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

Yanguang Chen,Jian Feng

doi:10.1155/2017/5243287

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 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.

Highlights

Cities as systems and systems of cities are scale-free complex systems, which cannot be effectively described by the traditional mathematical methods based on characteristic scales in many respects
The algorithm adopted in this study is the ordinary least squares (OLS) method, which can be applied to double logarithmic linear regression
A new method based on the maximumlikelihood estimation (MLE) is developed by Clauset et al [34] to address the power-law distribution in empirical data

Summary

Introduction

Cities as systems (individuals) and systems of cities (groups) are scale-free complex systems, which cannot be effectively described by the traditional mathematical methods based on characteristic scales in many respects. Two correlated scaling laws are often employed to analyze a hierarchy of cities: one is Zipf ’s law, and the other is the law of allometric growth. Zipf ’s law reflects urban growth [1, 9], and the allometric scaling law can be derived from dual Zipf ’s models of rank-size distributions of urban population and area [18]. This suggests that Zipf ’s law and the allometric scaling law represent different sides of the same coin. We can develop a new approach to studying urban systems

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