The SEEK filter method for data assimilation in oceanography: a synthesis

This paper reviews the developments of the singular evolutive extended Kalman (SEEK) filter method used for data assimilation in oceanography, since the original paper by Pham et al. (J Mar Syst 16:3-4, 323-340 1998a). First, a short review is presented of the context of data assimilation in oceanography and of the variety of numerical ocean codes and configurations in which the SEEK filter has been implemented using different data sets for assimilation. Then, the paper provides an exposition of the different versions of the SEEK filter developed during the past 10 years and discusses their relative merits for scientific or operational implementations. A classification of the algorithmic variants is proposed, and several possible improvements of the generic methodology are mentioned in the perspective of new assimilation challenges. [PUBLICATION ABSTRACT]