Hybrid SEIK algorithm for oceanographic data assimilation

The singular evolutive interpolated Kalman filter (SEIK) as a variant of the ensemble Kalman filter has been implemented and tested for application in oceanography assimilating altimetric data within twin experiments framework. Previous studies suggest that this filter is reasonably well-behaved in the presence of instability. In the SEIK assimilation algorithm, the analysis error covariance matrix is approximated by a covariance matrix whose rank corresponds to the number of ensemble members used for representing the forecast error covariance. In order to achieve a computationally efficient algorithm, the rank of this covariance matrix is often chosen to be small, leading to problems with the convergence of the filter.