Radial Density Profiles

Radial density profiles follow the method developed by Alain Bertaud to characterize the spatial structure of cities. They measure how population density varies with distance from the city centre.

Method

1. Centre identification — the population-weighted centroid of each city is computed from H3 cells
2. Ring construction — concentric rings of 1 km width are drawn outward from the centre
3. Density aggregation — for each ring, we compute the average population density (persons/km²) of all H3 cells whose centroids fall within the ring
4. Profile output — the result is a distance-density curve that reveals whether a city is monocentric (steep gradient), polycentric (multiple peaks), or dispersed (flat profile)

Why H3?

Radial profiles use the H3 hexagonal grid (resolution 8, ~0.74 km² per cell) rather than the regular 1 km grid. H3 cells have uniform area and compact shape, which reduces edge effects when assigning cells to distance rings.

Interpretation

• Steep exponential decay — classic monocentric city (e.g., Paris, Buenos Aires)
• Plateau then drop — large dense core (e.g., Mumbai, Dhaka)
• Multiple peaks — polycentric structure (e.g., Ruhr area, Randstad)
• Flat profile — dispersed, low-density sprawl (e.g., Atlanta, Houston)

Methodology

This page describes the analytical methods used to transform raw satellite data into the statistics and visualizations shown on The Urban World.

City definitions

Cities are defined using the GHSL Urban Centre Database (GHS-UCDB), which delineates functional urban areas based on population density contiguity rules. Each urban centre has a unique boundary polygon used to clip raster data.

Population and density

For each city and epoch, we sum population grid cells (GHS-POP) falling within the city boundary to get total population. Density is computed as population divided by the built-up area (GHS-BUILT-S) within the boundary.

Rankings

City rankings are computed per epoch. Population rank orders cities by total population. Density rank uses population-weighted density to avoid distortion from low-density periphery cells.