Urban Scaling as Validation for Predictions of Imperviousness From Population

Abstract

Strategies for creating quantitative projections for human systems, especially impervious surfaces, are necessary to consider the human drivers of climate and ecosystem change. There are models that generate predictions of how impervious surfaces may change in response to different potential futures, but few tools exist for validating those predictions. We seek to fill that gap. We demonstrate a statistically robust sublinear scaling relationship between population and urban imperviousness across a 15 year history. We show that Integrated Climate and Land-Use Scenarios (ICLUS) urbanization projections are also consistent with theory. These results demonstrate a theory that can be used to validate other models' predictions of urban growth and land cover change, analogous to the ways in which allometric scaling laws in biology have been used to validate process-based models of ecosystem composition under different climate scenarios. Plain Language Summary The decisions human organizations like cities or countries make can have a big influence on the environment, and the environment can influence our decisions. Scientists have some tools for modeling long-term interactions between cities and the environment. It is hard to learn if these tools are working, because even if we know how a particular decision-if made-would influence the environment, we are not good at predicting what decisions will be made. We show that there is a specific mathematical shape to the relationship between a city's population and the total built-up area: things like roads, parking lots, or buildings. This mathematical relationship shows us that in cities with larger populations, there is less space available per person and so built-up areas are more intensely used. We then test whether other researchers' predictions about interactions between urban population and built-up areas predict that these places will be more intensely used, like we showed. We show that the other researchers' predictions do correctly represent some important things we know about cities. This helps us know more about how reliable our predictions of interactions between human organizations and the environment might be.

The detection of natural cities in the Netherlands—Nocturnal satellite imagery and Zipf’s law

“…When looking at the panel analysis we recognize neglegible differences between the simple linear regression and the between estimates. This also corresponds with the results found by Brelsford et al (2020) who explored US Metropolitan Statistical Areas based on census data. The elasticities estimated in that study are close to 5/6 and similar to our results.…”

“…The total impervious area of a sample of n differently large cities with size P1 to Pn is thus: = with α and β pre-estimated. Brelsford et al (2020) (for the USA) and Bettencourt and Lobo (2015) 2 (for European countries) report βestimates in the range between 0.81 (USA) and 1.09 (Spain). For German functional cities larger than 500,000 inhabitants authors found a β-estimate of 0.95.…”

“…In these regressions the simple comparison of those five years could disregard a possible temporal influence of earlier on later years. Therefore (iii), as proposed by Brelsford et al (2020) we additionally use a between estimator:…”

“…Brelsford et al (2020) specify the between estimator with dummy variables for the years. Our results obtained with this method are almost identical but not reported.…”

Divergent urban land trajectories under alternative population projections within the Shared Socioeconomic Pathways

“…On the other hand, changes in LULC can also induce significant feedbacks on population characteristics. Elevated rates of urbanization may attract immigration from other areas, resulting in compounded population growth (Mulder 2006, Brelsford et al 2020, Koomen et al 2023. Understanding these interdependent relationships helps address sustainability challenges by increasing the realism of urban land projections, based on anticipated shifts in population growth (Gao and O'Neill 2021).…”