Variation in the reference Shields stress for bed load transport in gravel‐bed streams and rivers

The present study examines variations in the reference shear stress for bed load transport (τ r ) using coupled measurements of flow and bed load transport in 45 gravel‐bed streams and rivers. The study streams encompass a wide range in bank‐full discharge (1–2600 m 3 /s), average channel gradient (0.0003–0.05), and median surface grain size (0.027–0.21 m). A bed load transport relation was formed for each site by plotting individual values of the dimensionless transport rate W * versus the reach‐average dimensionless shear stress τ*. The reference dimensionless shear stress τ* r was then estimated by selecting the value of τ* corresponding to a reference transport rate of W * = 0.002. The results indicate that the discharge corresponding to τ* r averages 67% of the bank‐full discharge, with the variation independent of reach‐scale morphologic and sediment properties. However, values of τ* r increase systematically with average channel gradient, ranging from 0.025–0.035 at sites with slopes of 0.001–0.006 to values greater than 0.10 at sites with slopes greater than 0.02. A corresponding relation for the bank‐full dimensionless shear stress τ* bf , formulated with data from 159 sites in North America and England, mirrors the relation between τ* r and channel gradient, suggesting that the bank‐full channel geometry of gravel‐ and cobble‐bedded streams is adjusted to a relatively constant excess shear stress, τ* bf − τ* r , across a wide range of slopes.