Mathematical modeling for planning water-food-ecology-energy nexus system under uncertainty: A case study of the Aral Sea Basin

A bi-level decentralized chance-constrained programming (BDCP) method is developed for planning water-foodecology-energy (WFEE) nexus system. The BDCP method has advantages in balancing the tradeoff between twolevel stakeholders in hierarchical structure and reflecting the synergy effect among multiple divisions under random uncertainty. Then, a BDCP-WFEE model is formulated for the Aral Sea Basin, where the upper-level model aims to maximize system benefit, and the multiple divisions at the lower-level model aim to maximize food production, ecological water allocation, and electricity generation. Compared with the conventional singlelevel model, results obtained from the BDCP-WFEE model under multiple scenarios reveal that (i) the food production would increase by 2.0%-3.6% , implying that the food demand of additional 0.7 million people can be met; (ii) the ecological water allocation would increase by 0.9%-3.0%, denoting that the amount of water to the Aral Sea would reach 23.4 km3 at the end of planning period; (iii) the electricity generation would increase by 5.4%-8.5%. Besides, under the premise of ensuring food security, the proportion of agricultural water allocation in the Aral Sea Basin would reduce by 17.0%, indicating that the BDCP-WFEE model can effectively optimize the water allocation pattern and alleviate the conflict of water resources allocation among competetive users. These findings can provide policy support for managers to solve the problems of water shortage, food crisis, ecological degradation, and electricity insecurity.