Construction of response operators to small external forcings for atmospheric general circulation models with time periodic right-hand sides

Fluctuation-dissipation relations make it possible to connect the response operators of system statistical characteristics to small external perturbations with the statistical characteristics of the unperturbed system (providing statistical stationary of the system). This gives a possibility to estimate the sensitivity of the system directly from modeling or observational data. The problem becomes much more complex if the right hand side of the system contains a component periodically dependent on time (as applied to the problems of modeling the atmosphere, this corresponds to the annual cycle regime experiments). Recently obtained generalized fluctuation-dissipation relations (see Majda and Wang, 2010 11]) allow (at least theoretically) to construct response operators in the former case as well. In this work we formulate the algorithm for constructing an approximate response operator and test it numerically on the example of the National Center for Atmospheric Research (NCAR) CAM3 atmospheric general circulation model.