Evidence for the homothetic scaling of urban forms

Abstract

The size and form of cities influence their social and environmental impacts. Whether cities have the same form irrespective of their size is still an open question. We analyse the profile of artificial land and population density, with respect to the distance to their main centre, for the 300 largest European cities. Our analysis combines the GMES/Copernicus Urban Atlas 2006 land use database at 5 m resolution for 300 larger urban zones with more than 100,000 inhabitants and the Geostat population grid at 1 km resolution. We find a remarkable constancy of radial profiles across city sizes. Artificial land profiles scale in the two horizontal dimensions with the square root of city population, while population density profiles scale in three dimensions with its cube root. In short, cities of different size are homothetic in terms of land use and population density, which challenges the idea that larger cities are more parsimonious in the use of land per capita. 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. Our findings also yield homogenous spatial definitions of cities, from which we can re-question urban scaling laws and Zipf’s law for cities.

Alonso and the Scaling of Urban Profiles

“…He opened up a vast literature strand in geographical research, based on allometric urban growth and urban scaling laws (Lee ; Batty 2008b, 2010, 2013; Bettencourt ; Arcaute et al ; Jiang ). Recently, Lemoy and Caruso () endorsed this idea with new data on European cities and empirically identified the homothetic transformations that affect density and developed land profiles across population sizes. A logical extra step is then to address the second of these needs: assessing whether observed scaling behaviors can be related to socioeconomic factors by means of an explicative model.…”

Linking socio-economic and physical dynamics in spatial planning

“…The scaling behaviour of these profiles is then evaluated by minimizing a signal-over-noise ratio. The resulting scaling powers will refine previous insights on the scaling of population density profiles by confronting housing development intensity to the housing land profiles studied in Lemoy and Caruso (2018).…”

“…We focus on the most fundamental differentiation regarding urban land use: has it been artificialised for human uses (residence or roads for instance) or is it natural, or at least undeveloped (Prokop et al, 2011) Using spatially detailed data from the EU Copernicus Urban Atlas, the profiles of artificial land use (ALU) are calculated and compared between two years, 2006 and 2012. Based on the homothety of urban forms found by Lemoy and Caruso (2018), a simple scaling law is used to compare cities after controlling for population and allows for the internal structure of cities, as determined by distance to the city centre, to be compared across years. Examining cities from a monocentric perspective, with respect to distance to the main centre is long established in urban geography and economics (Alonso, 1964;Clark, 1951;Fujita, 1989;McDonald, 1989;Von Thünen, 1875).…”

“…Such a radial description has proven to be a useful concept cross disciplines, linking together the monocentric model of urban economics (Fujita and Thisse 2013), the urban sprawl analysis of urban geographers (Dieleman and Wegener 2004) and the compactness debate of urban planners (Ewing et al 2014). More recently, the radial description of urban attributes has been brought into the urban allometry research strand by Lemoy and Caruso (2018). They showed that land use and population density profiles turn out to scale with city size, respectively in proportion to the square root and to the cubic root of total urban population.…”

Regional science: economy and geography in France and French‐speaking countries

“…Economists and geographers collaborated for building models of urban morphologies under equilibrium constraints, as in a group formed by Pierre Henri Derycke, Jean‐Marie Huriot and Dominique Peeters, or Jacques Thisse and his team on spatial competition and agglomeration economies. However, recent investigations have led to propose introducing some complex processes in those models at equilibrium, as for instance by Geoffrey Caruso and Remy Lemoy in Luxembourg University renormalizing the distribution of intra‐urban densities (Lemoy & Caruso, ). A few scholars also developed land rent theory, with contributions coming from different perspectives and cross explorations: it encompasses planning theory and practice (Paul Lacaze), public finance (V. Renard), economic‐marxist perspective (Lipiez), land economics (Derycke, Sallez and Granelle), and political science (Guigou, ).…”