Estimating shear velocity and roughness length from velocity profiles

In turbulent boundary layer flows, shear velocity u * , and roughness length z 0 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 z 0 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 z 0 , 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 z 0 .