Errors in the Bed Shear Stress as Estimated from Vertical Velocity Profile

In this study, errors in determining bed shear stress caused by errors in theoretical bed surface data or roughness size selection using one-point velocity, two-point velocity, or a group of velocity measurements within the log-velocity region are systematically and quantitatively analyzed. The smaller the roughness element, the smaller the error in the bed shear stress estimate. For a fixed roughness size and absolute error in selecting the theoretical bed data, the closer to the bed the velocity measurement is taken, the larger the error in the friction velocity estimate. The velocity profile near the bed is very sensitive to the selection of the theoretical bed surface data. The velocity profile near the bed will deviate significantly from the true log profile if the theoretical bed surface data is over- or underestimated by 5mm or more. This study shows conclusively that using the upper measurement data points, instead of the near-bed measurement, in the regression analysis yields better roughness size and bed shear stress estimates.