Abstract

Commentary: On the Efficiency of Covariance Localisation of the Ensemble Kalman Filter Using Augmented Ensembles

Highlights

  • In discussing Equation (39) (Equation (25) of Bocquet [1]), Farchi and Bouquet [2] state that “This perturbation update has been rediscovered by Bishop et al [3] and included in their gain ETKF (GETKF) algorithm

  • The update formula used in the GETKF is prone to numerical cancellation errors as opposed to Equation (39)”

  • We note: (i) The predecessor of the GETKF eigenvalue form of the modified gain matrix equation appeared in Posselt and Bishop [4, 5]—before Bocquet [1]

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Summary

Introduction

In discussing Equation (39) (Equation (25) of Bocquet [1]), Farchi and Bouquet [2] state that “This perturbation update has been rediscovered by Bishop et al [3] and included in their gain ETKF (GETKF) algorithm. We note: (i) The predecessor of the GETKF eigenvalue form of the modified gain matrix equation appeared in Posselt and Bishop [4, 5]—before Bocquet [1]. (iii) The eigenvalue form enables Wang et al.’s [6] corrections for ensemble rank deficiency. Since the columns of C associated with zero eigenvalues cannot contribute to products of the matrix H Zf with other vectors, it is more efficient to work with the concise svd given by H Zf

Results
Conclusion

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