On the Use of Cost-Effective Valid-Time-Shifting (VTS) Method to Increase Ensemble Size in the GFS Hybrid 4DEnVar System

Valid-time-shifting (VTS) ensembles, either in the form of full ensemble members (VTSM) or ensemble perturbations (VTSP), were investigated as inexpensive means to increase ensemble size in the NCEP Global Forecast System (GFS) hybrid four-dimensional ensemble–variational (4DEnVar) data assimilation system. VTSM is designed to sample timing and/or phase errors, while VTSP can eliminate spurious covariances through temporal smoothing. When applying a shifting time interval (τ = 1, 2, or 3 h), VTSM and VTSP triple the baseline background ensemble size from 80 (ENS80) to 240 (ENS240) in the EnVar variational update, where the overall cost is only increased by 23%–27%, depending on the selected τ. Experiments during a 10-week summer period show the best-performing VTSP with τ = 2 h improves global temperature and wind forecasts out to 5 days over ENS80. This could be attributed to the improved background ensemble distribution, ensemble correlation accuracy, and increased effective rank in the populated background ensemble. VTSM generally degrades global forecasts in the troposphere. Improved global forecasts above 100 hPa by VTSM may benefit from the increased spread that alleviates the underdispersiveness of the original background ensemble at such levels. Both VTSM and VTSP improve tropical cyclone track forecasts over ENS80. Although VTSM and VTSP are much less expensive than directly running a 240-member background ensemble, owing to the improved ensemble covariances, the best-performing VTSP with τ = 1 h performs comparably or only slightly worse than ENS240. The best-performing VTSM with τ = 3 h even shows more accurate track forecasts than ENS240, likely contributed to by its better sampling of timing and/or phase errors for cases with small ensemble track spread.