Stochastic Averaging of Idealized Climate Models

Abstract

ariability in the climate system involves interactions across a broad range of scales in space and time. While models of slow ?climate? variability may not explicitly account for fast ?weather? processes, the dynamical influence of these unresolved scales cannot generally be ignored. Perspectives from statistical physics indicate that if the scale separation between slow and fast scales is sufficiently large, deterministic parameterizations are appropriate, while for smaller scale separations the parameterizations should be nondeterministic. The method of ?stochastic averaging? provides a framework for the reduction of coupled fast?slow systems into an effective dynamics of the slow variables. This study describes the hierarchy of approximations associated with stochastic averaging and applies this reduction methodology to two idealized models: a Stommel-type model of the meridional overturning circulation and a model of coupled atmosphere?ocean boundary layers. Finally, stochastic averaging is compared to other stochastic reduction strategies that have been applied to climate models.