Global evidence for a consistent spatial footprint of intra-urban centers

Abstract

Urban space is highly heterogeneous, with population and human activities concentrating in localized centers. However, the global organization of such intra-urban centers remains poorly understood due to the lack of consistent, comparable data. Here we develop a scalable geospatial framework to identify intra-urban activity centers worldwide using nighttime light observations. Applying this approach to more than 9,500 cities, we construct a high-resolution global dataset of over 15,000 centers. We uncover a striking regularity: despite vast differences in city size, regional development, and population density, the built-up area associated with individual centers remains remarkably consistent. Across cities, total urban area scales proportionally with the number of centers, yielding a stable mean spatial footprint. This regularity holds at the micro-scale, where Voronoi-based service areas exhibit a characteristic size that is persistent across countries and independent of local population concentration. As a geometric consequence, this polycentric multiplication maintains stable average distances to the nearest center as cities expand, preventing the accessibility decay inherent in monocentric growth. These findings reveal a universal organizing principle whereby urban expansion is accommodated through the replication of activity centers with a consistent spatial extent, providing a new empirical foundation for understanding the nature of urban growth.

Figures (13)

• Figure 1: Scheme of the urban center identification methods. (a) Nighttime light distribution around Shanghai, China. (b) Contour maps of the region under different minimum contour area values. (c) Centers under different minimum contour area values. The one with the highest POI density is labeled as the main center. (d) Majority voting across all minimum contour area values. The insets display close-up satellite views of the identified main center (top) and a subcenter (bottom). Imagery from Google.
• Figure 2: Geographic distribution of global urban centers. (a) Heatmap of centers worldwide. Developed or densely populated regions typically have a high density of centers. (b) Average area per center relative to the center number of cities. Cities with $\ge$20 centers are aggregated. Triangles indicate the mean, error bars represent the standard deviation and the purple line denotes the average value of the means. (c) Scaling analysis between the total built-up area and center number. Squares represent individual cities, and triangles indicate group means. The line represents the fitting to the group means (triangles) of cities with more than one center ($n=46$) on a log-log scale. The scaling exponent $\beta = 1.03$. (d) The identified urban centers in Los Angeles, US; London, UK; Luanda, Angola; Lusaka, Zambia; and Beijing, China. Note that for simplicity, the extents of some cities are not fully depicted. The locations of the CBDs are collected from official government reports and online documents. The spatial proximity of the identified main centers (purple stars) to the CBDs (white stars) partially validates the accuracy of our center identification procedure.
• Figure 3: Spatial distribution of centers within the city. (a) The Voronoi Diagram of centers in Los Angeles, US. (b) The kernel density estimation of the area distribution of cities with 1, 2, 3, 4, and 5 centers. The vertical dashed line represents the average area for each city group. The average area of monocentric cities, i.e., cities with a single center, is obviously smaller than the difference in average area between cities with consecutive numbers of centers. (c) Area distribution of centers' voronoi polygons in monocentric and polycentric cities for China, Germany, the UK, the US and Japan. The average coverage area of centers in polycentric cities remains stable across different countries. (d) Area distribution of centers' voronoi polygons in ten cities. Squares indicate the mean, error bars represent the standard deviation and the dashed purple line denotes the average value of the means. (e) The area versus population density of centers' voronoi polygons. The $R^2$ values of the linear regression are rather small.
• Figure 4: Population-weighted average distance to the center. (a) Two types of average distance. For the average distance to the nearest center, we overlay the population grid on the urban area, calculate the distance to the nearest center of each grid, and average it by the population of grid. For the average distance to the main center, the distance to the main center of each grid is used. (b) Average distance relative to the center number of the urban area. Urban areas are grouped by the center number and those with at least 20 centers are grouped together. While the distance to the main center increases significantly with the number of centers, the distance to the nearest center remains stable. The scatters represent the mean and the error bars represent the standard deviation. The line for the main center represents the fitting to $y = ax^b$, and the line for the nearest center represents the average value of the means.
• Figure 5: Population density decay from urban center to peripheries. Scatter plots show population density distributions around the main and sub-centers for Los Angeles (US); Beijing (China); Berlin (Germany); and London (UK). Each point represents the average population density within a 2-km-wide concentric ring. Lines represent the linear regression fits to $\log y = \log a + bx$. Generally, density decays more steeply around main urban centers than subcenters, as indicated by the larger decay coefficients $b$.