## 5 Verification and Comparison of the Developed Lower-Depth Soil Temperature Evaluation Model
### Experimental Verification of the Developed Lower-Depth Soil Temperature Evaluation Model  
In order to verify the proposed method for lower-depth soil temperature evaluation, additional data from the other site (site C in Figure 2) were collected. The soil temperature measurements at the uppermost depth are plotted in Figure 10. Following the procedure presented in Section 5.1, the parameters \(A\), \(Z\), and \(CRCST_{i,mmax}\) were obtained (Table 3). Implementing the developed model using the values in Table 3 for different depths, we can compare the measured soil temperatures and the corresponding predicted values using \(T_{ud}\) data (Figure 11). Figure 10: Daily average soil temperature at the uppermost depth in the site C.  
The average and the maximum measured soil temperatures at the depth of 10 cm were 7.1 \({}^{\circ}\)C and 14.5 \({}^{\circ}\)C, respectively, while their predicted values were 6.6 \({}^{\circ}\)C and 17.5 \({}^{\circ}\)C, respectively. The average and the maximum measured soil temperatures (the corresponding predicted values are in parentheses) were 6.0 \({}^{\circ}\)C (4.7 \({}^{\circ}\)C) and 11.4 \({}^{\circ}\)C (12.4 \({}^{\circ}\)C), respectively, for the depth of 15 cm, 5.2 \({}^{\circ}\)C (3.8 \({}^{\circ}\)C) and 10.0 \({}^{\circ}\)C (9.6 \({}^{\circ}\)C), respectively, for the depths of 20 cm, and 2.7 \({}^{\circ}\)C (2.7 \({}^{\circ}\)C) and 5.9 \({}^{\circ}\)C (7.1 \({}^{\circ}\)C), respectively, for the depth of 30 cm. The difference in the average and the maximum soil temperatures between the measured and the predicted values ranged 0-1.4 \({}^{\circ}\)C and 0.4-3.0 \({}^{\circ}\)C, respectively. These differences in soil temperature prediction result from imperfection of soil temperature model. The developed soil temperature prediction model in this study has an advantage of simplicity associated with fewer calculations using only three fitting parameters, and reasonably predicts shallow depth soil temperatures. Figure 12 compares the measured and predicted soil temperatures at each depth of the site C. From the regression analysis, it can be seen that the relationship between the measured and the predicted values produced a high R\({}^{2}\) value (ranging from 0.8733 to 0.9106). This result is an improvement of the previously proposed model [56]. From Figure 12, the soil temperature prediction at the depth of 10 cm showed the highest uncertainty, resulting in the highest scatteredness of data point and the lowest R\({}^{2}\) value. It was noted that the uncertainty of soil temperature tends to slightly decrease as the soil temperature at the deeper depth is less influenced by the dynamic variation of air temperature. Figure 11: Measured and predicted temperature curves for additional data at depths of (**a**) 10 cm; (**b**) 15 cm; (**c**) 20 cm; and (**d**) 30 cm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Depth (cm)** & **Fitting Parameter _A_** & **Fitting Parameter _Z_** & \(CRCST_{i,mmax}\) \\ \hline
10 & 3.8452 & 1.3804 & 621.259 \\
15 & 3.8812 & 1.1687 & 407.675 \\
20 & 3.9070 & 1.9046 & 302.345 \\
30 & 3.9436 & 2.2992 & 198.401 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Values of the fitting parameters \(A\) and \(Z\) and \(CRCST_{i,mmax}\) for the site C.  
As pointed out by [PERSON] et al. [57], the advantage of using long-term data of the daily average temperature for several seasons or longer is that it reduces the deviation of prediction and the variation of temperature, which is mainly caused by climatic and ground conditions. Thus, this study used long-term lower-depth soil temperature data to develop depth profiles of soil temperature and to experimentally verify the prediction model. Consequently, an effective and practical lower-depth soil temperature prediction model was developed. The model enables the estimation of soil temperature in various areas and strata, instead of predicting the soil temperature at one elevation.