3.1.3. Environmental Variables

The introduction of environmental variables into a downscaling analysis can improve the quality of satellite-retrieved precipitation data [13–20]. Therefore, environmental variables that are closely related to satellite precipitation data, such as the slope (SLP), aspect (ASP), curvature (CVT), hillshade (HSHD) [29,30], topographic wetness index (TWI) [31], and NDVI, were selected in this study. The NDVI data were obtained from the 1-km MOD13A3 monthly average vegetation index provided by the MODerate resolution Imaging Spectroradiometer (MODIS), and digital elevation model (DEM) data were taken from the Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM), with a native resolution of 30 m. To maintain consistency with the NDVI data, the resolution was resampled to 1 km using the pixel averaging method, that is, the data from all high-resolution pixels within a given coarse-resolution pixel were averaged to obtain the corresponding coarse-resolution estimate. The topographic variables were obtained from the DEM data using Geographic Information System (GIS) software.

For the selected environmental variables, such as the NDVI, DEM, ASP, SLP, HSHD, TRI, and CVT, experiments were performed on each of the variables individually and on various combinations of variables. Moreover, the variance inflation factor (VIF) method was utilized to prevent multicollinearity. The VIF is a measure of the severity of multicollinearity in an MLR model, where multicollinearity refers to linear correlations between independent variables. The VIF is calculated when filtering variables. When the VIF value is closer to one, the multicollinearity is weaker, and vice versa. Specifically, when performing the experiments, variables were added to the existing variable group one by one. If adding a particular variable resulted in multicollinearity according to the VIF, that variable was deleted from the variable group. The variables were then introduced into the GWR model separately or in various combinations to obtain the downscaling outcomes. After a comparison of the results, the NDVI was found to have the best downscaling effect and thus was selected as the final explanatory variable for further study.
