An intelligent and uncertain optimization framework for water-nitrogen synergistic management under extreme supply and demand water risks

Extreme climate conditions, such as droughts and floods, are becoming more frequent, prolonged, and severe due to global warming. The multiscenario water–nitrogen resource allocation program (WNRAP) not only addresses the risks associated with uncertainty in water supply and demand in extreme climates but also reduces the likelihood of these extreme events by decreasing carbon emissions. Therefore, to increase the ability of agricultural water–nitrogen management systems (AWNMS) to cope with extreme hydrological events, a multidimensional uncertainty model combined with an intelligent optimization framework that integrates the R-vine copula and interval two-stage stochastic programming (RITSP-IGWO) was developed. First, the R-vine copula model was used to characterize the non-Gaussian correlations among rainfall, runoff, and crop actual evapotranspiration (ET_c,act). Second, the interval two-stage stochastic programming (ITSP) model was employed to address uncertainties in the environmental parameters. Finally, the multistrategy improved gray wolf optimization (IGWO) algorithm was utilized to solve the ITSP model and obtain the WNRAP results for 27 scenarios. The optimization results revealed that the water and nitrogen fertilizer use efficiencies in the WNRAP increased by 18.69% and 21.83%, respectively, whereas the CO₂ emissions decreased by 11.63%, and the solution efficiency improved by 67.99%. This framework can generate accurate and robust WNRAPs, providing effective theoretical support and practical guidance for sustainable agriculture to address the risks of extreme climate uncertainty.