Using Low-Rank Ensemble Kalman Filters for Data Assimilation with High Dimensional Imperfect Models 1

Low-rank square-root Kalman lters were developed for the ecien t estimation of the state of high dimensional dynamical systems. These lters avoid the huge computa- tional burden of the Kalman lter by approximating the lter's error covariance matrices by low-rank matrices. Accounting for model errors with these lters would cancel the ben- ets of the low-rank approximation as the insertion of the model error covariance matrix in the lter's equations increases the rank of the lter's covariance matrices by the rank of the model error after every forecast step, making the lter's computation cost again prohibitive. This papers discusses this problem and presents several approaches to allow the numerical implementation of an advanced low-rank ensemble Kalman lter with high dimensional imperfect models. Numerical experiments were carried out to assess the rele- vance of these approaches with a realistic general circulation ocean model of the tropical Pacic Ocean. c 2007 European Society of Computational Methods in Sciences and Engineering