On the relation between transversal and longitudinal scaling in cities

Abstract

Does the scaling relationship between population sizes of cities with urban metrics like economic output and infrastructure (transversal scaling) mirror the evolution of individual cities in time (longitudinal scaling)? The answer to this question has important policy implications, but the lack of suitable data has so far hindered rigorous empirical tests. In this paper, we advance the debate by looking at the evolution of two urban variables, GDP and water network length, for over 5500 cities in Brazil. We find that longitudinal scaling exponents are city-specific. However, they are distributed around an average value that approaches the transversal scaling exponent provided that the data is decomposed to eliminate external factors, and only for cities with a sufficiently high growth rate. We also introduce a mathematical framework that connects the microscopic level to global behaviour, finding good agreement between theoretical predictions and empirical evidence in all analyzed cases. Our results add complexity to the idea that the longitudinal dynamics is a micro-scaling version of the transversal dynamics of the entire urban system. The longitudinal analysis can reveal differences in scaling behavior related to population size and nature of urban variables. Our approach also makes room for the role of external factors such as public policies and development, and opens up new possibilities in the research of the effects of scaling and contextual factors.

City size based scaling of the urban internal nodes layout

“…For example, once the urban population increases, the number of network nodes increases accordingly, which may affect the structure of the entire network and its k value. A recent research confirmed the relationship between urban development and the law of urban size using longterm datasets [37]. Therefore, in future research, the time dimension can also be introduced to describe the relationship between the urban structure and law of urban size.…”

More from Less? Environmental Rebound Effects of City Size

“…In contrast, infrastructure variables such as urbanized area, total electrical cables length, total street length, gasoline consumption, number of petrol stations and number of schools, among others [15,43,46], present β < 1, or a sub-linear regime. It means that larger cities require less infrastructure per-capita (Y/N).…”

“…Examples of such variables are the number of households and household water consumption [43]. The fact that the values of such exponents are nearly the same, showing similar behavior for different urban variables and different countries, suggests a potential universality in urban scaling [15][16][17]43,46,47], being also observed in the dynamic growth of individual cities [46,48]. Moreover, some theoretical works [16,17,49] suggest that socio-economic and infrastructure scaling exponents are in fact interrelated, in a way that β = 1 + δ for socio-economic variables, and β = 1 − δ for infrastructure variables, where δ ≈ 0.15 (obtained empirically) is the parameter that establishes an interrelation between these two regimes.…”

Spatial Scaling of Land Use/Land Cover And Ecosystem Services Across Urban Hierarchical Levels: Patterns And Relationships

“…for certain quantities reflecting wealth creation and innovation and <1 for certain material infrastructural quantities) (Bettencourt et al 2007;Bettencourt et al 2010;Ribeiro et al 2020).…”