The use of an ensemble approach to study the background error covariances in a global NWP model

The estimation of the background error statistics is a key issue for data assimilation. Their time average is estimated here using an analysis ensemble method. The experiments are performed with the nonstretched version of the Action de Recherche Petite Echelle Grande Echelle global model, in a perfect-model context. The global (spatially averaged) correlation functions are sharper in the ensemble method than in the so-called National Meteorological Center (NMC) method. This is shown to be closely related to the differences in the analysis step representation. The local (spatially varying) variances appear to reflect some effects of the data density and of the atmospheric variability. The resulting geographical contrasts are found to be partly different from those that are visible in the operational variances and in the NMC method. An economical estimate is also introduced to calculate and compare the local correlation length scales. This allows for the diagnosis of some existing heterogeneities and anisotropies. This information can also be useful for the modeling of heterogeneous covariances based, for example, on wavelets. The implementation of the global covariances and of the local variances, which are provided by the ensemble method, appears moreover to have a positive impact on the forecast quality.