A spatial hierarchical learning module based cellular automata model for simulating urban expansion: case studies of three Chinese urban areas

Understanding the spatio-temporal evolution of urban expansion is essential for urban planning and sustainable development. Recently, cellular automata (CA)-based models have emerged as highly effective and widely utilized approaches for simulating urban expansion. However, they suffered from complex structural information inherent in neighborhood effects, including spatio-temporal dimension disjunction and neighborhood sensitivity. To address these issues, herein, we propose a spatial hierarchical learning module based cellular automata model (SH-CA). Specifically, to tackle the spatio-temporal dimension disjunction, we take spatial dependence and historical expansion trends into consideration. We redefine the neighborhood structure and introduce lightweight convolutional neural networks to capture the complex spatio-temporal interaction in neighborhood effects. For the neighborhood sensitivity, we develop a gate filter to aggregate multiscale neighborhood effects for ensuring the synthesis of diverse neighborhood effects disparities. The proposed SH-CA model was implemented to simulate urban expansion in three distinct main urban areas of Beijing, Guangzhou, and Chengdu in China during 2010-2015. The results showed that the proposed SH-CA greatly improves the figure of merit and simulates the most real land-use patterns compared with other four sophisticated CA models. Moreover, the hierarchical learning module effectively modeled spatio-temporal interaction in neighborhood effects, mitigated neighborhood sensitivity, and showed a strong scalability to existing popular CA-based models.