Impact of flow-dependent analysis-error covariance norms on extratropical singular vectors

Flow-dependent analysis-error covariances are estimated from the 128 member analysis ensembles of a preoperational implementation of the ensemble Kalman filter. Singular vectors are then computed with the initial-time norm defined using the inverse of these error covariances and the final-time norm defined by the total energy over North America. An optimization time interval of either 24 or 48 hours is used and the horizontal resolution of the singular vectors is 3 degrees. Provided that the analysis-error covariance estimates are accurate, these singular vectors should optimally explain the forecast error at the final time. To reduce the sampling error due to the small ensemble size, the analysis-error covariances are spatially localized. The impact of using the analysis-error covariance norm, with or without spatial localization, on the 20 leading singular vectors is measured relative to using the total-energy norm. In addition, the singular vectors are also compared with sets of 20 randomly selected members of the analysis ensembles. The results are generally consistent with those of previous studies with the maximum impact from the initial-time norm seen at the initial time. The growth is significantly reduced by using the analysis-error covariance norm instead of total energy and the smallest growth is obtained when no covariance localization is applied. The total-energy singular vectors are slightly more effective at explaining forecast error for most lead times than the analysis-error covariance singular vectors. This may point to errors in the covariance estimates, the importance of model error in affecting forecast-error evolution, or shortcomings with the tangent linear model used to compute the singular vectors. The use of a random selection of members from the analysis ensembles shows an even larger impact. In contrast with the singular vectors that continuously grow over the 72 It period examined, the total energy of the ensemble members initially decays during tangent linear model integrations. Also, the amount of forecast error explained by the ensemble members is significantly less than for all types of singular vectors. This suggests that, with respect to predicting forecast uncertainty over North America, the current approach of randomly selecting analysis ensemble members to initialize the ensemble prediction system may be improved.