## 3 Results and Discussion
### Comparison of the Spatial Distribution of Errors in Estimating Soil Temperature  
Spatial distributions of the performance in estimating T\({}_{\rm s}\) for the data-driven models with all climatic variables as inputs (M5P1, RF1, and XGBoost1 models) are shown in Figure 4. Generally, the models all performed well in estimating T\({}_{\rm s}\) at the majority of stations, with the values of RMSE less than 2.0 \({}^{\circ}\)C and the values of MAE less than 1.50 \({}^{\circ}\)C at 76.8% of all stations studied. Overall, there was some spatial variation in model performance between climatic zones. The accuracy of the model was relatively better in the CC and SC regions than in other regions, while the model performance was relatively poor in the NEC region, especially in the northeast provinces of China. Among the three models, M5P1 had the worst performance in estimation, with RMSE values greater than 2.01 \({}^{\circ}\)C and MAE values greater than 1.50 \({}^{\circ}\)C in up to 47.7% of the stations in all regions, except for the CC region where only a small fraction of stations had similar poor performance. On the contrary, the XGBoost1 model had the most satisfactory in estimating T\({}_{\rm s}\), with RMSE values less than 1.51 \({}^{\circ}\)C and MAE values less than 1.25 \({}^{\circ}\)C in most stations of all regions, except for the NEC region. The performance of the M5P2, RF2, and XGBoost2 models for estimating T\({}_{\rm s}\) are illustrated in Figure S1. The three models were trained using T\({}_{\rm mean}\) as the only input available. The three models generally had a positive performance in estimating T\({}_{\rm s}\) at the majority of stations, with RMSE values greater than 2.01 \({}^{\circ}\)C and MAE values greater than 1.50 \({}^{\circ}\)C at 48.8% of the stations. Although there was still relatively good estimating accuracy in some stations of the CC and SC regions, the overall performance of the three models was poor in other regions of this study. In particular, the IM and NEC regions had up to 71.9% of the stations with model RMSE values greater than 2.51 \({}^{\circ}\)C and MAE values greater than 2.00 \({}^{\circ}\)C. Overall, the estimation accuracy of the XGBoost2 model was slightly greater than both other models. These results suggest that there is space for improvement in the estimation accuracy of the three models when using T\({}_{\rm mean}\) as the only input. Our findings also confirm the conclusion of [PERSON]'s study that the appropriate addition of other meteorological factors to T\({}_{\rm mean}\) could effectively improve model performance in estimating T\({}_{\rm s}\)[59]. The spatial distribution of the performance for the data-driven models (M5P3, RF3, and XGBoost3 models) on T\({}_{\rm s}\) estimation with T\({}_{\rm mean}\) and RH as inputs is illustrated in Figure S2. The models generally had positive performance in estimating T\({}_{\rm s}\) at the majority of stations, with RMSE values less than 2.0 \({}^{\circ}\)C and MAE values less than 1.50 \({}^{\circ}\)C at56.2% of the stations. Among the climatic zones, the three models performed relatively better in the CC region than other regions, while the poorest model performance was observed in the NEC region, where the RMSE and MAE values in 78.5% of the stations were greater than 2.51 \({}^{\circ}\)C and 2.00 \({}^{\circ}\)C, respectively. Models showed very similar estimating performance between the NWC and the QTP regions. Compared with the M5P1, RF1, and XGBoost1 models, the accuracy of models with only T\({}_{\text{mean}}\) and RH as inputs was slightly worse. Therefore, reducing the number of meteorological factors as inputs would lower the estimation performance of each model, which is consistent with findings obtained by [PERSON] et al. [60]. This result suggests that using a complete set of relevant meteorological factors as inputs in studies of T\({}_{\text{s}}\) estimation could effectively improve the estimating performance of models, which confirms the findings from previous studies [61].