Unpacking the law of spatial directionality on urban expansion morphology and carbon emissions

Implementing spatial planning measures for compact cities requires examining the most carbon emission-efficient urban forms. However, past studies on urban form metrics have primarily focused on patterns, neglecting the directional aspects of urban expansion. This study analyses building footprint data within urbanized areas from 90 cities and 850 counties across China, to examine the relationship between urban forms and carbon emissions. Findings reveal that from 2000 to 2018, urban built-up areas predominantly expanded through elongation rather than sprawl. Representing the interbuilding distance, urban mean distance showed accelerated growth (94.6 %), but slowed down significantly after 2010 (9.22 %), with ongoing polycentric growth nationally. Urban shape and footprint indexes scale sub-linearly, while polycentricity and population size scale linearly with carbon emissions. Urban mean distance also exhibits a sub-linear scaling relationship. Elongation significantly influences carbon emissions at the city level, whereas GTWR and MGWR analyses confirm that sprawl contributes more significantly at the county scale. Furthermore, a threshold effect was identified: moderate urban distances mitigate emissions, while extended distances exacerbate them. Importantly, these findings advance the theoretical understanding of spatial directionality as a critical but underexplored dimension of urban form shaping long-term carbon lock-in. Directional urban expansion leads to morphological divergence and contributes to spatial heterogeneity in carbon lock-in effects. Consequently, effective low-carbon spatial planning requires jointly addressing urban density, the morphological structure defined by urban area, and the directional configuration of spatial expansion.