Understanding the mesoscopic scaling patterns within cities

Yu Liu,Zhou Huang,Jiang Zhang,Lei Dong

doi:10.1038/s41598-020-78135-2

Yu Liu, Zhou Huang + Show 2 more

Open Access

https://doi.org/10.1038/s41598-020-78135-2

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Abstract

Understanding quantitative relationships between urban elements is crucial for a wide range of applications. The observation at the macroscopic level demonstrates that the aggregated urban quantities (e.g., gross domestic product) scale systematically with population sizes across cities, also known as urban scaling laws. However, at the mesoscopic level, we lack an understanding of whether the simple scaling relationship holds within cities, which is a fundamental question regarding the spatial origin of scaling in urban systems. Here, by analyzing four extensive datasets covering millions of mobile phone users and urban facilities, we investigate the scaling phenomena within cities. We find that the mesoscopic infrastructure volume and socioeconomic activity scale sub- and super-linearly with the active population, respectively. For a same scaling phenomenon, however, the exponents vary in cities of similar population sizes. To explain these empirical observations, we propose a conceptual framework by considering the heterogeneous distributions of population and facilities, and the spatial interactions between them. Analytical and numerical results suggest that, despite the large number of complexities that influence urban activities, the simple interaction rules can effectively explain the observed regularity and heterogeneity in scaling behaviors within cities.

Highlights

Understanding quantitative relationships between urban elements is crucial for a wide range of applications
Current urban scaling frameworks ‘ignore’ those heterogeneous distributions as they usually model a city as a whole and study the macroscopic scaling across cities[6,9,14,22,23,24] or the temporal dynamics of individual cities25–27. (Ref.[28] compares the cross-sectional and temporal scaling analyses at the macroscopic level.) Several key questions at the mesoscopic level remain unanswered: do sub-units within a single city follow the power-law scaling as observed for systems of cities? What is the mechanism behind the potential scaling patterns within cities? Answering these questions is critical to reach a better understanding of urban systems
To incorporate the temporal dynamics and derive a better measure of the population distribution, we employ the concept of the active population (AP), which is a more appropriate proxy than simple residential or employment population for estimating socioeconomic a ctivity[15]

Summary

Introduction

Understanding quantitative relationships between urban elements is crucial for a wide range of applications. In spite of the complexity and variety of cities, it turns out that various macroscopic properties related to urban activities Y, such as gross domestic product and infrastructure, scale with the population size P in a surprisingly simple power-law manner: Y ∼ Pβ , where β is a scaling exponent (or an elasticity, in economic terms) that characterizes the non-linear properties of urban systems[1]. Our limited understanding of intra-urban scaling stems from the lack of granular data documenting the spatial distributions of urban elements such as population, infrastructure, and socioeconomic activity. Benefiting from the revolution of big data, we analyze the quantitative relationships between population, infrastructure, and socioeconomic activity at the mesoscopic level of ten Chinese cities: Beijing, Chengdu, Hangzhou, Jinan, Nanjing, Shanghai, Shenzhen, Suzhou, Xi’an, and Zhengzhou (Supplementary Table 1).

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