Rethinking the Roughness Height: An Improved Description of Temperature Profiles over Short Vegetation

Abstract

In this study, we present an extension to the Monin–Obukov similarity theory (MOST) for the roughness sublayer (RSL) over short vegetation. We test our theory using temperature measurements from fiber optic cables in an array-shaped set-up. This provides a high vertical measurement resolution that enables us to measure the sharp temperature gradients near the surface. It is well-known that MOST is invalid in the RSL as the flow is distorted by roughness elements. However, to derive the surface temperature, it is common practice to extrapolate the logarithmic profiles down to the surface through the RSL. Instead of logarithmic behaviour defined by MOST near the surface, our observations show near-linear temperature profiles. This log-to-linear transition is described over an aerodynamically smooth surface by the Van Driest equation in classical turbulence literature. Here we propose that the Van Driest equation can also be used to describe this transition over a rough surface, by replacing the viscous length scale with a surface length scale \(L_s\) that represents the size of the smallest eddies near the grass structures. We show that \(L_s\) scales with the geometry of the vegetation and that the model shows the potential to be scaled up to tall canopies. The adapted Van Driest model outperforms the roughness length concept in describing the temperature profiles near the surface and predicting the surface temperature.