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Performance of Ensemble Kalman Filters in Large Dimensions
Author(s) -
Majda Andrew J.,
Tong Xin T.
Publication year - 2018
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21722
Subject(s) - ensemble kalman filter , data assimilation , kalman filter , covariance , dimension (graph theory) , fidelity , mathematics , algorithm , ensemble learning , statistical physics , computer science , extended kalman filter , artificial intelligence , statistics , meteorology , geography , physics , telecommunications , pure mathematics
Contemporary data assimilation often involves more than a million prediction variables. Ensemble Kalman filters (EnKF) have been developed by geoscientists. They are successful indispensable tools in science and engineering, because they allow for computationally cheap low‐ensemble‐state approximation for extremely large‐dimensional turbulent dynamical systems. The practical finite ensemble filters like EnKF necessarily involve modifications such as covariance inflation and localization, and it is a genuine mystery why they perform so well with small ensemble sizes in large dimensions. This paper provides the first rigorous stochastic analysis of the accuracy and covariance fidelity of EnKF in the practical regime where the ensemble size is much smaller than the large ambient dimension for EnKFs with random coefficients. A challenging issue overcome here is that EnKF in huge dimensions introduces unavoidable bias and model errors that need to be controlled and estimated. © 2017 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematics and Wiley Periodicals, Inc.