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Treating Sample Covariances for Use in Strongly Coupled Atmosphere‐Ocean Data Assimilation
Author(s) -
Smith Polly J.,
Lawless Amos S.,
Nichols Nancy K.
Publication year - 2018
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/2017gl075534
Subject(s) - data assimilation , covariance matrix , covariance , sampling (signal processing) , computer science , noise (video) , eigenvalues and eigenvectors , algorithm , rank (graph theory) , statistics , mathematics , meteorology , artificial intelligence , physics , filter (signal processing) , quantum mechanics , combinatorics , image (mathematics) , computer vision
Strongly coupled data assimilation requires cross‐domain forecast error covariances; information from ensembles can be used, but limited sampling means that ensemble derived error covariances are routinely rank deficient and/or ill‐conditioned and marred by noise. Thus, they require modification before they can be incorporated into a standard assimilation framework. Here we compare methods for improving the rank and conditioning of multivariate sample error covariance matrices for coupled atmosphere‐ocean data assimilation. The first method, reconditioning, alters the matrix eigenvalues directly; this preserves the correlation structures but does not remove sampling noise. We show that it is better to recondition the correlation matrix rather than the covariance matrix as this prevents small but dynamically important modes from being lost. The second method, model state‐space localization via the Schur product, effectively removes sample noise but can dampen small cross‐correlation signals. A combination that exploits the merits of each is found to offer an effective alternative.