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Considering the multiple uncertainties in agricultural water resources management systems, this paper established an agricultural water optimal allocation model under uncertainty for Shijin irrigation district (ID). Uncertainties of four parameters, in- cluding precipitation, available groundwater, purchase prices of crops and crop cultivated area, were fully considered. Agricultural wa- ter allocation schemes were obtained based on the distribution characteristics simulation of the four parameters using Monte Carlo sim- ulation technique. In order to thoroughly analyze the results, the relationship between system benefits and water amounts was shown using 3D diagram. The optimized results show that total water use amount of 2016 ([217.460, 218.017] × 106 m3 for surface water irri- gation and [51.765, 66.266] × 106 m3 for groundwater irrigation) remains fairly static compared with the average level from 2003 to 2013, and irrigation water allocated to winter wheat is considerably larger than that to maize. The significant drop of the purchase price of maize has an apparent effect on water allocation. For winter wheat, surface water allocation of 2016 increases from 129.445 × 106 to 174.905 × 106 m3, and groundwater allocation increases from 24.511×106 m3 to 35.379 × 106 m3. For maize, surface water allocation of 2016 decreases from 88.329 × 106 to 42.846 × 106 m3, and groundwater allocation decreases from 34.733 × 106 to 23.865 × 106 m3. Water allocation amounts for the five subareas of Shijin ID are 54.326 × 106, 31.187 × 106, 51.899 × 106, 39.311 × 106, and 33.779 × 106 m3 respectively during the irrigation period of winter wheat, and are 16.693 × 106, 8.677 × 106, 16.151 × 106, 14.004×106, and 10.752 × 106 m3 during the irrigation period of maize. Moreover, cumulative probability distribution functions of surface water and ground- water allocation amounts for winter wheat and maize were obtained. Further, the linear relations between the difference in purchase price and the difference in water allocation of winter wheat and maize were obtained as well. These results will help decision makers learn detailed water distribution information and thus help make comprehensive irrigation schemes under uncertainty in future.
Keywords: agricultural water allocation; optimization; uncertainty; Monte Carlo simulation