## 6 Conclusions  
Aiming to improve the fitting accuracies of the general models used in SM analyses (e.g., downscaling, interpolation, and forecasting), the WT technique was introduced here to implement the required fitting procedures in the WT space rather than the regular space. As a test, four general regression models--i.e., ATA, ER, RF and NN--were selected and applied to the specific SM problem of spatial downscaling. By coupling (OWCMs) and uncoupling (GMs) the wavelet transformation, empirical relationships between the 0.25\({}^{\circ}\)\(\times\) 0.25\({}^{\circ}\) RFSM and 0.01\({}^{\circ}\)\(\times\) 0.01\({}^{\circ}\) GLASS FVC, LAI, albedo, and TRIMS LST were constructed. As a result, eight downscaled fine-RES SM datasets were produced using the trained GMs and OWCMs. The performances of the GMs and OWCMs were demonstrated by validating and analyzing the fine-RES SM datasets from two aspects: One was based on direct comparisons with in situ SM measurements. The other was based on indirect intercomparisons of the spatial and temporal consistencies between the aggregated OWCM-/GM-derived SM and the original RFSM dataset. Overall, the OWCM-derived SM was generally closer to the in situ SM and better matched with the in situ SM dynamic change during the unfrozen season compared to the corresponding GM-derived SM products, showing fewer time changes and more stable trends. Moreover, the OWCM-derived SM represents a significant improvement over the corresponding GM-derived SM regarding the RFSM in terms of spatial distribution and temporal variation. As discussed in Section 4.2, these improvements can possibly be attributed to two main factors, i.e., the application of OWCMs, which implement the fitting procedures in the WT space, and the selection of grid cells with low spatial heterogeneity. Since WT separates the high- and low-frequency feature information, implementing the fitting procedure between the same WT components of SM and the same attributes can better capture the relationships between them. In addition, for both GM- and OWCM-derived SM products, an in situ measurement site with lower spatial heterogeneity has better representativeness of the overall grid cell and, therefore, minimizes errors due to the point versus grid-cell upscaling differences, consequently improving our statistical indices, i.e., generally higher R values and lower RMSEs and ubRMSEs. Since the direct comparisons with in situ SM measurements were implemented only over grids with low spatial heterogeneity, the impacts of spatial heterogeneity (indicated by \(CV_{LST}\), \(CV_{LAI}\), \(CV_{TVDI}\), and \(CV_{SEE}\)) on the fitting accuracy of OWCMs and GMs--i.e., the correlation coefficient R between aggregated GM-/OWCM-derived SM and RFSM--were further analyzed and discussed based on a GAM. The results show that, despite the selection of only spatially representative sites for validation, spatial heterogeneity still substantially impacts the fitting accuracy of both GMs and OWCMs. Generally, the contribution to the correlation coefficient R decreases from positive (or around zero) to negative as the spatial heterogeneity increases. It is worth noting that the method of characterizing the spatial heterogeneity to identify the in situ nodes with maximal spatial representativeness, as described in Section 3.2.1, is arguably subjective due to its selection of the empirical coefficients adopted in Equations (4)-(6). However, the use of alternative coefficients does not significantly influence the spatial heterogeneity ranking over the grids with in situ measurement sites. OWCMs significantly improve the fitting effect of soil moisture on the QTP. In the future, it will be necessary to further verify this optimization effect in other regions and in situ networks, to determine its applicability in different related SM analysis topics (e.g., gap-filling, forecasting, and downscaling) that require SM fitting models. [PERSON] and [PERSON] designed the work.