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.