SUMMARYMost operational assimilation schemes rely on linear estimation theory. Under this assumption, it is shown how simple consistency diagnostics can be obtained for the covariances of observation, background and estimation errors in observation space. Those diagnostics are shown to be nearly cost-free since they only combine quantities available after the analysis, i.e. observed values and their background and analysis counterparts in observation space. A first application of such diagnostics is presented on analyses provided by the French 4D-Var assimilation. A procedure to refine background and observation-error variances is also proposed and tested in a simple toy analysis problem. The possibility to diagnose cross-correlations between observation errors is also investigated in this same simple framework. A spectral interpretation of the diagnosed covariances is finally presented, which allows us to highlight the role of the scale separation between background and observation errors.

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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.

SUMMARYWe present an overview of the 3D-Var data assimilation in the framework of the ALADIN/France model. The purpose of this system is to provide improved precipitation forecasts at mesoscale and in the short range, up to 18 hours. The goal of the paper is threefold. Firstly, we present initial considerations for the design of the 3D-Var system. Secondly, we discuss in more detail the specification of the background-error covariance matrix, by comparing three different error simulation techniques, namely two variants of the NMC method and an ensemble-based approach. The formal, diagnostic and impact studies have led to the selection of the ensemblebased covariances for the ALADIN/France assimilation. Thirdly, scores of quantitative precipitation forecasts are shown in order to illustrate the robustness and the preliminary meteorological performance of the ALADIN/France assimilation suite. The results indicate that the tested configuration improves some aspects of the precipitation forecast, while being neutral for others, when compared with the spin-up model.We conclude the paper by providing a more explicit insight into the future evolution of limited-area variational analysis towards convective-scale data assimilation.