Hasselmann’s stochastic climate model viewed from a statistical mechanics perspective

Abstract

Hasselmann’s stochastic climate model asserts that weather fluctuations randomly force the climate system in the same way that fluid molecules force Brownian ink particles. Langevin’s equation is used to model this physical process. This essay compares Hasselmann’s stochastic climate model and its Langevin equation to the role that the Langevin equation plays in the description of a classical N-particle system. The theory of classical N-particle systems is well developed. There exist a well defined hierarchy of models. One distinguishes between the micro-, meso-, and macroscopic levels of description obtained by successive coarse graining. Statistical mechanics and other synthetic analyses relate the different levels to each other. The Langevin equation is a mesoscopic equation. It ignores the details of the molecular interactions but retains information about the distribution of molecules in position and momentum space. The theory of the climate system is less developed. There exists a gallery rather than a hierarchy of models. Hasselmann’s stochastic climate model is a mesoscopic description. It ignores the details of the weather fluctuations. In its original version, it is a cognitive model, aimed at understanding a specific physical process. It has not yet been advanced to a comprehensive and realistic model of the climate system on the mesoscopic level.