摘要

Density analysis lies at the core of studies on urban expansion; however, many methods in urban land density analysis are arbitrary and suffer from the lack of an established foundation. We observed an "Inverse S-shape Rule" for urban land density that varies outward from an urban center by investigating 28 major cities in China at three time points. We proposed an inverse S-shaped function to formulate urban land density, which fit well for all of the cities in our sample using a nonlinear least squares fitting method. The parameters of the function explicitly describe the basic properties of an urban form. Based on the fitted functions, we derived an established method for the concentric partitioning of urban area and further proposed indicators to measure the urban compactness, urban expansion rate, and degree of urban sprawl. These indicators are practical for characterizing urban form and urban sprawl for either a single city or for multiple cities. A case study on major Chinese cities from 1990 to 2010 reveals that most of the cities expanded rapidly and became less compact and more dispersed during those two decades. However, most of the cities grew faster and showed more sprawl in the second decade compared to the first one. Discussions show that the model is also applicable for non-monocentric cities and possibly can be applied to many other geographical phenomena.