The study of introducing ensemble forecast errors in the GRAPES global 4DVar Part Ⅱ：Parameters determination and numerical experiments

In the first part of the study, the scientific scheme of how to effectively apply ensemble forecast errors is discussed, and the framework for the application of ensemble forecast errors in the global four dimensional variational data assimilation (4DVar) of the Global Regional Assimilation and PrEdiction System (GRAPES) is identified. Based on this work, the present paper further studies the application of ensemble forecast errors in the GRAPES global 4DVar. The study is focused on solving computational efficiency issues for efficient generation of ensemble samples close to or exceeding 100, as well as key parameters determination issues for matching with the GRAPES global 4DVar. The 4DVar based Ensemble of Data Assimilations (EDA) method is chosen to generate the ensemble samples. By using the preconditioning information generated during the minimization iteration of the first sample to precondition the minimization of other samples, the computational efficiency is increased by a factor of two. By using the Valid-Time-Shifting Perturbation (VTSP) method, the ensemble members are enlarged by a factor of three. The ensemble forecast errors variance inflation method is used, and the horizontal localization scale is selected to be 1.4 times of the horizontal length scale of the stream-function background error. The weight coefficients of background error and ensemble forecast errors are determined by numerical experiments, and the best weight for ensemble forecast error is 0.7 for 60 ensemble members. The results of two 52 d numerical experiments over the winter and summer seasons show that the improvement of ensemble four dimensional variational data assimilation (En4DVar) over 4DVar in the northern and southern hemisphere is mainly concentrated at 700—30 hPa in winter season and 400—150 hPa in the summer season. The tropical region is less affected by seasonal changes, and the improvement of geopotential height, wind field and temperature are obvious with En4DVar, and the improvement of meridional wind field is the most significant. The method developed in this study for the application of ensemble forecast errors in GRAPES Global 4DVar is reasonable and feasible.