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Open AccessArticle

The Size Distribution, Scaling Properties and Spatial Organization of Urban Clusters: A Global and Regional Percolation Perspective

Potsdam Institute for Climate Impact Research (PIK), Potsdam 14473, Germany
Institute of Earth and Environmental Science, University of Potsdam, Potsdam-Golm 14476, Germany
Authors to whom correspondence should be addressed.
Academic Editors: Martin Behnisch, Gotthard Meinel and Wolfgang Kainz
ISPRS Int. J. Geo-Inf. 2016, 5(7), 110;
Received: 7 April 2016 / Revised: 22 June 2016 / Accepted: 27 June 2016 / Published: 12 July 2016
Human development has far-reaching impacts on the surface of the globe. The transformation of natural land cover occurs in different forms, and urban growth is one of the most eminent transformative processes. We analyze global land cover data and extract cities as defined by maximally connected urban clusters. The analysis of the city size distribution for all cities on the globe confirms Zipf’s law. Moreover, by investigating the percolation properties of the clustering of urban areas we assess the closeness to criticality for various countries. At the critical thresholds, the urban land cover of the countries undergoes a transition from separated clusters to a gigantic component on the country scale. We study the Zipf-exponents as a function of the closeness to percolation and find a systematic dependence, which could be the reason for deviating exponents reported in the literature. Moreover, we investigate the average size of the clusters as a function of the proximity to percolation and find country specific behavior. By relating the standard deviation and the average of cluster sizes—analogous to Taylor’s law—we suggest an alternative way to identify the percolation transition. We calculate spatial correlations of the urban land cover and find long-range correlations. Finally, by relating the areas of cities with population figures we address the global aspect of the allometry of cities, finding an exponent δ ≈ 0.85, i.e., large cities have lower densities. View Full-Text
Keywords: Zipf’s law; city clusters; percolation; Taylor’s law Zipf’s law; city clusters; percolation; Taylor’s law
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Fluschnik, T.; Kriewald, S.; García Cantú Ros, A.; Zhou, B.; Reusser, D.E.; Kropp, J.P.; Rybski, D. The Size Distribution, Scaling Properties and Spatial Organization of Urban Clusters: A Global and Regional Percolation Perspective. ISPRS Int. J. Geo-Inf. 2016, 5, 110.

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