## 2 Materials and Methods
### Optimal Allocation of Water Resources
#### 2.2.4 Establishment of Optimal Allocation Model of Water Resources
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Period** & **Crop Period** & **Mar.** & **Apr.** & **May** & **Jun.** & **Jul.** & **Aug.** & **Sep.** & **Oct.** \\ \hline Current & Spring wheat & 1.4 & 2.7 & 11.9 & 13.4 & 8.5 & 0.0 & 0.0 & 0.0 \\ Corn & 0.0 & 4.0 & 11.9 & 15.7 & 29.2 & 28.5 & 15.7 & 4.7 \\ Flax & 1.4 & 2.6 & 11.9 & 16.3 & 22.3 & 11.7 & 0.0 & 0.0 \\ Current & Potato & 0.0 & 0.2 & 15.1 & 16.0 & 29.2 & 28.5 & 15.0 & 0.0 \\ Melon & 1.4 & 2.6 & 11.9 & 14.1 & 11.8 & 0.0 & 0.0 & 0.0 \\ Goji berry & 0.0 & 0.2 & 14.4 & 15.4 & 28.0 & 24.6 & 11.0 & 0.0 \\ Forest fruits & 1.4 & 2.6 & 11.9 & 15.4 & 29.2 & 28.5 & 12.8 & 2.1 \\ \hline \end{tabular}
\begin{tabular}{c c c c c c c c c} \hline
**Spring wheat** & 1.3 & 3.4 & 11.4 & 14.9 & 9.8 & 0.0 & 0.0 & 0.0 \\ Corn & 0.0 & 5.0 & 11.4 & 17.3 & 33.6 & 32.3 & 15.0 & 5.3 \\ Flax & 1.4 & 3.3 & 11.4 & 18.1 & 25.7 & 13.2 & 0.0 & 0.0 \\ Short-term & Potato & 0.0 & 0.3 & 14.6 & 17.7 & 33.6 & 32.3 & 14.4 & 0.0 \\ Melon & 1.4 & 3.3 & 11.4 & 15.6 & 13.5 & 0.0 & 0.0 & 0.0 \\ Goji berry & 0.0 & 0.2 & 13.9 & 17.0 & 32.2 & 27.9 & 10.5 & 0.0 \\ Forest fruits & 1.4 & 3.3 & 11.4 & 17.0 & 33.6 & 32.3 & 12.3 & 2.3 \\ \hline \end{tabular}
\begin{tabular}{c c c c c c c c c} \hline
**Spring wheat** & 0.9 & 3.6 & 11.6 & 15.8 & 10.4 & 0.0 & 0.0 & 0.0 \\ Corn & 0.0 & 5.3 & 11.6 & 18.4 & 35.6 & 34.3 & 14.4 & 5.6 \\ Flax & 0.9 & 3.5 & 11.6 & 19.1 & 27.2 & 14.0 & 0.0 & 0.0 \\ Potato & 0.0 & 0.3 & 14.8 & 18.8 & 35.6 & 34.3 & 13.8 & 0.0 \\ Melon & 0.9 & 3.5 & 11.6 & 16.5 & 14.4 & 0.0 & 0.0 & 0.0 \\ Goji berry & 0.0 & 0.2 & 14.1 & 18.0 & 34.2 & 29.6 & 10.1 & 0.0 \\ Forest fruits & 0.9 & 3.5 & 11.6 & 18.0 & 35.6 & 34.3 & 11.8 & 2.5 \\ \hline \end{tabular}
\end{table} 
Table 3: Monthly effective precipitation (mm) during the crop period. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Period** & **Corp Type** & **Mar.** & **Apr.** & **May** & **Jun.** & **Jul.** & **Aug.** & **Sep.** & **Oct.** & **Total** \\ \hline Current & Spring wheat & 13.9 & 63.1 & 193.0 & 174.2 & 22.1 & 0.0 & 0.0 & 0.0 & 466.3 \\ Corn & 0.0 & 46.8 & 128.7 & 161.6 & 162.4 & 138.4 & 67.6 & 21.1 & 726.6 \\ Flax & 16.4 & 119.2 & 185.7 & 199.3 & 74.1 & 21.5 & 0.0 & 0.0 & 616.2 \\ Current & Potato & 0.0 & 2.3 & 76.0 & 155.3 & 156.1 & 130.4 & 43.9 & 0.0 & 564.1 \\ Melon & 23.8 & 121.6 & 179.8 & 166.3 & 36.3 & 0.0 & 0.0 & 0.0 & 527.8 \\ Goji berry & 0.0 & 1.2 & 43.9 & 86.3 & 100.9 & 68.5 & 17.4 & 0.0 & 318.2 \\ Forest fruits & 21.3 & 83.0 & 131.6 & 141.2 & 141.9 & 121.0 & 29.2 & 2.0 & 671.2 \\ \hline \end{tabular}
\end{table} 
Table 5: Monthly crop water requirement (mm) during the crop period. (3) Return flow  
Irrigation water diversion is an important factor affecting the return flow in irrigation areas, and the return flow coefficient reflects the proportion of return flow in irrigation water diversion. In addition, the return flow is also affected by precipitation, evaporation, groundwater level, crop planting structure, and other factors. Under the combined influence of various factors, the return flow and return flow coefficient exhibit a degree of uncertainty. This paper utilizes interval numbers to characterize the uncertainty of return flow in irrigation areas. According to the monitoring data of return flow (Table 6), the interval of the return flow coefficient is determined as [0.274, 0.338]. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multirow{2}{*}{**Return Flow (10\({}^{6}\) m\({}^{3}\))**} & **Irrigation** & **Return Flow** \\  & & **Diversion (10\({}^{6}\) m\({}^{3}\))** & **Coefficient** \\ \hline
2018 & 46.571 & 137.859 & 0.338 \\
2019 & 47.691 & 147.839 & 0.323 \\
2020 & 44.406 & 162.358 & 0.274 \\ \hline \hline \end{tabular} (4) Crop parameters  
According to the statistical data of the study area from 2001 to 2020, Table 7 determines the crop yield per unit area, crop unit price, crop planting cost, and the minimum and maximum planting area of each crop.  
\end{table} 
Table 6: Return flow coefficient of study area.