Some Tests and Developments of a Statistical Theory of Synoptic-Scale Meteorology

Abstract

A statistical theory of meteorological measurements and predictions was developed previously. It furnishes a priori minimum-error, maximum-probability distributions. In the present investigation, observed measurement and prediction errors are compared with theoretical errors to test whether the latter actually are smaller. In each of six arbitrarily chosen synoptic situations, standard deviations of observed and theoretical errors were computed and compared. In addition, standard deviations of theoretical 24-hr prediction errors from Rossby's wave-speed formula and Cressman's observed errors using this formula were compared. Results of each of these seven tests support the theory. Furthermore, two alternative methods are considered for investigating a synoptically observed variable: 1. The variable can be specified at points in space and time, but its value then is uncertain. In this connection, meteorological uncertainty relations which were derived earlier, are obtained in more exact form from the present theory. 2. The variable can be averaged over space or time to reduce these uncertainties, but details are lost in the process. Expressions are derived for reduced variances of averaged variables, in this case. These alternatives are regarded as mutually exclusive but complementary procedures.