A STATISTICAL THEORY OF METEOROLOGICAL MEASUREMENTS AND PREDICTIONS

Abstract

A statistical theory of synoptic-scale measurements and predictions is developed and presented with the aid of numerical examples. In place of standard meteorological variables which are important in classical theory, there are a priori probability distributions of these variables in the present theory. The probabilities are for measured and predicted values to differ from hypothetically true values by specified amounts. These differences generally must be regarded as minimal because complexities of atmospheric phenomena cannot be completely observed or encompassed in prediction procedures. The minimum-error, maximum-probability distributions are Gaussian with standard deviations dependent on observation-network densities. Classical kinematic and dynamic equations are used in prediction to transform initial probability distributions into final ones. The procedure is very similar to procedures of quantum mechanics and statistical mechanics, as is illustrated by a numerical example. It is shown that uncertainties associated with forecasts of unstable phenomena can be described quantitatively by the theory. The theory is general and capable of wide use. Classical deterministic methods are limiting cases of it.