Data Assimilation Meetings at Reading

Date Meeting type Speakers
26 September 2012

Room change: GU10

Informal DARC meeting Sarah Dance (UoR)
On the stability of the ensemble square root filter with finite ensemble size
The ensemble Kalman filter is a data assimilation algorithm that uses a finite size ensemble of model states in order to calculate analyses. Much of the published analysis of the filter to date focusses on statistical properties. In this talk we take a deterministic view and consider filter stability for finite ensemble sizes. We derive conditions for filter stability and show that rank deficient ensemble approximations of the forecast error covariance can cause filter divergence. Methods suitable for regularizing the forecast error covariance in the context of the square root filter are discussed, including the commonly used techniques of covariance localization and inflation, and a novel approach of matrix augmentation based on the ideas of Tikhonov regularization, that can be interpreted as a model error term. It is shown that model error matrix augmentation is more numerically robust than covariance inflation. Our results are illustrated using a simple linear model.

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