## 5 Discussion
### Discussion of the Impacts of Spatial Heterogeneity on the Fitting Accuracy  
According to Section 3.3, the impacts of spatial heterogeneity on the fitting accuracy of OWCMs and GMs are further analyzed and discussed. Based on GAM, the partial deviance explained by each factor (e.g., \(CV_{LAI}\), \(CV_{LST}\), \(CV_{TVDI}\) and \(CV_{SEE}\)) for the fitting accuracy of each OWCM/GM was determined. Since the spline change trends for the fitting accuracies of the eight GMs and OWCMs are similar, only the top four explained deviances are plotted in Figure 9 for a clear presentation. The gray shaded area indicates 90% confidence intervals. Unless otherwise specified, all discussion below is based on these intervals.  
Overall, spatial heterogeneity shows a substantial impact on the fitting accuracy. The contribution to the correlation coefficient R (between aggregated GM-/OWCM-derived SM and RFSM) decreases from positive (or around zero) to negative as the spatial heterogeneity increases--especially under high-CV conditions. Specifically, when \(CV_{LST}\) increases, the explained partial deviance decreases almost monotonously (Figure 9a). This indicates that the LST heterogeneity negatively impacts the fitting accuracy, i.e., a higher \(CV_{LST}\) corresponds to lower fitting accuracy. LST has been regarded as a strong indicator of SM  
Figure 9: GAM partial effect splines presenting the dynamic changes in the fitting accuracy R with (**a**) \(CV_{LST}\), (**b**) \(CV_{LAI}\), (**c**) \(CV_{TVDI}\), and (**d**) \(CV_{SEE}\). In (**a**–**d**), the dotted lines indicate the zero value (\(y\)-axis) and the means of explanatory variables (\(x\)-axis), while the shaded areas are the 90% confidence intervals. Moreover, the small vertical lines at the bottoms of the figures represent data points.  
in previous studies due to the controlling effect of SM on surface energy exchange and partition [37; 91]. The pixel spatial heterogeneity brings uncertainty to the SM fitting process because the pixel values of LST at different scales might not represent one another well [85]. Figure 9b shows that the explained partial deviances fluctuate around zero for small \(CV_{LAI}\) values, but decrease slightly when \(CV_{LAI}\) increases. This implies that low vegetation heterogeneity has no significant impact on the fitting accuracy, but still has a solid negative impact during conditions of high vegetation heterogeneity. This could be explained by the more complex couplings and feedback between SM and vegetation conditions (i.e., LAI) when LAI is distributed heterogeneously within the pixel [92]. Figure 9c shows four upside-down 'U' spline shapes for \(\text{CV}_{TVDI}\), with the explained partial deviance shifting from negative to positive, and then back to negative. This indicates that the fitting accuracies are less affected by moderate \(\text{CV}_{TVDI}\) levels, but substantially negatively affected by low- and high-\(\text{CV}_{TVDI}\) conditions. In Figure 9d, the explained partial splines for \(\text{CV}_{SEE}\) show a clear downward trend similar to those for \(\text{CV}_{LST}\), drawing the same conclusions as discussed above for \(\text{CV}_{LST}\).