Sampling error is a fundamental limitation of assimilation schemes, such as the EnKF, that employ the sample covariance from an ensemble of forecasts. Despite the fact that the EnKF is typically applied in situations where the ensemble size is small compared to the system dimension, most of what is known about the effect of sampling error comes from low-dimensional examples or asymptotic results valid when the ensemble size is large.

I will show how progress can be made for high-dimensional systems and small ensembles by leveraging (i) the diagonal form of the Kalman-filter update in the optimal coordinates of Snyder and Hakim (2022) and (ii) basic results from the theory of random matrices.

Lieu
École normale supérieure – PSL
24 rue Lhomond 75005 PARIS
Aile Erasme • Salle SERRE – E509
Accès par la cage d’escalier D