## 3 Results
### Single-Objective Optimisation Parameters  
In this section, we first show the results of single-objective optimizations, where the objective variables are any one of \(\theta\), \(T\), \(h\), \(q\). The optimal parameters obtained under these four single-objective scenarios, which show differences in estimated hydraulic and thermal parameters, are presented in Table 2. In particular, the disparity is obvious when using \(T\) as the objective variable. To visually compare the simulation results, we normalize Table 2 according to the parameter ranges and plot a radar chart (Figure 2). The figure shows that when \(T\) (red circles) is used as the objective variable, most of the optimal parameters, particularly \(\theta_{r}\), \(\theta_{s}\), and \(n\), differ from those obtained for other objectives. Additionally, under different single-objective scenarios, parameters \(b_{1}\), \(b_{2}\), and \(b_{3}\) exhibit significant variability. This reflects the differing behaviors of water and heat transport dynamics in parameter inversion. Based on this, we speculate that \(T\) has low sensitivity to hydraulic parameters. Based on these optimal hydraulic and thermal parameters, we simulate the coupled water vapor heat transport during 1 July 2019-31 October 2019, and compare the model predicted values of \(\theta\), \(T\), \(h\), \(q\) with those of \"true\" observations. The period from 1 July-30 September is used as the calibration period, and from 1 October-31 October as the validation period. Figure 3 shows the variations in \(\theta\) (Figure 3a), \(T\) (Figure 3b), \(h\) (Figure 3c), and \(q\) (Figure 3d) at depths of 5 cm, 10 cm, 20 cm, 50 cm, and 100 cm under different single-objective functions, where the black circles represent the observed values, and the black, blue, green, and red lines represent the simulated values when the objective variable is \(\theta\), \(T\), \(h\), and \(q\), respectively. In general, the simulation performs better when using \(\theta\) or \(h\) as the objective variable, particularly for the simulation of \(\theta\) and \(h\). However, the simulation results are poorer when \(T\) is used as the objective variable, except for the simulation of \(T\) itself, which performs well. This also corresponds to Figure 2, where the optimal parameters obtained under this objective function are different from compared to those obtained with other objectives. Additionally, when \(q\) is used as the objective variable, the simulation of water movement performs better than when \(T\) is used, but the accuracy is not as high as when \(\theta\) or \(h\) is used as the objective variable. Therefore, we infer that \(\theta\) and \(h\) are important factors in water movement, and thus using \(\theta\) or \(h\) as the objective variable \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{4}{c}{**Objectives**} \\ \cline{2-5}  & \(\theta\) & \(T\) & \(h\) & \(q\) \\ \hline \(\theta_{\mathrm{r}}\) & 0.014 & 0.010 & 0.015 & 0.018 \\ \(\theta_{\mathrm{s}}\) & 0.291 & 0.316 & 0.288 & 0.288 \\ \(\alpha\) & 0.071 & 0.108 & 0.058 & 0.099 \\ \(n\) & 1.558 & 1.716 & 1.607 & 1.500 \\ \(K_{\mathrm{s}}\) & 457.088 & 512.861 & 457.088 & 977.237 \\ \(l\) & 0.160 & 0.440 & 0.700 & 0.520 \\ \(b_{1}\) & 127.900 & 133.500 & 129.100 & 135.700 \\ \(b_{2}\) & \(-\)503.500 & \(-\)509.900 & \(-\)510.000 & \(-\)516.600 \\ \(b_{3}\) & 1511.000 & 1511.100 & 1503.900 & 1512.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters obtained from single-objective optimization. can better simulate water movement. In contrast, \(T\) has limited effectiveness in simulating hydraulic parameters, and thus cannot simulate water movement well. \(q\), which combines both thermal and hydraulic processes, can better simulate water movement when used as the objective variable.