An Area-Adaptive Gravity Model Addressing Spatial Heterogeneity in Urban Mobility

Accurately modeling human mobility is fundamental for understanding and managing urban systems. Among various approaches, the gravity model, derived from Zipf’s law and long used to describe human movement between two locations, is one of the most widely adopted frameworks to predict human movement between areas. However, when applied to intra-city mobility, the model’s parameters show strong sensitivity to the resolution of units, limiting its accuracy and generalizability in real urban environments, which consist of irregular and unequal regions rather than idealized uniform grids. In this study, we systematically examine how spatial scale, the side of spatial unit based on grid partitioning of cities, shapes model behavior and identify two mechanisms: the scale-combination benefit and the scale-disparity penalty. Empirical analyses show that each 1 km increase in the sum of grid sizes improves CPC by 0.012, whereas each 1 km increase in their absolute difference reduces it by 0.020. Further analysis reveals a strong positive linear relationship between model parameters and the logarithm of the product of origin and destination scales. Extending these findings, we develop an area-adaptive gravity model that adapts to regions of varying sizes and is particularly effective for capturing intra-city mobility. Evaluation across grid, irregular, and sub-district partitions using five performance metrics demonstrates that the proposed model achieves superior adaptability and predictive power.