A risk-based stochastic model for supporting resources allocation of agricultural water-energy-food system under uncertainty

The interactive water-energy relationship is a major restriction on food production in agricultural irrigation systems. Applying water-saving irrigation systems can further intensify the interrelationship between water and electricity and trigger a water-energy joint risk. Currently, there are no approaches capable of effectively assessing the various uncertainties and water-energy joint risks in irrigation districts. In this study, a novel mathematical programming method termed copula-based interval two-stage stochastic mixed-integer programming (CITSMIP) is proposed. CITSMIP quantifies water-energy joint risks in food production and provides an optimal resource allocation plan and water-saving irrigation application schemes under different joint risk levels. CITSMIP was applied to solve an irrigation resource management problem in northwest China. The results show that under a certain water-energy joint risk, planting sunflowers would be the first choice for water-saving irrigation applications. As water-saving applications have become increasingly common over time, the watersaving volume is expected to increase to [74.65, 84.46] x 107 m3 by 2035. Moreover, under a certain joint risk, compared with the water risk, fluctuations in energy risk would have a greater impact on the total benefit of the system and the total consumption of resources. Compared with single water risk or energy risk management, the joint risk management results would have a lower degree of uncertainty and higher lower-bound benefits. Establishing CITSMIP can provide valuable insights into informing stakeholders to allocate resources and maximize benefits under water-energy joint risk.