Abstract

The ensemble Kalman filter (EnKF) can be interpreted in the more general context of linear regression theory. The recursive filter equations are equivalent to the normal equations for a weighted least-squares estimate that minimizes a quadratic functional. Solving the normal equations is numerica... Show moreThe ensemble Kalman filter (EnKF) can be interpreted in the more general context of linear regression theory. The recursive filter equations are equivalent to the normal equations for a weighted least-squares estimate that minimizes a quadratic functional. Solving the normal equations is numerically unreliable and subject to large errors when the problem is ill-conditioned. A numerically reliable and efficient algorithm is presented, based on the minimization of an alternative functional. The method relies on orthogonal rotations, is highly parallel and does not 'square' matrices in order to compute the analysis update. Computation of eigenvalue and singular-value decompositions is not required. The algorithm is formulated to process observations serially or in batches and therefore easily handles spatially correlated observation errors. Numerical results are presented for existing algorithms with a hierarchy of models characterized by chaotic dynamics. Under a range of conditions, which may include model error and sampling error, the new algorithm achieves the same or lower mean square errors as the serial Potter and ensemble adjustment Kalman filter (EAKF) algorithms. Show less