Covariance modeling by means of eigenfunctions of Laplace operator

Abstract

A reliable covariance model and estimation procedure is a key element in data assimilation methods. However, sample covariance matrix based on a small ensemble of model states suffers from several drawbacks like low rank and presence of spurious correlations.

In this paper, we deal with estimation and modelling techniques relying on transformation of the state to the spectral space and assuming a particular covariance structure based on the Laplace operator.

Keywords

• Data assimilation
• discrete Fourier transform
• spectral
• diagonal covariance
• maximum likelihood