## 2 Numerical Aspects and Experimental Designs
### Settings of the Model Experiments  
The flow chart of the DA system constitutes two parts as shown in Figure 1. For the first part of EnKF, MPAS with 120 km cell spacing was used with 36 ensemble members whose perturbations are created by RANDOMCV, i.e., adopting the module from WRFDA (see [44; 45]). The NCEP GFS data are used as the background field in the experiments. To update these EnKF prior ensembles within the MPAS-GSI EnSRF, the 120 km MPAS fields were interpolated to a Gaussian T-106 grid (approximately 125 km horizontal grid spacing). Compared to the one-way system developed in [PERSON] et al. [22] that uses the CWB global spectral model in DA but applies MPAS for the main forecast, the DA system in this study may be called a two-way system since the same forecast model, MPAS, is used in both DA and the main forecast. The background error covariances (BECs) of EnKF are generated by the 36 members at a 6 h forecast for each DA cycle. The 12 and 24 h forecasts in one month of July 2016 by MPAS with 60-15 km resolution were used to derive the static background error covariance using the NMC method [22]. In the second part, hybrid-3 DVAR is used with the resolution of MPAS 60-15 km (or 60-15-3 km for higher resolution) with the weighted BECs to update the analysis at each cycle. The 6 h forecast of MPAS is then conducted with the updated analysis for the next DA cycle. For the hybrid DA system in this study, combined BECs are used by weighting BECs with 75% (flow-dependent) from EnKF and 25% (static/climatological) from 3 DVAR, respectively [22; 46; 47]. The choice of BECs is based on the operational forecast of the global model at CWB that suggests a combination of less static and more flow-dependent BECs. The optimization of BECs for MPAS-GSI was not pursued in this study and it may be sub-optimal compared to the use of full flow-dependent BECs (e.g., Feng and Wang [48]). After DA at each cycle, recentering is performed with the hybrid analysis to replace the ensemble mean and update the ensembles with their perturbations in order to maintain a better stability of split assimilation by the two parts. The homogeneous isotropic horizontal and vertical ensemble localization scale (km) are set to 800 km and 0.8 in Inp unit, respectively. There are two outer loops applied for the GSI-hybrid system, in which 100 and 150 iterations are used in the inner loop. The RO observation errors for both RO operators use the defaults of GSI [22]. The total DA time window with 6 h cycles is two days, from 0000 UTC 2 July 2016 to 0000 UTC 4 July, for the experiments conducted in this study. Figure 1: The flowchart of the GSI hybrid data assimilation. The data assimilation is divided into two parts that include the EnKF and GSI systems. The EnKF system uses \(n\) members (\(n\) is 36 in this study) at the lower resolution to provide background error covariances for the GSI system. The GSI system at the higher resolution provides the analysis for the EnKF system to re-center all ensemble members with the coarser resolution for MPAS forecasts, and then the new ensemble members can be updated for use in the next cycling. The DVI then can be applied to the analysis after the final DA cycle prior to free forecasts. The numerical experiments conducted in this study are listed in Table 1. All the experiments are conducted for 5-day forecasts from 0000 UTC 4 July 2016 to 0000 UTC 9 July 2016. The experiment GTS at 60-15 km resolution assimilates conventional soundings together with all other non-conventional data including satellite radiances (AMSU-A, AISR, and IASI). The conventional data include GTS soundings, aircraft, satellite-tracked winds, surface pressure observations, ships, and buoys used operationally at CWB. NoDA is the experiment that uses the NCEP FNL as the initial guess (without any data assimilation) and may be used to provide a reference guide for the impact of the hybrid DA.