基于三维生态足迹的京津冀城市群自然资本可持续利用分析@@@Sustainability evaluation of natural capital utilization based on a three-dimensional ecological footprint model: A case study of the Beijing-Tianjin-Hebei Metropolitan region

： Ecological footprint analysis is an important method of sustainability assessment. Three-dimensional ecological footprint model (3DEF) can distinguish and track the occupation of natural capital stock and the consumption of natural capital flows, and consequently elucidating the core issues of sustainable development. To date, studies that apply the 3DEF method for the evaluation of sustainable utilization of natural capital are relatively few and mainly concerned with the global or the national scale. Taking the Beijing- Tianjin- Hebei region as the study area, this research evaluated natural capital utilization sustainability based on a 3DEF model at the scale of metropolitan region. Using statistical data in 2010, this research first calculated the ecological footprint depth (EFdepth) and footprint size (EFsize) of 13 cities. It then, analyzed the difference in the composition of the 13 cities' EFdepth and EFsize, as well as its influencing factors and examined the pattern of the Beijing-Tianjin-Hebei Metropolitan region's natural capital use in 2010. Lastly, it examined the ecological sustainability status of this metropolitan region. The main conclusions of the study are as follows: Ecological deficit is prevalent in the 13 cities of the metropolitan region. EFdepth is deeply influenced by the amount and structure of fossil energy consumption. The relationship between EFdepth and economic development may be described by the environmental Kuznets curve (EKC) with an inverted N shape. According to the relationship between the depletion of stocks and the appropriation of flows, the 13 cities in the Beijing- Tianjin- Hebei Metropolitan region are divided into four categories, namely, the depletion of stocks is seriously, significantly, or generally ahead of the appropriation of flows, and the average level of the depletion of stocks and the appropriation of flows are the same. The ecological sustainability status of these four types of cities is, respectively, the weakest, weaker, stronger, and the strongest. The results presenting the natural capital utilization at the metropolitan region scale based on the 3DEF model are better than that with traditional ecological footprint model method.