Removing Population Size, World Cities Leave on Land a Footprint of Wealth
Résumé
Urban expansion builds on rich and easily accessible arable land, which is a concern for agricultural production, in a context of global climate change. It also affects ecosystems, contributing to the biodiversity crisis, and human health, for instance through air pollution. Soil sealing is linked to an increased flood risk as well. Worldwide measures aim to alleviate the impacts of urban expansion and sprawl, in small and large cities. However, the link between urban extent and population size is still unclear, as the literature displays contradictory results on this matter. In this work, we uncover a radial scaling law governing built-up land in 1800+ global urban areas, of more than 300,000 inhabitants each (gathering more than 30% of the world population in total). We use for this UN World Urbanization Prospects and Copernicus' GHSL built land data for the year 2020. We study these urban areas through a mix of radial (center-periphery) analysis and scaling laws, a method which we refer as radial scaling analysis. We observe that world cities have homothetic (or isometric) radial land use profiles, and that built-up footprint is proportional to total population. We obtain these results through two independant but coherent analyses. On the one hand, through a rescaling of radial built land profiles, which provides a nice data collapse. And on the other hand, through non-linear regression methods, which additionally show that the mathematical shape of these profiles is roughly exponential. The spatial scaling law which we observe is important for the understanding and the definition of urban areas, to help build a science of cities using robust empirical stylized facts, and to make cities more sustainable. It implies that small and large urban areas have similar internal (radial) structures, and that built-up area per capita is constant across city sizes. This suggests that efforts to curb land take (for instance in the frame of no net land take NNLT objectives) are needed equally in large and small cities. These results also lead us to define a new scale-free indicator of urban built land per capita, which captures the remaining variations. At the national scale, we find that these variations are very strongly correlated to wealth, measured by gross domestic product per capita. This very strong link means that land take on the one side and economic activity (measured by gross domestic product) on the other side are quite fundamentally intertwined in our societies -- which is not very encouraging for NNLT objectives. This actually suggests a pick between economic development and sustainability.