Effects of bed-elevation uncertainty on bed shear stress estimated using log-law profiles

Owing to their simplicity and theoretical foundation, log-law velocity profiles have been widely used to estimate bed shear stress. Such estimates depend on both the measured velocities and the wall-normal coordinate referenced to the bed elevation. However, in natural environments, bed elevation may be uncertain because of factors such as bed microtopography and changes in bed elevation between bed surveys and velocity profile measurements. This uncertainty can introduce a systematic bias into the regression-based bed shear stress. In this study, the effects of bed-elevation uncertainty on the bed shear stress estimated using log-law velocity profiles are analytically quantified. The analytical solutions reveal notable asymmetry, whereby the overestimation of the bed shear stress induced by negative bed-elevation error is greater than the underestimation caused by positive errors of equal absolute magnitude. Fixed-bed flume velocity profiles are then used to conduct a controlled sensitivity assessment of the theoretical error mechanism, with elevation shifts applied exclusively during postprocessing rather than during physical bed evolution. These findings provide a quantitative indication of the potential bias caused by bed-elevation uncertainty in log-law-based shear stress estimation.