Stochastic parametrization of subgrid‐scale processes in coupled ocean–atmosphere systems: benefits and limitations of response theory

Abstract

A stochastic subgrid‐scale parametrization based on the Ruelle's response theory and proposed by Wouters and Lucarini is tested in the context of a low‐order coupled ocean–atmosphere model for which a part of the atmospheric modes is considered as unresolved. A natural separation of phase‐space into an invariant set and its complement allows for an analytical derivation of the different terms involved in the parametrization, namely the average, fluctuation and long memory terms. In this case, the fluctuation term consists of 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 parametrizations in multiscale systems used for climate forecasts.