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A Simple Approximate Method of Stochastic-Dynamic Prediction for Small Initial Errors and Short Range

Philip D. ThompsonNational Center for Atmospheric Research, Boulder, CO 80307

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Abstract

Starting with the vorticity equation for barotropic flow, we derive a system of stochastic differential equations that determines the time-evolution of the local variance of vorticity error originating in a large ensemble of initial states containing random and statistically isotropic initial errors. Those equations show that the local growth or decay of error variance depends primarily on the detailed structure of the true vorticity field; in general, the most rapid growth of error can be expected in concentrated regions of strong vorticity gradient.

Those stochastic differential equations provide the basis for a simple method of stochastic-dynamic prediction. It requires only a modest increase over the total volume of computation for deterministic prediction.

Abstract

Starting with the vorticity equation for barotropic flow, we derive a system of stochastic differential equations that determines the time-evolution of the local variance of vorticity error originating in a large ensemble of initial states containing random and statistically isotropic initial errors. Those equations show that the local growth or decay of error variance depends primarily on the detailed structure of the true vorticity field; in general, the most rapid growth of error can be expected in concentrated regions of strong vorticity gradient.

Those stochastic differential equations provide the basis for a simple method of stochastic-dynamic prediction. It requires only a modest increase over the total volume of computation for deterministic prediction.

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