Stochastic parameterization of subgrid-scale processes in coupled ocean-atmosphere systems: Benefits and limitations of response theory

A stochastic subgrid-scale parameterization based on the Ruelle's response theory and proposed in Wouters and Lucarini [2012] is tested in the context of a low-order coupled ocean-atmosphere model for which a part of the atmospheric modes are considered as unresolved. A natural separation of the phase-space into an invariant set and its complement allows for an analytical derivation of the different terms involved in the parameterization, namely the average, the fluctuation and the long memory terms. In this case, the fluctuation term is an additive stochastic noise. Its application to the low-order system reveals that a considerable correction of the low-frequency variability along the invariant subset can be obtained, provided that the coupling is sufficiently weak. This new approach of scale separation opens new avenues of subgrid-scale parameterizations in multiscale systems used for climate forecasts.