Grid, Patch, or Multi‐Scale Integration? A Comparative Analysis for Cellular Automata‐Based Urban Growth Simulations

ABSTRACT Capturing patch features can significantly enhance the performance of cellular automata (CA)‐based land use modeling. However, current research has yet to comprehensively explore the definition of patch‐based CA simulation rules and their integration with grid‐based rules. This study proposes a generalized urban CA framework that integrates grid‐ and patch‐based rules across scales. Using Beijing's urban growth from 2000 to 2020 as a case study, we evaluated the simulation performance of CA under different rule‐integration modes. The results demonstrate that patch‐level assessment of urban growth potential improves the model's temporal generalizability, robustness, and accuracy. However, using patches as cells for local interactions reduces simulation performance and efficiency, whereas grid‐based neighborhoods produce better results by more closely resembling complex boundary buffer neighborhoods. Furthermore, treating patches as basic units for urban expansion control enhances simulated urban morphology and accuracy. Integrating these optimal rules across scales within the proposed framework yields the best‐performing CA model. This study offers a methodological reference for grid‐patch integration in land use modeling, which can facilitate pre‐assessing urban growth‐induced land degradation risks and achieving reasonable spatial planning, supporting sustainable urban development.