Modelling multi-regional urban growth with multilevel logistic cellular automata

Simulation models based on cellular automata (CA) are useful for revealing the complex mechanisms and processes involved in urban growth and have become supplementary tools for urban land use planning and management. Although the urban growth mechanism is characterized by multilevel and spatiotemporal heterogeneity, most existing studies focus only on simulating the urban growth of singular regions without considering the heterogeneity of the urban growth process and the multilevel factors driving urban growth within regions that consist of multiple subregions. Thus, urban growth models have limited performance when simulating the urban growth of multi-regional areas. To address this issue, we propose a multilevel logistic CA model (MLCA) by incorporating a multilevel logistic regression model into the traditional logistic CA model (LCA). In the MLCA, multilevel driving factors are considered, and the multilevel logistic model allows the transition rules to not only vary in space, but also change when the subregional level factors change. To verify the MLCA's validity, it was applied to simulate the urban growth of Tongshan County, located in China's Xuzhou Prefecture. The results were compared with three comparative models, LCA1, which only considered grid cell-level factors; LCA2, which considered both grid cell- and subregional-level factors; and artificial neural network CA. Urban growth data for the periods 2000-2009 and 2009-2017 were used. The results show that the MLCA performs better on both visual comparison and indicators for accuracy verification. The Kappa of the results increased by < 5%, but the improvement was significant, while increases for the accuracy of urban land and figure of merit were much higher than 5%. In addition, the results of MLCA had the smallest mean absolute percentage error when allocating new urban land areas to the various subregions. The results reveal that higher-level (e.g., town level) factors either strengthened or weakened the effects of grid cell-level factors on urban growth, which indirectly affected the spatial allocation of new urban land. The MLCA model is an effective step towards simulating nonstationary urban growth of multi-regional areas, using the comprehensive effects of multilevel driving factors.