An interval multi-objective fuzzy-interval credibility-constrained nonlinear programming model for balancing agricultural and ecological water management

This study presents an interval multi-objective fuzzy-interval credibility-constrained nonlinear programming (IMFICNP) model combined with spatial water requirement of ecological vegetation (SEWR) estimation for solving the problem of allocation of agricultural and ecological water in irrigation districts under uncertainties. Through techniques of remote sensing (RS) and geographic information system (GIS), the ecological vegetation is subdivided into three types including forest land, grassland and shrubland and the water requirement of ecological vegetation is extended from site-specific sample to spatial decision-making unit (DMU), which provides a set of spatial data for input parameters of constraints. The IMFICNP model can be formulated through combination of interval parameter programming, multi-objective programming and fuzzy-interval credibility-constrained programming, which can handle the conflicts of multiple objectives under uncertainties such as single uncertainty (interval and fuzzy parameters) and dual-uncertainties (fuzzy-interval sets), and finally generate optimal water allocation schemes for crop and ecological vegetation under different credibility levels. The interval quadratic crop water production functions (IQCWPFs) are introduced to express the nonlinear relationships between crop yield and irrigation amount. Then, this model is applied to a case study of Huangyang Irrigation District (HID) in Shiyang River Basin to demonstrate its applicability. The results indicate that a higher credibility level is accompanied by less amount of water allocation and lower system benefit. The amount of water allocation at the DMU is dominated by planting area of crops and ecological vegetation, but there are few exceptions that optimal solutions are determined by the economic value. In addition, SEWR enables to reflect spatial heterogeneity of the DMU at a larger scale. IMFICNP model can coordinate conflicts among multiple objectives and it can tackle the violation of system constraints with fuzzy-interval sets. Therefore, these results can effectively balance the agricultural and ecological water management in irrigation districts, and provide valuable basis for the sustainable development of arid and semi-arid areas.