*4.6. Residual Correction*

A series of improvements in downscaling methods for satellite precipitation products have been achieved, from the original ER model proposed by Immerzeel et al. [13] and the MLR model proposed by Jia et al. [14] to the GWR approach proposed by Xu et al. [17] and Chen et al. [20]. Residual correction is a key step in both ER and MLR [17]. In this study, residual correction for GWR was analyzed in detail.

Using DS\_CIMERG as an example, the residual correction processes for GWR downscaling in July 2016 and September 2017 were analyzed, and the results are shown in Figure 13; Figure 14, respectively. Figure 13a shows the CIMERG data before downscaling. Figure 13b shows the estimated precipitation based on the low-resolution (10 km) regression coefficients (i.e., Predicted Precipitation (10 km) in Figure 2). Figure 13c shows the 10-km residuals obtained by subtracting CIMERG from the 10-km precipitation predictions. Figure 13d shows the 1-km residuals obtained after applying the spline interpolation technique to the 10-km residuals. Figure 13e shows the DS\_CIMERG precipitation estimates, which are based on the high-resolution (1 km) regression coefficients. Finally, Figure 13f presents the residual-corrected downscaling results obtained by summing the 1-km residuals and the 1-km precipitation estimates. As shown in this figure, the precipitation estimates (Figure 13b) obtained with the low-resolution parameters already exhibited high consistency with CIMERG (Figure 13a), and their residual values were generally small, ranging between -10 and 10 mm (Figure 13c), indicating that the low-resolution estimated precipitation data obtained via the GWR method were close to the initial precipitation data. In contrast, the high-resolution precipitation estimates obtained based on the 1-km regression coefficients (Figure 13e) not only were highly consistent with the initial precipitation distribution but also reflected the detailed structure of the precipitation distribution. The results shown in Figure 14 are similar to those in Figure 13, except that they correspond to a different month. Table 2 summarizes the detailed error statistics. The CC, RMSE, and MAE values after residual correction were worse than those before residual correction. Therefore, the addition of residual correction to the GWR model transferred the errors of the original IMERG precipitation data to the final downscaling outcomes, thereby decreasing the reliability of the outcomes, as the residuals were obtained by subtracting the 10-km precipitation predictions from the original IMERG precipitation data.

**Figure 13.** Comparison of the DS\_CIMERG product in July 2016 before and after residual correction. (**a**) CIMERG; (**b**) predicted precipitation (10 km); (**c**) residuals (10 km); (**d**) residuals (1 km); (**e**) DS\_CIMERG; (**f**) downscaled precipitation after residual correction.

**Figure 14.** Comparison of the DS\_CIMERG product in September 2017 before and after residual correction. (**a**) CIMERG; (**b**) predicted precipitation (10 km); (**c**) residuals (10 km); (**d**) residuals (1 km); (**e**) DS\_CIMERG; (**f**) downscaled precipitation after residual correction.

To further evaluate the results through additional validation tests, the data before and after residual correction from 2010 to 2018 were also processed and evaluated. The results were consistent with those presented in Table 2. The CC, RMSE, and MAE values respectively increased from 0.576, 26.92 mm, and 18.12 mm before residual correction to 0.59, 26.55 mm, and 17.63 mm after residual

correction. Therefore, the residual correction step is not necessary in GWR downscaling; this conclusion is consistent with the findings of Xu et al. [17].


**Table 2.** Comparison of evaluation metrics before and after residual correction.
