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Xuguang Wang and Ting Lei


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.

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Bo Huang, Xuguang Wang, Daryl T. Kleist, and Ting Lei


A scale-dependent localization (SDL) method was formulated and implemented in the Gridpoint Statistical Interpolation (GSI)-based four-dimensional ensemble-variational (4DEnVar) system for NCEP FV3-based Global Forecast System (GFS). SDL applies different localization to different scales of ensemble covariances, while performing a single-step simultaneous assimilation of all available observations. Two SDL variants with (SDL-Cross) and without (SDL-NoCross) considering cross-wave-band covariances were examined. The performance of two- and three-wave-band SDL experiments (W2 and W3, respectively) was evaluated through 1-month cycled data assimilation experiments. SDL improves global forecasts to 5 days over scale-invariant localization including the operationally tuned level-dependent scale-invariant localization (W1-Ope). The W3 SDL-Cross experiment shows more accurate tropical storm–track forecasts at shorter lead times than W1-Ope. Compared to the W2 SDL experiments, the W3 SDL counterparts applying tighter horizontal localization at medium-scale wave band generally show improved global forecasts below 100 hPa, but degraded global forecasts above 50 hPa. While the outperformance of the W3 SDL-NoCross experiment versus the W2 SDL-NoCross experiment below 100 hPa lasts for 5 days, that of the W3 SDL-Cross experiment versus the W2 SDL-Cross experiment lasts for 3 days. Due to local spatial averaging of ensemble covariances that may alleviate sampling error, the SDL-NoCross experiments show slightly better forecasts than the SDL-Cross experiments at shorter lead times. However, the SDL-Cross experiments outperform the SDL-NoCross experiments at longer lead times, likely from retention of more heterogeneity of ensemble covariances and resultant analyses with improved balance. Relative performance of tropical storm–track forecasts in the W2 and W3 SDL experiments are generally consistent with that of global forecasts.

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