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Results of the analysis defined the discharge necessary to initiate motion of particle sizes ranging from 10- 150 mm. 5.4.3 Derivation of Hydraulic Geometry Relationships. A critical factor in incipient motion analysis is accurate calculation of boundary shear stress. As indicated above, the shear stress relationship based on velocity and depth (Equation 5.4) was considered preferable to the slope based relation (Equation 5.3), in part due to difficulties in defining energy slope in a riffle-pool environment over a wide range of flow conditions. Use of the velocity-depth relationship for boundary shear stress requires knowledge of the mean velocity in the vertical for a given depth, which is precisely the information collected during stream gaging. Therefore, given the stream gaging data in the canyon available from the National Park Service investigation (O'Brien, 1984), accurate calculation of boundary shear stress in various cobble bar environments was possible. Based on stream gaging field data, presented in the NPS data notebooks, power curve relationships between total discharge and velocity or flow depth were derived for specific portions of a cobble bar. At Mathers Hole (rm 17.5), the velocity and depth data only for those verticals located on the cobble bar were utilized in the regressions. ragure 5.5a and b are plots of available data and the resulting regression relationship. Given that incipient motion conditions were expected to occur at higher discharges, the regressions were based only on data for 8,000 cfs and greater, in order to provide the best fit at higher discharges. At the spawning bar (rm 16.5) the measured data were limited; however, given the importance of this location as an observed spawning area, it was considered important to complete the analysis with the best available data. Regression relationships were derived for the central portion of the left bank channel around the spawning bar, based on four relatively low discharges. It is recognized that limited data may affect the accuracy of the analysis; however, given that power curve relationships typically fit hydraulic geometry data quite well, it was felt that the resulting relationships could be used and extrapolated to higher discharge with some confidence. F'tgures 5.6a and b present the derived relationships. 5.4.4 Results of Incipient Motion Analysis. Based on the spawning bar (rm 16.5) subsurface particle size gradation curves, the subsurface dSO necessary for evaluation of critical dimensionless shear stress by the Andrews (1983) relationship ranges from about 28 to 42 mm (see rag. 5.7). These values were considered indicative ofthe range of values that might be found in a cobble bar (rm 16.5) in the Yampa Canyon and were used to evaluate a range of incipient motion conditions for both river mile 16.5 and 17.5. At Mathers Hole (rm 17.5, Site 1), the surface ds4 was 86mm and at river mile 16.5, the surface d84 was 72 mm (see Figure 5.9). These values were obtained from the gradation curves presented in Figure 3.9. These values were used in the incipient motion computations to determine the bed roughness height, Ks' Based on the subsurface dSO values obtained from Figure 5.7, the range of critical dimensionless shear stress for a 75 mm particle ranges from 0.035 to 0.05. This compares to the value reported in National Park Service report of 0.03 (O'Brien, 1984, pg. 42). Tabulated incipient motion results for Site 1 at Mathers Hole are presented in Tables 5.5a and b. Similarly, Tables 5.5c and d provide incipient motion results for the spawning bar at river mile 16.5. These results are illustrated in graphical form in Figures 5.& and b for the Mathers Hole site and the spawning bar site respectively. At Mathers Hole, for surface particles larger than or equal to the subsurface D50 the range of incipient motion discharge is from approximately 18,000 to 23,000 cfs, given a subsurface DSO of 28mm. For a subsurface DSO of 42mm the incipient motion ranged from approximately 28,000 to 34,000 cfs. 5-16 I I I I I I I I I I I I I I I I I I I