Using low-rank ensemble kalman filters for data assimilation with high dimensional imperfect models

Low-rank square-root Kalman filters were developed for the efficient estimation of the state of high dimensional dynamical systems. These filters avoid the huge computational burden of the Kalman filter by approximating the filter's error covariance matrices by low-rank matrices. Accounting for model errors with these filters would cancel the benefits of the low-rank approximation as the insertion of the model error covariance matrix in the filter's equations increases the rank of the filter's covariance matrices by the rank of the model error after every forecast step, making the filter'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 filter with high dimensional imperfect models. Numerical experiments were carried out to assess the relevance of these approaches with a realistic general circulation ocean model of the tropical Pacific Ocean.