A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991-2014

TL;DR

This study analyzes the hierarchical allometric scaling of Chinese cities from 1991 to 2014, revealing clearer scaling relations over time, persistent long-term evolution, and implications for urban planning based on fractal and allometric principles.

Contribution

It introduces a hierarchical cascade model and R/S analysis to study city scaling laws, highlighting the evolution and long-term memory of urban growth patterns in China.

Findings

Hierarchical scaling relations became clearer from 1991 to 2014.

Global allometric exponent fluctuated around 0.85.

Hurst exponent > 0.5 indicates persistent urban evolution.

Abstract

The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in observational data. In theory, both the allometric growth law and Zipf's law are related to the hierarchical scaling laws associated with fractal structure. In this paper, the scaling laws of hierarchies with cascade structure are used to study Chinese cities, and the method of R/S analysis is applied to analyzing the change trend of the allometric scaling exponents. The results show that the hierarchical scaling relations of Chinese cities became clearer and clearer from 1991 to 2014 year; the global allometric scaling exponent values fluctuated around 0.85, and the local scaling exponent approached to 0.85. The Hurst exponent of the allometric parameter change is greater than 0.5, indicating persistence and a long-term memory of urban evolution. The main conclusions can be reached as follows: the allometric scaling law of cities represents an evolutionary order rather than an invariable rule, which emerges from self-organized process of urbanization, and the ideas from allometry and fractals can be combined to optimize spatial and hierarchical structure of urban systems in future city planning.