The “peak carbon” target has triggered wide-ranging and profound systemic changes and transformations that have left the provinces along the basin facing the dual dilemma of implementing carbon reduction actions and socioeconomic development. The allocation of carbon emission quotas is a fundamental task that reflects the division of labour and collaboration within a river basin to achieve the “peak carbon” target. Therefore, the fair and efficient allocation of industrial carbon emission quotas is the key to the implementation of carbon emissions trading and the establishment of carbon offset mechanisms. In the study, based on the description of the spatial and temporal evolution of the industrial carbon footprint and its carrying capacity, the industrial carbon offset area and industrial carbon reimbursement area are divided. Moreover, the allocation method of industrial carbon emission quotas is proposed by accounting for the principles of fairness, efficiency, and sustainability, and is verified using the provinces along the Yellow River Basin in China as a case. The results show that the industrial carbon carrying capacity is “unbalanced”. The provinces with strong carrying capacity are in the middle and upper reaches, and provinces with weak carrying capacity are in the middle and lower reaches. Moreover, the industrial carbon offset in the basin as a whole is higher than the industrial carbon compensation, which is potentially conducive to the implementation of cross-basin carbon offset. The weights of the equity, efficiency and sustainability indicators are 0.46, 0.23 and 0.31, respectively. The two industrial carbon compensated provinces can transfer the surplus industrial carbon emission quotas to the two industrial carbon offset provinces after obtaining the corresponding financial compensation. The Gini coefficient is 0.26, which is relatively fair. The study not only reveals the mechanism of the relationship among industrial carbon carrying capacity, carbon emission quota and carbon offset, but also provides a scientific basis for the establishment of a carbon emission quota trading market and the strengthening of the inter-provincial coordinated emission reduction incentives in the basin.
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