Copula–information gain-based identification of GPP response thresholds under multiscale agricultural drought

Scientifically determining the threshold at which gross primary productivity (GPP) enters a significantly drought-affected state is a critical prerequisite for effective drought risk mitigation and agricultural management. Previous studies have predominantly relied on empirical criteria or probability-based analyses to determine this threshold, while objective, information-driven frameworks to characterize nonlinear drought–ecosystem response thresholds across multiple time scales are lacking. To address this limitation, we propose a Copula–Information Gain (Copula–IG) framework that integrates copula-based joint dependence modeling with information-theoretic discrimination, thereby enabling probabilistic and information-driven identification of GPP drought thresholds across multiple temporal scales. The results indicate pronounced spatiotemporal heterogeneity and strong scale dependence in agricultural drought responses across China. As the drought duration extends from short-term to medium- and long-term periods, the discriminative performance of the Copula–IG model consistently improves, while the GPP drought threshold gradually shifts from a spatially dispersed pattern toward greater convergence and stability. IG values were primarily concentrated within the range of 0.05–0.10, indicating enhanced separation between drought-affected and non-affected GPP states. Meanwhile, the mechanism underlying GPP drought threshold formation transitions from a rapid, evapotranspiration-dominated short-term response to a structurally constrained suppression process governed by cumulative soil moisture deficits under prolonged drought conditions. Overall, this study presents a probabilistic, quantitative, and spatially refined framework for identifying agricultural drought–ecosystem response thresholds, thereby providing valuable scientific support for high-resolution agricultural climate monitoring and ecological early-warning systems.