Marie Turcicova, Institute of Computer Science of the CAS

Modelling diagonal covariance matrix in spectral space

Jan Mandel, Krystof Eben


A reliable covariance model and estimation procedure is a key element in ensemble data assimilation methods. It is well known that the sample covariance matrix computed from a small ensemble of model states suffers from low rank and spurious correlations may occur. In this contribution, we present parametric estimators based on transformation of the ensemble into the spectral space and taking diagonal approximation. Diagonal entries of the resulting matrix are noisy estimates of the true spectral covariance matrix. We propose to model these terms by parametric methods in order to make the diagonal smoother. Performance of the estimators, measured by the Frobenius norm, is illustrated by a simulation.

Acknowledgement: partially supported by NSF grant DMS-1216481 and Czech Science Foundation grant GA13-34856S.