Research on the spatial-temporal distribution of three-dimensional carbon footprint in different urban agglomerations in China

This study expands the original two-dimensional carbon footprint model into a three-dimensional model form. Introduce two indicators of carbon footprint depth (CF_depth) and size (CF_size) to form a three-dimensional carbon footprint model (CF_3D), which is used to respectively represent the occupation and consumption of natural capital reserves by human activities' carbon emissions. Based on the 3D carbon footprint model, this paper calculated the CF_size, CF_depth, and CF_3D for four different urban agglomerations of China (BTH, YRD, PRD, and CY) spanning from 2000 to 2017. Building on this, the study analyzed the spatial-temporal and dynamic characteristics of the multivariate collaboration between CF_size, CF_depth, and GDP using a multivariate collaborative relationship model. The research findings reveal that (1) from 2000 to 2017, the utilization of natural capital stock in the Beijing-Tianjin-Hebei (BTH), Yangtze River Delta (YRD), Pearl River Delta (PRD), and Chengyu (CY) urban agglomerations were in an unsustainable development state, with their CF_depth exceeding 1. Among these regions, the degree of natural capital consumption was PRD > BTH > YRD > CY. (2) There manifests an obvious regional complementary characteristic of CF_size and CF_depth. Regions coupled with abundant land resources (such as Chengde and Hangzhou) tend to have high CF_size and low CF_depth, whereas area with fewer land resources (such as Tianjin and Shanghai) exhibits the opposite pattern. (3) In four urban agglomerations, the relationship of temporal multivariate collaboration among CF_size, CF_depth, and GDP exhibits a declining trend from 2000 to 2017, with an average value ranging from 0.4 to 0.6. The change in their multivariate spatial collaboration was not pronounced throughout the course of the study.