Unifying the Scaling of Urban Heat Island With Surface Heat Flux Under Calm Conditions

Abstract How the urban heat island effect (UHI) responds to surface heat flux is a central question in urban climate research. Previous studies have reported two distinct scaling relations: nighttime UHI scales with heat flux to the one‐third power, while daytime UHI scales with heat flux to the two‐thirds power. However, the physical origin of this nighttime‐daytime difference and how the scaling transitions between the regimes remains elusive. We reconcile these scaling laws through a set of large‐eddy simulations (LES) in which the atmosphere is initialized with a mixed layer of depth beneath a linear potential temperature profile. LES reveals that the power‐law scaling of the UHI depends on . When (nocturnal conditions), the scaling exponent approaches one‐third, while for large (daytime conditions), it approaches two‐thirds. This scaling transition is explained through a theoretical framework that accounts for the dependence of boundary‐layer height on surface heat flux.