The shapes of US cities: Revisiting the classic population density functions using crowdsourced geospatial data

The declining pattern of population density from city centres to the outskirts has been widely observed in American cities. Such a pattern reflects a trade-off between housing price/commuting cost and employment. However, most previous studies in urban population density functions are based on the Euclidean distance, and do not consider commuting cost in cities. This study provides an empirical evaluation of the classic population density functions in 382 metropolitan statistical areas (MSA) in the USA using travel times to city centres as the independent variable. The major findings of the study are: (1) the negative exponential function has the overall best fit for population density in the MSAs; (2) the Gaussian and exponential functions tend to fit larger MSAs, while the power function has better performance for small MSAs; (3) most of the MSAs appear to show a decentralisation trend during 1990–2016, and larger MSAs tend to have a higher rate of decentralisation. This study leverages crowdsourced geospatial data to provide empirical evidence of the classic urban economic models. The findings will increase our understanding about urban morphology, population–job displacement and urban decentralisation. The findings also provide baseline information to monitor and predict the changing trend of urban population distribution that could be driven by future environmental and technological changes.