An Exploration of Multivariate Fluctuation Dissipation Operators and Their Response to Sea Surface Temperature Perturbations

The fluctuation–dissipation theorem (FDT) has been proposed as a method of calculating the mean response of the atmosphere to small external perturbations. This paper explores the application of the theory under time and space constraints that approximate realistic conditions. To date, most applications of the theory in the climate context used univariate, low-dimensional-state representations of the climate system and an arbitrarily long sample size. The authors explore high-dimensional multivariate FDT operators and the lower bounds of sample size needed to construct skillful operators. It is shown that the skill of the operator depends on the selection of variables and features representing the climate system and that these features change once memory (slab ocean) is added to the system. In addition, it is found that the FDT operator has skill in estimating the response to realistic sea surface temperature (SST) patterns, such as El Niño–Southern Oscillation (ENSO), despite the fact that these patterns were not part of the data used to produce the operator. The response of clouds is also studied; for variables that represent cloud properties, the decrease in skill in relation to decrease in sample size still maintains the key features of the response.