城市标度律及应用

Urban scaling law and its application

城市标度律刻画了城市系统某一指标和人口规模的幂函数缩放关系,包括超线性(社会交互类指标)、次线性(基础设施类指标)和线性(个人需求类指标)3种标度关系。本文从城市标度律的验证、解释、应用和质疑4个方面总结梳理了2007—2020年间的研究进展,重点分析了城市标度律和城市时序发展的异速增长律的明显差异,单个城市时序发展不会遵循城市系统的截面标度律。城市规模修正指标为更加客观地评价城市表现提供了新思路。考虑城市规模效应后,2017年中国经济产出效率较高的城市主要位于东南沿海、长江中游和新疆,而东北和中原地区城市经济产出效率较低。城市标度律的机制解释、城市系统动态演化模型和城市内部标度律是未来值得关注的研究方向。

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 scaleadjusted 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.