Theoretical insight into diagnosing observation error correlations using observation‐minus‐background and observation‐minus‐analysis statistics. (26th October 2015)

• Record Type: Journal Article
• Authors: Waller, J. A.; Dance, S. L.; Nichols, N. K.
• Is Part Of: Quarterly journal of the Royal Meteorological Society. Volume 142:Number 694(2016)
• Page Start: 418
• Page End: 431
• Publication Date: 2015-10-26
• Subjects: data assimilation diagnostic -- correlated observation errors -- innovation statistics; Meteorology -- Periodicals; 551.5
• DOI: 10.1002/qj.2661
• Languages: English
• ISSNs: 0035-9009

Abstract

Abstract : 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.