Dual non-deterministic bi-level programming method for collaborative management of water-energy-food-ecology nexus: A case study of Ordos

In the collaborative management of water-energy-food-ecology (WEFE) nexus, uncertainties existing in many system parameters and their interrelationships could intensify the conflict-laden issue of water allocation among competing interests. This study develops a dual non-deterministic bi-level programming (DNBP) method for WEFE nexus management under dual uncertainties and bi-level objectives. DNBP is a hybrid methodology of non-deterministic optimization and bi-level programming, which has advantages in analyzing trade-offs between competing stakeholders and tackling uncertainties characterized by randomness and vagueness. A DNBP-WEFE model is then formulated for Ordos (one city with severe shortage of water resource in Northern China) during 2026–2050, where 72 scenarios are designed to examine the impacts of energy, food and ecological demands, constraint-violation probabilities as well as system credibility levels. Results reveal that (i) energy transition (i.e., the development of clean energy) can reduce energy water intensity (to 1.22 m³/t of standard coal by the end of the planning period) and thereby save water consumption; (ii) compared with 2023, the proportion of unconventional water would increase by 6.40%–12.00% during 2046–2050; improving the utilization of unconventional water can reduce the consumptions of surface water and groundwater; (iii) water allocation and system benefit would increase with an increasing p level and recycled water would decrease with an increasing α level, demonstrating that policymakers should attach importance to the impact of uncertainties on system benefit and resource conservation. The findings provide feasible schemes for ensuring food security, energy supply and ecological protection under the framework of water and economy sustainable development.