Stochastic Climate Models

The proceedings of the summer 1999 Chorin workshop on stochastic climate models captures well the spirit of enthusiasm of the workshop participants engaged in research in this exciting field. It is amazing that nearly 25 years after the formal theory of natural climate variability generated by quasi-white-noise weather forcing was developed, and almost 35 years after J . M. Mitchell first suggested this mechanism as the origin of sea-surf ace-temperature fluctuations and climate variability, there have arisen so many fresh perspectives and new applications of the theory. The workshop has succeeded admirably in high­ lighting these new aspects while clarifying the position of stochastic climate modelling within the general framework of climate research and mathematical modelling. The organizers can be congratulated in bringing together leading researchers covering a wide range of scientific expertise, from mathematicians concerned with the derivation of stochastic models from first principles, to app­ lied climate modellers trying to understand the dynamics of the complex climate system. Following the first burst of stochastic modelling papers in the decade from the mid-seventies to the mid-eighties, in which the viability of the concept was demonstrated using relatively simple conceptual models, there was a lull of work in this field. One awaited the development of more sophisticated climate models with which one could carry out realistic quantitative analyses of the implications of stochastic forcing for the global climate system. Now that these models have become widely available, it is natural that one is witnessing a resurgence of stochastic modelling investigations. Front Matter....Pages i-xxvii Front Matter....Pages 1-1 A gallery of simple models from climate physics....Pages 3-63 Simple climate models....Pages 65-100 Complex climate models — tools for studying the origin of stochasticity in the climate system....Pages 101-116 Some mathematical aspects of the GCMs....Pages 117-138 Front Matter....Pages 139-139 Hasselmann’s program revisited: the analysis of stochasticity in deterministic climate models....Pages 141-157 Thermodynamic formalism, large deviation, and multifractals....Pages 159-169 Averaging and climate models....Pages 171-188 Dynamical systems with time scale separation: averaging, stochastic modelling, and central limit theorems....Pages 189-209 Front Matter....Pages 211-211 Energy balance models — viewed from stochastic dynamics....Pages 213-240 Exponential stability of the quasigeostrophic equation under random perturbations....Pages 241-256 A mini course on stochastic partial differential equations....Pages 257-284 Hasselmann’s stochastic climate model viewed from a statistical mechanics perspective....Pages 285-295 Front Matter....Pages 297-297 Constrained stochastic forcing....Pages 299-308 Stochastic resonance and noise-induced phase coherence....Pages 309-323 Stochastic confinement of Rossby waves by fluctuating eastward flows....Pages 325-343 Some mathematical remarks concerning the localisation of planetary waves in a stochastic background flow....Pages 345-368 Rossby waves in a stochastically fluctuating medium....Pages 369-384 Passive tracer transport in stochastic flows....Pages 385-398 This book presents a collection of articles written by mathematicians and physicists, designed to describe the state of the art in climate models with stochastic input. They are based on a selection of lectures given at the interdisciplinary Workshop on Stochastic Climate Models held in Chorin, Germany, from May 31 to June 2, 1999. The emphasis is on reduced models tractable with advanced tools from the area of stochastic processes, stochastic analysis and random dynamical systems. They include popular examples such as box models for the thermohaline ocean circulation and simple models for El Niño. Among the main topics addressed are a comprehensive survey of the hierarchy of climate models ranging from general circulation models to simple energy balance models; a discussion of the origin of stochasticity in climate modelling by separation of fast and slow scale processes such as weather phenomena or astronomical events; a review of relevant mathematical tools such as stochastic partial differential equations, aspects of stochastic dynamics, large deviations, and averaging techniques; several concrete reduced models are discussed together with methods for their approach such as stochastic resonance, localization of waves, or tracer transport in stochastic flows. The book is aimed at mathematicians, physicists or scientists of any area interested in an overview of the state of the art in reduced climate models. In particular, mathematicians will find a survey of simple models, while physicists will encounter mathematically relevant techniques at work.