# Comparison of Various Models for Optimal Water Distribution in Canal Systems
## 3 Results
### Results Analysis  
#### 3.2.1 Model Results  
The five water distribution models discussed in this paper were applied to the Fengqigou branch canal. The results of the water distribution are as follows; Table 2 presents the results of the water distribution duration for each tertiary canal in the five models: \begin{table}
\begin{tabular}{c c c c} \hline
**Name of Canal** & **Design Flow Rate (m\({}^{3}\)s\({}^{-1}\))** & **Crop Area (ha)** & **Water Requirement (m\({}^{3}\))** \\ \hline Tertiary canal 7 & 0.6 & 49.5 & 26,730 \\ Tertiary canal 8 & 0.6 & 71.9 & 38,826 \\ Tertiary canal 9 & 0.5 & 45.7 & 24,678 \\ Tertiary canal 10 & 0.8 & 104.2 & 56,268 \\ Tertiary canal 11 & 0.5 & 61.8 & 33,372 \\ Tertiary canal 12 & 0.8 & 94.1 & 50,814 \\ Tertiary canal 13 & 0.8 & 115.8 & 62,532 \\ Tertiary canal 14 & 0.8 & 74.8 & 40,392 \\ Tertiary canal 15 & 0.5 & 54.9 & 29,646 \\ Tertiary canal 16 & 0.5 & 84.3 & 45,522 \\ Tertiary canal 17 & 0.5 & 64.2 & 34,668 \\ Tertiary canal 18 & 0.5 & 68.5 & 36,990 \\ Tertiary canal 19 & 0.6 & 54.3 & 29,322 \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 3: Schematic diagram of canal location. Figures 4 and 5 show the start and end times of water distribution for each tertiary canal in Irrigation Model 1 and Irrigation Model 2, respectively. These two models follow an upstream-to-downstream sequence for the tertiary canals. When the water distribution of the upstream tertiary canal is completed and the flow rate in the branch canal meets the flow rate requirement of the next tertiary canal, the next canal begins its water distribution. During the water distribution process, water will not bypass an upstream canal to be distributed to a downstream canal. These two types of irrigation model are still widely used in major irrigation districts due to their simplicity and lack of complex logical relationships. The total water distribution times for Irrigation Model 1 and Irrigation Model 2 are 127.19 h and 122.84 h, respectively. Figure 6 shows the start and end times of water distribution for each tertiary canal in Irrigation Model 3, \"Continuous Irrigation Between Groups and Rotational Irrigation Within Groups\". Canals within the same group are irrigated in a rotational manner, while canals between different groups are irrigated simultaneously. The model divides 19 tertiary canals into three groups, as shown in Table 3. During the water distribution process, the duration for each group is the sum of the water distribution times for all canals within the group. Therefore, the distribution durations for the first, second, and third groups are 120.98 h, 121.91 h, and 121.45 h, respectively. The total water distribution duration for the canals is determined by the longest duration among the three groups, which is 121.91 h.  
Figure 5: Start and end times for each tertiary canal in Irrigation Model 2. Figure 6: Start and end times for each tertiary canal in Irrigation Model 3. Figure 7 shows the start and end times of water distribution for each tertiary canal in Irrigation Model 4. In this model, canals are irrigated rotationally between groups, while canals within the same group are irrigated simultaneously. The model divides 19 tertiary canals into six groups, as shown in Table 4. The water distribution duration for each group is determined by the canal with the longest distribution duration within that group. The irrigation durations for each group, from Group 1 to Group 6, are 18.99 h, 17.88 h, 21.71 h, 25.69 h, 19.54 h, and 16.98 h, respectively. The total duration for all canals is the sum of the durations for the six groups, which is 120.79 h. The differences in irrigation durations for canals within the same group are minimal. If the difference is small enough, as determined by a rational optimization model, the manager can operate the gates of the canals simultaneously, making canal management more convenient. Figure 8 shows the start and end times of water distribution for each tertiary canal in Irrigation Model 5.