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 forcing that will produce a given response in the AGCM. In the few cases where the operator is not accurate, it appears that the fact that the operator was constructed in a reduced space is at least partly responsible.As an example of the potential utility of a response operator with the accuracy found here, the FDTbased operator is applied to a problem that is difficult to solve with an AGCM. It is used to generate an influence function that shows how well heating at each point on the globe excites the AGCM's Northern Hemisphere annular mode (NAM). Most of the regions highlighted by this influence function, including the Arctic and tropical Indian Ocean, are verified by AGCM solutions as being effective locations for stimulating the NAM.

A generalization of the fluctuation-dissipation theorem (FDT) that allows generation of linear response operators that estimate the response of functionals of system state variables is tested for a system defined by an atmospheric general circulation model (AGCM). A sketch of the proof of this generalization is provided, followed by comparison of response estimates based on the theory and actual responses of the AGCM for various idealized anomalous equatorial heat sources. Tested response quantities include precipitation, variances of bandpass and low-pass streamfunction, and momentum and heat fluxes. The solutions from the FDT operators are very similar to the AGCM solutions in terms of structure while overestimating response amplitudes by about 20%. As an example of an application of such response operators, the FDT operator that estimates the response of bandpass upper-tropospheric streamfunction variance is used to find the most efficient means of disturbing the Atlantic storm tracks by tropical heating. The results of the study suggest that the generalized FDT is an attractive method for systematically studying response attributes of the climate system that are of interest to climate scientists and society.

We study the response of a simple quasi-geostrophic barotropic model of the atmosphere to various classes of perturbations affecting its forcing and its dissipation using the formalism of the Ruelle response theory. We investigate the geometry of such perturbations by constructing the covariant Lyapunov vectors of the unperturbed system and discover in one specific case -orographic forcing -a substantial projection of the forcing onto the stable directions of the flow. This results into a resonant response shaped as a Rossby-like wave that has no resemblance to the unforced variability in the same range of spatial and temporal scales. Such a climatic surprise corresponds to a violation of the fluctuation-dissipation theorem, in agreement with the basic tenets of nonequilibrium statistical mechanics. The resonance can be attributed to a specific group of rarely visited unstable periodic orbits of the unperturbed system. Our results reinforce the idea of using basic methods of nonequilibrium statistical mechanics and high-dimensional chaotic dynamical systems to approach the problem of understanding climate dynamics.