Using singular value decomposition in conjunction with data assimilation procedures

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 regularizaron theory. Numerical results are presented. © Springer-Verlag Berlin Heidelberg 2007.