## 3 Result Analysis and Verification
### Comparison under the Hypothesis of Uniform Moisture Content  
The situation for the uniform moisture content distribution along the depth direction is first considered. A soil column model was established using the soil parameters in Table 1 to analyze the infiltration process, as shown in Figure 5, by setting the middle part as a monitoring section to observe the distribution of the moisture content. Meanwhile, the flow boundary was specified on the top surface (AB) to represent different rainfall intensities, and the others (AC, CD, BD) were assumed to be airtight. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameters** & \(K_{y}\)**(m/s)** & \(\theta_{s}\) & \(\theta_{r}\) & \(\theta_{0}\) & \(\alpha\)**/m\({}^{-1}\)** & \(n\) \\ \hline Value & \(5.8\times 10^{-6}\) & 0.4 & 0.015 & 0.2 & 1.5 & 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model calculation parameters. The comparative calculation under five rainfall intensities were carried out (1 \(\times\) 10\({}^{-7}\) m/s, 5 \(\times\) 10\({}^{-7}\) m/s, 1 \(\times\) 10\({}^{-6}\) m/s, 2 \(\times\) 10\({}^{-6}\) m/s, 4 \(\times\) 10\({}^{-6}\) m/s), and it should be noted that the selected rainfall intensity was numerically smaller than the saturated permeability coefficient because it is an unsaturated infiltration process. After theoretical calculation and numerical simulation, the distribution of the soil moisture profile at different times is shown in Figure 6, taking two rainfall intensities (\(q\) = 1 \(\times\) 10\({}^{-6}\) m/s and \(q\) = 1 \(\times\) 10\({}^{-7}\) m/s) as examples. It can be seen that with the increase in time, the scope of the soil wetting zone continued to expand, while the surface moisture content was higher, and gradually decreased towards the interior. In addition, the stratification of the soil moisture content profile can be clearly observed, that is, after the moisture content reaches the critical value, it will not change, but gradually and stably increase from top to bottom within the limit of critical moisture content. At the same time, the results between the proposed model and simulation are in good agreement, and the maximum error is no more than 5%, as shown in Table 2. Compared with the horizontal wetting front hypothesis of the traditional model, the result of the proposed model is more in line with the actual wetting front shape. Figure 5: Schematic diagram of model. Figure 6: Distribution map of soil moisture content profile at different moments under different rainfall intensities. The variation trend of the soil surface moisture content with time under different rainfall intensities can be obtained using Equation (8), following numerical simulation calculation and comparison, for which the results obtained are shown in Figure 7. It can be seen that the surface moisture content obtained by the improved model and simulation results have the same trend, and the maximum error is no more than 5%, as shown in Table 3, which proves the validity of model. Moreover, in the early stage, the surface soil moisture content increases nonlinearly, and it will gradually tend to a certain value after a while, that is, the critical moisture content. The rainfall intensity has a great impact on the increase rate, and the greater the rainfall intensity, the faster the increase in the moisture content, and the shorter the time required to reach the critical moisture content. Figure 8 shows the variation law of the wetting front depth with time for the improved model. It can be seen that the wetting front depth increases nonlinearly with time at first, and the lower the rainfall intensity, the longer the nonlinear duration, which corresponds to the transition stage. After a while, the wetting front depth increases linearly with time, and the greater the rainfall intensity, the greater its growth rate, which corresponds to the stable stage.