## 3 Results and Discussion
### Analysis of Factors Affecting the Model's Estimation of Soil Temperature
For example, the variability of T\({}_{\rm s}\) at different soil depths generally vary, with greater variability between measured and estimated values observed in deeper soils. The literature indicates that the thermal conductivity of soil decreases with increasing soil porosity but increases with increasing soil water content [74]. Therefore, both enhanced rainfall and reduced porosity could improve the thermal conductivity of the soil, which could make T\({}_{\text{s}}\) less variable [75]. In addition, the increase in the organic matter content of the soil also reduces the thermal conductivity [76]. The degree of irrigation, similar to precipitation, can indirectly affect the soil water content. The increase in soil water content increases the heat capacity in the soil, which results in a smaller range of variation in T\({}_{\text{s}}\)[74]. With combination 5 (i.e., including T\({}_{\text{max}}\) and T\({}_{\text{min}}\)) as inputs (Figure S6), the accuracy of each model at each station was lower than the accuracy of its corresponding model with the complete input combination, indirectly suggesting that adding more relevant meteorological factors to the inputs would improve the model performance in estimating T\({}_{\text{s}}\). This result is consistent with the conclusion made by [PERSON] et al. [2] and [PERSON] and [PERSON] [6]. Among the selected stations, the best-performing models were observed at station 56,188, where the R\({}^{2}\) values of the M5P, RF, and XGBoost models were 0.969, 0.971, and 0.976, respectively (Figure S6). For station 56,188 (within the CC region) and station 59,287 (within the SC region), the range of variations in T\({}_{\text{s}}\) was smaller than other stations within other climatic zones, resulting in the scatters of the regression at the two stations being denser than at other stations. This outcome might be due to the fact that these two stations are located at regions where the climatic difference between them is similar, but they are distinct from other stations in terms of climate. Similar patterns were found by other studies, in which the estimation of reference crop evapotranspiration (ET\({}_{0}\)) in different climatic zones was conducted [50]. Figure 5: Scatter plot of estimated T\({}_{\text{s}}\) versus measured T\({}_{\text{s}}\) from the three machine learning models with T\({}_{\text{mean}}\), RH, R\({}_{\text{s}}\), and U\({}_{\text{2}}\) as inputs. For combination 6 (i.e., including T\({}_{\rm mean}\) and U\({}_{2}\) as inputs), XGBoost models outperformed both RF and M5P models in terms of estimating accuracy, similar to other input combinations (Figure S7). Across the selected stations, the R\({}^{2}\) values of XGBoost models averaged 0.966, slightly higher than the RF and M5P models, which had the same estimating accuracy on average (both averaged R\({}^{2}\) = 0.960). Under this input combination, the accuracies of the M5P and RF models were very close at each of the stations. At some of the stations (e.g., stations 56,188 and 59,287), the M5P model even slightly outperformed the RF model. Among these stations, the best model performance in estimating T\({}_{\rm s}\) was observed in station 51,744, where the XGBoost model had the highest accuracy (R\({}^{2}\) = 0.976). Compared to models with input combination 5, there were improvements to some extent in the estimating accuracy of models with input combination 6 at all selected stations, except for station 59,287. The estimating accuracies of the M5P, RF, and XGBoost models at station 59,287 decreased by 2.0%, 2.5%, and 2.1%, respectively, when comparing the input combinations. This result might be due to the high variability of wind speeds in the region where station 59,287 was located, which could impair the model accuracy in estimation. A previous study by [PERSON] and [PERSON] (2018) had similar findings, which confirmed that U\({}_{2}\) could significantly affect the performance of estimated T\({}_{\rm s}\).