Scale Dependence and Nonlinear Effects of Urban Functional Zone Form on Carbon Emission Intensity: Evidence from Yangtze River Delta Agglomeration

Urban functional zones (UFZ) serve as fundamental units of human activity, and their spatial configurations significantly influence urban carbon emissions. However, current research often overlooks the heterogeneity of UFZ forms and the complex, multi-scale relationships underlying their impact on emissions. To address this gap, this study investigates the Yangtze River Delta (YRD) urban agglomeration by delineating UFZ from the dual perspectives of block function and form. By integrating multi-scale spatial analysis with explainable machine learning, this study establishes a morphological indicator system covering three dimensions: density, morphology, and structure. The results reveal a pronounced scale dependency in the effects of UFZ form on carbon emission intensity (CEI), with optimal analytical scales identified at 14 km for density, 5 km for morphology, and 7 km for structure. Notably, variations within these dimensions lead to distinct patterns of impact intensity, even within the same functional category. Furthermore, most indicators exhibit nonlinear, threshold-dependent effects on CEI. These findings provide actionable guidance for fine-grained urban planning and carbon mitigation strategies.