## 1. Introduction

[2] Estimates of bed load transport are used in the analysis of a wide range of practical and theoretical problems in hydrology, including the specification of environmental maintenance flows; computation of sediment loads; development of numerical models of channel evolution; and assessments of the effects of watershed disturbance and river management. Ideally, transport estimates should be based on field measurements of bed load taken over a range of flows. However, the effort involved in taking such measurements and the uncertainty associated with the data are often quite large, and thus it sometimes becomes necessary to compute transport rates on the basis of an empirical relation. Although the application of a transport relation is conceptually straightforward, this approach has its own set of limitations. Key among the limitations is the specification of a critical dimensionless shear stress (or Shields stress), τ*_{c}, for incipient motion. Existing data sets indicate that for a given grain size and shear stress, there is at least a threefold range in τ*_{c} [*Buffington and Montgomery*, 1997]. Some of the variation in τ*_{c} is due to differences in measurement methods [*Buffington and Montgomery*, 1997]; some is due to changes in bed surface structures and channel morphology [*Church et al.*, 1998]; and some is due to differences in flow properties arising from changes in bed roughness and channel gradient [*Ashida and Bayazit*, 1973; *Bathurst et al.*, 1987; *Graf*, 1991; *Shvidchenko and Pender*, 2000]. Uncertainties in the selection of τ*_{c} can lead to large errors in computed transport rates because entrainment is a nonlinear function of flow strength; these effects are particularly important in the range of flows slightly above the threshold for motion, where transport rates increase by orders of magnitude for small changes in shear stress.

[3] The present study examines variations in the threshold shear stress for bed load transport in 45 gravel-bed streams and rivers in the western United States and Canada. We use coupled measurements of flow and bed load transport to formulate a series of bed load rating curves, and from these curves estimate the reference Shields stress τ*_{r}, corresponding to a dimensionless transport rate *W** = 0.002 [*Parker et al.*, 1982]. This approach avoids some of the ambiguity in defining transport thresholds for poorly sorted gravels, which can be entrained over a relatively wide range of shear stress [*Milhous*, 1973; *Diplas*, 1987; *Ashworth and Ferguson*, 1989; *Wilcock and McArdell*, 1993; *Wathen et al.*, 1995; *Powell et al.*, 2001; *Church and Hassan*, 2002]. In the present study the reference transport rate (*W** = 0.002) is assumed to represent flows that are just high enough to begin mobilizing sediment from the armor layer, i.e., bed surface particles larger than sand and granules (>4 mm). We focus on differences in τ*_{r} associated with changes in channel gradient and relative roughness. As gradient and relative roughness increase, large particles alter the vertical distribution of velocity and fluid momentum, reducing the shear stress available for sediment transport (skin friction). Modeling sediment transport under these conditions requires either a downward adjustment in the total boundary shear stress, τ_{o}, to account for friction losses due to boulders or woody debris (drag-partitioning; see *Wiberg and Smith* [1991]), or an upward adjustment in τ_{r} to reflect changes in the fluid and gravitational forces acting on grains. Flume experiments show that the net effect of changes in flow and bed structure as channel gradient increases is to initiate transport at much higher Shields stresses than is normally assumed [*Ashida and Bayazit*, 1973; *Bathurst et al.*, 1987; *Graf*, 1991; *Tsujimoto*, 1991; *Shvidchenko and Pender*, 2000]. The relation for τ*_{r} developed here is based on field data from natural streams. We assume that flow measurements taken at the time of bed load sampling include the effects of form drag, averaged over a suitable area of the bed. The change in effective stress due to large roughness elements carries over into observed relations between shear stress and bed load transport. In a graphical sense the primary effect of increased flow resistance is to shift the position of the bed load rating curve toward higher stresses [*Reid and Laronne*, 1995]. Flow resistance typically increases as relative submergence decreases and streams become steeper, smaller, and coarser near their headwaters [*Knighton*, 1998; *Bathurst*, 2002], which will likely have a primary effect on trends in τ*_{r}. A simple method for estimating τ*_{r} based on morphologic properties would be straightforward to implement, and the uncertainty in estimated values of τ*_{r} is perhaps no worse than that generated through a drag-partitioning model. Additional relations for the reference discharge *Q*_{r} and bank-full dimensionless shear stress τ*_{bf} are developed independently to test the hypothesis that channel morphology in gravel-bed rivers is linked consistently to bed load transport thresholds of the surface bed material.