Atmospheric sensitivity to tropical heating as determined from the Fluctuation-Dissipation Theorem

For applications ranging from El Nino to global change, one would like to have a linear response operator that accurately estimates the atmospheric response to an arbitrary heating distribution. Given such an operator one can answer optimal forcing questions that cannot be addressed with complex models, including AGCMs. Unfortunately a simple linearization of the governing equations is not an adequate means of producing such a response operator because this leaves out important dynamical and diabatic processes. An alternative suggested by Leith (1975) is to employ the fluctuation-dissipation theorem (FDT) for construction of a response operator. This is the approach we use in this study.

To test the approach, we use the theorem to construct a response operator designed to match the behavior of an AGCM. This operator gives the mean response of AGCM state variables to a steady forcing. We then compare the operator response and the AGCM response to identical forcing functions and find they are remarkably similar thus validating the methodology. The conventional FDT only allows one to estimate the response of mean state variables, but a recent generalization by Majda et al. (2005) enables construction of response operators for functionals of state variables. Using this generalization we produce response operators for variances and covariances and find they also give very accurate estimates of how the AGCM responds to tropical heating.

Having determined that the response operators for means, variances and covariances give reliable response estimates, we then use them to find optimal ways of forcing system properties of interest. For example, using singular vector techniques, we find the tropical heating distribution that has the largest impact on bandpass variance in the Atlantic stormtrack. And we find the Green's function that indicates how heating at each point in the tropics contributes to stimulation of the North Atlantic Oscillation.