Several variants of hybrid data assimilation algorithms have been developed and tested within recent years, particularly for numerical weather prediction (NWP). The hybrid algorithms are designed to combine the strengths of variational and ensemble-based techniques while at the same time attempting to mitigate their weaknesses. One such variational-based algorithm is under development for use with the National Centers for Environmental Prediction's (NCEP) global forecast system (GFS) model. In this work, we attempt to better understand the impact of utilizing a hybrid scheme on the quality of analyses and subsequent forecasts, as well as explore alternative extensions to make better use of the ensemble information within the variational solver.

A series of Observing System Simulation Experiments (OSSEs) are carried out.  It is demonstrated that analysis and subsequent forecast errors are generally reduced in a 3D-hybrid scheme relative to 3DVAR.  Several variational-based 4D extensions are proposed and tested, including the use of a variety of dynamic constraints.  A simple approach for hybridizing the 4D-ensemble with a time-invariant contribution is proposed and tested.  The 4D variants are shown to be superior to the 3D-hybrid, with positive contributions from static B as well as the dynamic constraint formulations.  It is clear from both the 3D and 4D experiments that more sophisticated methods for dealing with inflation and localization in the ensemble update are needed even within the hybrid paradigm.  Lastly, a method for applying piecewise scale-dependent weights is proposed and successfully tested.

The 3D OSSE-based results are also compared with results from an experiment using real observations to corroborate the findings.  It is found that in general, most of the results are comparable, though the positive impact in the real system is more consistent and impressive.