ABSTRACT

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.

摘要

齐普夫定律，表征城市规模或人口的等级分布，已广泛应用于城市研究。以往对齐夫定律的研究主要集中在城市规模和人口的空间维度上，对其时间动态的考虑有限。在这里，我们提出了一个概念模型，使用 Zipf 定律的方法和全球城市范围数据的大约 30 年时间序列来表征城市群的空间蔓延模式。首先，我们量化了过去 30 年全球特大城市和小型定居点的城市面积增量。使用提出的概念模型，从 Zipfian 动力学中揭示了城市蔓延模式（即平衡、扩散和聚合）。然后，我们在不同的空间尺度上描述了城市蔓延模式。总体，全球小城市群的扩张速度略快于大城市群。在大陆尺度上，亚洲和非洲的扩张格局呈现平衡格局，而其他大陆则主要呈现弥散扩张格局。总体而言，对于发展中地区（例如，北非和西非），观察到聚集的蔓延模式，而对于那些高度发达的地区（例如，加拿大和西欧），则以扩散蔓延模式为主。本研究揭示的城市扩张模式反映了不同规模的城市群的不同增长率，促进了我们对城市发展路径的理解。齐夫定律在多个空间和时间维度上的相对稳健的表现表明城市扩张背后的城市演化的自组织机制，