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• Distribution effect of carbon-food nexus for Chinese cities were explored. • Several methods built using the spatial decoupling index were proposed. • Chinese cities exhibited varying degrees of the distribution effect over the period. • Driver pattern of carbon-food nexus has changed over the years. Climate change mitigation and food security are sustainable development goals (SDGs) of the United Nations. Despite extensive studies focused on the nexus of different SDGs and corresponding mechanisms, the distribution effect of carbon-food nexus and its driver has received limited attention, hindering policy making for balancing pathways of regional emission reduction and food production improvement. The present study explored the distribution effect (i.e., spatial performance) of carbon-food nexus from multiple perspectives (namely, status quo, drivers, and trend) based on a unique city-level dataset from 2005 to 2017. To this end, we proposed the spatial decoupling index, the corresponding decomposition and nonparametric models for capturing the multi-perspective distribution effects. The results indicated that Chinese cities, categorized by population scale and economic structure, exhibited varying degrees of distributions of carbon-food nexus over the period. Moreover, the driver pattern of carbon-food nexus was noted to have changed, wherein investment efficiency and scale were positive drivers. Furthermore, we showed that a more developed city's economy was statistically significantly associated with higher carbon emission and lower food production. Therefore, related stakeholders should take more actions such as strengthening capital accumulation and joint management of carbon intensity, for improving the distribution effect of the overall city-level carbon-food nexus. [ABSTRACT FROM AUTHOR]

[Display omitted] • A bi-level joint-probabilistic programming approach is developed. • It can handle leader–follower issues and joint-probabilistic constraints. • The proposed approach is applied to China's multi-regional energy system model. • The optimal schemes during 2021–2050 under three mitigation scenarios are obtained. • Results are helpful to achieve low-carbon goals in multi-regional energy system. Climate change mitigation and renewable resources utilization are becoming particularly urgent for energy system management. In this study, a bi-level joint-probabilistic programming (BJPP) method is developed for planning multi-regional energy system under different mitigation policies and uncertainties. BJPP can handle leader–follower issues in decision-making process as well as examine the risk of violating joint-probabilistic constraints. Based on the BJPP method, a China's multi-regional energy system (named as BJPP_CMES) model is formulated to provide optimal scheme for energy system planning of China over a long-term horizon (2021–2050) by synergistically minimizing carbon dioxide (CO 2) emission and system cost. A series of scenarios associated with different carbon capture and storage (CCS) levels and violation risks of energy-demand constraints are examined. Results reveal that: (i) the share of non-fossil energy in China's energy supply would keep increasing in 2021–2050, and the highest growth of the renewable supply would occur in Ningxia (rising 47.7%); (ii) Sichuan, Inner Mongolia, and Gansu would be the top three suppliers of renewable electricity; (iii) the CO 2 emission of China would reach a peak of [44.3, 54.8] billion tonnes during the period of 2026–2030; Shandong, Inner Mongolia, and Shanxi would be main contributors of CO 2 emission in the future; (iv) compared with the single-level model, the CO 2 emission from the BJPP_CMES model would reduce by [2.7, 5.7]%; (v) among developed regions, the individual probability level of Jiangsu-Zhejiang-Shanghai is the most significant parameter for both CO 2 emission and system cost. The findings are helpful for decision makers to optimize multi-regional energy system (MES) with a low-carbon and cost-effective manner, as well as to provide useful information for renewable energy utilization and regional sustainable development. [ABSTRACT FROM AUTHOR]