The effect of Surface Heterogeneity on the Temperature-Humidity Correlation and the Relative Transport Efficiency

We derive a conceptual model of the flow over heterogeneous terrain consisting of patches with contrasting Bowen ratios. Upward moving eddies are assumed to carry heterogeneous properties, whereas downward moving eddies carry homogeneous properties. This results in a decorrelation of temperature and humidity as the contrast between the patches increases. We show that this model is able to reproduce the relationship developed by Lamaud and Irvine (Boundary-Layer Meteorol. 120:87¿109, 2006). Some details differ from their expression but are in accordance with data obtained over African savannah. We extend the conceptual model to a combination of any scalars, not necessarily linked through the surface energy balance (as is the case for temperature and humidity). To this end we introduce a new parameter that describes the surface heterogeneity in surface fluxes. The results of the current model can be used to predict the discrepancy between similarity relationships for different scalars over heterogeneous terrai