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A robust formulation of the ensemble Kalman filter
Author(s) -
Thomas S. J.,
Hacker J. P.,
Anderson J. L.
Publication year - 2009
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.372
Subject(s) - kalman filter , ensemble kalman filter , mathematics , context (archaeology) , algorithm , filter (signal processing) , eigenvalues and eigenvectors , quadratic equation , computation , computer science , mathematical optimization , extended kalman filter , statistics , paleontology , physics , geometry , quantum mechanics , computer vision , biology
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 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. Published in 2009 by John Wiley and Sons, Ltd.