The effect of improved ensemble covariances on hybrid variational data assimilation

Hybrid four-dimensional ensemble-variational (4DEnVar) data assimilation is a method which avoids using a linear and adjoint model by relying on an input ensemble to propagate analysis increments in time. Previous studies have shown that hybrid 4DEnVar performs worse than hybrid four-dimensional variational (4D-Var) assimilation. Given hybrid 4DEnVar's heavy reliance on the ensemble, this comparison may be affected by the quality of the input ensemble. Here we investigate how improvements to the ensemble system affect hybrid 4D-Var and how they affect the comparison with hybrid 4DEnVar. Using the Met Office's operational ensemble generation scheme (the ensemble transform Kalman filter, ETKF) it is found that hybrid 4D-Var gains little benefit from using an enlarged ensemble as input (176 as opposed to 23 members). By contrast, hybrid 4DEnVar benefits more from the increased ensemble size, and it benefits further when the weighting given to the ensemble covariance is increased. Both data assimilation methods benefit when the input ensemble is changed from using the ETKF to using an ensemble of 4DEnVars. Both schemes also show further benefit when a large ensemble (200 members) of 4DEnVars is used, and when a large weight is given to the covariance information from this ensemble. Thus, improving the ensemble covariance used in assimilation (ensemble generation method and ensemble size) and increasing its weight can have substantial benefits. Given that both hybrid 4D-Var and hybrid 4DEnVar benefit from improvements to the input ensemble, the relative performance is largely unaffected by the ensemble changes and hybrid 4D-Var performs better than hybrid 4DEnVar for all input ensembles.