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Zhiyong Meng
Fuqing Zhang


Ensemble-based data assimilation is a state estimation technique that uses short-term ensemble forecasts to estimate flow-dependent background error covariance and is best known by varying forms of ensemble Kalman filters (EnKFs). The EnKF has recently emerged as one of the primary alternatives to the variational data assimilation methods widely used in both global and limited-area numerical weather prediction models. In addition to comparing the EnKF with variational methods, this article reviews recent advances and challenges in the development and applications of the EnKF, including its hybrid with variational methods, in limited-area models that resolve weather systems from convective to meso- and regional scales.

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Loïk Berre
Gérald Desroziers


The use of local spatial averaging to estimate and validate background error covariances has received increasing attention recently, in particular in the context of variational data assimilation for global numerical weather prediction. First, theoretical and experimental results are presented to examine spatial structures of sampling noise and signal in ensemble-based variance fields in this context. They indicate that sampling noise tends to be relatively small scale, compared to the signal of interest. This difference in spatial structure motivates the use of spatial averaging techniques.

Based on the usual linear estimation theory, it is shown how this information can be taken into account in order to calculate and apply an objective spatial filter. This kind of approach can also be used to compare and validate ensemble-based variances with innovation-based variances. The use of spatial averaging is even more important for innovation-based variances because local innovations correspond to single error realizations.

Similar ideas can be considered for the estimation of correlation functions. The spatial structures of sampling noise and signal in correlation length scale fields suggest that space-averaging techniques could also be applied to correlation functions. The use of wavelets for this purpose is presented in particular. Connections with related approaches in different contexts such as ensemble Kalman filters and probabilistic forecasting are also discussed.

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