Treating sample covariances for use in strongly coupled atmosphere-ocean data assimilation

Smith, P. J. ORCID: https://orcid.org/0000-0003-4570-4127, Lawless, A. S. ORCID: https://orcid.org/0000-0002-3016-6568 and Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220 (2018) Treating sample covariances for use in strongly coupled atmosphere-ocean data assimilation. Geophysical Research Letters, 45 (1). pp. 445-454. ISSN 0094-8276 doi: 10.1002/2017gl075534

Abstract/Summary

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 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 localisation 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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/74247
Identification Number/DOI	10.1002/2017gl075534
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO) Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Uncontrolled Keywords	Coupled data assimilation, Forecast error covariances, Localisation, Re-conditioning
Publisher	American Geophysical Union
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