On the Application of Linear Regression to Surface-Layer Wind Profiles for Deducing Roughness Length and Friction Velocity

Abstract

In a steady, spatially homogeneous neutral stability flow dominated by mechanical turbulence, the friction velocity ($$ u_{*} $$) and the roughness length (z0) can be estimated by applying linear regression to measurements of wind speed (u) at several heights (z). Surface-layer wind profile plots in the scientific literature normally have ln(z) on the vertical axis and u on the abscissa, which might suggest a linear regression, such as the ordinary least-squares method, which minimizes the vertical residuals, i.e., the ln(z) deviations, from the fitted line. Here, we show that ordinary least-squares fitting of the profile data is sensitive to the choice of the variable whose residuals are being minimized, and that the linear regression should be computed as u versus ln(z), i.e., minimizing the u deviations. This is equivalent to ln(z) being the independent variable and u the dependent variable. The differences in the estimated values of $$ u_{*} $$ and z0 compared to those resulting from the ln(z) versus u linear regression can be expressed as a function of the coefficient of determination (r2) of the wind-profile data. Applying the ordinary least-squares method while minimizing the deviations of ln(z) leads to systematic overestimation of the $$ u_{*} $$ and z0 values. Using these values as input into the atmospheric dispersion model AERMOD leads to increased shear-induced turbulence and consequently enhanced dilution of the plume.