Abstract:The relationship between carbon emissions and carbon absorption is unbalanced, and the carbon cycle system is facing tremendous ecological pressure at present in China. In this paper, a carbon footprint size and depth measurement model was firstly established based on the three-dimensional ecological footprint method. Then we used this model to distinguish the natural capital flow and stock occupied by absorbing carbon emissions. Furthermore, the carbon footprint size and depth of 30 provinces were calculated on the basis of energy consumption from 2000 to 2016. The spatial correlation of carbon footprint size (depth) was analyzed by spatial autocorrelation method. The results showed as follows:(1) The carbon footprint size in China was affected by carbon footprint and carbon ecological carrying capacity. It showed an increase from 0.173 hm2/person to 0.329 hm2/person and then decrease to 0.301 hm2/person. The high-value areas of carbon footprint size were the northeast, northwest and southwest regions where the natural capital flow was not yet fully occupied. The low-value areas were mainly distributed in the eastern coast and the central regions where the natural capital flow was insufficient to compensate for carbon emissions. (2) The provincial carbon footprint depth has exceeded the natural length of 1, and the depth increased from 1.04 to 1.42 and then decreased to 1.31 since 2008. The carbon footprint depth in 10 provinces was always at the natural length of 1 from 2000 to 2016. The high-value areas of carbon footprint depth were the eastern coast and the central regions where the natural capital stock was consumed by carbon emissions and the ecological sustainability was weak, while the highest depth occurred in Shanghai with 298.83. There existed the regional complementarity between natural capital flow and natural capital stock for absorbing carbon emissions. (3) Using the global spatial autocorrelation analysis, we found that carbon footprint size and depth showed the positive correlation and significant spatial agglomeration in all provinces of China. Through the local spatial autocorrelation analysis, the High-High agglomeration areas of carbon footprint size were mainly distributed in the northeast and northwest regions, and there was a tendency of number decrease of High-High agglomeration areas. Moreover, the High-High agglomeration areas of carbon footprint depth were mainly distributed in the eastern coastal areas and there was an obvious spread trend toward the adjacent regions. By introducing the two indexes of carbon footprint size and carbon footprint depth, the research methods of carbon footprint are further improved, and the evaluation results are more accurate and reasonable than the results by the traditional carbon footprint theory.