Acta Geographica Sinica ›› 2021, Vol. 76 ›› Issue (2): 251-260.doi: 10.11821/dlxb202102001

• Theoretical Exploration •     Next Articles

Urban scaling law and its application

GONG Jianya1(), XU Gang1(), JIAO Limin2, QIN Kun1   

  1. 1. School of Remote Sensing and Information Engineering, Wuhan University, Wuhan 430079, China
    2. School of Resource and Environmental Sciences, Wuhan University, Wuhan 430079, China
  • Received:2019-07-30 Revised:2020-12-26 Online:2021-02-25 Published:2021-04-25
  • Contact: XU Gang;
  • Supported by:
    Ministry of Education in China Project of Humanities and Social Sciences(20YJCZH195);China Postdoctoral Science Foundation(BX20190251);China Postdoctoral Science Foundation(2019M662699);National Natural Science Foundation of China(41971368)


The introduction of complexity science in urban geography has provided a new perspective to understand cities. Urban scaling law is one of the simple rules behind complex urban systems, which describes how urban indicators scale with urban population size within the system of cities. Social interaction-related urban indicators, such as GDP and innovation, super-linearly scale with urban population in a power law form, while infrastructure-related urban indicators, such as roads and gas stations, sub-linearly scale with population. Other urban indicators linearly scale with population, which are related to human individual needs, such as jobs and household electricity consumption. In this study, we first summarize the content and progress of urban scaling law during the past decade (2007-2020) from the following four aspects: the validation of urban scaling law, the explanation on the mechanism of urban scaling law, the application of urban scaling law, and the criticism of urban scaling law. We further compare the fundamental differences between the urban scaling law and urban allometric growth. Urban scaling law describes quantitative relationships between urban indicators and population size across cities, while urban allometric growth emphasizes the temporal growth of individual cities. Our analysis indicates that the cross-sectional urban scaling law cannot be applied to predict temporal trajectories of individual cities. Finally, we introduce the scale-adjusted metropolitan indicator (SAMI) for the evaluation of economic performance and urban land use efficiency in 291 Chinese cities, which is based on the theory of urban scaling law. The conventional evaluation of cities based on per capita indicators ignores the non-linear scaling relationship between urban indicators and population size. For example, the GDP per capita of large cities ranks high thanks to their advantages of population size. SAMI eliminates the influence of city size and can compare urban performance more objectively. Cities with higher SAMIs of GDP experience a higher efficiency in economic output (GDP) and they are concentrated in southeast coastal regions, middle reaches of the Yangtze River, and Xinjiang. On the contrary, cities in the northeastern China and Central China Plains experience a relatively low efficiency in economic output. Future studies are encouraged to focus on the mechanism of urban scaling law, the unified model for the evolving urban system across cities and over time, and the scaling law within cities.

Key words: urban geography, science of cities, complex urban system, scaling law, scale-adjusted metropolitan indicator (SAMI)