Planning a Water–Food–Energy–Ecology Nexus System toward Sustainability: A Copula Bi-level Fractional Programming Method

A copula bi-level fractional programming (CBFP) method is developed for planning the water–food–energy–ecology (WFEE) nexus system. CBFP has advantages in (i) dealing with ratio-objective problems, (ii) balancing the conflicts between hierarchical decision levels, and (iii) reflecting joint risks of correlated uncertain variables. Then, a CBFP–WFEE model is formulated to the Ili-Balkhash basin in Central Asia, in which 108 scenarios associated with different irrigation efficiencies, ecological-flow demands (EBW), and water–land resources have been examined. Solutions of water allocation, hydropower generation, and land-use pattern are obtained. Our major findings are as follows: (i) from 2021 to 2050, water allocation to livestock in East Kazakhstan would remarkably increase (by 40.9%) when water allocation to food is satisfied; (ii) hydropower generation would increase with the rising ecological flows and arable land resources; (iii) EBW is the key factor influencing the water inflow to the Balkhash Lake; (iv) the share of ecosystem water allocation would exceed 17.5% by 2050, and grassland area would rank in the first place of the ecosystem. Compared with conventional bi-level stochastic programming and single-level fractional programming models, the CBFP–WFEE model can achieve a higher ecosystem service value and higher efficiency of water–land resources, which can provide more feasible and sustainable alternatives for the WFEE nexus system. The obtained results can help balance the contradictions among water shortage, economic development, and ecology protection, as well as provide synergic management strategies for regional sustainability.