The Evolution of Dispersion Spectra and the Evaluation of Model Differences in an Ensemble Estimation of Error Statistics for a Limited-Area Analysis

An ensemble of limited-area forecasts has been obtained by integrating the Aire Limitée Adaptation Dynamique Développement International (ALADIN) limited-area model, in cold-starting mode, from an ensemble of Action de Recherche Petite Echelle Grande Echelle (ARPEGE) global analyses and forecasts. This permits error covariances of the ALADIN 6-h forecast and of the ARPEGE analysis to be estimated. These two fields may be combined in a future ALADIN analysis. The evolution of dispersion spectra is first studied in a perfect model framework. The ARPEGE analysis reduces the large-scale dispersion of the ARPEGE background by extracting some information from observations. Then, the digital filter initialization reduces the small-scale dispersion by removing the noise caused by interpolation of the ARPEGE analysis onto the ALADIN grid. Finally, the ALADIN 6-h forecast strongly increases the small-scale dispersion, in accordance with its ability to represent small-scale processes. Some model error contributions are then studied. The variances of the differences between the ALADIN and ARPEGE forecasts, which are started from the same ARPEGE analysis, are of smaller scale than are the ALADIN and ARPEGE perfect model dispersions. The small-scale part of these ARPEGE–ALADIN model differences is shown to correspond to structures that are represented by ALADIN and not by ARPEGE. Therefore, this part may be added to the ARPEGE analysis dispersion. The residual large-scale part is more ambiguous, but it may be added to the ALADIN dispersion; this may reflect some effects of the coupling inaccuracies, and strengthen (in a future ALADIN analysis) the use of the large-scale information from the ARPEGE analysis.