A copula-based security risk evaluation and probability calculation for water-energy-food nexus

Water-energy-food (WEF) are essential for human survival and development and they interact complexly. The research on Water-energy-food-coupling security risk (WEF-CSR) is crucial to promoting multi resource collaborative management. In this study, a comprehensive index system was constructed using three dimensions: reliability (Ra), coordination (C), and resilience (Rs). We selected the middle and upper reaches of the Yellow River Basin in China to study WEF-CSR conflicts, coupled with the Copula method of risk probability calculation. The results showed that: 1) from 2005 to 2021, the WEF-CSR index in the study area showed a progressively increasing trend, with a mean value of 0.49 in a critical safety state and lower values in the upper reaches of Ningxia and Gansu provinces. 2) The Ra-indexes in the criterion layer is not clearly affected by resource endowment conditions between annual periods; C-indexes are growing rapidly, with their annual growth rate four times as fast as the Ra-indexes, and Rs-indexes growing at about 2.7 times faster. 3) "Energy consumption per capita, carbon emissions, and water-related indicators" are the six main limiting factors, with a combined impediment degree of over 35 %, water resources are major constraint. 4) The Ra-C, C-Rs, and Ra-C-Rs indexes are well fitted by Clayton copula, and the C-Rs indexes are well fitted by Frank copula. The three-dimensional joint distribution risk probability, Ra-C-Rs (Ra ≤ 0.4, C ≤ 0.4, Rs ≤ 0.4) is 0.29. When the Ra or C indexes increases, the probability of unsafe Rs rises to 40 %-50 %, meaning future development must emphasize synergy, especially in Rs. In future, the five provinces in the middle and upper reaches of the Yellow River should focus on reducing energy pressure, improving water shortage conditions, and enhancing the overall resilience to avoid single-factor adverse conditions affecting WEF's coordinated and sustainable development.