## 3 Results
### Feature Partial Dependence Analysis  
Subsequently, we undertook a more in-depth investigation into the impacts of precipitation and exchangeable K on soil organic matter content. This choice was driven by the results of the DT and RF analyses, which highlighted these variables as being within the top two regarding Shapley-based feature importance (Figures 3 and 4). In Figure 5, we present _PD_ plots illustrating how the three models portrayed the connections between precipitation and organic matter content; all models consistently showed a positive correlation between them. Nonetheless, we identified disparities in the strength and form of the relationships across the models. Specifically, the DT model exhibited a distinct, step-like association centered around a precipitation value of 1400 mm (Figure 5). However, both RF and GB models suggested a positive yet nonlinear relationship. Figure 4: Shapley-based feature importance of environmental variables for global explanations of soil organic matter content, expressed as mean Shapley values. For abbreviations, refer to Table 1.  
Figure 3: Global feature explanation through the Shapley additive explanation for three tree-based models. The range of Shapley values was computed for each explanatory variable to determine its impact on soil organic matter content. For abbreviations, refer to Table 1.  
When scrutinizing the association between soil organic matter content and other variables, all three models concurred on the positive nature of these relationships for precipitation, exchangeable K, and available P. Notably, only the DT model revealed a conspicuous stepwise linkage, discernible at the values of precipitation (1400 mm), K (1 cmol\({}^{+}\) kg\({}^{-1}\)), and available P (600 mg kg\({}^{-1}\)). Two-dimensional _PD_ plots were employed to visually determine the interaction effects between precipitation and exchangeable K (Figure 6). All models indicated that organic matter is contingent upon both precipitation and K. The observed patterns across all models displayed distinct divisions in the patterns along the K contents around the value of 1 cmol\({}^{+}\) kg\({}^{-1}\) and along the amount of precipitation of approximately 1400 mm. This observation strongly suggests the presence of an interaction effect between these variables. The presentation of _PD_ plots focusing on precipitation while conditioning on varying K thresholds effectively demonstrates this interaction effect (Figure 6). Specifically, as precipitation increased within the 1400-1700 mm range, the RF model showed a more gradual rise in soil organic matter content from 30.53 g kg\({}^{-1}\) to 33.66 g kg\({}^{-1}\) and 36.79 g kg\({}^{-1}\), smoothing out the potential anomalies through averaging multiple outputs, while the GB model displayed fluctuations, with predicted values falling from 7.48 g kg\({}^{-1}\) to 4.82 g kg\({}^{-1}\) before rising again to 7.48 g kg\({}^{-1}\), due to its sequential approach that may capture complex patterns as well as anomalies. In contrast, for DT and RF, the most important variables are precipitation and K, while for GB, the most crucial variables are precipitation and P, with K ranking fourth in importance, suggesting why there were fluctuations. The GB model recognized exchangeable K as one of the top five predictors but assigned it relatively lower importance (Figure 4),  
Figure 5: Partial dependence plots of soil organic matter content with precipitation (RN), exchangeable potassium (K), available phosphate (AP), and exchangeable calcium (Ca) (global explanations). indicating a different predictive behavior that might lead to the observed fluctuations. In contrast, the DT showed a different type of fluctuation, where the predicted values shifted from 30.89 g kg\({}^{-1}\) to 37.13 g kg\({}^{-1}\) and then settled at 34.01 g kg\({}^{-1}\), potentially reflecting overfitting to the training data, resulting in abrupt threshold effects.