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The model runs provide, among other things, estimates of the flow depth It and energy slope Sf at <br />each cross section. This information is used with (4) and (5) to calculate the dimensionless shear <br />stress at each cross section, and to formulate an empirical relation between Q and z, as shown in <br />Figure 23. A power-law fit of the average values of f for this site gives a curvilinear relation with <br />an exponent of 0.73. The value of the exponent is slightly higher than the uniform-flow value <br />(0.60) because, here, the Sf increases from 0.0018 to 0.0021 over the range of flows considered. <br />0.08 <br />0.06 <br />0.04 <br />0.02 <br />0.00 <br />Discharge (m3/S) <br />3.0 <br />2.5 <br />2.0 <br />ti/2 <br />c <br />1.5 <br />1.0 <br />0.5 <br />0.0 <br />Figure 23. Relation between discharge and dimensionless shear stress, RKM 345. <br />From the above relation, we estimate that the threshold for initial motion in this reach is exceeded at <br />a discharge of -210 m3/s (recall that initial motion is the flow corresponding to f = 0.030, which is <br />the point where a few framework particles are just beginning to move). The bankfull flow (or the <br />point where most all of the framework particles are moving) is reached at a discharge of about 390 <br />mN. These discharges are somewhat low in comparison to our reach-average estimates (see <br />below) because the grain size measured at this site (48 mm) is small in comparison to the reach- <br />average value for this segment of the Colorado River (57 mm; Table 1). <br />Similar measurements and calculations were done at two additional sites in the lower part of the <br />study area. One site is located at RKM 150, about 4 km downstream of the Cisco gauge; the other <br />site is located at RKM 106, about 4 km upstream of the Moab bridge. Water surface elevations <br />were measured at site RKM 150 on three different occasions, and at RKM 106 on four different <br />occasions. These measurements allow us to verify model results over a broad range of discharges, <br />rather than relying on a single set of observations as was done at the site discussed above. We <br />obtained excellent agreement between the observed and calculated water surface elevations at the <br />upper site (RKM 150) by choosing n values of 0.027-0.029 (Fig. 24a). Similar results were <br />obtained at the lower site (RKM 106) choosing n values of 0.025-0.026 (Fig. 24b). <br />34 <br />0 100 200 300 400 500 600 700