Variation in Zero Plane Displacement and Roughness Length for Momentum Revisited

Abstract

Zero plane displacement height (\(d_0\)) and momentum roughness length (\(z_{0m}\)), describe the aerodynamic characteristics of a vegetated surface. Usually, \(d_0\) and \(z_{0m}\) are assumed to be constant functions of the physical characteristics of the surface. Prior evidence collected from the literature and our examination of flux tower data show that \(d_0\) and \(z_{0m}\) vary in time at sites with tree and shrub canopies, but not grasslands. The conventional explanations of these variations are based on linear functions of wind velocity and friction velocity, with little theoretical basis. This study explains the variation in aerodynamic parameters by matching four analytical canopy velocity models to a logarithmic above-canopy velocity profile at canopy height. \(d_0\) and \(z_{0m}\) come out as functions of 2 non-dimensional terms, the canopy momentum absorption capacity (parameter) and a (measurable) Péclet number. To test the theories of variation, we analysed the velocity profiles from Ozflux and Ameriflux sites. None of the theories could recreate \(d_0\) and \(z_{0m}\) at half-hourly intervals. However, the canopy velocity models were able better to recreate the distribution of the variations in \(d_0\) and \(z_{0m}\). Additionally, the estimates of canopy momentum absorption capacity varied consistently with phenological changes in the canopies, whereas, the fitting parameters of the linear regression of using wind speed and friction velocity did not exhibit physically interpretable variations. The canopy velocity models may offer better predictions with an accurate estimation of the canopy height, a horizontally homogeneous and rigid canopy, and incorporation of the roughness sublayer.