Time-expanded sampling for ensemble-based filter with covariance localization: assimilation experiments with a shallow-water equation model

A time-expanded sampling approach is proposed for ensemble-based filters with covariance localization in data assimilation. This approach samples a series of perturbed state vectors from each prediction run within a subsynoptic-scale time window in the vicinity of the analysis time. As all the sampled state vectors are used to construct the ensemble and compute the localized covariance, the number of required prediction runs can be much smaller than the ensemble size, and this can reduce the computational cost significantly. The conventional approach, however, requires the number of prediction runs to be as large as the ensemble size, so the ensemble size can be severely limited by the computational cost for an intended operational application. By properly setting the sampling time interval, the proposed approach can improve the ensemble spread and ensemble representation of the forecast probability distribution and thus improve the filter performance even thought the number of prediction runs is greatly reduced. The potential merits of the proposed time-expanded sampling are demonstrated by assimilation experiments with a shallow-water equation model.