similar in structure and amplitude to the corresponding GCM responses. The operator is also able to give accurate estimates for the inverse problem in which one derives the forci...