## 3 Results and Discussion  
### Comparison of the Accuracy of Various Machine Learning Models  
The overall and average performance of each data-driven model in the seven different climatic zones is shown in Tables 2 and 3, respectively. As listed in Table 2, averaged across the six input combinations and the seven climatic zones, the XGBoost model (on average R\({}^{2}\) = 0.964, RMSE = 2.066 \({}^{\circ}\)C, MAE = 1.597 \({}^{\circ}\)C) overall performed better in T\({}_{\rm s}\) estimation than the RF (on average R\({}^{2}\) = 0.959, RMSE = 2.130 \({}^{\circ}\)C, MAE = 1.647 \({}^{\circ}\)C) and M5P models (on average R\({}^{2}\) = 0.954, RMSE = 2.280 \({}^{\circ}\)C, MAE = 1.742 \({}^{\circ}\)C). Among the six input combinations, models with the complete combination of meteorological variables as inputs (i.e., the input combination 1) had the greatest estimating accuracy in each of the seven climatic zones (Table 3). Under this input combination, averaged across the meteorological stations in each climatic zone, the ranges of the mean statistical indicator values for M5P1, RF1, and XGBoost1 at different climatic zones were 1.722-2.875 \({}^{\circ}\)C, 1.354-2.257 \({}^{\circ}\)C, and 1.342-2.208 \({}^{\circ}\)C for RMSE, 0.928-0.975, 0.956-0.984, and 0.959-0.985 for R\({}^{2}\), and 1.245-2.106 \({}^{\circ}\)C, 1.028-1.702 \({}^{\circ}\)C, and 0.992-1.651 \({}^{\circ}\)C for MAE, respectively. The second best estimating accuracy among input combinations was observed in models with the combination of T\({}_{\rm mean}\) and R\({}_{\rm s}\) (i.e., the input combination 4) as inputs, which were M5P4, RF4, and XGBoost4 (with corresponding ranges of 1.658-2.830 \({}^{\circ}\)C, 1.506-2.556 \({}^{\circ}\)C, and 1.446-2.435 \({}^{\circ}\)C for RMSE, 0.929-0.975, 0.941-0.980, and 0.9494-0.983 for R\({}^{2}\), and 1.214-2.093 \({}^{\circ}\)C, 1.119-1.915 \({}^{\circ}\)C, and 1.084-1.840 \({}^{\circ}\)C for MAE, respectively). Although input combination 4 yielded slightly worse model accuracy than the complete combination, it required less input variables and a much smaller dataset. It was noted that models with T\({}_{\rm mean}\) as inputs all achieved relatively good performance in estimation, including models with the complete input combination (M5P1, RF1, and XGBoost1) and the combinations of T\({}_{\rm mean}\) and RH (M5P3, RF3, and XGBoost3), T\({}_{\rm mean}\) and R\({}_{\rm s}\) (M5P4, RF4, and XGBoost4) and T\({}_{\rm mean}\) and U\({}_{2}\) (M5P6, RF6, and XGBoost6). These results confirm the argument that temperature is the most fundamental meteorological factor for data-driven models in estimating T\({}_{\rm s}\). Among the other three meteorological factors, R\({}_{\rm s}\) had the highest degree of influence on estimating accuracy, followed by RH, and then U\({}_{2}\). Therefore, considering the model estimating accuracy and the size of input data jointly, models using the input combination of T\({}_{\rm mean}\) and R\({}_{\rm s}\) would have a higher potential in T\({}_{\rm s}\) estimation across different climatic zones in China than models with other input combinations. For the three algorithms in this study, the overall model performance was generally ranked as XGBoost > RF > MSP with any of the input combinations in any of the climatic zones, with the exception that M5P2 was always better than RF2 in all climatic zones and even better than XGBoost2 in some climatic zones (e.g., NWC, IM, and QTP).