A risk-averse stochastic quadratic model with recourse for supporting irrigation water management in uncertain and nonlinear environments

Abstract

Agricultural water management system are subject to a variety of uncertainties and nonlinearity, which complicate the decision-making process and exaggerate water-shortage risks. Previously, few studies could tackle multiple uncertainties and the associated system risks in nonlinear problems. In this paper, a novel risk-averse optimization model was developed for supporting irrigation water management to mitigate these problems. Based on a risk measurement tool, Conditional Value-at-Risk (CVaR), a CVaR-based interval fuzzy two-stage stochastic quadratic programming (CIFTSQP) was proposed. CIFTSQP could not only provide risk-averse solutions with recourse in response to extreme economic risk quantified as CVaR and water-shortage risk expressed as fuzzy credibility level, but also handle and quantify the nonlinearity in a stochastic program caused by the economy-of-scale effects of facilities. The proposed method has been applied to an irrigation water management case in the northern China. Results suggested that, in response to severe water shortage, sunflowers would be preferred. Meanwhile, groundwater use in Wuyuan County and surface water consumption of Urad Qianqi and Urad Zhongqi should be reduced. Moreover, desired water-allocation strategies with varied risk-aversion levels were generated under different water inflow levels. Results reveal that the highest economic benefits could be achieved when risk aversion degree reaches 30 %, 40 % and 70 % under the low, medium and high inflow levels, respectively. Results reveal that higher risks would bring higher returns under the low and medium inflow levels, and the highest economic benefits could be achieved when risk aversion degree reaches 70 % under the high inflow level.reveal that higher would bring higher returnsunder the low and medium inflow levels, andthe highest economic benefits could be achieved when risk aversion degree reaches 70 % under the high inflow level. The developed CIFTSQP method provided valuable insights into informed irrigation decision-making with respect to economy-of-scale effects, risk aversion and recourse in an agricultural water allocation system. It can also be applied to address other resource allocation problems under uncertainty and risk.