Ensemble‐derived stationary and flow‐dependent background‐error covariances: Evaluation in a quasi‐operational NWP setting

In this study several approaches for obtaining more accurate background‐error covariances for atmospheric data assimilation are evaluated. Experiments are conducted by replacing the covariances in the operational three‐dimensional variational analysis system at the Canadian Meteorological Centre. In the current system, these covariances are computed using the so‐called NMC method that is known to suffer from several deficiencies. The approaches evaluated in this study attempt to more realistically sample the probability distribution of background error by simulating (using a Monte Carlo approach) the error generated at each stage of the forecast‐analysis process. The ensemble Kalman filter and a simpler approach applied to an existing forecast‐analysis system are both used to generate these error samples. In addition, error samples are generated directly from the covariances of the operational system to allow the effects of sampling error to be quantified. Several strategies for estimating the full covariance matrix from a relatively small number of error samples are then employed. Approaches include the use of a spatially localized ensemble representation of the correlations that allows the usual assumptions of homogeneity and isotropy to be relaxed. In addition, the use of a weighted average between such a covariance matrix and a covariance matrix with homogeneous and isotropic correlations is evaluated. Several diagnostic results from the estimated background‐error covariances are presented in addition to verification statistics computed from two‐week forecast‐analysis experiments. Modest forecast improvements are obtained by using the new background‐error covariance estimates, mostly in the southern hemisphere. However, additional results suggest that further improvements may be gained by increasing the number of error samples and a preliminary quantitative estimate of the expected gain is computed. © Crown copyright, 2005. Royal Meteorological Society