The Roughness Length for Water Vapor Sensible Heat, and Other Scalars

An expression is presented for the roughness length of water vapor (or sensible heat, etc.) that is the surface value intercept of the straight line resulting from a semi-logarithmic plot of the mean specific humidity (or potential temperature, etc.) profile in the dynamic sublayer. The derivation is based on the standard assumption of continuity in the mean profile at the interface between the interfacial transfer sublayer and the fully turbulent surface sublayer. It is found that the resulting formulation yields similar results for a number of empirical and theoretical equations for the interfacial transfer that are available in the literature. The roughness length of any scalar admixture depends not only on the nature of the surface but also on the intensity of the surface shear stress and on the molecular diffusivity and the viscosity. In meteorological applications under rough flow conditions this roughness length may be considerably smaller than the aerodynamic roughness length Z0, whereas under smooth flow conditions it is usually somewhat larger.