Application of Stochastic Dynamic Prediction to Real Data

Abstract

The technique of stochastic dynamic prediction proposed by Epstein is applied to atmospheric data. The motivation for the approach is discussed and a review is given of the development of the stochastic dynamic equations which, subject to the third-moment discard approximation, describe the evolution of the first two moments of a probability density characterizing an ensemble of possible true states. The method of “least squares” is used to extract the moments directly from radiosonde observations of the 500 mb geopotential height field. Approaching the analysis problem from a Bayesian standpoint leads to a weighted average of the new observations and the forecast, the appropriate weighting for the latter being supplied by the stochastic forecast itself. The basic physical model employed is a spectral form of the equivalent barotropic. The effects of the simplicity of the dynamical model on the growth of error (external error growth) must be considered explicitly when making stochastic forecasts, and two parameterizations are tested. To simulate these error sources, additional random forcing terms are used in each spectral equation. The output of each forecast is an estimate of the expected state of the atmosphere, as well as the uncertainty associated with that estimate as supplied by the variance-covariance information. During the forecast period, the uncertainty patterns undergo significant changes in response to model dynamics. The second parameterization of external error growth is found to be somewhat successful. Implications are drawn for more complicated models with reference to the treatment of external error growth. In addition, it is suggested that computing economies may be realized through the use of Monte Carlo methods.