Surface Thermal Heterogeneities and the Atmospheric Boundary Layer: The Thermal Heterogeneity Parameter

Representing land–atmosphere exchange processes at the ground surface of numerical-weather-prediction models remains a challenge in spite of the recent advances in computing. Previous studies investigating the effects of spatial surface heterogeneities have been viewed from a turbulence perspective, mostly assuming the existence of a blending length scale above which surface-induced perturbations are modelled using an ad hoc bulk surface parameter representing a pseudo-equivalent surface condition. While these types of approaches can generate reasonable results, they fail to account for the long-lasting spatial perturbations that modify the mean flow. In this work, the interactions between the characteristic scales of surface thermal heterogeneities and the mean resolved fluid dynamics are investigated for a broad range of unstable atmospheric conditions. Thermal dispersive fluxes, which naturally appear as a means to account for persistent-in-time advection fluxes generated by unresolved spatial heterogeneities, provide a quantification of the interaction between surface thermal heterogeneities and the atmospheric boundary-layer mean flow. Hence, they also provide a deterministic approach for including the effect of unresolved processes on the mean flow. We introduce a new non-dimensional number (i.e., the heterogeneity parameter) that can be used to identify the flow conditions and surface configurations in which heterogeneity effects become important. The heterogeneity parameter can be used to distinguish cases with high and low dispersive-flux contributions based on the mean flow and characteristics of the thermal heterogeneities. These results suggest that under weak geostrophic forcing, surface heterogeneity effects should be accounted for in numerical-weather-prediction models.