Stochastically Driven Large-scale Circulations with Multiple Equilibria

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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 ... 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 ...

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