Stochastic climate models: Part I. Theory

Abstract

A stochastic model of climate variability is considered in which slow changes of climate are explained as the integral response to continuous random excitation by short period "weather" disturbances. The coupled ocean-atmosphere-cryosphere-land system is divided into a rapidly varying "weather" system (essentially the atmosphere) and a slowly responding "climate" system (the ocean, cryosphere, land vegetation, etc.). In the usual Statistical Dynamical Model (SDM) only the average transport effects of the rapidly varying weather components are parameterised in the climate system. The resultant prognostic equations are deterministic, and climate variability can normally arise only through variable external conditions. The essential feature of stochastic climate models is that the non-averaged "weather" components are also retained. They appear formally as random forcing terms. The climate system, acting as an integrator of this short-period excitation, exhibits the same random-walk response characteristics as large particles interacting with an ensemble of much smaller particles in the analogous Brownian motion problem. The model predicts "red" variance spectra, in qualitative agreement with observations. The evolution of the climate probability distribution is described by a Fokker-Planck equation, in which the effect of the random weather excitation is represented by diffusion terms. Without stabilising feedback, the model predicts a continuous increase in climate variability, in analogy with the continuous, unbounded dispersion of particles in Brownian motion (or in a homogeneous turbulent fluid). Stabilising feedback yields a statistically stationary climate probability distribution. Feedback also results in a finite degree of climate predictability, but for a stationary climate the predictability is limited to maximal skill parameters of order 0.5.

Sensitivity of a double-gyre ocean model to details of stochastic forcing

“…4. In all experiments an overall red-noise behaviour is observed, as expected from the stochastic climate scenario proposed by Hasselmann (1976). The red oceanic spectrum is a consequence of the amplification of lowfrequency weather fluctuations.…”

Scale-Dependent Reconstruction of the NAO Index

“…Concerning the low-frequency variations of the NAO on decadal and interdecadal time scales, one important issue is the role of the North Atlantic Ocean. It is broadly accepted that the passive response of the ocean is in agreement with the statistical climate model concept of Hasselmann (1976), but the active role of the ocean on the NAO dynamics is still open to debate. Studies based on observational data have shown that extratropical SST anomalies could force the atmospheric circulation (Czaja and Frankignoul 2002).…”

Disentangling multi-level systems: averaging, correlations and memory

“…On the other hand, Earth Models of Intermediate complexity [9,23], which are tailored for such problems, are definitely not competitive if our aim is to describe the variability of the present climate and the short-term climate change. The problem of providing a satisfactory description of the dynamical processes that cannot be explicitly be represented has long been addressed at various levels of rigour by the climate community [20,31,11,10,3,28,22]. The solutions that are being used in practical applications today go by the name of parametrizations.…”