[Spatial Correlation Analysis of Urban Vitality and Carbon Emissions in Mountainous Cities]

Urban vitality serves as a crucial indicator for measuring urban development quality and sustainability, reflecting the interaction intensity between human activities and urban spaces. As urban vitality increases, the spatial agglomeration of human activities and high-intensity development of the built environment often intensify energy consumption and exacerbate carbon emission pressures. Against the backdrop of global warming, cities, as primary sources of carbon emissions, warrant a deeper understanding of the spatial correlation characteristics between urban vitality and carbon emissions. This understanding holds significant implications for optimizing urban spatial organization and achieving high-quality development. Taking central Chongqing as a case study, this study constructed an evaluation index system for urban vitality in mountainous cities based on multi-source data integrating economic, social, cultural, environmental, and spatial dimensions and evaluated it using the entropy weight-TOPSIS method. Bivariate spatial autocorrelation and Geodetector were employed to investigate the spatial relationships between urban vitality and carbon emissions and explore their underlying mechanisms. The results showed the following： ① As a typical mountainous city, affected by topography, the comprehensive urban vitality in central Chongqing exhibited an irregular "center-periphery" structure, with significant vitality clusters forming in the inner-ring area and peripheral secondary group centers, while different dimensions of vitality showed both similarities and differences in spatial distribution. ② Comprehensive, economic, social, cultural, and spatial vitality all demonstrated significant positive spatial correlations with carbon emissions, with social vitality showing the highest spatial autocorrelation. The high-high clusters were mainly distributed in the inner-ring area and some peripheral groups, while low-low clusters were primarily located in the marginal areas of the central city. ③ The Geodetector analysis revealed that, in the context of restricted and highly concentrated construction space in mountainous cities, among various vitality factors, the population activity variability and agglomeration demonstrated the strongest explanatory power for carbon emissions, followed by the density of functional facilities and functional mix. Moreover, the interactions between different vitality factors all exhibited bivariate enhancement relationships. Notably, the interaction between population activity variability and functional mix showed the most significant impact on carbon emissions. These findings provide a scientific basis for mountainous cities to achieve coordinated development of carbon reduction and vitality enhancement.