Economic approach for optimal allocation of irrigation water in water-scarce region

Optimizing irrigation water allocation is critical for maximizing grain yields in water-scarce regions. Traditional algorithms face challenges such as lack of interpretable criteria, the curse of dimensionality, and instability. This study proposes an economic approach to spatial irrigation allocation, based on the marginal benefit criterion, to improve both the explainability and efficiency of the optimization process. A groundwater-enhanced SWAT model was used to derive the “irrigation amount-crop yield” (IRR-YLD) functions for multiple hydrological response units. The Karush-Kuhn-Tucker (KKT) optimality conditions were then applied to these functions to determine the optimal water allocation. The proposed approach was implemented in a representative region suffering from shallow groundwater overexploitation in the North China Plain, with the goal of optimizing the allocation of potential supplementary surface water benefitting from the South-to-North Water Diversion project. Results showed that under the first-type KKT optimality conditions (i.e., assuming sufficient water resources), where the marginal benefit of the IRR-YLD functions equals zero, winter wheat production reached its maximum, yielding 4.4 × 10⁴ tons more than current levels, requiring approximately 33.23 × 10⁸ m³ of surface water. Under the second-type KKT optimality conditions (i.e., assuming insufficient water resources), which equalized marginal benefits across 48 counties, 8.62 × 10⁸ m³ of surface water—satisfied for one round of supplementary irrigation—could increase wheat yield by 20.7 × 10⁴ tons compared to an equal allocation scheme providing 75 mm of water per county. This study further explores the mathematical, economic, and physical implications of the optimal irrigation water allocation. This research offers insights and policy recommendations for optimizing the use of groundwater and surface in this globally significant region, which faces the dual challenges of water scarcity and the need for increased crop production.