Spatial Scale Selection for Urban Systems: A Complexity–Heterogeneity Balancing Method

Cities are complex systems with socioeconomic activities exhibiting diverse spatial distributions, where selecting an appropriate observation scale is vital for understanding urban complexity. However, the traditional methods for this task are often limited, either because they rely on subjective judgments or lack generalizability before being applied across the diverse functions of a city. To address this issue, we introduce a complexity-heterogeneity balancing method, which employs renormalization group techniques to generate distribution matrices across different scales, striking a balance between complexity and heterogeneity to objectively identify appropriate observation scales. We implement this method on freight, enterprise and restaurant distribution data derived from major Chinese cities to identify their appropriate spatial scales. The results properly reflect the characteristic spatial organization structure of each urban function, meaning that the method provides a robust framework for determining appropriate scales in urban spatial analysis tasks. Our study has potential applications in enhancing the logistics optimization, industrial zoning and commercial planning processes and identifying urban functions and morphological features, thereby contributing to sustainable urban development.