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Table 2. General characteristics of flow modeling sites <br /> average bankfull conditions surface (subsurface) sediment <br />River Mile width, depth, slope, D84, D50, D16, <br />(RM) m m m/m mm mm mm <br />------------------ <br />184.2 ------------------ <br />85 ------------------ <br />2.89 ------------------- <br />0.0024 ------------------ <br />140 -------------- <br />75 ----------- <br />32 <br /> (120) (26) (1.4) <br />177.3 75 3.23 0.0020 100 48 24 <br /> (64) (30) (0.7) <br />166.0 126 3.27 0.0020 86 57 34 <br /> (64) (30) (1.4) <br />162.4 148 3.36 0.0015 105 55 27 <br /> (72) (16) (0.5) <br />159.0 148 2.86 0.0017 90 46 25 <br /> (n/a) (n/a) (n/a) <br />139.5 106 4.19 0.0012 90 50 25 <br /> (80) (25) (2.4) <br />134.0 137 3.22 0.0014 80 50 35 <br /> <br />------------------ <br />------------------ <br />------------------ <br />------------------- (80) <br />------------------ (48) <br />-------------- (16) <br />----------- <br />The key problem in estimating discharge thresholds for sediment transport and channel change is to <br />develop appropriate measures of the boundary shear stress, r, and the critical shear stress,'r, The <br />average boundary shear stress is given by <br />i = p g R Sf (1) <br />where p is the density of water, g is the gravitational acceleration, R is the hydraulic radius (which <br />in wide channels is very nearly equal to the flow depth, h), and Sf is the friction slope or energy <br />gradient. We used a series of observations over a range of flows to calibrate a one-dimensional <br />hydraulic model for each study site (we adapted the step-backwater modeling procedure outlined <br />by Henderson, 1966, to a spreadsheet program). The step-backwater model finds Sf at individual <br />stream channel cross sections using an iterative solution to the energy equation: <br />S f - dx - dx (u2 + h + z) (2) <br />g <br />where dH/dx is the gradient in total energy, u is the mean velocity, z is the average bed elevation, <br />and x is the downstream direction. The model results allow us to evaluate the boundary shear <br />stress and the roughness (Manning's n) for a range of discharges. <br />In the absence of direct observations of particle entrainment from tracer gravels or bed load <br />samples, the only practical means for estimating r, is to use the Shields' criterion: <br />i* - iC (3) <br />c - (R-P)gD <br />where z, is the critical dimensionless shear (Shields) stress, p, is the density of sediment, and D is <br />the particle diameter. <br />13