THE EFFECT OF INITIAL UNCERTAINTIES ON PREDICTIONS MADE WITH SOME BAROTROPIC AND BAROCLINIC MODELS

Abstract

A statistical theory developed previously is applied to predictions made with three simple atmospheric models under similar boundary and initial conditions. The theory gives minimum variances in height fields of various isobaric levels. The governing equations of each model are utilized to transform these initial variances to final variances of forecast fields. These variances are a measure of the theoretical minimum errors expected at any future states due to presence of initial uncertainties. Using the normal frequency function, these theoretical variances are further transformed to probabilities of obtaining forecast heights within specified magnitudes of true heights. These theoretical probabilities are compared with observed probabilities of errors in forecast fields obtained by various models for three synoptic situations. The theoretical probabilities are found to be larger everywhere than the observed ones, in support of the statistical theory that provides limiting probabilities not to be exceeded. A comparison of theoretical minimum variances indicates that the growth of these variances is more pronounced in more complex models that incorporate additional terms in the governing equations. The effect of hypothetically increasing the number of reporting stations indicates that a substantial reduction in initial and final variances is realized when the number of reporting stations is increased by two to three times the present number. The results of this study offer a possibility of choosing an optimum model to obtain the most reliable short-range weather prediction for a given synoptic situation.