Hybrid variational ensemble data assimilation with initial condition and model physics uncertainty

This study has evaluated an existing hybrid three-dimensional variational ensemble transform Kalman filter (3DVAR-ETKF) ensemble data assimilation system using the Weather Research and Forecasting (WRF) model in realistic numerical weather prediction experiments. The study was divided into three parts: Part one assessed the skill of the ETKF ensemble generation scheme with and without implicit mode error included in the ensemble. Part two assessed the benefit of including flow-dependent information into the hybrid cost function. Part three proposed an alternative to ETKF and tested its performance in cycling experiments. The ETKF perturbations as an ensemble-generation scheme performed well in single and multiphysics ensemble approaches. The multi-physics ETKF ensemble performed best maintaining the appropriate variance and dependence on covariance inflation. The multi-physics ETKF ensemble was characterized by larger (smaller) error growth (reduction) during the model integration than the single-physics ensemble. Using the ensemble mean as the first guess in the 3DVAR cost function significantly improved the skill of the analyses. Tuning the static 3DVAR background error covariances using the ETKF ensemble perturbations instead of time-lagged perturbations improved the skill of the deterministic and ensemble 3DVAR analyses as measured by 12- through 48-h deterministic forecast skill. Incorporating ensemble-based flow-dependent error covariances from limited 20-member ensembles into the hybrid cost function added skill to the analyses. This added skill was in addition to that achieved by using the ensemble mean as the first guess and using the tuned background error covariances. The greatest improvements in analysis skill were observed when a multi-physics ensemble was used to supply the error covariances to the hybrid cost function. Vertical localization added some skill to the analyzed wind speeds, mostly at longer lead times and when the localization length scale is less restrictive. The proposed hybrid Lanczos ensemble filter (HLEF) ensemble generation scheme was shown to be equivalent to the ETKF scheme when no inflation was applied and the HELF perturbations did not include the effect of covariance localizations or hybridization. Both vertical and horizontal covariance localization in the HLEF perturbations ameliorated the under estimation of analysis uncertainty. 10-day cycling experiments with inflated and localized HLEF perturbations required less than 30% of the magnitude of the inflation required by ETKF. Experiments that addressed the possibility of producing analysis perturbations that are consistent with the hybrid variational cost function produced encouraging results.