Modelling of flow-dependent ensemble-based background-error correlations using a wavelet formulation in 4D-Var at Meteo-France

The use of a wavelet formulation and ensemble data assimilation is considered in this study, in order to specify flow-dependent background-error correlations for the Meteo-France global 4D-Var system. This wavelet model is calibrated by using a temporal series of recent perturbed backgrounds, which is sampled in a sliding way. This approach is compared to a homogeneous and static spectral formulation of error correlations. Diagnostic studies are conducted in order to illustrate the representation of heterogeneous and flow-dependent correlation features, corresponding for instance to smaller horizontal length-scales in the vicinity of midlatitude lows and to larger vertical correlations in vertically unstable regions. The positive impact of the flow-dependent wavelet formulation on the forecast quality is then shown during two contrasting three-week periods. The impact of an increased ensemble size when using this approach is also illustrated, in terms of length-scale dynamics and forecast quality.