Evaluation of an ensemble-based incremental variational data assimilation

In this work, we aim at studying ensemble based optimal control strategies for data assimilation. Such formulation nicely combines the ingredients of ensemble Kalman lters and variational data assimilation (4DVar). In the same way as variational assimilation schemes, it is formulated as the minimization of an objective function, but similarly to ensemble lter, it introduces in its objective function an empirical ensemble-based background-error covariance and works in an o-line smoothing mode rather than sequentially like sequential lters. These techniques have the great advantage to avoid the introduction of tangent linear and adjoint models, which are necessary for standard incremental variational techniques. They also allow handling a time varying background covariance matrix representing the error evolution between the estimated solution and a background solution. As this background error covariance matrix { of reduced rank in practice { plays a key role in the variational process, our study particularly focuses on the generation of the analysis ensemble state with localization techniques. Besides, to clarify well the dierences between the dierent methods and to highlight the potential pitfall and advantages of the dierent methods, we present key theoretical properties associated to dierent choices involved in their setup. We compared experimentally the performances of several variations of an ensemble technique of interest with an incremental 4DVar method. The comparisons have been leaded on the basis of a Shallow Water model and have been carried out both with synthetic data and through a close experimental setup. The cases where the system’s components are either fully observed or only partially have been in particular addressed.