Evaluating Coupling Security and Joint Risks in Northeast China Agricultural Systems Based on Copula Functions and the Rel–Cor–Res Framework

Ensuring the security of agricultural systems is essential for achieving national food security and sustainable development. Given that agricultural systems are inherently complex and composed of coupled subsystems—such as water, land, and energy—a comprehensive and multidimensional assessment of system security is necessary. This study focuses on Northeast China, a major food-producing region, and introduces the concept of agricultural system coupling security, defined as the integrated performance of an agricultural system in terms of resource adequacy, internal coordination, and adaptive resilience under external stress. To operationalize this concept, a coupling security evaluation framework is constructed based on three key dimensions: reliability (Rel), coordination (Cor), and resilience (Res). An Agricultural System Coupling Security Index (AS-CSI) is developed using the entropy weight method, the Criteria Importance Through Intercriteria Correlation (CRITIC) method, and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method, while obstacle factor diagnosis is employed to identify key constraints. Furthermore, bivariate and trivariate Copula models are used to estimate joint risk probabilities. The results show that from 2001 to 2022, the AS-CSI in Northeast China increased from 0.38 to 0.62, indicating a transition from insecurity to relative security. Among the provinces, Jilin exhibited the highest CSI due to balanced performance across all Rel-Cor-Res dimensions, while Liaoning experienced lower Rel, hindering its overall security level. Five indicators, including area under soil erosion control, reservoir storage capacity per capita, pesticide application amount, rural electricity consumption per capita, and proportion of agricultural water use, were identified as critical threats to regional agricultural system security. Copula-based risk analysis revealed that the probability of Rel–Cor reaching the relatively secure threshold (0.8) was the highest at 0.7643, and the probabilities for Rel–Res and Cor–Res to reach the same threshold were lower, at 0.7164 and 0.7318, respectively. The probability of Rel–Cor-Res reaching the relatively secure threshold (0.8) exceeds 0.54, with Jilin exhibiting the highest probability at 0.5538. This study provides valuable insights for transitioning from static assessments to dynamic risk identification and offers a scientific basis for enhancing regional sustainability and economic resilience in agricultural systems.