Abstract: Revealing the spatial differentiation cause and spatiotemporal matching characteristic of ecological loads in the Beijing-Tianjin-Hebei urban agglomeration (BTHUA) holds significant strategic importance for regional sustainable development. We explored natural capital utilization of the BTHUA by using the three-dimensional ecological footprint model. Based on the spatial-temporal geographically weighted regression model and the barycenter theory, we identified the causes for the spatial differentiation of the three-dimensional ecological footprint and its spatial-temporal matching characteristic with energy utilization and economic development. Results showed that the regional per capita three-dimensional ecological footprint showed an overall fluctuating downward trend and remained in a long-term ecological deficit state (exceeding the carrying capacity by 5.2 times). Footprint size fluctuated steadily from 0.21 to 0.22 hm²·cap^-1. Cultivated land was the main source of the differentiation in per capita three-dimensional ecological footprint and footprint size. Footprint depth showed a fluctuating downward trend between 8.26 and 11.46, with grassland being the main contributor. The effect of socio-economic indicators on the three-dimensional ecological footprint shifted from strong positive effect (0.27) to strong negative effect (-0.20). The ecological construction indicator exhibited a continuous weak negative impact, while energy consumption remained an important driver of ecological footprint growth in the later stage, with its impact shifting from negative to positive after 2010. The results of multivariate spatiotemporal matching indicated that footprint depth, total energy consumption, and per capita GDP exhibited strong coordination at the spatiotemporal scale (mean value 0.73), being significantly higher than single temporal (mean value 0.55) and spatial matching degrees (mean value 0.67), demonstrating a high level of coordination between natural capital utilization, energy use, and economic development in the region at the spatiotemporal scale.

Key words: three-dimensional ecological footprint, natural capital utilization, driving mechanism, barycenter theory, multivariate spatial-temporal matching