Towards sustainability for water-agriculture-energy-ecosystems nexus with interconnected uncertainty: A vine copula-based fixed-mix stochastic programming method

The collaborative management of the water-agriculture-energy-ecosystems (WAEE) nexus is of great significance for promoting sustainable development; however, some parameters associated with interconnected uncertainty (i.e., joint-random uncertainty) existing in the WAEE nexus can introduce additional complexity and intensify the conflict-laden issue of water allocation among agriculture, energy and ecosystems. This study develops a vine copula-based fixed-mix stochastic programming (VCFSP) method that can capture joint violation risks among multiple random variables and handle uncertainties represented as probability distributions in the WAEE nexus. A VCFSP-WAEE model is then formulated for synergistically managing the WAEE nexus of the Kaidu-Kongque River Basin in northwest China, where 96 scenarios involving different utilization rates of brackish water and joint violation probabilities are examined. Results reveal that, with the increase of brackish water utilization rate: (i) the total amount of water (allocated to agriculture, energy and ecosystems) would rise from 13.5 × 10⁹ m³ to 16.0 × 10⁹ m³ during 2046–2050, while the amount of conventional water resources would decrease by 209.4 × 10⁶ m³; (ii) the agricultural cultivated area would increase by 0.4 × 10⁶ ha, and the food yield would increase by 4.7 × 10⁹ kg at the end of planning period. In order to alleviate the pressure of local surface water and groundwater shortages, it is suggested to enhance the utilization efficiency of unconventional water resources and develop low-cost desalination technologies. Compared with the current situation, during the planning period, the proportion of agricultural water allocation would show a general decrease trend (from 73.2 % to 55.9 %), while the proportion of ecological water allocation would present an increase trend (from 6.5 % to 17.7 %). This discloses that increasing the utilization of unconventional water (especially brackish water) is beneficial for increasing ecological water supply, thereby improving the eco-environment in arid regions.