Improving NCEP GFS 4DEnVar System Using Cost-Effective Methods to Increase Ensemble Size

A few methods were proposed for the purpose of inexpensively increasing ensemble size in the ensemble-based data assimilation system. The first method shifts the ensemble perturbations from the forecasts initialized at the same time but valid at different times, to the analysis time. The shifted ensemble perturbations will be combined with the ensemble perturbations at the analysis time to compute the error covariance. This method is called valid time lagging (VTL) method. VTL can improve the error covariance estimate by increasing the degree of freedom of the perturbations to better represent location, structure forecast errors. Theoretical analysis proves that the estimated error covariance by VTL will result in a temporal and spatial-smoothing which favorably removes the remote spurious correlations caused by the use of the limited ensemble size. In the second method called initial time lagging (ITL) method, the shifted ensemble perturbations will be introduced by the forecasts initialized from previous different analysis times but valid at the same time. ITL method may better represent the model errors due to the use of the ensemble forecasts with different leading times. To take into account that the forecasts with different leading times in ITL may not have the equal skills in representing the background forecast errors, a scaling method is applied to weight the ensemble perturbations differently in different lagged groups (referred to as ITLS method). The computational cost increase in the above methods will only result from running the ensemble forecasts by several additional hours. The three methods were investigated in the GSI-based four dimensional ensemble-variational (4DEnVar) hybrid data assimilation system for the NCEP Global Forecast System (GFS). Experiments were conducted within the 5-week summer period during August 2013.

In VTL method, the ensemble perturbations at three hours before and after the analysis time was shifted to the analysis time, which results in an increase of the ensemble size from 80 (ENS80) to 240 (VTL240M80) in 4DEnVar update while both experiments will still keep using the original 80 members in EnKF update. VTL240M80 only increases 10% of the cost relative to ENS80. Estimations of both the self- and cross- variable error correlation by VTL240M80 were improved over ENS80. Specifically a larger improvement was seen for the small correlation than the large correlation. There was no significant spread difference in both experiments. VTL240M80 improved both the global forecasts and the tropical cyclone track forecasts over ENS80. The analysis generated by VTL240M80 is more balanced than ENS80. While VTL240M80 increases cost by 10% and directly increasing ensemble size to 240 (ENS240) triples the cost, VTL240M80 recovers more than 50% of the improvement of ENS240.

In ITL method, combining with the original 80 members, three (twelve) lagged groups with 80 (20) members in each lagged group were selected to configure the 320-member experiment of ITL320M80 (ITL320M20). Due to the use of the longer forecasts, the cost of ITL320M80 almost doubles that of ENS80 and halves the cost by directly increasing the ensemble size to 320 (ENS320). But ITL320M20 does not incur additional cost since the 20-member longer forecasts are freely available in the Global Ensemble Forecast System (GEFS). Estimation of the error correlation in ITL320M80 didn’t show a significant difference from ENS80 while ITL320M20 show a significant degradation. Both experiments exhibited a larger spread and caused more imbalance than ENS80, especially for ITL320M20. In terms of the verification of global forecast and tropical cyclone track forecasts, ITLM320M80 generally showed neutral or negative impacts except that an improvement was seen for the temperature forecasts, while ITL320M20 showed consistent degradation.

In ITLS method, the scaling coefficients were calculated by comparing the spread in each lagged group with the original 80-member ensemble. Following the configuration in ITL method, ITLS320M80 and ITLS320M20 were carried out. Results from ITLS method didn’t show a significant difference from ITL method except that the larger spread in ITL method was reduced.