## 3 Results and Discussion
### Optimal Allocation Considering Return Flow (Model II)
#### 3.3.3 Results of Optimal Allocation of Water Resources (Model II)  
Table 14 presents the optimization results of irrigation water resources across different periods. When return flow resources are utilized for irrigation, the total water allocation for the current, short-term, and long-term years is 170, 162, and 159 million m\({}^{3}\), respectively. This represents an increase of 25, 17, and 14 million m\({}^{3}\) compared to the total water allocation without considering return flow. After reusing return flow resources, the irrigation diversion water allocation for the current, short-term, and long-term years ranges from [127, 133], [121, 127], and [119, 125] million m\({}^{3}\), respectively. These allocations are [12, 18], [18, 24], and [20, 26] million m\({}^{3}\) less than the irrigation diversion without considering return flow. Table 15 shows the optimization results of water allocation for crops over different periods. Only the water allocation for corn and flax has increased after utilizing return flow resources, while the water allocation for other crops remains unchanged. This is because corn and flax have high water productivity, and return flow resources are prioritized for crops with high water productivity to enhance irrigation efficiency. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Crop Type**} & \multicolumn{2}{c}{**Current**} & \multicolumn{2}{c}{**Short-Term**} & \multicolumn{2}{c}{**Long-Term**} \\ \cline{2-7}  & **Ignore Return** & **Consider** & **Ignore Return** & **Consider** & **Ignore Return** & **Consider** \\  & **Flow** & **Return Flow** & **Flow** & **Return Flow** & **Flow** & **Return Flow** \\ \hline Spring wheat & 15.90 & 15.90 & 15.40 & 15.40 & 15.18 & 15.18 \\ Corn & 35.34 & 35.51 & 33.73 & 33.90 & 33.13 & 33.29 \\ Flax & 2.95 & 27.61 & 9.49 & 26.60 & 12.03 & 26.16 \\ Potato & 16.73 & 16.73 & 15.77 & 15.77 & 15.43 & 15.43 \\ Melon & 9.57 & 9.57 & 9.31 & 9.31 & 9.19 & 9.19 \\ Goji berry & 13.12 & 13.12 & 12.08 & 12.08 & 11.67 & 11.67 \\ Forest fruits & 51.40 & 51.40 & 49.20 & 49.20 & 48.36 & 48.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Results of water allocation optimization for various crops during different periods (10\({}^{6}\) m\({}^{3}\)). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Period**} & \multicolumn{2}{c}{**Ignore Return**} & \multicolumn{2}{c}{**Consider Return Flow**} & \multicolumn{2}{c}{**Reduction of**} \\ \cline{2-5}  & **Irrigation** & **Total Water** & **Irrigation** & **Return Flow** & **Irrigation** \\  & **Diversion** & **Volume** & **Diversion** & **Return Flow** & **Diversion** \\ \hline Current & \(145\) & 170 & [127, 133] & [37, 43] & [12, 18] \\ Short-term & \(145\) & 162 & [121, 127] & [35, 41] & [18, 24] \\ Long-term & 145 & 159 & [119, 125] & [34, 40] & [20, 26] \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Optimization results of irrigation water in different periods (10\({}^{6}\) m\({}^{3}\)). In conclusion, utilizing return flow resources for farmland irrigation offers multiple benefits. It increases the amount of irrigation water available, improves efficiency, and avoids negative impacts on the Yellow River's water ecological environment. Additionally, it reduces the amount of water diverted from the Yellow River, conserves water resources, and lowers the power costs associated with irrigation and water extraction. Currently, some scholars are researching the optimization of water resources and surplus energy in irrigation systems [36]. The primary focus of optimal water resource allocation in irrigation areas is on upstream river inflow and groundwater [37], with insufficient research on the optimal allocation of return flow resources. Numerous factors affect return flow in irrigation areas, leading to uncertainty in the return flow coefficient and the amount of return flow. Using a deterministic model for optimization diminishes the reference value of the allocation results [38].