Understanding the mesoscopic scaling patterns within cities

TL;DR

This study investigates how urban infrastructure and socioeconomic activities scale within cities, revealing sub- and super-linear patterns influenced by population heterogeneity and spatial interactions, thus advancing understanding of intra-city scaling laws.

Contribution

It provides the first detailed analysis of mesoscopic scaling patterns within cities and introduces a conceptual framework explaining observed heterogeneity based on population and facility distributions.

Findings

Infrastructure volume scales sub-linearly with active population.

Socioeconomic activity scales super-linearly with active population.

Scaling exponents vary among cities of similar size.

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.