Modeling urban growth using spatially heterogeneous cellular automata models: Comparison of spatial lag,spatial error and GWR

Many methods can be used to construct geographical cellular automata (CA) models of urban land use, but most do not adequately capture spatial heterogeneity in urban dynamics. Spatial regression is particularly appropriate to address the problem to reproduce urban patterns. To examine the advantages and disadvantages of spatial regression, we compare a spatial lag CA model (SLM-CA), a spatial error CA model (SEM-CA) and a geographically-weighted regression CA model (GWR-CA) by simulating urban growth at Nanjing, China. Each CA model is calibrated from 1995 to 2005 and validated from 2005 to 2015. Among these, SLM and SEM are spatial autoregressive (SAR) models that consider spatial autocorrelation of urban growth and yield highly similar land transition probability maps. Both SAR-CA and GWR-CA accurately reproduce urban growth at Nanjing during the calibration and validation phases, yielding overall accuracies (OAs) exceeding 94% and 85%, respectively. SAR-CA is superior in simulating urban growth when measured by OA and figure-of-merit (FOM) while GWR-CA is superior regarding the ability to address spatial heterogeneity. A concentric ring buffer-based assessment shows OA valleys that correspond to FOM peaks, where the ranges of valleys and peaks indicate the areas with active urban development. By comparison, SAR-CA captures more newly-urbanized patches in highly-dense urban areas and shows better performance in terms of simulation accuracy; whereas, GWR-CA captures more in the suburbs and shows better ability to address spatial heterogeneity. Our results demonstrate that spatial regression can help produce accurate simulations of urban dynamics featured by spatial heterogeneity, either implicitly or explicitly. Our work should help select appropriate CA models of urban growth in different terrain and socioeconomic contexts.