Noise-Induced Transitions in a Barotropic β-Plane Channel

Abstract

The concepts of multiplicative stochastic perturbations and noise-induced transitions are applied to a quasigeostrophic ?-plane model of barotropic flow over topography. The spectral three-component low-order representation of this configuration yields the Charney?DeVore (CDV) model. The externally prescribed damping of the system is allowed to scatter around a mean value. The stochastic representation of the damping term leads to a multiplicative stochastic forcing. The Fokker?Planck equation and the stochastic differential equation of the low-order CDV model are solved numerically. It is found that the qualitative behavior of the system is a function of the multiplicative noise level. In particular, the effect of multiplicative noise is not simply a smoothing of the probability density function, as it would be for pure additive noise. Rather, multiplicative noise leads to the high-index state being favored over the low-index state. The concept of noise-induced transitions explains this behavior. The noise-induced transition of the stochastic low-order model is confirmed by numerical integrations of a corresponding gridpoint model with many more degrees of freedom than the spectral model. It is suggested that the statistics of the unresolved physical processes could be an important factor in understanding the behavior of midlatitude large-scale atmospheric dynamics.