On the Use of Valid Time Lagging (VTL) Ensembles to Increase Ensemble Size in GFS Hybrid 4DEnVar System
Sampling error is one of the major concerns in the ensemble-based data assimilation (DA) systems. It is caused by the use of small-sized ensemble for the consideration of limited computational resources. Directly increasing the ensemble size was proven to positively improve the ensemble-based DA systems, but the cost was also significantly increased. Instead of running a large-sized ensemble, the ensemble forecasts at different valid times were explored as an inexpensive means to increase the ensemble size in the Global Forecast System (GFS) hybrid four-dimensional ensemble-variational (4DEnVar) system. Directly introducing the valid time lagging ensemble members (VTLM) could contribute to sampling the phase errors but is likely to incur unrealistic ensemble perturbations. To remedy the deficiency in VTLM, the method of leveraging the valid time lagging ensemble perturbations (VTLP) was proposed. VTLP was proven functioning because it performs temporally and spatially smoothing of the ensemble covariances by its construction. However, VTLP may not be as efficient as VTLM in sampling the phase errors.
Both methods with 1-, 2- and 3-hour lagging time intervals were implemented and evaluated within the GFS hybrid 4DEnVar system. With respect to the ensemble covariances, VTLP improved the ensemble correlation accuracy and increased the effective rank, incurring little ensemble spread change. On the other hand, VTLM increased the total ensemble spread, degraded the ensemble correlation estimate and was not as efficient as VTLP in increasing the effective rank. The results from the ten-week summer DA cycling experiments showed that VTLP generally improved the global temperature and wind forecasts over the five-day forecast lead times, especially when using 2-hour lagging time interval, while VTLM only showed limited positive impacts on the temperature and wind forecasts above 100 hPa. In terms of the track forecasts from 22 tropical storms, both VTLP and VTLM improved the track forecasts. VTLM with 3-hour lagging time interval even showed more accurate track forecasts even than directly increasing ensemble size. The computational cost of each method is also discussed.