A Comparison of Hybrid Ensemble Transform Kalman Filter3DVAR and Ensemble Square-Root Filter Analysis Schemes


A hybrid ensemble transform Kalman filter (ETKF)-3DVAR analysis scheme is compared to an ensemble square-root filter (EnSRF) analysis scheme in a two-layer primitive equation modelunder perfect-modelassumptions. The ETKF-3DVAR updates the ensemble mean with a hybridized ensemble covariance and the 3DVAR covariance, and it can be incorporated to the operational3DVAR data assimilation framework conveniently. The ensemble perturbations are generated by the computationally efficient ETKF scheme. The EnSRF runs comparatively expensive parallel data assimilation cycles for each member and serially assimilates the observations. The EnSRF background-error covariance is estimated fully from the ensemble, and covariances are localized. The intent of this study is to determine whether the hybrid ETKF-3DVAR method provides much of the potential improved accuracy of the EnSRF. It was found that depending on the norm, the analyses of the hybrid ETKF3DVAR corresponding to the optimal linear combination coefficient were slightly less accurate or similar to the EnSRF using its optimal covariance localization scale. The ETKF-3DVAR system was less prone to spurious gravity wave activity than the EnSRF that requires covariance localization. Maximal growth in the ETKF ensemble perturbation space exceeded that in the EnSRF ensemble perturbation space. The skill of the ETKF ensemble variance to estimate the ensemble mean error variance is similar to that of the EnSRF ensemble. It was also found that applying covariance localization to the ensemble part of the hybrid error covariance when updating the mean did not improve its analysis. The hybrid ETKF-3DVAR approach is thus judged to be a promising, less expensive approach to utilize ensemble forecasts effectively in data assimilations.

Xuguang Wang, Thomas M. Hamill, Jeffrey S. Whitaker, and Craig H. Bishop