On the efficiency of covariance localisation of the ensemble Kalman filter using augmented ensembles.

The ensemble Kalman filter (EnKF) has been successfully applied to a wide range ofgeophysical systems. However, when the ensemble size is small, ensemble estimates areunreliable, which is why localisation has been introduced. In the EnKF, two types oflocalisation methods have emerged: domain localisation and covariance localisation. Domainlocalisation is simple to implement and yields parallelisable algorithms. On the other hand,EnKF algorithms using covariance localisation rely on a single global analysis with alocalised background covariance. Their implementation is in general more complex,especially in a deterministic context. At the same time, the ability to assimilatenon-local observations becomes increasingly important with the prominence ofsatellite observations. With domain localisation, non-local observations cannotbe assimilated without ad hoc approximations, which limits the accuracy of theanalysis. In this presentation, we discuss the implementation of covariance localisationin the deterministic EnKF using augmented ensemble during the analysis step,that is when the ensemble size during the analysis step is larger than during theforecast step. The focus is on two crucial points: the accurate representation ofa localised background covariance and the perturbation update. We identify andpresent two methods. The first is based on a factorisation property and alreadyknown in the literature under the term modulation. The second relies on randomisedsingular value decomposition and has not been applied in this context. The qualitativeproperties of both methods are illustrated using a simple one-dimensional covariancemodel. For both method, we then derive an ensemble square root Kalman filter withcovariance localisation (LEnSRF). We compare the performance of the resultingalgorithms using twin simulations of the Lorenz 1996 (L96) model. Finally, weintroduce a realistic extension of the LEnSRF that uses domain localisation in thehorizontal and covariance localisation in the vertical. Using twin simulations of amultilayer extension of the L96 model, we show that this approach is adequate toassimilate satellite radiances, for which domain localisation alone is insufficient. [ABSTRACT FROM AUTHOR]