GSI-Based Four-Dimensional Ensemble–Variational (4DEnsVar) Data Assimilation: Formulation and Single-Resolution Experiments with Real Data for NCEP Global Forecast System

A four-dimensional (4D) ensemble–variational data assimilation (DA) system (4DEnsVar) was developed, building upon the infrastructure of the gridpoint statistical interpolation (GSI)-based hybrid DA system. 4DEnsVar used ensemble perturbations valid at multiple time periods throughout the DA window to estimate 4D error covariances during the variational minimization, avoiding the tangent linear and adjoint of the forecast model. The formulation of its implementation in GSI was described. The performance of the system was investigated by evaluating the global forecasts and hurricane track forecasts produced by the NCEP Global Forecast System (GFS) during the 5-week summer period assimilating operational conventional and satellite data. The newly developed system was used to address a few questions regarding 4DEnsVar. 4DEnsVar in general improved upon its 3D counterpart, 3DEnsVar. At short lead times, the improvement over the Northern Hemisphere extratropics was similar to that over the Southern Hemisphere extratropics. At longer lead times, 4DEnsVar showed more improvement in the Southern Hemisphere than in the Northern Hemisphere. The 4DEnsVar showed less impact over the tropics. The track forecasts of 16 tropical cyclones initialized by 4DEnsVar were more accurate than 3DEnsVar after 1-day forecast lead times. The analysis generated by 4DEnsVar was more balanced than 3DEnsVar. Case studies showed that increments from 4DEnsVar using more frequent ensemble perturbations approximated the increments from direct, nonlinear model propagation better than using less frequent ensemble perturbations. Consistently, the performance of 4DEnsVar including both the forecast accuracy and the balances of analyses was in general degraded when less frequent ensemble perturbations were used. The tangent linear normal mode constraint had positive impact for global forecast but negative impact for TC track forecasts.