Journal article
Efficient ensemble covariance localization in variational data assimilation
CH Bishop, D Hodyss, P Steinle, H Sims, AM Clayton, AC Lorenc, DM Barker, M Buehner
Monthly Weather Review | AMER METEOROLOGICAL SOC | Published : 2011
Abstract
Previous descriptions of how localized ensemble covariances can be incorporated into variational (VAR) data assimilation (DA) schemes provide few clues as to how this might be done in an efficient way. This article serves to remedy this hiatus in the literature by deriving a computationally efficient algorithm for using nonadaptively localized four-dimensional (4D) or three-dimensional (3D) ensemble covariances in variational DA. The algorithm provides computational advantages whenever (i) the localization function is a separable product of a function of the horizontal coordinate and a function of the vertical coordinate, (ii) and/or the localization length scale is much larger than the mode..
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Funding Acknowledgements
The authors wish to acknowledge the contributions of Ricardo Todling whose comments, as a reviewer, significantly improved the paper. Among other things, Ricardo improved the conciseness of the proof of the square root theorem. The authors also acknowledge the helpful criticism of the Editor, Herschel Mitchell, and the insightful suggestions of an anonymous reviewer. CHB expresses his gratitude to the "Centre for Australia Weather and Climate RESEARCH-a collaboration between the Bureau of Meteorology and CSIRO" for their support of a visit to the Centre during which this paper was conceived. CHB and DH gratefully acknowledge financial support from ONR Project Element 0602435N, Project BE-435-003, and ONR Grant N0001407WX30012.