Estimating shear velocity and roughness length from velocity profiles

In turbulent boundary layer flows, shear velocity u*, and roughness length z0 are commonly derived from semilogarithmic flow velocity profiles by fitting a straight line by ordinary least squares regression to the profile and calculating estimates of u*, and z0 from the slope and intercept of the computed regression equation. However, it is not clear from the literature whether the appropriate regression is of flow velocity u on the logarithm of height above the bed In z or of ln z on u. In order to calculate estimates of u* and z0, the true or structural relation between u and In z must be established. Because u is generally observed with much greater error than is In z, the structural relation may be estimated by regressing u on ln z; regressing ln z on u is incorrect. An analysis of 24 stream channel flow velocity profiles indicates that even in situations where the correlation between u and ln z exceeds 0.9, performing the incorrect regression can result in the considerable overestimation of u* and z0.