https://orcid.org/0000-0002-3249-2818
Abstract
In geophysics, the direct application of covariance matrix dynamics described by the Kalman filter (KF) is limited by the high dimension of such problems. The parametric Kalman filter (PKF) is a recent alternative to the ensemble Kalman filter, where the covariance matrices are approximated by a covariance model featured by a set of parameters. The covariance dynamics is then described by the time evolution of these parameters during the analysis and forecast cycles. This study focuses on covariance model parametrized by the variance and the local anisotropic tensor fields (VLATcov). The analysis step of the PKF for VLATcov in a 2D/3D domain is first introduced. Then, using 2D univariate numerical investigations, the PKF is shown to be able to provide a low numerical cost approximation of the Kalman filter analysis step, even for anisotropic error correlation functions. Moreover the PKF has been shown able to reproduce the KF over several assimilation cycles in a transport dynamics. An extension toward the multivariate situation is theoretically studied in a 1D domain.
Acknowledgments
We would like thank Isabelle Mirouze, Marc Bocquet and Richard Ménard, for interesting discussions and comments on the manuscript. We would like to thank the two anonymous referees for their fruitful comments which have contribute to improve the manuscript. This work was supported by the French national program LEFE/INSU (Étude du filtre de KAlman PAramétrique, KAPA).
Disclosure statement
No potential conflict of interest was reported by the author.