A Hybrid Ensemble Kalman Filter / 3D-Variational Analysis Scheme

A hybrid 3-dimensional variational (3D-Var) / ensemble Kalman filter analysis scheme is demonstrated using a quasigeostrophic model under perfect-model assumptions. Four networks with differing observational densities are tested, including one network with a data void. The hybrid scheme operates by computing a set of parallel data assimilation cycles, with each member of the set receiving unique perturbed observations. Background error covariances for the data assimilation are estimated from a linear combination of time-invariant 3D-Var covariances and flow-dependent covariances developed from the ensemble of short-range forecasts. The hybrid scheme allows the user to weight the relative contributions of the 3D-Var and ensemble-based background covariances.

The analysis scheme was cycled for 90 days, with new observations assimilated every 12 h. Generally, it was found that the analysis performs best when background error covariances are estimated almost fully from the ensemble, especially when the ensemble size was large. When small-sized ensembles are used, some lessened weighting of ensemble-based covariances is desirable to reduce the impact of spurious analysis corrections over long distances. The relative improvement over 3D-Var analyses was dependent upon the observational data density; generally, there is less improvement for data-rich networks than for data poor networks, with the largest improvement for the network with the data void. As expected, errors depend on the size of the ensemble, with errors decreasing as more ensemble members are added. The sets of initial conditions generated from the hybrid are generally well-calibrated and provide an improved set of initial conditions for ensemble forecasts.