# The light pollution as a surrogate for urban population of the US cities

## TL;DR

This paper investigates how different definitions of city boundaries affect the relationship between night-time light and population in US cities, highlighting the importance of boundary choice for urban scaling analyses.

## Contribution

It demonstrates that natural clustering methods reveal an isometric relation between light pollution and population, unlike traditional geopolitical definitions which show sublinear scaling.

## Key findings

- City boundary definitions significantly influence scaling behavior.
- Natural clustering yields an isometric relation between light and population.
- CCA-based measures are more consistent and suitable for urban studies.

## Abstract

We show that the definition of the city boundaries can have a dramatic influence on the scaling behavior of the night-time light (NTL) as a function of population (POP) in the US. Precisely, our results show that the arbitrary geopolitical definition based on the Metropolitan/Consolidated Metropolitan Statistical Areas (MSA/CMSA) leads to a sublinear power-law growth of NTL with POP. On the other hand, when cities are defined according to a more natural agglomeration criteria, namely, the City Clustering Algorithm (CCA), an isometric relation emerges between NTL and population. This discrepancy is compatible with results from previous works showing that the scaling behaviors of various urban indicators with population can be substantially different for distinct definitions of city boundaries. Moreover, considering the CCA definition as more adequate than the MSA/CMSA one because the former does not violate the expected extensivity between land population and area of their generated clusters, we conclude that, without loss of generality, the CCA measures of light pollution and population could be interchangeably utilized in future studies.