The Dynamics of Cities: Assessing Scaling Relations of Past and Projected Urban Population and Infrastructure to Analyze Trajectories of Urbanization in the 21st Century

Abstract:

Future projections of population estimate that Earth will add 2.5 billion urban inhabitants by 2050. Rapid urbanization will occur to meet the demands of increasing populations. Bettencourt’s theory of urban scaling states (1) that properties of urban infrastructure (Y) are power law functions of population (N), described as Y=Y₀N^β, where β < 1.0 for urban infrastructure, and (2) that the relationship is scale-invariant. Studies by Bettencourt and colleagues provide evidence to support urban scaling using a range of urban infrastructure variables, such as impervious surface area or road volume as a power law function of population size. We tested the theory of urban scaling using, as a metric of urban infrastructure, the percent developed imperviousness (%ISA) data product at 30 m spatial resolution from the USGS National Land Cover Database for 2001, 2006, and 2011. We examined the scaling relations between %ISA and population for all metropolitan and micropolitan statistical areas (MSAs) in the conterminous U.S. We compared the parameter coefficients derived from data in the recent past (2001-2011) to the parameter coefficients estimated using two different urban growth projections for 2010-2100. Both urban growth datasets included projections based on the IPCC SRES storylines. As expected, we found β < 1.0 for urban infrastructure properties using both the recent data and future projections. We found β to decrease over time for both urban projection datasets, suggesting increased densification of MSAs in the future. We calculated change in %ISA and population to investigate the impacts of the SRES storylines on future urban density. We found three major patterns in projections of future urban area and population by MSA: (1) increased densification of urban areas along the border with Mexico; (2) stagnant to decreasing population by 2100 yet increasing %ISA (small MSAs); and (3) a linear trend where increases in population coincide with increases in %ISA.