Diversity in global urban sprawl patterns revealed by Zipfian dynamics

Zipf’s law, characterizing the rank-size distribution of city size or population, has been widely applied in urban studies. Previous studies on Zipf’s law mainly focused on the spatial dimension of urban size and population, with limited consideration of its temporal dynamics. Here, we proposed a conceptual model to characterize the spatial sprawl pattern of urban clusters using the approach of Zipf’s law and approximately 30-year time series of global urban extent data. First, we quantified increments of urban areas in global megacities and small settlements over the past three decades. Urban sprawl patterns (i.e., equilibrium, diffuse, and aggregated) were revealed from the Zipfian dynamics, using the proposed conceptual model. Then, we characterized urban sprawl patterns at different spatial scales. Overall, the sprawl of small urban clusters is slightly faster than those of large clusters globally. At the continental scale, the sprawl pattern shows equilibrium patterns in Asia and Africa, whereas other continents mainly present diffuse sprawl patterns. In general, for developing regions (e.g., North and West Africa), an aggregated sprawl pattern was observed, whereas, for those highly developed regions (e.g., Canada and West Europe), the diffuse sprawl pattern dominated. Patterns of urban sprawl revealed in this study reflect different growth rates of varying sizes of urban clusters, advancing our understanding of urban development pathways. The relatively robust performance of Zipf’s law over multiple spatial and temporal dimensions suggests the self-organized mechanism of city evolution behind urban sprawl, which contributes to the development of future urban growth models.