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Ensemble propagation and continuous matrix factorization algorithms
Author(s) -
Bergemann Kay,
Gottwald Georg,
Reich Sebastian
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.457
Subject(s) - orthogonalization , ensemble kalman filter , singular value decomposition , kalman filter , algorithm , factorization , mathematics , matrix decomposition , ensemble forecasting , matrix (chemical analysis) , extended kalman filter , computer science , artificial intelligence , physics , statistics , eigenvalues and eigenvectors , materials science , quantum mechanics , composite material
We consider the problem of propagating an ensemble of solutions and its characterization in terms of its mean and covariance matrix. We propose differential equations that lead to a continuous matrix factorization of the ensemble into a generalized singular value decomposition (SVD). The continuous factorization is applied to ensemble propagation under periodic rescaling (ensemble breeding) and under periodic Kalman analysis steps (ensemble Kalman filter). We also use the continuous matrix factorization to perform a re‐orthogonalization of the ensemble after each time‐step and apply the resulting modified ensemble propagation algorithm to the ensemble Kalman filter. Results from the Lorenz‐96 model indicate that the re‐orthogonalization of the ensembles leads to improved filter performance. Copyright © 2009 Royal Meteorological Society