Agricultural Water Management Model Based on Grey Water Footprints under Uncertainty and its Application

The grey water footprint theory was introduced into a fractional programming model to alleviate non-point source pollution and increase water-use efficiency through the adjustment of crop planting structure. The interval programming method was also incorporated within the developed framework to handle parametric uncertainties. The objective function of the model was the ratio of economic benefits to grey water footprints from crop production, and the constraints contained water availability constraints, food security constraints, planting area constraints, grey water footprint constraints and non-negative constraints. The model was applied to the Hetao Irrigation District of China. It was found that, based on the data in the year of 2016, the optimal planting plans generated from the developed model would reduce 34,400 m³ of grey water footprints for every 100 million Yuan gained from crops. Under the optimal planting structure, the total grey water footprints would be reduced by 21.9 million m³, the total economic benefits from crops would be increased by 1.138 billion Yuan, and the irrigation water would be saved by 44 million m³. The optimal results could provide decision-makers with agricultural water use plans with reduced negative impacts on the environment and enhanced economic benefits from crops.