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.

SUMMARYFollowing the a posteriori diagnosis approach proposed by some authors, a practical computation of the expectation of sub-parts of the value of a cost function at the minimum is shown to be feasible by using a randomization technique based on a perturbation of observations or background fields. These computations allow the tuning of observation-error weighting parameters by applying a simple iterative fixed-point procedure.The procedure is first tested in a simplified variational scheme on a circular domain and then in a similar scheme but with the addition of the vertical coordinate. The relationship between the proposed approach and the Generalized Cross Validation is also shown. A test in the French Action de Recherche Petite Echelle Grande Echelle (ARPEGE) three-dimensional variational framework with both simulated observations and background fields is finally performed. It shows that a complete description of observation-error parameters can be retrieved with only a few iterations and, thus, at a reasonable cost.

AROME-France is a convective-scale numerical weather prediction system running operationally at Météo-France since the end of 2008. It uses a 3D-Var assimilation scheme to determine its initial conditions. Climatological background-error covariances of such a system are calculated using differences between forecasts from an AROME ensemble assimilation. These statistics are compared with the lowerresolution ALADIN-France system ones: they provide 3D-Var analysis increments that are more intense and more localized, in accordance with the actual AROME model resolution. AROME ensemble-assimilation (ENS DA) covariances have also been compared with covariances calculated with an AROME ensemble of forecasts run in spin-up mode (ENS SU). On the one hand, ENS SU appears to be a reasonable approximation of ENS DA compared with ALADIN-France covariances, by representing a large part of the small-scale variance increase. On the other hand, ENS DA allows for a fully cycled development of small-scale forecast perturbations, which leads to a further enhancement of small-scale covariances. This aspect is shown to be beneficial in terms of assimilation diagnostics and forecast performance and in a case study.