This study first attempts to use the parameterized quadratic Directional Distance Function (DDF) approach to calculate China's provincial carbon abatement cost and carbon reduction potential (CRP) under different scenarios from 2000 to 2017. Afterward, considering three different scenarios, we analyze the Spatio-temporal characteristics and the dynamic evolution pattern of CRP. We also conduct the spatial autocorrelation test and spatial Durbin model to analyze the spatial spillover effects and influencing factors of CRP. The results are obtained as follows: CRP across the three scenarios varies considerably across provinces and different-located groups. CRP higher areas are mainly located in the economically developed eastern coastal regions, while most provinces with low CRP are concentrated in the western region. The spatial autocorrelation test indicated that provinces with a similar CRP showed a significant geographic agglomeration, and the agglomeration effect was strengthened first and then weakened. Simultaneously, the local spatial distribution of MCRP, FCRP, and ECRP shows a slight spatial polarization feature. Finally, through the SDM analysis and spillover effect decomposition, we find that improvement of regional CRP not only depends on economic development, industrial structure adjustment, and energy efficiency elevation, but also involves energy structure optimization, low-carbon innovation, and population. The low-carbon innovation provides critical support for local CRP under the efficiency scenario but restrains the local CRP under the fairness scenario. Therefore, the central government should emphasize local conditions and the ex-ante scenario assessment, strengthen regional interactive governance, optimize energy efficiency, and promote the application of clean energy to enhance CRP.
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