City boundaries and the universality of scaling laws

This paper investigates the universality and robustness of scaling laws for urban systems, according to the work by Bettencourt, Lobo and West among others, using England and Wales as a case study. Initial results employing the demarcations for cities from the European Statistical Commission digress from the expected patterns. We therefore develop a method for producing multiple city definitions based on both morphological and functional characteristics, determined by population density and commuting to work journeys. For each of these realisations of cities, we construct urban attributes by aggregating high resolution census data. The approach produces a set of more than twenty thousand possible definitions of urban systems for England and Wales. We use these as a laboratory to explore the behaviour of the scaling exponent for each configuration. The analysis of a large set of urban indicators for the full range of system realisations shows that the scaling exponent is notably sensitive to boundary change, particularly for indicators that have a nonlinear relationship with population size. These findings highlight the crucial role of system description when attempting to identify patterns of behaviour across cities, and the need for consistency in defining boundaries if a theory of cities is to be devised.