A comparison of two models to measure the distance decay of urban land density to the city center

As the distance to the city center increases, the density of urban land decays. The distance decay of urban land density can be quantitatively described by the urban land density function (also known as the inverse-S function) and the Geographic Micro-Process (GMP) model. However, the differences between the two models in the aspects of the fitting results and application scope are not clear. Taking Hefei as an example, this paper interpreted Landsat images to obtain land use data at three time points and combined the concentric-ring analysis method to compare the differences between the two models. The results show that the two models can both fit the distance decay of urban land density well, and both provide quantitative indicators for measuring urban compactness. However, the inverse-S function is an empirical model. Although it can describe the distance decay of urban land density and the urban expansion processes with higher accuracy, it cannot provide a mechanistic explanation. In contrast, the GMP model is a theoretical model derived based on explicit assumptions, which can reveal the reasons for the inverse-S shaped decay pattern of urban land density and the change of urban compactness from a process perspective. This study provides references for the method selection of fitting urban land density spatial decay and the modeling of urban land-use change.