Variability of Reference Shear Stress in Gravel-Bed Streams

The prediction of sediment transport in gravel bed streams is complicated by heterogeneous bed material and armoring of the bed surface, thus affecting both the availability and mobility of grains on the bed. The application of standard bed-load transport formulae in high gradient, coarse-bedded streams may produce inaccurate results, related to difficulty in defining the critical shear stress for sediment motion (τ _c) as well as in estimating the shear stress available for sediment transport (skin friction). Failure of transport functions to match existing bed-load data sets is related to problems in defining these two parameters. The present study examines possible sources of variation in the reference shear stress (τ _ref) using coupled measurements of flow and bed load transport in more than 30 gravel-bed streams and rivers. The study streams encompass a wide range in bankfull discharge (1-650 cms), slope (0.2-5%), and median surface grain size (0.027-0.21 m). Dimensionless sediment transport rates, W^*, were calculated for the bed-load measurements, and then plotted as a function of the reach-average dimensionless shear stress (τ ^*). The dimensionless reference shear stress (τ^*_ref) was then estimated by selecting the value of τ^* corresponding to a small non-zero transport rate (W^* = 0.002). Resulting values of τ^*_ref were found to be positively correlated to reach slope, ranging from as little as 0.015 at low-gradient sites to greater than 0.100 at steeper slopes. Bankfull dimensionless shear stress (τ ^*_bf) likewise increases as slope increases and is highly correlated to τ^*_ref, resulting in a consistent ratio of excess shear stress, τ^*_bf/τ^*_ref, over the range of study sites. These data suggest that the reference shear stress is likely to vary between streams and within drainage basins, especially at slopes greater than 1%, while maintaining a consistent relationship between sediment initiation and bankfull channel morphology.