Theoretical insight into diagnosing observation error correlations using observation-minus-background and observation-minus-analysis statistics

Waller, J. A., Dance, S. L. ORCID: https://orcid.org/0000-0003-1690-3338 and Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220 (2016) Theoretical insight into diagnosing observation error correlations using observation-minus-background and observation-minus-analysis statistics. Quarterly Journal of the Royal Meteorological Society, 142 (694). pp. 418-431. ISSN 1477-870X doi: 10.1002/qj.2661

Abstract/Summary

To improve the quantity and impact of observations used in data assimilation it is necessary to take into account the full, potentially correlated, observation error statistics. A number of methods for estimating correlated observation errors exist, but a popular method is a diagnostic that makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. The accuracy of the results it yields is unknown as the diagnostic is sensitive to the difference between the exact background and exact observation error covariances and those that are chosen for use within the assimilation. It has often been stated in the literature that the results using this diagnostic are only valid when the background and observation error correlation length scales are well separated. Here we develop new theory relating to the diagnostic. For observations on a 1D periodic domain we are able to the show the effect of changes in the assumed error statistics used in the assimilation on the estimated observation error covariance matrix. We also provide bounds for the estimated observation error variance and eigenvalues of the estimated observation error correlation matrix. We demonstrate that it is still possible to obtain useful results from the diagnostic when the background and observation error length scales are similar. In general, our results suggest that when correlated observation errors are treated as uncorrelated in the assimilation, the diagnostic will underestimate the correlation length scale. We support our theoretical results with simple illustrative examples. These results have potential use for interpreting the derived covariances estimated using an operational system.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/43719
Identification Number/DOI	10.1002/qj.2661
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	Royal Meteorological Society
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