Using singular value decomposition in conjunction with data assimilation procedures

Authors:
Gabriel Dimitriu
Affiliations:
University of Medicine and Pharmacy, Faculty of Pharmacy, Department of Mathematics and Informatics, Iasi, Romania
Venue:
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Year:
2006

Citing 2
Cited 2

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Abstract

In this study we apply the singular value decomposition (SVD) technique of the so-called 'observability' matrix to analyse the information content of observations in 4D-Var assimilation procedures. Using a simple one-dimensional transport equation, the relationship between the optimal state estimate and the right singular vectors of the observability matrix is examined. It is shown the importance of the value of the variance ratio, between the variances of the background and the observational errors, in maximizing the information that can be extracted from the observations by using Tikhonov regularization theory. Numerical results are presented.