Evaluation of new estimates of background- and observation-error covariances for variational assimilation

In this study new estimates for the observation- and background-error covariances in a three-dimensional variational analysis system at the Canadian Meteorological Centre are evaluated. In the current system, the observation errors are assumed uncorrelated with the variances estimated following a more or less ad hoc approach for each instrument type. The background-error covariances are computed using the so-called NMC method. The new estimate for the observation error variances is obtained using a practical approach developed at Meteo-France that computes the maximum likelihood estimate of the variances. Two new estimates for the stationary background-error covariances are evaluated. The first simply involves tuning the variances in the operational background-error covariances. For the second, the NMC method is replaced by a Monte Carlo approach applied to the existing analysis system. Both the variances and spatial covariances of the innovations are computed and compared with the corresponding quantities derived from each set of error covariances used by the analysis system. This comparison shows a significantly improved consistency for radiosonde data when using the new error covariances, especially with the Monte Carlo approach. In contrast, the interchannel innovation covariances for ATOVS AMSU-A observations are more consistent when using background-error covariances obtained with the NMC method. In addition, modest forecast improvements are obtained by using the new observation- and background-error covariance estimates, most notably for the tropics.