## 4 Discussion and Conclusions  
The main contribution of this study lies in exploring the variations in the predictive performance of different TC estimations to different input errors in ATPRK-based spatial downscaling. To fill the gap from previous studies based on a single attribute and/or a small number of data [26, 27], the sensitivity analysis in this study was based on extensive comparisons using synthetic and real datasets. As error information of real satellite-derived products is usually unavailable, a direct comparison of results from the real dataset may not be compatible with those from the synthetic dataset with known errors. Despite the limitation of using error information from a limited number of actual observation sites in the real SM dataset, common results could be derived from the two experimental datasets in this study. The results from two experiments indicate that the quality of the spatial downscaling result depends heavily on the accuracy of input data. When input data become more erroneous, the prediction accuracy decreases accordingly. For input data with no or few errors, residual correction is recommended to improve the prediction accuracy. TC normalization is also effective when nonlinear regression models are employed for TC estimation. However, in spatial downscaling of coarse resolution data with significant errors (i.e., SM dataset in this study), residual correction and TC normalization cannot achieve better prediction performance, and the use of TC estimate as a prediction result is more effective. These findings were not reported in most spatial downscaling studies where input errors were not considered in spatial downscaling of satellite-derived products [16, 17, 18, 19]. When noisy coarse resolution data are used as input for spatial downscaling, the RCs that remain after regression modeling inevitably include input errors, depending on the explanatory power of the applied regression model. As a result, the errors of the coarse resolution RCs propagate to the ATPK-based RC predictions. In addition, the TC normalization procedure aiming at reproducing the patterns of the erroneous input data also yields a worse result. As found in the previous study [26], the higher explanatory power of regression modeling for TC estimation does not always lead to better prediction accuracy. When downscaling the coarse resolution data with significant errors (the SM dataset in this study), the prediction accuracy was not clearly correlated to the explanatory power. Instead, the regression model with higher explanatory power (RF in this study) predicted worse than other modes with relatively lower explanatory power. Quantitative relationships modeled at a coarse resolution are directly applied to auxiliary variables at a fine resolution for the TC estimation. Thus, a possible explanation for the worse prediction in the case with higher explanatory power is that the relationships at a coarse resolution distorted by overfitting to the noisy input (too higher \(R^{2}\) values) are likely to generate erroneous TC estimates at a fine resolution. It should be noted that the superiority of SVR to LR and RF in this study does not indicate that SVR is an optimal TC estimator in spatial downscaling. Instead, using the magnitude of explanatory power in the TC estimation as a direct indicator to select an optimal regression model requires caution, particularly when the input data contain errors. Recently, geographically weighted regression (GWR) has often been applied in ATPRK-based spatial downscaling [35, 36, 37]. As regression coefficients are estimated locally, the explanatory power of GWR is likely to be higher than that of other regression models. As a result, GWR may be more susceptible to input errors than other models in some cases. Therefore, it is worthwhile to analyze the impact of input errors on the predictive performance of GWR-based spatial downscaling to confirm the results of this study.