Edward Epstein's Stochastic-Dynamic Approach to Ensemble Weather Prediction

In the late 1960s, well before the availability of computer power to produce ensemble weather forecasts, Edward Epstein (1931-2008) developed a stochastic-dynamic prediction (SDP) method for calculating the temporal evolution of mean value, variance, and covariance of the model variables: the statistical moments of a time-varying probability density function that define an ensemble forecast. This statistical-dynamical approach to ensemble forecasting is an alternative to the Monte Carlo formulation that is currently used in operations. The stages of Epstein's career that led to his development of this methodology are presented with the benefit of his oral history and supporting documentation that describes the retreat of strict deterministic weather forecasting. The important follow-on research by two of Epstein's proteges, Rex Fleming and Eric Pitcher, is also presented. A low-order nonlinear dynamical system is used to discuss the rudiments of SDP and Monte Carlo and to compare these approximate methods with the exact solution found by solving Liouville's equation. Graphical results from these various methods of solution are found in the main body of the paper while mathematical development is contained in an online supplement. The paper ends with a discussion of SDP's strengths and weaknesses and its possible future as an operational and research tool in probabilistic-dynamic weather prediction.