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

Abstract

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.

An OSSE-Based Evaluation of Hybrid Variational–Ensemble Data Assimilation for the NCEP GFS. Part II: 4DEnVar and Hybrid Variants

“…Buehner et al (2010b) performed an intercomparison study for the Canadian operational global NWP model, and found that the 4DEnVar improved upon their operational, nonhybrid 4DVar in the tropics and Southern Hemisphere, but not in the Northern Hemisphere. Finally, Wang and Lei (2014) performed a comparison study of hybrid 4DEnVar with 3DEnVar using the NCEP GFS (model) at low resolution. Buehner et al (2013), again using the operational Canadian system, found that while the use of 4D instead of 3D ensemble covariances did result in small, consistent improvements in their EnVar for deterministic NWP, the gains were not as large as found when going from 3DVar to 4DVar.…”

Impact of hybrid GSI analysis using ETR ensembles

“…It can be seen that improvement with hybrid experiment can be seen at all levels on taking global average, while in tropics middle levels, hybrid experiment performs inferior to 3D Var in comparison with radiosonde observations. Using NCEP/GSI system it is observed in previous studies that hybrid produced neutral or negative impact on temperature forecasts in tropics at some vertical levels in comparison with 3D Var (Wang et al 2013;Wang and Lei 2014). The improvement in wind field not seen in temperature at some vertical levels might be due to improper coupling of wind and mass fields in tropics.…”

“…Due to the nature of global observing system with large number of mass-type observations, assimilation system can anchor temperature analysis errors through assimilation of satellite radiances (Kleist and Ide 2015) and more improvement with hybrid experiment is expected in wind. It is noted in some previous studies that hybrid assimilation produced largest improvement in wind than other variables (Wang et al 2008b;Wang and Lei 2014). In this section, model wind at different pressure levels in the analysis and forecasts are compared against conventional observations assimilated in the model.…”

Application of 3-D ensemble variational data assimilation to a Baltic Sea reanalysis 19892013

“…Large-scale atmospheric experiments using real observations were done later by, e.g. Buehner et al (2010b), Liu and Xiao (2013), and Wang and Lei (2014). These authors compared the results with other methods (EnKF, 3DVar, 3DVar-FGAT, Ensemble-based 3DVar, 4DVar, Hybrid 4DVar).…”