## 3 Results
### Influence of Check Dam Heights and Spacings on Infiltration Rate of Grassed Channel  
The influence of check dam heights and spacings of a grassed channel on the amount of runoff reduction by infiltration process was evaluated using the newly developed model. It was assumed that the channel section was trapezoidal with a length = 60 m, bottom width = 0.2 m, side slope \(m=3\), and longitudinal slope = 0.3%. The channel was assumed to be uniformly covered with a similar type of soil and grass cover. A steady inflow rate of \(Q\) = 0.055 m\({}^{3}\)/s was considered as a design discharge. The effects of check dam heights and spacing on the infiltration rate of grassed channel were investigated using five check dam system cases, as detailed in Table 3. Different sections were created in the grassed channel to represent the spacing between two check dams (Figure 9). The evaluation of the water depth, flow variations, and infiltration rates was performed at the middle of each channel section. Figure 9: Side view of the channel for different check dam design cases: (**a**) case 1, case 2, and case 3; (**b**) case 4; (**c**) case 5. The values of \(t_{\rm d}\), \(t_{\rm p}\), and \(y\) for all design cases were calculated by fitted non-linear regression equations, as shown in Figure 6a-c. For example, the value of \(y\) (m) for Section 1 in case 1 was determined using the equation presented in Figure 6c. The obtained values of \(Q_{in}\) and \(y_{\rm p}\) were 0.055 m\({}^{3}\)/s and 0.2053 m, respectively. The depth was observed to decrease along the channel due to an infiltration-induced reduction of flow rate. The equations in Figure 6a,b were used to calculate the values of \(t_{\rm d}\) and \(t_{\rm p}\) at Section 1 for \(h_{w}\) = 10 cm, \(L\) = 10 m, and \(Q_{in}\) = 0.055 m\({}^{3}\)/s. Obtained values were \(t_{\rm d1}\) = 0.244 min (or 14.6 s), and \(t_{\rm p1}\) = 0.284 min (or 17 s). The values of \(t_{\rm d}\) and \(t_{\rm p}\) for the rest of the sections were calculated in the same manner by considering the flow rates. Moreover, the flow variations at channel sections and related water levels were estimated from the infiltration rate at different times. Because Figure 6a,b was developed from a channel with 10 m spacing of downstream check dams, the values of \(t_{\rm d}\) and \(t_{\rm p}\) were multiplied by 2 and 3 in cases 4 and 5, respectively, in order to fit their spacing of 20 and 30 m (Figure 9). The differences in the water levels for different check dam design cases are shown in Figure 10. The figure shows a decrease in the water level in the downstream of the channel due to infiltration through the channel. However, the water level showed a time-dependent increase in each section due to the lower rate of infiltration along the channel over time. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Height \(h_{\rm d}\) (cm)** & **Spacing \(L_{d}\) (m)** & **Number of Sections** \\ \hline
1 & 10 & 10 & 6 \\
2 & 15 & 10 & 6 \\
3 & 20 & 10 & 6 \\
4 & 20 & 20 & 3 \\
5 & 20 & 30 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Details of the check dam system design cases used for the estimation of the effects of check dam heights and spacing on the infiltration rate of grassed channel. Figure 10: \(Cont.\)  
Figure 11 presents the variations in \(F\) over time for the five considered cases. Figure 11a-c shows a higher value of \(F\) for a higher value of \(h_{w}\) at all channel sections. For the comparisons among Figure 11c-e, the values of \(F\) in all sections were summed at a specific time due to the differences of section lengths. The comparison revealed that a decrease in spacing of check dams had a very low impact on the infiltration rate. For more clarification, the total inflow, outflow, and infiltration volumes after 90 min for the five cases are presented in Table 4, whereas Figure 12 shows a comparison of the percentage of the total volume of conveyed water and the total volume of infiltrated water.