Title: Theoretical insight into diagnosing observation error spatial correlations using background and analysis innovation statistics

Author: Sarah L Dance (University of Reading)
J. A. Waller (University of Reading)
N. K. Nichols (University of Reading)

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 background and analysis innovations. 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 for the multivariate case that demonstrates that it is still possible to obtain useful results when the background and observation error length-scales are similar. 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. In general, 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 (see Waller et al abstract).

GMAO Head: Steven Pawson Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: Feb 9 2015