## 3 Results and Discussion
### Comparison of the Spatial Distribution of Errors in Estimating Soil Temperature
The spatial distribution of estimating performance for M5P4, RF4, and XGBoost4 models that were trained with T\({}_{\text{mean}}\) and R\({}_{\text{s}}\) as inputs are illustrated in Figure S3. The models all showed positive performance in modeling T\({}_{\text{s}}\) for a large proportion of stations, with RMSE values less than 2.0 \({}^{\circ}\)C and MAE value less than 1.50 \({}^{\circ}\)C at up to 71.6% of the stations. Among the climatic zones, the estimating accuracy of the three models was relatively excellent in the CC and SC regions, with RMSE values less than 1.50 \({}^{\circ}\)C and MAE values less than 1.25 \({}^{\circ}\)C at 45.5% of the stations, while in contact the model performance in the NEC region was relatively poor, with up to 64.9% of the stations showing values of RMSE and MAE greater than 2.51 \({}^{\circ}\)C and 1.75 \({}^{\circ}\)C, respectively. Among the three models, the estimating performance of XGBoost4 was slighter better than RF4, but both of them obviously outperformed M5P4. Overall, patterns of the spatial variability in model performance for this input combination (i.e., T\({}_{\text{mean}}\) and R\({}_{\text{s}}\)) were very similar to patterns shown in models with the complete combination of meteorological variables as inputs, indicating that the removal of RH and U\({}_{2}\) from the inputs did not noticeably decrease the estimation accuracy of models in this study. Moreover, the input combination of T\({}_{\text{mean}}\) and R\({}_{\text{s}}\) required far less meteorological data than the complete input combination. Therefore, it can be concluded that T\({}_{\text{mean}}\) and R\({}_{\text{s}}\) are key input variables for estimating T\({}_{\text{s}}\) in different climate zones, consistent with findings obtained by [PERSON] [59] and [PERSON] [21]. For the data-driven models with T\({}_{\text{max}}\) and T\({}_{\text{min}}\) as inputs (i.e., M5P5, RF5, and XGBoost5), the spatial distribution of their estimating performance is demonstrated in Figure S4. Overall, the three models performed poorly in estimating T\({}_{\text{s}}\) at most stations, with 55.8% of the stations showing the values of RMSE and MAE above 2.01 \({}^{\circ}\)C and 1.50 \({}^{\circ}\)C, respectively. Models with T\({}_{\text{max}}\) and T\({}_{\text{min}}\) as input variables performed worse than the M5P1, RF1, and XGBoost1 models, indicating that using temperature as the only input climatic variable would not be sufficient enough to obtain satisfactory model performance. The spatial distributions of the estimating performance for the M5P6, RF6, and XGBoost6 models that were trained using T\({}_{\text{mean}}\) and U\({}_{2}\) as inputs are shown in Figure S5. The three models showed poor performance in modeling T\({}_{\text{s}}\) at most stations, with RMSE values greater than 2.01 \({}^{\circ}\)C and MAE values greater than 1.50 \({}^{\circ}\)C at 58.7% of the stations. Although the estimating accuracy of the three models was relatively good in the CC region, their estimating performance was poor in other regions. For instance, in the IM and NEC regions, up to 78.4% of the stations showed values of RMSE and MAE greater than 2.51 \({}^{\circ}\)C and 2.00 \({}^{\circ}\)C, respectively. A combined comparison of Figures S2-S5 indicates that the models showed an overall trend of decreasing accuracy from south to north. This would lead us to think that it is related to latitude, whereas latitude could affect T\({}_{\text{s}}\) due to the angle of incidence by solar radiation [62]. Regarding the effect of latitude on T\({}_{\text{s}}\), scholars have reached similar conclusions in studies from other countries. In a study conducted by [PERSON] and [PERSON] [63] in the USA, it was concluded that T\({}_{\text{s}}\) decreased with increasing latitude. The model with inputs T\({}_{\text{mean}}\) and R\({}_{\text{s}}\) would be slightly more accurate in estimation than under several other combinations of inputs, which was very close to the performance of each model at full input of the parameter variables.