## 3 Results
### Multi-Objective Optimisation Parameters  
Subsequently, we continue to explore the impact of multiple objectives (\(\theta+T+h\), \(\theta+T\) + \(q\), \(\theta+h+q\), \(T+h+q\), and \(\theta+T+h+q\)) on parameter optimization. The 3D and 4D Pareto surfaces yield dual-objective trade-off fronts similar to those obtained in the dual-objective case, so they are not presented here. Simulation of the hydrothermal dynamics of soil based on a compromise solution obtained using multi-objective optimization. Figure 9 presents the simulation results of \(\theta\) (Figure 9a), \(T\) (Figure 9b), \(h\) (Figure 9c), and \(q\) (Figure 9d) at depths of 5 cm, 10 cm, 20 cm, 50 cm, and 100 cm under different triple- and quadruple-objective functions. Compared with the dual-objective optimization, considering one or two more variables can improve the simulation results to a certain extent. However, due to the interaction between these variables, considering multiple variables simultaneously does not necessarily lead to better simulation results.  
To more clearly reflect the differences in parameter inversion under different objectives, we present the \(R^{2}\), \(RMSE\), \(MAE\), and \(d\) values for the entire profile during the calibration and validation periods, comparing the simulated and observed values (Tables 3 and 4). In general, some of the simulation results during the validation period are better than those during the calibration period. We speculate that this is primarily due to two reasons: first, the climate in October shows less variation, and the fluctuations in the surface layer of the soil are smoother, leading to better simulation results; second, the validation period we selected might be relatively short. From an economic perspective, since \(\theta\) and \(T\) data are  
Figure 8: The 1:1 line plots of \(\theta\) (**a–f**), \(T\) (**g–l**), \(h\) (**m–r**), and \(h\) (**s–x**) for dual-objective functions optimization (\(\theta+T\), \(\theta+h\), \(\theta+q\), \(T+h\), \(T+q\), \(h+q\)). The dark blue, red, green, light blue, and orange circles represent observation depths of 5 cm, 10 cm, 20 cm, 50 cm, and 100 cm, respectively.  
relatively easy to obtain and can be measured simultaneously in the field, we compare the simulation performance when using \(\theta\), \(T\), and \(\theta+T\) as objective variables. We find that, based on \(\theta\) as the objective variable, incorporating \(T\) improves the simulation performance. Therefore, using both \(\theta\) and \(T\) as objective variables enables the model to more effectively simulate the soil water, vapor, and heat processes.  
Figure 9: Comparisons of simulated and observed values of (**a**) \(\theta\), (**b**) \(T\), (**c**) \(h\), and (**d**) \(q\) at depths of 5 cm, 10 cm, 20 cm, 50 cm, and 100 cm for different multi-objective functions, where the black circles represent the observed values and the black, green, dark blue, light blue, and red lines represent the simulated values when the objective variable are \(\theta+T+h\), \(\theta+T+q\), \(\theta+h+q\), \(T+h+q\), \(\theta+T+h+q\), respectively.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Water content**} & \multicolumn{4}{c}{**Temperature**} & \multicolumn{4}{c}{**Male potential**} & \multicolumn{4}{c}{**Heat flux**} \\
**Objectives** & \(R^{2}\) & \(RMSE\) & \(MAE\