Outer Loops in 4D Hybrid Ensemble-Variational Data Assimilation for the NCEP GFS

The use of hybrid covariance models, which combine a fixed climatological estimate with and ensemble-based representation, has become quite popular for numerical weather prediction (NWP). One such method for incorporating localized covariances from an ensemble within the variational framework utilizes an augmented control variable (ensemble-var, or EnVar), and has been implemented in the operational NCEP data assimilation system (gridpoint statistical interpolation, GSI). By taking the existing 3D EnVar algorithm in GSI and allowing for four-dimensional ensemble perturbations, coupled with the 4DVAR infrastructure already in place, a 4D EnVar capability has been developed. The 4D EnVar algorithm has a few attractive qualities relative to 4DVAR, including the lack of need for tangent-linear and adjoint model as well as reduced computational cost. Preliminary results using real observations have been encouraging, showing forecast improvements nearly as large as were found in moving from 3DVAR to hybrid 3D EnVar. 4D EnVar is the method of choice for the next generation assimilation system for use with the operational NCEP global model, the global forecast system (GFS).

The use of an outer-loop has long been the method of choice for 4DVar data assimilation to help address nonlinearity. An outer loop involves the re-running of the (deterministic) background forecast from the updated initial condition at the beginning of the assimilation window, and proceeding with another inner loop minimization. Within 4D EnVar, a similar procedure can be adopted since the solver evaluates a 4D analysis increment throughout the window, consistent with the valid times of the 4D ensemble perturbations. In this procedure, the ensemble perturbations are kept fixed and centered about the updated background state. This is analogous to the quasi-outer loop idea developed for the EnKF. Here, we present results for both toy model and real NWP systems demonstrating the impact of incorporating outer loops to address nonlinearity within the 4D EnVar context. The appropriate amplitudes for observation and background error covariances in subsequent outer loops will be explored.