# Comparison of Various Models for Optimal Water Distribution in Canal Systems
## 3 Results
### Results Analysis
#### 3.2.2 Model Comparison Results  
The total duration of water distribution is a key index in irrigation management. During the water distribution process, managers aim to develop a scheme with the shortest total duration. The total water distribution times for the five models are 127.19 h, 122.84 h, 121.91 h, 120.79 h, and 159.98 h, respectively. Irrigation Model 4 has the shortest total water distribution time, while Irrigation Model 5 has the longest. The total duration of water distribution is similar in Models 1 through 4, with minimal differences being exhibited. Figure 9 shows changes in flow rate in the branch canal in the five models. The design flow of the branch canal is 1.8 m\({}^{3}\)/s, and the flow rate should be maintained between 1.08 and 1.8 m\({}^{3}\)/s. The flow rates for the canals in Irrigation Models 1 to 5 fluctuate within ranges of 1.08 to 1.8 m\({}^{3}\)/s, 1.08 to 1.8 m\({}^{3}\)/s, 1.6 to 1.8 m\({}^{3}\)/s, and 1.1 to 1.8 m\({}^{3}\)/s, respectively. Throughout the entire water distribution process, the gates in Irrigation Models 1 to 5 are adjusted eleven times, six times, eleven times, five times, and nine times, respectively. Compared with the other models, Irrigation Model 4 exhibits the least fluctuation in flow rate, and requires the fewest gate adjustments. This model optimizes the engineering capacity of the canal, reduces flow rate fluctuations, and ensures a relatively stable flow rate in the branch canal. In contrast, Irrigation Models 1, 2, and 3 exhibit wider fluctuations in flow rate, particularly during the later stages of water distribution. This is because, as most canals complete their water distribution, the number of active canals decreases, resulting in a corresponding decrease in the flow rate of the branch canal. Operability for managers primarily concerns the sequence of opening and closing gates, whether from upstream to downstream or vice versa, during the water distribution process. Figure 10 shows the opening sequence of the tertiary canals in the five models. A greater fluctuation in the gate-opening curve indicates more operational complexity for the manager. In Irrigation Model 1, each gate is opened sequentially from Canal 1 to Canal 19, and the downstream canal gates will not be opened before the upstream gates. Similarly, in Irrigation Model 2, the gates are opened one by one, but in reverse order, from  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Tertiary** & **Flow Rate** & **Flow Rate** & **Flow Rate** & **Flow Rate** & **Flow Rate** \\
**Canal** & **of Model 1** & **of Model 2** & **of Model 3** & **of Model 4** & **of Model 5** \\
**(m\({}^{3}\)s\(  
Canal 19 to Canal 1. In Irrigation Model 3, all canals are divided into three groups, and in Irrigation Model 4, they are divided into six groups. This type of distribution model leads to grouping of canals with long distances between upstream and downstream, causing the gate-opening sequence curves to fluctuate more widely. Irrigation Model 5 exhibits the most significant fluctuations in the curves, indicating that managers need to travel frequently between upstream and downstream sections of the branch canal to open the gates. Figure 11 shows the closing sequences of the tertiary canals in the five models. Due to variations in the duration of each canal's water distribution, the order in which the gates are closed differs from the opening order. In Irrigation Models 1 and 2, the gates are not closed in the same upstream-to-downstream order as during opening. Figure 10: Opening sequences of the tertiary canals in the five models. Figure 9: Flow rates of the branch canal in the five models. The leakage losses for Irrigation Models 1 to 5 are 28 \(\times\) 10\({}^{3}\) m\({}^{3}\), 27 \(\times\) 10\({}^{3}\) m\({}^{3}\), 33 \(\times\) 10\({}^{3}\) m\({}^{3}\), 36 \(\times\) 10\({}^{3}\) m\({}^{3}\), and 48 \(\times\) 10\({}^{3}\) m\({}^{3}\), respectively. Irrigation Model 2 exhibits the smallest leakage loss, while Irrigation Model 5 has the largest leakage loss.