## 3 Results and Discussion
### Optimal Allocation of Irrigation Water Diversion (Model I)  
#### 3.2.1 Optimization Results of Irrigation Benefits (Model I)  
Figure 6 illustrates the net profit optimization results across different periods. For the current years, the optimized net profit increased from USD [41.35, 54.81] million to USD [59.62, 78.98] million, reflecting a rise of USD [18.27, 24.18] million, accompanied by a significant improvement in irrigation efficiency. In the upcoming year, the projected net profits for the short-term and long-term are estimated at USD [61.81, 81.46] million and USD [62.64, 82.42] million, respectively, representing increases of USD [2.20, 2.47] million and USD [3.02, 3.43] million compared to the current years. These gains are attributed to an increase in precipitation by 6.1 mm and 8.9 mm in the short term and long term, respectively, relative to the current years. The augmented precipitation reduces crop irrigation requirements, thereby enhancing both irrigation area and efficiency. Additionally, reference evapotranspiration decreased by 11.6 mm in the short term and by 15.5 mm in the long term, which further reduces crop water demand, subsequently lowering the crop irrigation quota and enhancing irrigation efficiency.  
Water productivity refers to the net profit generated by the consumption of irrigation water per unit volume for crops and is a crucial factor in optimizing water resource allocation. Figure 7 illustrates the significant variation in water productivity across different crops. Goji berries exhibit the highest water productivity ([1.15, 1.41] USD/m\({}^{3}\)), followed by forest fruits and potatoes ([0.60, 0.81] and [0.39, 0.55] USD/m\({}^{3}\), respectively). Spring wheat and corn have the lowest water productivity ([0.08, 0.11] and [0.06, 0.09] USD/m\({}^{3}\), respectively).  
Figure 5: Prediction of the monthly average reference evapotranspiration in different periods.  
Table 9 presents the net profit optimization results for each crop across different periods. In the current years, the net profit of each crop after optimization changes significantly compared to the pre-optimization values. Specifically, the net profits of spring wheat, corn, and flax, which have lower water productivity, decrease by USD [0.98, 1.27], [1.13, 1.65], and [1.43, 1.61] million, respectively. On the other hand, the net profits of potato, melon, goji berry, and forest fruits, which have higher water productivity, increase by USD [3.82, 5.30], [0.53, 0.74], [6.72, 8.26], and [10.77, 14.50] million, respectively. The optimization results indicate that in the future years, only the net profit of flax shows a significant increase. Specifically, in the short-term and long-term future years, the net profit of flax increased by USD 0.55 to 2.80 million and USD 2.22 to 3.14 million, respectively, compared to the current years. This suggests that climate change will increase the availability of distributable irrigation water in the future, which will be allocated to expand the planting area of flax, ultimately improving the irrigation efficiency of the region.  
Figure 6: Optimization results for net profit in different periods.  
Figure 7: Water productivity of different crops.