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ON STOCHASTIC DYNAMIC PREDICTION UDC 551.508.313 1. The Energetics of Uncertainty and the Question of Closure

By Rex J. Fleming

Abstract

In this, the first part of a two-part study, we examine the rationale of the stochastic dynamic approach to numerical weather prediction. Advantages of the stochastic dynamic method are discussed along with problems associated with the method. This method deals with the initial uncertainty by considering an infinite ensemble of initial states in phase space, relative frequencies within the ensemble being proportional to probability densities. The evolution of this ensemble in time, given by the stochastic dynamic equation set, is based upon the original deterministic hydrodynamic equation set. One may consider the latter set as a subset of the former. Insight into the nature of these equations is obtained by deriving the energy transformations associated with them. A simple baroclinic model is used to isolate the energy concepts and relations. The energetics yield qualitative and quantitative information on the nature of the growth of uncertainty. It is found that the baroclinic instability mechanism is responsible for most of the error growth as would be expected. Previous predictability studies have considered that the simulation of the forces governing the atmosphere has been perfect. The effects of imperfect forcing can be viewed with the stochastic dynamic equations by adding another dimension to phase space for each parameter considered to be uncertain. The effect of the inclusion of this imperfect forcing is shown by the new energetic relations that result, and by numerical calculation of the changes in th

Year: 1971
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