A methodology to quantify the neighborhood decay effect of urban cellular automata models

Spatial heterogeneity is an essential feature of land use change. It is important for cellular automata (CA)-based urban expansion modeling to consider the spatial heterogeneity of neighborhood effect. According to the first law of geography, there exists a distance decay effect in the neighborhood space of the urban CA models. But no research has ever been able to accurately quantify the neighborhood decay effect and apply it to models. In this study, we propose a methodology to accurately quantify the neighborhood decay effect of CA models with large neighborhood size, including the design of neighborhood configuration and the selection and optimization of decay strategies. Taking Wuhan and Guangzhou as examples, we show the implementation process of the methodology and simulate urban expansion of two areas for the periods 2000-2010 and 2010-2015 by CA models with distance decay neighborhood to reveal the advantages and characteristics of modeling the neighborhood decay effect. The results show that the simulation accuracy of CA models with the spatial heterogeneous neighborhood and the hybrid neighborhood (HYN) is higher than that of CA models with homogeneous neighborhood, and in most cases, the HYN can more accurately describe the neighborhood decay effect.