Hasselmann's Program Revisited: the Analysis of Stochasticity in Deterministic Climate Models

In his seminal 1976 paper on \Stochastic Climate Models", K. Hassel-mann proposed to improve deterministic models for the \climate" (slow variables) by incorporating the innuence of the \weather" (fast variables) in the form of random noise. We will recast this program in the language of modern probability theory as follows: While the transition from a GCM (general circulation model) to an SDM (statistical dynamical model) (both deterministic) is facilitated by the method of averaging, stochasticity comes into the picture when studying the error made in the averaging procedure, provided that the fast variables are suuciently \chaotic". The study of normal deviations from the averaged system is described by the central limit theorem, while the study of large deviations from the average (events happening on an exponential time scale) is done by the theory of large deviations. We feel that the latter should be particularly appealing to meteorologists, as one can, for example, describe the \hop-ping" of the climate between its various local attractors due to the forcing by chaotic weather.