[1] This paper presents field data on channel geometry and potential control variables from 47 field settings representing a diverse range of environments. These data are used to evaluate existing scaling relationships used in models of the evolution of bedrock channel geometry and to test the hypothesis that channel width (w) increases more slowly and depth (d) more rapidly in relation to discharge (Q) or drainage area (A) as substrate resistance increases. For this data set, w $ A 0.3 , w $ Q 0.5 , d $ A 0.2 , and d $ Q 0.3 . The w-A and w-Q relations are close to those found by previous investigators. The d-A and d-Q relations have not previously been reported for bedrock channels. Examination of trends within the data does not support the hypothesis and, instead, suggests that the erosional resistance of channel boundaries is not the primary control on scaling relations for channel geometry. Scaling Relations for Bedrock Channels[2] The most widely used approach to modeling bedrock channel incision in the context of landscape evolution assumes that incision rate (E) is proportional to stream power [Howard et al., 1994], which is a function of discharge (Q), or the commonly used surrogate drainage area (A), and channel gradient (S)where k is a dimensional constant for erodibility that depends on bedrock properties, and m and n are dimensionless exponents. Recent papers on bedrock channel processes in the context of landscape evolution consistently cite the need for further field data to test model assumptions about how bedrock erodibility influences incision rate and about how bedrock channel geometry scales with A, S, and Q in field settings with differing lithology, discharge, sediment supply, and tectonic uplift [Montgomery and Gran, 2001;Whipple, 2004;Wobus et al., 2006]. In this paper, we present new field data that can be used to test assumptions of scaling in bedrock channels. Scaling of bedrock channel geometry is particularly critical in models of bedrock channel evolution through time and space.[3] The simplest way to scale bedrock channel geometry is to use downstream hydraulic geometry relations established for alluvial channels. Downstream hydraulic geometry relations for width (w) and depth (d) take the form ofIn their original formulation of downstream hydraulic geometry on the basis of data from 10 rivers, Leopold and Maddock [1953] proposed that average values of exponents for alluvial channels are b = 0.5 and f = 0.4. Subsequent studies drawing on larger data sets [Park, 1977] expanded the range of values for b (0.03-0.89) and f (0.09-0.70), but 0.5 and 0.4 remain accurate averages for alluvial channels worldwide.[4] The rationale behind downstream hydraulic geometry is that channel shape, expressed via w and d, determines the distribution of velocity (v) and shear stress, which in turn interact with the erodibility of the bed and banks to control cross-sectional shape and boundary roughness as Q and sediment supply change downstream [Leopold and Maddock, 1953]. The rates at which w, d, an...

[1] Detailed channel and water surface surveys were conducted on 15 mountain stream reaches (9 step-pool, 5 cascade, and 1 plane-bed) using a tripod-mounted Light Detection and Ranging scanner and laser theodolite. Reach-average velocities were measured at varying discharges with dye tracers and fluorometers. Multiple regressions and analysis of variance tests were used to test hypothesized correlations between Darcy-Weisbach friction coefficient, f, and potential control variables. Gradient (S 0 ) and relative grain submergence (R h /D 84 ) individually explained a low proportion of the variability in f (R 2 = 0.18), where R h is hydraulic radius, D 84 is the 84th percentile of the cumulative grain size distribution, and R 2 is equal to the coefficient of determination. Because channel type, grain size, and S 0 are interrelated, we tested the hypothesis that f is highly correlated with all three of these variables or a combination of the above variables with flow period (a categorical variable) or dimensionless unit discharge (q*). Total resistance correlated strongly (adj-R 2 = 0.74, 0.69, and 0.64) with S 0 , flow period, wood load (volume of wood/m 2 of channel), q*, and channel type (step-pool, cascade, plane-bed). Total resistance differed between step-pool and plane-bed and between cascade and plane-bed reaches. Significant differences in f in step-pool and cascade reaches were found at the same values of flow and S 0 . The regression analyses indicate that discharge explains the most variability in f, followed by S 0 when discharge is similar among channel reaches, but that R h /D 84 is not an appropriate variable in these steep mountain streams to represent variations in both resistance and discharge. Results also indicate that the forms of resistance among channel types are sufficiently different to change the relationship of the control variables with f in each channel type. These results can be used to further the development of predictive equations for high-gradient mountain streams.

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[1] Total flow resistance can be partitioned into its components of grain (ff grain ), form (ff step ), wood (ff wood ), and spill (ff spill ) resistance. Methods for partitioning flow resistance developed for low-gradient streams are commonly applied to high-gradient systems. We examined the most widely used methods for calculating each component of resistance, along with the limitations of these methods, using data gathered from 15 high-gradient (0.02 < S 0 < 0.195) step-pool, cascade, and plane-bed reaches in Fraser Experimental Forest. We calculated grain resistance using three equations that relate relative submergence ( R/D m ) to ff grain as well as using an additive drag approach. The drag approach was also used for calculating ff wood and ff step . The ff grain contributed the smallest amount toward all reaches at all flows, although the value varied with the method used. The Parker and Peterson (1980) equation using D 90 best represented ff grain at high flows, whereas the Keulegan (1938) equation using D 50 best characterized ff grain at base flows, giving a lower bound for grain resistance. This suggests that ff grain may be better represented if two grain sizes are used to calculate this component of resistance. The drag approach, which is used to calculate wood resistance, overestimated the significance of individual logs in the channel. The contribution of ff spill was reduced at higher flows when form drag around the step is accounted for at higher flows. We propose a method for evaluating the contribution of ff step that accounts for form drag around the steps once they are submerged at higher flows. We evaluated the potential sources of error for the estimation of each component of resistance. Determination of the drag coefficient was one of the major sources of error when calculating drag around wood, steps, or boulders.

