Statistical-Dynamical Predictions

Abstract By analogy with Gibbs' statistical mechanics, a statistical-dynamical theory is described which can be applied to the problem of atmospheric predictions from synoptic charts. The m variables and constants whose measurement is needed to characterize an initial state are regarded as coordinates of an m dimensional phase space. In this space, the probability density ψ of the ensemble of possible initial measurements is used to define the “true” values of these quantities and to furnish probabilities of initial measurements lying within prescribed limits of true values. Dynamical equations provide standard deterministic predictions here, while a general continuity equation for ψ transforms initial probability distributions into final ones which, in turn, yield probability forecasts. This continuity equation is resolvable into component equations of probability diffusion for all coordinates of the phase space. It is found that predictability increases (decreases) with time if the atmosphere is diverge...