314 – Environmental Model Estimation and Inference
Covariance Modeling by Means of Eigenfunctions of Laplace Operator
Marie Turcicova
Charles University in Prague
Jan Mandel
University of Colorado Denver
Krystof Eben
Institute of Computer Science AS CR
Large dimension of both state vector and data is a well-known challenge in environmental modeling (e.g., numerical weather forecast) and, in particular, in data assimilation. The Ensemble Kalman Filter addresses this problem by estimating the current system state and its uncertainty via their sample counterparts. However, sample covariance matrix based on a small ensemble is not a sufficiently good estimate of the true covariance. In this paper, we deal with techniques relying on transformation of the state to the spectral space and assuming a particular covariance structure based on the Laplace operator. Parameters, which this special structure depends on, are estimated by a least squares method and a maximum likelihood method. The behavior of both estimators is illustrated by a simulation. Both methods have a smaller error in Frobenius norm than the sample covariance, moreover, the latter method performs better than the former one, which corresponds to its stronger assumptions.