3.2.1. Overall Flow Chart of the Study

In this study, monthly IMERG precipitation data were used for downscaling. As shown in Figure 2, first, the original IMERG precipitation data (OIMERG) and the observed precipitation data (OBS) were merged using OI to obtain 10-km OI-corrected IMERG precipitation data (CIMERG). The OI technique was originally developed by Eliassen [32] and Gandin [33]. In this study, OI was used to calibrate and adjust the satellite precipitation data based on OBS; hence, the corrected results possessed the combined advantages of satellite precipitation data and OBS (see Section 3.2.2 for details). Then, since it was found that the NDVI showed the best performance among all considered environmental variables (DEM, SLP, ASP, CVT, HSHD, TWI, and NDVI) in the downscaling of precipitation data, we included only the NDVI variable in this study, which was resampled from its original 1 km resolution to a 10 km resolution. With the 10-km NDVI as the independent variable, the spatial downscaling of CIMERG was performed using GWR to obtain a 1-km monthly precipitation dataset (DS\_CIMERG) for the Tianshan Mountains. For comparison with previous methods, two additional sets of data were generated and used for further validation: DS\_OIMERG, obtained via GWR downscaling with OIMERG (the original uncorrected IMERG precipitation data) as the dependent variable, and DS\_Spline, obtained by using the spline interpolation method for OIMERG precipitation downscaling. The steps highlighted in the red dashed box in Figure 2 constitute the process of residual correction, which is necessary for the verification of the downscaling method proposed in this study.

**Figure 2.** The flow chart of this study. The red dashed box indicates the residual correction process, and the blue boxes represent the three categories of downscaling estimation data. OIMERG, original IntegratedMulti-satellitE Retrievals for GPM; OBS, observed precipitation data; OI, optimum interpolation; NDVI, normalized difference vegetation index; CIMERG, OI-corrected IMERG precipitation data; GWR, geographically weighted regression; DS\_CIMERG, obtained via GWR downscaling with CIMERG; DS\_OIMERG, obtained via GWR downscaling with OIMERG; DS\_Spline, obtained by using the spline interpolation method for OIMERG precipitation downscaling.
