The Effect of Analysis Errors on Some Predictions Made with the Spectral Vorticity Equation

Abstract

A theoretical method of determining minimum variances was applied to predictions made with the barotropic vorticity equation written in spectral form. The theory was first tested on hypothetical data, and then three synoptic cases were examined. If we assume a particular frequency function, we may obtain probabilities from the variances. Because the theoretical variances are minimum variances, the probabilities that we obtain are maximum probabilities. This means that the actual probability that an error will be less than a particular amount should not be greater than the theoretically computed value. The Gaussian frequency function was used to obtain probabilities from the theoretical variances. The theoretical probabilities were compared with observed probabilities of errors in spectral components and components of kinetic energy. The observed and theoretical probabilities were approximately the same for the hypothetical case. The theoretical probabilities were definitely maximum probabilities for the three synoptic cases.