In an ensemble Kalman filter, at each assimilation step, there is an intrinsic need of evaluating the covariance matrix of the propagated ensemble. In the "standard" ensemble Kalman, this is done with the empirical covariance matrix of the ensemble. This has strong drawbacks. The size of the ensemble being often smaller than the size of the system, there is an intrinsic lack of information. Usually, this is solved by inflation (increase of the overall value of the covariance matrix by a factor) and localisation (reduction of the off-diagonal elements of the matrix). The tuning of localisation and inflation is done empirically, and has a computational cost that can be huge.
The aim of this project is to develop and algorithm where inflation and localisation are optimally tuned by the algorithm itself. Pr. Marc Bocquet, in NPG (2015)
expanded the ensemble Kalman filter using bayesien hierarchical methods. This leads to a natural emergence of inflation and its optimal value in the algorithm. We are now aiming with Dr. Alexis Hannart to use a shrinkage estimator for the covariance matrix (JMVA (2014)
) that would replace localisation.