Spatially distributed footprint families-based simulation–optimization approach for agricultural-ecological resources management under uncertainty

The nonlinear relationships across spatially-distributed irrigation, actual evapotranspiration and crop yield, and interactions between agriculture and ecology aggravate difficulties in water, land and fertilizer resources optimization. To address the above problems, this paper developed a framework of footprint families based multi-objective type-2 fuzzy random chance constrained programming (FFMOT2FRCCP). It integrated the multi-objective programming (MOP), footprint families, interval type-2 AHP (IT2AHP), type-2 fuzzy random chance constrained programming (T2FRCCP) with spatially-distributed water production functions. Spatially distributed irrigation-yield functions and irrigation-actual evapotranspiration functions were fitted simultaneously to simulate spatial heterogeneous yield considering nonlinear relationships across irrigation, actual evapotranspiration and yield. It overcomes disadvantages of traditional functions in neglecting spatially-distributed water transfers between irrigation and evapotranspiration. Interactive relationships between agricultural and ecological effects were measured by footprint families containing water, carbon ecological and energy footprint concurrently based on the life cycle approach. Besides, both water shortage risk and yield loss risk were quantified and controlled with consideration of their conduction machines. Moreover, weights across footprint families and risks were determined by the IT2AHP approach by taking compound uncertainties of subjectivities of mangers into account. In addition, uncertainties of the runoff were handled by T2FRCCP approach. The model was applied to Yingke irrigation district to verify its application. Resulted showed that (1) ecological footprint decreased, energy footprint, carbon footprint and risks enlarged when flow levels changed though its high, medium and low levels; (2) yield loss risk varied from 0 to 0.27 while water shortage risk changed from 0.13 to 0.32, and crop yield losses occurred after water shortage risk took place; (3) the actual evapotranspiration presented mismatching variations with yield because of their various irrigation thresholds. The results could offer insight in how to measure and handle nonlinear relationships amid distributed actual evapotranspiration and yield under various water allocation schemes. Besides, the results could provide optimal decisions giving consideration of agricultural and ecological balances for managers.