Stochastically Driven Large-scale Circulations with Multiple Equilibria

Abstract

The dynamic climatology of a simple model of barotropic stochastically forced β-plane flow over topography is studied. Except for the forcing, the model is similar to the three-component systems studied by Charney and DeVore (1979) and Hart (1979). In certain regions of parameter space there are two stable equilibria, a high-index flow with strong zonal winds and a low-index flow with a pronounced wave component. A random forcing is added in order to incorporate crudely the impact of the truncated flow modes on those retained in the model. The Fokker-Planck equation for this system is solved numerically and the steady-state probability distribution of the system is evaluated. It is found that the probability density distribution has maxima at the equilibria but that there also is a finite probability for intermediate states. This situation corresponds to that in the atmosphere where certain types of circulation like a high-index flow are met more frequently than others. It is also found that the predictability of the flow system studied depends strongly on the location of the initial state in phase space.