A variational assimilation ensemble and the spatial filtering of its error covariances: increase of sample size by local spatial averaging
Berre, Loïk ; Pannekoucke, Olivier ; Desroziers, Gérald ; Stefanescu, Simona Ecaterina ; Chapnik, Bernard ; Raynaud, Laure
An ensemble of perturbed assimilations is a powerful technique to simulate the space and time dynamics of errors in an operational assimilation system. Using an ensemble of variational assimilations is relatively straightforward, as its basic elements can be directly derived from the operational variational scheme. Moreover, with respect to the analysis update of the perturbations, the potential benefit is both to adequately simulate the effect of the operational variational gain matrix, and to take advantage of its realism (e.g. non linear mass/wind balances), of its appropriate filtering, and of its full rank. This includes available spectral and wavelet covariance tools also, which are believed to ease both an optimal estimation of filtered (possibly hybrid) ensemble covariances, and their use in the construction of the analysis members (including a careful filtering of sampling noise). It is also noticed that with e.g. an ensemble of 3D-Fgat, the analysis part of the assimilation ensemble cost is relatively small, compared to the forecast part. In order to reduce the amplitude of sampling noise, local spatial averaging can be applied, as it allows the ensemble size to be multiplied by a 2D spatial sample size. A methodology, based on the comparison of statistics of two independent ensembles which have the same size, is also presented to estimate signal and sampling noise statistics. It is shown that the spatial structure of sampling noise is relatively small scale. This justifies the application of spatial filtering. Following the usual linear estimation theory, it is shown that signal-to-noise ratios can be used also as objective and optimal filtering coefficients. The results indicate that a small ensemble (with typically 3 to 10 members) can provide relevant and robust information about flow-dependent error standard deviations, with e.g. larger values near troughs than near ridges. Comparison with innovation-based estimates and impact experiments tend to support these results. The (expected and effective) localized and positive nature of the flow-dependent modifications and impacts is also shown. The use of wavelets for correlation modelling can also be seen as a spatial filtering tool applied to raw ensemble correlations, in order to improve their accuracy. These attractive filtering properties are illustrated too.
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