Validation of the ECMWF ensemble prediction system using empirical orthogonal functions

Empirical orthogonal function (EOF) analysis of deviations from the ensembl e mean was used to validate the statistical properties of T(L)159 51-member ensemble forecasts run at the European Centre for Medium-Range Weather For ecasts (ECMWF) during the winter of 1996/97. The main purpose of the analys is was to verify the agreement between the amount of spread variance and er ror variance accounted for by different EOFs. A suitable score was defined to quantify the agreement between the variance spectra in a given EOF subsp ace. The agreement between spread and error distribution for individual pri ncipal components (PCs) was also tested using the nonparametric Mann-Whitne y test. The analysis was applied at day 3, 5, and 7 forecasts of 500-hPa he ight over Europe and North America, and of 850-hPa temperature over Europe. The variance spectra indicate a better performance of the ECMWF Ensemble Pr ediction System (EPS) over Europe than over North America in the medium ran ge. In the former area, the excess of error variance over spread variance t ends to be confined to nonleading PCs, while for the first two PCs the erro r variance is smaller than spread at day 3 and in very close agreement at d ay 7. When averaged over a six-EOF subspace, the relative differences betwe en spread and error PC variances are about 25% over Europe, with the smalle st discrepancy (15%) for 850-hPa temperature at day 7. Overall, the distrib ution of variance between different EOFs produced by the EPS over Europe is in good agreement with the observed distribution, the differences being of comparable magnitude to the sampling errors of PC variances in individual seasons.