Analyzing urban scaling laws in the United States over 115 years

The scaling relations between city attributes and population are emergent and ubiquitous aspects of urban growth. Quantifying these relations and understanding their theoretical foundation, however, is difficult due to the challenge of defining city boundaries and a lack of historical data to study city dynamics over time and space. To address this issue, we analyze scaling between city infrastructure and population across 857 United States metropolitan areas over an unprecedented 115 years using dasymetrically refined historical population estimates, historical urban road network models, and multi-temporal settlement data to define dynamic city boundaries based on settlement density. We demonstrate the clearest evidence that urban scaling exponents can closely match theoretical models over a century if cities are defined as dense settlement patches. Despite the close quantitative agreement with theory, the empirical scaling relations unexpectedly vary across regions. Our analysis of scaling coefficients, meanwhile, reveals that a city in 2015 uses more developed land and kilometers of road than a city with a similar population in 1900, which has serious implications for urban development and impacts on the local environment. Overall, our results offer a new way to study urban systems based on novel, geohistorical data.