A diagnostic study of time variations of regionally averaged background error covariances

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Abstract
In variational data assimilation systems, background error covariances are often estimated from a temporal and spatial average. For a limited area model such as the Aire Limited Adaptation Dynamique Developpment International (ALADIN)/France, the spatial average is calculated over the regional computation domain, which covers western Europe. The purpose of this study is to revise the temporal stationarity assumption by diagnosing time variations of such regionally averaged covariances. This is done through examination of covariance changes as a function of season (winter versus summer), day (in connection with the synoptic situation), and hour (related to the diurnal cycle), with the ALADIN/France regional ensemble Three‐Dimensional Variational analysis (3D‐Var) system. In summer, compared to winter, average error variances are larger, and spatial correlation functions are sharper horizontally but broader vertically. Daily changes in covariances are particularly strong during the winter period, with larger variances and smaller‐scale error structures when an unstable low‐pressure system is present in the regional domain. Diurnal variations are also significant in the boundary layer in particular, and, as expected, they tend to be more pronounced in summer. Moreover, the comparison between estimates provided by two independent ensembles indicates that these covariance time variations are estimated in a robust way from a six‐member ensemble. All these results support the idea of representing these time variations by using a real‐time ensemble assimilation system.

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