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<br />100 C (9797 kg/m2s2), R is the hydraulic radius of the channel at the indicated stage, and <br /> <br />. <br /> <br />S is the water surface slope at the indicated stage. When channel width is much greater <br /> <br />than depth, mean depth is a good approximation of hydraulic radius. All of the cross- <br /> <br />sections measured in the study reach fit this criteria, and we approximated the hydraulic <br /> <br />radius with mean depth, calculated as the cross-sectional area divided by the top-width of <br /> <br />the channel. The slope of the water surface at the desired stages was not directly <br /> <br />measured because we did not observe high discharges during our field work. We' used a <br /> <br />reach average slope of 0.0014, which is the average slope of the line connecting surveyed <br /> <br />elevations of the high-water marks, and of the flood plain and terrace surfaces. <br /> <br />We used the Shields relation, as discussed by Andrews (1983), to calculate the <br /> <br />critical shear stress necessary to entrain the D50 or median particle size. Andrews (1983) <br /> <br />showed that in a naturally sorted gravel bedded stream, a range of particle sizes is <br /> <br />I <br /> <br />mobilized at nearly the same discharge. Assuming "equal mobility" of a range of particle <br /> <br />sizes allows the use of a "reference" particle in the Shields relation and provides a means <br /> <br />to calculate the critical shear stress necessary to entrain a range of bed material sizes. <br /> <br />The Shields relation is calculated as: <br /> <br />tcr = t* 50 (gs-g,JD50 <br /> <br />(4) <br /> <br />where tcr is the critical shear stress necessary to entrain a particle, in N/m2, t* 50 is the <br /> <br />critical dimensionless shear stress, which for most gravel-bedded streams is between <br /> <br />0.033 and 0.086 (Andrews 1983; Buffington and Montgomery, 1997), gs is the specific <br /> <br />weight of the particle, which is assumed to be 2650 kglm2s2, and gw is the specific weight <br /> <br />ofthe fluid. Shields (1936) assumed t* 50 values of 0.06, and this determination has been <br /> <br />widely used (Andrews 1983). However, recent findings by Buffington and Montgomery <br /> <br />17 <br />