Mechanisms of Vertical Sensible Heat Flux Divergence in the Urban Roughness Sublayer: Insights from Observations and LES

Eddy-covariance (EC) fluxes collected on urban rooftops are commonly interpreted as representative of turbulent fluxes above the roughness sublayer when sensors are installed well above the mean building height. However, extended EC observations from a tall rooftop in Enschede, the Netherlands, reveal vertical divergence in sensible heat flux (SHF), with measurements at 10 m above the roof sometimes substantially differing from those at 5 m. To investigate the mechanisms behind this behaviour, we integrate dual-level EC measurements with building-resolved large-eddy simulations (LES) performed using the PALM4U model over a realistic urban environment and synoptic conditions. Two clear-sky case studies are examined: a windy spring episode dominated by mechanical shear and organized convective rolls, and a calm , hot summer event characterized by buoyancy-driven convective cells. The LES captures both the diurnal cycle of SHF and the enhanced vertical divergence observed during the calm conditions. Analysis of the flow structure indicates that the windy case dominated by mechanical shear with nearly aligned streamlines, weak flow deflection, and predominantly local turbulent transport, while the calm case is associated with pronounced streamline deformation, inclined thermal structures, and stronger non-local transport contributions. Evaluation of flux-gradient relationships based on K-theory suggests that local gradient-based parameterizations perform well under windy conditions, whereas they break down under calm, convective regimes, indicating that horizontal advection due to flow distortion and non-local turbulent transport dominates under convective conditions. Double-averaging further shows that dispersive flux contributions are largely restricted to the immediate canopy layer and remain negligible at the EC measurement heights. Overall, the findings demonstrate that vertical divergence of SHF above urban rooftops is mainly controlled by flow distortion and non-local transport processes due to thermal stratification. Our results demonstrate that commonly used height-based criteria (i.e. 2–5 times the mean building height) are insufficient to ensure representative EC measurements in complex urban settings and LES can serve as a powerful tool to understand the flow in complex urban settings before installing EC instruments for flux measurements.