Ensemble-smoothing can be used as a cost-efficient addition to ensemble square root Kalman filters to improve a reanalysis in data assimilation. To correct a past state estimate, the smoothing method utilizes the cross-covariances between the present filtered state ensemble and a past ensemble at the time instance where the smoothing should be performed. Using the cross-covariances relies on the assumption that dynamics of the system under consideration are linear. Thus, for nonlinear models, it can be expected that the smoothing is suboptimal. We discuss the influence of nonlinearity on the performance of ensemble-smoothing based on numerical experiments with the Lorenz-96 model and a realistic ocean circulation model. The experiments show that there exists an optimal smoothing time interval, which depends on the strength of the nonlinearity. Under some circumstances, the smoothing can also deteriorate the quality of state estimates compared to assimilating only current observations by filtering.
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