Title: Scaling evidence of the homothetic nature of cities,
Abstract: In this paper we analyse the profile of land use and population density with
respect to the distance to the city centre for the European city. In addition
to providing the radial population density and soil-sealing profiles for a
large set of cities, we demonstrate a remarkable constancy of the profiles
across city size.
Our analysis combines the GMES/Copernicus Urban Atlas 2006 land use database
at 5m resolution for 300 European cities with more than 100.000 inhabitants and
the Geostat population grid at 1km resolution. Population is allocated
proportionally to surface and weighted by soil sealing and density classes of
the Urban Atlas. We analyse the profile of each artificial land use and
population with distance to the town hall.
In line with earlier literature, we confirm the strong monocentricity of the
European city and the negative exponential curve for population density.
Moreover, we find that land use curves, in particular the share of housing and
roads, scale along the two horizontal dimensions with the square root of city
population, while population curves scale in three dimensions with the cubic
root of city population. In short, European cities of different sizes are
homothetic in terms of land use and population density. While earlier
literature documented the scaling of average densities (total surface and
population) with city size, we document the scaling of the whole radial
distance profile with city size, thus liaising intra-urban radial analysis and
systems of cities. In addition to providing a new empirical view of the
European city, our scaling offers a set of practical and coherent definitions
of a city, independent of its population, from which we can re-question urban
scaling laws and Zipf's law for cities.