## 3 Results and Discussion
### Comparison of the Accuracy of Various Machine Learning Models
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Different**} & \multicolumn{3}{c}{**MSP**} & \multicolumn{3}{c}{**RF**} & \multicolumn{3}{c}{**XGBoost**} \\ \cline{2-10}  & **RMSE** & **R\({}^{2}\)** & **MAE** & **RMSE** & **R\({}^{2}\)** & **MAE** & **RMSE** & **R\({}^{2}\)** & **MAE** \\ \hline NWC & 2.358 & 0.971 & 1.800 & 2.213 & 0.974 & 1.709 & 2.175 & 0.976 & 1.694 \\ IM & 2.679 & 0.967 & 2.071 & 2.486 & 0.971 & 1.944 & 2.417 & 0.974 & 1.907 \\ NEC & 2.912 & 0.957 & 2.211 & 2.700 & 0.963 & 2.075 & 2.584 & 0.967 & 1.988 \\ NC & 2.197 & 0.966 & 1.688 & 2.042 & 0.970 & 1.588 & 1.984 & 0.973 & 1.539 \\ CC & 1.748 & 0.961 & 1.302 & 1.643 & 0.965 & 1.239 & 1.608 & 0.970 & 1.202 \\ SC & 1.735 & 0.925 & 1.330 & 1.645 & 0.931 & 1.274 & 1.604 & 0.941 & 1.226 \\ QTP & 2.330 & 0.930 & 1.794 & 2.181 & 0.938 & 1.697 & 2.090 & 0.945 & 1.625 \\ \hline Mean & 2.280 & 0.954 & 1.742 & 2.130 & 0.959 & 1.647 & 2.066 & 0.964 & 1.597 \\ \hline \hline \end{tabular}  
* **Note:** RMSE and MAE are in \({}^{\circ}\)C.  
\end{table} 
Table 2: Summary of the performance of data-driven models for soil temperature in different climate zones of China. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**NWC**} & \multicolumn{3}{c}{**NWC**} & \multicolumn{3}{c}{**NWC**} & \multicolumn{3}{c}{**NWC**} & \multicolumn{3}{c}{**NWC**} & \multicolumn{3}{c}{**CC**} & \multicolumn{3}{c}{**SC**} & \multicolumn{3}{c}{**S**} & \multicolumn{3}{c}{**QTP**} \\ \cline{2-13}
**Model** & **RMSE** & \(\mathbf{R^{2}}  
The box plots of the RMSE values of the three data-driven models (i.e., M5P, RF, and XGBoost models) for estimating T\({}_{\rm s}\) with the six input combinations at the 689 stations of China are shown in Figure 3. The RMSE values of the XGBoost model under the six input combinations were 1.001-2.823 \({}^{\circ}\)C, 1.272-3.480 \({}^{\circ}\)C, 1.121-3.259 \({}^{\circ}\)C, 1.050-2.981 \({}^{\circ}\)C, 1.173-3.540 \({}^{\circ}\)C, and 1.231-3.422 \({}^{\circ}\)C, respectively, which overall were lower than the corresponding values of the M5P model (1.241-3.618 \({}^{\circ}\)C, 1.056-3.447 \({}^{\circ}\)C, 1.133-3.638 \({}^{\circ}\)C, 1.174-3.478 \({}^{\circ}\)C, 1.250-4.059 \({}^{\circ}\)C, and 1.107-3.758 \({}^{\circ}\)C, respectively) or the RF model (1.051-2.873 \({}^{\circ}\)C, 1.082-3.611 \({}^{\circ}\)C, 1.111-3.431 \({}^{\circ}\)C, 1.090-3.123 \({}^{\circ}\)C, 1.170-3.761 \({}^{\circ}\)C, and 1.153-3.619 \({}^{\circ}\)C, respectively). Averaged across all stations, the mean RMSE values for the XGBoost model under the six input combinations decreased by 23.1%, \(-\)1.4%, 5.5%, 13.2%, 11.2%, and 3.4% when compared with the M5P model, and by 3.0%, 1.4%, 1.9%, 4.3%, 4.5%, and 1.7% when compared with the RF model. The median RMSE values of the three models showed a similar pattern to the mean RMSE values. These results together indicated that, among the three models in this study, the XGBoost model had the highest overall performance, followed by the RF model and then the M5P model. Figure 3: Box plots of the RMSEs of the three models for estimating T\({}_{\rm s}\) under six input combinations (**a–f**).