Surface Velocity to Depth-Averaged Velocity—A Review of Methods to Estimate Alpha and Remaining Challenges

Abstract

The accuracy of discharge measurements derived from surface velocities are highly dependent on the accuracy of conversions from surface velocity us to depth-averaged velocity U. This conversion factor is typically known as the ‘velocity coefficient’, ‘velocity index’, ‘calibration factor’, ‘alpha coefficient’, or simply ‘alpha’, where α=U/us. At some field sites detailed in situ measurements can be made to calculate alpha, while in other situations (such as rapid response flood measurements) alpha must be estimated. This paper provides a review of existing methods for estimating alpha and presents a workflow for selecting the appropriate method, based on available data. Approaches to estimating alpha include: reference discharge and surface velocimetry measurements; extrapolated ADCP velocity profiles; log law profiles; power law profiles; site characteristics; and default assumed values. Additional methods for estimating alpha that require further development or validation are also described. This paper then summarises methods for accounting for spatial and temporal heterogeneity in alpha, such as ‘stage to alpha rating curves’, ‘site alpha vs. local alpha’, and ‘the divided channel method’. Remaining challenges for the accurate estimation of alpha are discussed, as well as future directions that will help to address these challenges. Although significant work remains to improve the estimation of alpha (notably to address surface wind effects and velocity dip), the methods covered in this paper could provide a substantial accuracy improvement over selecting the ‘default value’ of 0.857 for alpha for every discharge measurement.