Relationships between carbon emissions and urban population size and density, based on geo-urban scaling analysis: A multi‑carbon source empirical study

Urban sustainability focuses on coupled human-nature system and has attracted the attention of the world's policy and academia. This study applies geographically weighted regression and movement stratification regression in the urban scaling perspective. Multiple carbon sources were used to analyze the relationships between carbon emissions and urban population size, density. Results revealed the followings. (1) Overall, there are sub-linear scaling modes between urban size and total, industrial and residential carbon emissions. In contrast, a super-linear mode was found for transportation carbon emissions. (2) An examination of regional differences revealed disparities in carbon urban scaling exponents. (3) For total, industrial, and transportation carbon emissions, an oblique W-shape with a low left and high right side in the relationship between density urban scaling exponents and urban size was found. A U-shape relationship was found in residential carbon emissions. (4) One million urban population size is the threshold point. Increasing urban density can promote carbon reduction when the urban population is smaller than one million. In contrast, increasing urban density leads to more carbon emissions when the urban population exceeds one million. (5) Urban low-carbon development strategies should be developed according to each region's different urban densities and scale characteristics. • there is an optimal urban density value to maximize the efficiency of urban carbon emission. • urban density different impacts on carbon emissions differently for different city sizes. • total carbon emissions do have a scaling relationship with urban size. • Residential carbon emissions were most sensitive to city size. • the theoretical relationship between urban size and urban scaling exponents of density (TSDC hypothesis).