Optimal water allocation in irrigation districts considering scale coupling and hierarchical games

Irrigation district is one of the most complex agricultural systems, including multi-scale processes (from farmland irrigation and canal conveyance to district water supply and planning) with multi-level decision-makers, such as farmers and district administrators. Current water resource allocation cannot coordinate water quantity at different spatial scales and development levels, as well as dynamic interaction and feedback. It is often required for the integrity of the optimal water resource allocation in irrigation districts. In this study, an optimal model was established for water resource allocation in irrigation districts using scale coupling and hierarchical games. Large-scale system decomposition was also coordinated with bi-level programming. A dynamic feedback was linked to field irrigation, multi-level canal water allocation, and irrigation district water supply at various scales, particularly for the daily-scale refined water. An intelligent cyclic mechanism was also proposed for the ‘optimization-feedback’ at the regional scale, thus ensuring consistency between single-scale control and system-wide optimization. Irrigation water use efficiency was coordinated among different entities. A case study was taken of the Qinglongshan Irrigation District in Heilongjiang Province, China. A field test validated the effectiveness of the model. Results show that the optimal scheme increased water productivity by 18%, compared with conventional irrigation practices. The performance of the model was significantly superior to that of single-scale optimization. Only the field-scale model increased irrigation water use efficiency by 9%; Only the canal-scale bi-level programming model increased by 4.1% in water conveyance losses, thereby balancing benefit trade-offs at various scales. Compared with the integrated model, the standalone district-scale model increased water diversion by 24%, whereas economic water productivity was reduced by 19%. The unified framework effectively avoided resource waste and suboptimal solutions after local-scale optimization. The bi-level programming module effectively captured the hierarchical decision-making attributes among water users. The coordination index of water allocation was improved. A closed-loop "demand-allocation-supply" mechanism was established to balance system integrity and scale adaptability. The finding can provide a theoretical basis and practical tool for resilient, efficient, and coordinated agricultural water in large-scale irrigation districts, particularly with multiple water sources and administrative levels.