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On diagnosing observation error statistics with local ensemble data assimilation

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Waller, J. A., Dance, S. L. and Nichols, N. K. (2017) On diagnosing observation error statistics with local ensemble data assimilation. Quarterly Journal of the Royal Meteorological Society. ISSN 1477-870X (In Press)

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To link to this item DOI: 10.1002/qj.3117

Abstract/Summary

Recent research has shown that the use of correlated observation errors in data assimilation can lead to improvements in analysis accuracy and forecast skill. As a result there is increased interest in characterizing, understanding and making better use of correlated observation errors. A simple diagnostic for estimating observation error statistics makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. This diagnostic is derived assuming that the analysis is calculated using a best linear unbiased estimator. In this work, we consider if the diagnostic is still applicable when the analysis is calculated using ensemble assimilation schemes with domain localization. We show that the diagnostic equations no longer hold: the statistical averages of observation-minus-background and observation-minus-analysis residuals no longer result in an estimate of the observation error covariance matrix. Nevertheless, we are able to show that, under certain circumstances, some elements of the observation error covariance matrix can be recovered. Furthermore, we provide a method to determine which elements of the observation error covariance matrix can be correctly estimated. In particular, the correct estimation of correlations is dependent both on the localization radius and the observation operator. We provide numerical examples that illustrate these mathematical results.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:71224
Publisher:Royal Meteorological Society

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