An agricultural drought early warning threshold model with considering copula combined with diminishing marginal benefit theory: A case study in the Yellow River basin

Agricultural drought-induced yield reductions threaten socioeconomic stability and food security. Reliable early warning systems are essential for mitigating these threats. However, agricultural drought early warning based on meteorological conditions remains poorly explored, and prevalent conditional probabilities for determining drought propagation thresholds are largely subjective. In this study, an agricultural drought early warning threshold (ADEWarT) model was developed, combining Copula and diminishing marginal benefit theory, leveraging inherent regional drought propagation characteristics to objectively determine the thresholds. The ADEWarT model was applied and evaluated in the rain-fed agricultural areas of the Yellow River basin (raYRB) during the crop-growing seasons. Results showed that in most raYRB during the crop-growing seasons, early warning indicators for agricultural drought were the preceding meteorological drought conditions, while in the central-western raYRB during spring, they were the preceding compound drought and hot events. The performance metric, Matthews correlation coefficient (MCC), demonstrated that the ADEWarT model performed well (MCC > 0.4) across the raYRB. Compared with subjectively determined propagation thresholds, the proposed model exhibited superior performance during summer and autumn. The eXtreme Gradient Boosting combined with SHapley Additive exPlanations (XGBoost-SHAP) method revealed that the impacts of vegetation on early warning thresholds were modulated by hydrothermal conditions. Areas with lower absolute early warning thresholds were generally located on steep slopes, shady aspects, and at low elevations across the raYRB, indicating higher agricultural drought risk. This study provides technical guidance for agricultural drought risk management in the raYRB and offers a transferable framework applicable to other regions.