An extended patch-based cellular automaton to simulate horizontal and vertical urban growth under the shared socioeconomic pathways

Most contemporary urban cellular automata (CA) models primarily focus on the simulation of urban land expansion, and cannot effectively simulate vertical urban growth. This study addresses this drawback by extending a patch-based urban CA model with a component that can predict the building volumes of an urban land expansion scenario. The proposed model is evaluated through a case study in the Guangzhou-Foshan metropolitan area, China. The horizontal urban growth simulations achieve a mean 'Figure-of-merit' value of 0.1406 at the cell level and an agreement of 97% at the pattern level. The building volume prediction made by the methods of random forest and k-nearest-neighbor has a testing R-2 of 0.90 and a mean percentage absolute error of 22%. The proposed model is applied to the urban growth projections under the shared socioeconomic pathways (SSPs). The results successfully reflect the influences that different SSPs have on vertical urban developments. These results also complement related research of urbanization projections under the SSPs, because most existing studies consider the impacts of horizontal urban growth only. As building volumes and heights are fundamental parameters to urban climate modeling, the ability of the proposed model to project future change in vertical urban developments can support the mitigation of climate change effects on human settlements.