  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.
