## 4 Discussion
### Prediction Models  
Considering the compositional nature of soil PSFs, we applied ALR (additive log-ratio) and ILR (isometric log-ratio) transformations before model fitting in this study. Some studies also reported application of the log-ratio transformations coupled with machine learning approaches. For example, [PERSON] et al. [17] implemented the ALR and ILR transformation with the boosted regression tree (BRT), RF, and regression kriging for a river basin. The results indicated that machine learning approaches improved the mapping performance rather than regression kriging, and the ILR-RF model outperformed the ILR-BRT model. However, [PERSON] et al. [1] cast doubts on the necessity of using log-ratio transformations in soil PSFs prediction. They predicted transformed and untransformed PSFs byRF and applied the predictions to estimate available soil water capacity (AWC) and the total amount of irrigation water (TIW). The results indicated no apparent difference in the prediction of PSFs, AWC, and TIW. Moreover, they suggested that the log-transformations may lead to biased estimation of PSFs, and the bias can further propagate to pedo-transfer functions. Therefore, they believed the untransformed PSFs were still valid for predicting AWC (or TIW). Some other studies may also support this concept, for they applied Digital Soil Mapping (DSM) without log-ratio transformations in soil PSFs mapping but gained fairly good accuracy [8; 22]. More studies are still needed to testify to the rationality and the feasibility of log-ratio transformation in DSM at different scales. Former studies used the variable importance of the RF algorithm to interpret the relation between covariates and response variables. For example, [PERSON] et al. [5] found seven variables, including the freezing degree-days, thawing degree-days, leaf area index, snow cover days, elevation, soil moisture, and soil bulk density, are selected to estimate the mean annual ground temperature. The relative importance results in [PERSON] et al. [17] showed that soil organic carbon, NDVI, elevation, precipitation, and temperature were the main predictors to explain the variability of transformed PSFs in the Heihe River basin (area = 14.67 \(\times\) 10\({}^{5}\) km\({}^{2}\)). According to the study [1] at a region in southwestern Iran (area = 4600 ha), the relative importance showed that MRVBF, NDVI, elevation, slope, and band 3 of Landsat 8 were the significant covariates in predicting clay, silt, and sand when using terrain attributes and optical images. While on a larger spatial scale, [PERSON] et al. [66] indicated that climatic elements (precipitation and temperature), Landsat8 bands (band 2 and 3), elevation, and geology were the most influential predictors for the distribution of clay and sand in Nigeria. [PERSON] et al. [22] found that climatic elements (e.g., solar radiation, wind speed, temperature seasonality, daytime LST), altitude, and regolith thickness were the essential factors in predicting soil PSFs in China. [PERSON] et al. [8] illustrated that depth, climatic elements (precipitation, precipitable Water Vapor images, daytime, and nighttime LST), and terrain factors were the most influential covariates. For soil PSFs prediction, vegetation condition is more influential on a regional scale than a national or global scale. Climatic elements are more critical on a large spatial scale, such as national and global scales. In this study, variable importance by the parsimonious ILR-RF models at both the BQ and WQ regions were given in Figures S5 and S6. The variable importance in RF algorithm was given with two aspects. One is the mean decrease in accuracy and the other is the mean decrease in Gini index when a particular predictor variable is removed [58]. The VRM (Vector Ruggedness Measure) and s2_df_a_9 (multiyear average of maximum diurnal LST difference in summer) were the most important covariates for clay\({}_{\text{lit}}\) and silt\({}_{\text{lit}}\) prediction in the BQ region, respectively (Figure S5).