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A summary of n-verification data for hydraulic variables for the 21 sites is given in table 3. The few inconsistencies in the data (for example, the slopes at site II) are due to difficulties in data collection as a result of the extremely turbulent flow conditions. These data indicate the wide range of channel roughness accompanying depth of flow (in terms of hydraulic radius) for seven sites as shown in figures 10 and II. Where channel roughness changes dramatically with depth of flow, it is difficult to select n values by any of the available methods. These roughness-depth relations indicate the need for an accurate and reliable method of estimating n values on higher- gradient streams. Standard hydraulic theory and analysis indicate that when slope exceeds critical slope, that is, when the Froude number exceeds unity, greater veloc- ities and supercritical flow result, The onsite data collected for this study (table 3) and that of Barnes (1967), Limerinos (1970), and Thompson and Camp- bell (1979), and other data for slopes as steep as 0,052, indicate that Froude numbers computed from average section properties are less than unity, subcritical flow, in higher-gradient mountain streams. Davidian (1984) indicates Froude numbering rarely exceed unity for any time period in a natural stream with erodible banks. At velocities greater than those listed in table 3, the combined effects of channel and cross-section variations seem to create extreme turbulence and energy losses that result in increased flow resistance, Studies of the flow resistance of boulder-filled streams by Herbich and Shulits (1964) and Richards (1973) indicate that there is a spill-resistance component with increasing flow. Spill resistance is a result of increased turbulence and roughness resulting from the velocity of water striking the large area of protruding bed-roughness elements and eddy currents set up behind the larger boulders. Aldridge and Garrett (1973) believe the effect of the disturbance of water surrounding boulders and other obstructions increases with velocity and may overlap with nearby obstruction disturbances and further increase turbulence and hence roughness. In larger magnitude floods, additional energy is consumed transporting bed material, Several investigators have noted supercritical flow under certain condi- tions. These conditions have included flow in concrete, sand, or smooth rock channels. Dobbie and Wolf (1953), Thompson and Campbell (1979), and the author believe n values for cobble- and boulder-bed streams are much greater than those normally selected, and flows approach, but do not exceed, critical flow for any significant length of stream. For these conditions of steep slopes, cobble- and boulder-bed material channels, and extreme flows, a limiting assumption of subcritical to critical flow in subsequent hydraulic analyses seems reasonable. If supercritical flow is indicated in the hydraulic analysis for long lengths of channel, a reevaluation of roughness coefficients probably will show all energy losses were not accounted for. Most equations used to predict channel roughness need streambed particle- size information, which often is time-consuming and difficult to obtain, Cor- relation coefficients for selected hydraulic characteristics of the Colorado data are shown in table 4. The correlation coefficient for Manning's n is greater for friction slope than for streambed particle size. This implies that the channel roughness associated with streambed material size can be evaluated in terms of the more easily obtained friction slope. 28