Open Access

Yunfei Li, Fabiano L. Ribeiro, Bin Zhou, Diego Rybski

• City size is a primary determinant of the urban heat island (UHI) intensity, with its effects further nuanced by the urban form. But how to factor in the urban form into the UHI assessment remains unresolved. We propose an every-pair-interaction model that meaningfully incorporates urban size and fractal dimension to characterize the UHI intensity. Regression on the summertime surface UHI intensity of 5,000 European cities shows that the model outperforms the simple linear combination of logarithmic size and fractal dimension. Subject to the interplay between the range of the every-pair interaction and the urban fractal shape, the model also represents a generalization as it includes power-law, logarithmic, and saturating size dependence of UHI—all three possibilities have been reported empirically in the literature. Our theoretical framework indicates that the surface UHI intensity saturates with urban size, opening up new research perspectives around UHI intensity.