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 background error correlations are also assumed to be homogeneous and isotropic.

For this study, random samples of background error are generated by simulating (using a Monte Carlo approach) the error generated at each stage of the forecast-analysis process. This includes two different approaches for simulating model error: (1) additive random error drawn from a specified Gaussian distribution and (2) random perturbations to the physical parameterizations and boundary conditions of the forecast model. For both approaches a simple adaptive tuning procedure is employed to ensure the simulated background error variances are consistent with observation error variances and innovation variances. One of several strategies for estimating the full covariance matrix from a relatively small number of error samples is then employed. Approaches include the use of a wavelet representation and a spatially localized ensemble representation of the correlations. The first allows the usual assumption of homogeneity to be relaxed and the second allows both homogeneity and isotropy to be relaxed.

The error covariances are updated on a six-hourly basis using error samples pooled over a time period sufficiently long to obtain a robust estimate. The period over which error samples are pooled depends on the number of perturbed forecast-analysis experiments. For example, only a few perturbed experiments are required to compute seasonally varying covariances, whereas running O(100) experiments would provide fully flow-dependent covariances. Several diagnostic results from the estimated background error covariances are presented. In addition, verification statistics are compared from forecast-analysis experiments that use the new background error covariances and those from the currently operational system.