Accelerating and parallelizing minimizations in ensemble and deterministic variational assimilations

The specification of a correct background-error covariance matrix is a key issue in data assimilation schemes. The Ensemble Kalman Filter (EnKF) aims at providing simulations of analysis and background errors and then gives a way to determine this background-error covariance matrix. The EnKF can be transposed to variational ensemble assimilation, where a set of perturbed variational analyses are performed. In this case, however, there is an evident important additional cost associated with the use of multiple minimizations. The aim of the paper is to investigate different techniques to reduce the cost of the multiple minimizations that have to be performed. In particular, the use is investigated of a preconditioning technique based on Ritz eigenpairs resulting from a first minimization performed by a combined Lanczos/conjugate-gradient algorithm. The possibility is also studied of improving the starting point of a new perturbed solution, with Lanczos vectors issued from a single prior unperturbed or perturbed minimization. This appears to provide a first significant reduction in the cost of the new minimization. Finally, a new approach is proposed to generalize the previous idea to the use of multiple sets of Lanczos vectors issued from an ensemble of perturbed assimilations. The application of this procedure to a simplified analysis problem shows encouraging results, as it appears to be a possible way for reducing the global cost of an ensemble variational assimilation. Moreover, this seems to provide an efficient strategy for parallelizing such an ensemble variational assimilation but also the deterministic variational assimilation itself. Copyright (c) 2012 Royal Meteorological Society