Scaling of Urban 3D Form with Emissions and GDP in Chinese Cities

Rapid urbanization has permanently transformed the face of cities. As the physical manifestation of these transformations, urban form provides a key basis for examining its connections with urban outcomes. While previous studies have primarily focused on two-dimensional (2D) measures, cities are inherently three-dimensional (3D), and the increasing availability of spatial data has recently enabled more detailed 3D analyses. However, comprehensive frameworks that integrate both horizontal and vertical dimensions remain limited. Here, we analyze building height data for 296 Chinese prefecture-level cities in 2019, proposing a volume-constrained framework to explore cross-sectional scaling relationships of urban 3D form with transport emissions, building operation emissions, and GDP. Our results suggest that, conditional on comparable total building volumes, cities characterized by greater vertical development and smaller horizontal extent are statistically associated with lower transport and building operation emissions and higher GDP. We further examine heterogeneity in these associations across cities with different levels of economic development, population size, energy transition, and spatial structure. Additionally, we decompose building operation emissions by end use and show that the height-emission association varies substantially across regional contexts and energy structures, particularly in reliance on heating. This framework provides a systematic approach for incorporating 3D urban form into cross-city scaling analyses, highlighting the diversity of spatial configurations and their associations with urban performance.