Fast Identification of Urban Sprawl Based on K-Means Clustering with Population Density and Local Spatial Entropy

Lingbo Liu,Zhenghong Peng,Hongzan Jiao,Jie Zhao,Yang Yu,Hao Wu

doi:10.3390/su10082683

Abstract

As urban sprawl is proven to jeopardize the sustainability system of cities, the identification of urban sprawl is essential for urban studies. Compared with previous related studies which tend to utilize more and more complicated variables to recognize urban sprawl while still retaining an element of uncertainty, this paper instead proposes a simplified model to identify urban sprawl patterns. This is a working theory which is based on a diagram interpretation of the classic urban spatial structure patterns of the Chicago School. The method used in our study is K-means clustering with gridded population density and local spatial entropy. The results and comparison with open population data and mobile phone data verify the assumption and furthermore indicate that the accuracy of source population data will limit the precision of output identification. This article concludes that urban sprawl is mainly dominated by population and surrounding unevenness. Moreover, the Floating Catchment Area (FCA) local spatial entropy method presented in this research brings about an integration of Shannon entropy, Tobler’s first law of geography and the Moore neighborhood, improving the spatial homogeneity and locality of Batty’s Spatial Entropy model which can only be used in a general scope.

Highlights

Urban spatial expansion is described as a process in which the city encroaches surrounding open space and extends the territory of urban areas, due to its growing population, increasing incomes and decreasing commuting costs [1]
As a disfavored type of expansion, urban sprawl refers to excessive spatial growth of cities, which results in negative consequences such as rapid loss of farmland, despoiled ecological system and swelling traffic congestion in both the West and the East [2,3,4,5,6,7,8,9,10], which resulted in a wide range of economic [2], social [3], health [4] and environmental problems [11], jeopardizing the sustainability system of cities and becoming a major concern for urban studies
This study suggests the identification of urban sprawl based on K-means clustering with the merely gridded population and its local spatial entropy, wherein the Elbow method is used to verify the group number

Summary

Introduction

Urban spatial expansion is described as a process in which the city encroaches surrounding open space and extends the territory of urban areas, due to its growing population, increasing incomes and decreasing commuting costs [1]. This article hereby argues that the combination of the entropy method and urban sprawl indices presents an ideal way of identifying urban sprawl. Based on the reinterpretation of urban spatial structure models of the Chicago School with gridded population density map, this paper concludes that there exist five combination patterns of spatial population density in Moore neighborhood units, which helps to identify whether the central unit is in a sprawling area. This paper hereby presents a simplified urban sprawl measuring method based on K-means clustering with merely the population density of gridded units and their local spatial entropy which calculates the uneven distribution degree of population density of surrounding units. The final section summarizes the main findings and reflects on the methodology

Urban Expansion Diagrams of Gridded Population

FCA Local Spatial Entropy

Conclusions