he Ensemble Kalman Filter (EnKF), recently reformulated by itsinventor G. Evensen, is one of the most used filter algorithms fordata assimilation in meteorology and oceanography. The EnKF algorithmpromises to provide good data assimilation results while beingrelatively simple to implement and to apply. On the other hand, thealgorithm exhibits problems related to its computational cost forlarge-scale problems and approximations made by the EnKF. Thecomparison with the SEIK filter, introduced by D.T. Pham, shows thatthis alternative formulation of an ensemble based Kalman filterexhibits better properties with regard to computational costs andrequired approximations than the typical formulation of the EnKF. Wediscuss the differences between the two filter algorithms andadvantages of each filter. The practical consequences of the differentalgorithmic formulations are shown using results from an applicationof both filter algorithms to the finite element model FEOM in aconfiguration for the North Atlantic.