Measuring heterogeneity in urban expansion via spatial entropy

TL;DR

This paper introduces a spatial entropy-based method to quantify urban sprawl, providing a rigorous, interpretable measure that can compare urban expansion across different cities and over time.

Contribution

It develops a novel spatial entropy approach for measuring urban heterogeneity, improving the assessment of urban sprawl with a rigorous and comparative framework.

Findings

The proposed measures effectively quantify urban disorder.

Application to European cities demonstrates interpretability.

Method allows comparison of urban expansion across space and time.

Abstract

The lack of efficiency in urban diffusion is a debated issue, important for biologists, urban specialists, planners and statisticians, both in developed and new developing countries. Many approaches have been considered to measure urban sprawl, i.e. chaotic urban expansion; such idea of chaos is here linked to the concept of entropy. Entropy, firstly introduced in information theory, rapidly became a standard tool in ecology, biology and geography to measure the degree of heterogeneity among observations; in these contexts, entropy measures should include spatial information. The aim of this paper is to employ a rigorous spatial entropy based approach to measure urban sprawl associated to the diffusion of metropolitan cities. In order to assess the performance of the considered measures, a comparative study is run over alternative urban scenarios; afterwards, measures are used to quantify the degree of disorder in the urban expansion of three cities in Europe. Results are easily interpretable and can be used both as an absolute measure of urban sprawl and for comparison over space and time.