Detailed hydraulic measurements were made in nine step-pool, fi ve cascade and one plane-bed reach in Fraser Experimental Forest, Colorado to better understand at-a-station hydraulic geometry (AHG) relations in these channel types. Average values for AHG exponents, m (0·49), f (0·39), and b (0·16), were well within the range found by other researchers working in steep gradient channels. A principal component analysis (PCA) was used to compare the combined variations in all three exponents against fi ve potential control variables: wood, D 84 , grain-size distribution (σ), coeffi cient of variation of pool volume, average roughness-area (projected wetted area) and bed gradient. The gradient and average roughness-area were found to be signifi cantly related to the PCA axis scores, indicating that both driving and resisting forces infl uence the rates of change of velocity, depth and width with discharge. Further analysis of the exponents showed that reaches with m > b + f are most likely dominated by grain resistance and reaches below this value (m < b + f) are dominated by form resistance. Copyright © 2010 John Wiley & Sons, Ltd.KEYWORDS: at-a-station hydraulic geometry (AHG); hydraulic measurements; principal component analysis (PCA); channels At-a-station Hydraulic Geometry and Flow ResistanceAt-a-station hydraulic geometry (AHG) characterizes how changes in discharge affect specifi c hydraulic variables such as width, depth, velocity and friction. Leopold and Maddock (1953) fi rst coined the term 'hydraulic geometry' to describe systematic changes both downstream and at a cross-section for each of the above hydraulic variables. They proposed three power relations to describe how width (w = aQ b ), depth (d = cQ f ) and velocity (v = kQ m ) vary with discharge both downstream and at a given cross-section in a channel, where Q is discharge; w is water-surface width, d is mean depth; and v is velocity. These power relations are bound by the continuity equation (Q = wdv), so that the coeffi cients a, c, and k have a product equal to one and the exponents b, f, and m sum to one. Leopold and Maddock (1953) found that the rates of change of width, depth and velocity with discharge were related to the shape of the channel, the slope of the watersurface and the roughness of the wetted perimeter. They also found the sediment load to be an important control on the rates of change of both velocity and depth (Leopold and Maddock, 1953).Few studies have reported AHG values for steep mountain channels (Lee and Ferguson, 2002;Reid, 2005;Comiti et al., 2007). A better understanding of at-a-station changes in each of the above hydraulic variables can improve our understanding of the sources and magnitude of hydraulic roughness in these channels, which tend to have values of fl ow resistance as refl ected in Manning's n or Darcy-Weisbach friction factor (ff) that are much higher than values for channel reaches with gradient <1% (Jarrett, 1984;Bathurst, 1985Bathurst, , 1993.Steep mountain channels are divided into cascad...

Streamflow influences the distribution and organization of high water marks along rivers and streams in a landscape. The federal definition of ordinary high water mark (OHWM) is defined by physical and vegetative field indicators that are used to identify inundation extents of ordinary high water levels without any reference to the relationship between streamflow and regulatory definition. Streamflow is the amount, or volume, of water that moves through a stream per unit time. This study explores regional characteristics and relationships between field-delineated OHWMs and frequency-magnitude streamflow metrics derived from a flood frequency analysis. The elevation of OHWM is related to representative constant-level discharge return periods with national average return periods of 6.9 years using partial duration series and 2.8 years using annual maximum flood frequency approaches. The range in OHWM return periods is 0.5 to 9.08, and 1.05 to 11.01 years for peaks-over-threshold and annual maximum flood frequency methods, respectively. The range of OHWM return periods is consistent with the range found in national studies of return periods related to bankfull streamflow. Hydraulic models produced a statistically significant relationship between OHWM and bank-full, which reinforces the close relationship between the scientific concept and OHWM in most stream systems.

Photographic guidance is presented to assist with the estimation of Manning's n and Darcy-Weisbach f in high-gradient plane-bed, step-pool, and cascade channels. Reaches both with and without instream wood are included. These coefficients are necessary for the estimation of reachaverage velocity, energy loss, and discharge. Using data collected in 19 stream channels located in the State of Colorado and the Eastern Italian Alps, on slopes ranging from 2.4 to 21 percent, guidance is provided for low through bankfull flows. Guidance for low flow resistance estimation is additionally provided using data collected in 29 channels in the State of Washington, New Zealand, Chile, and Argentina. Bankfull n values range from 0.048 to 0.30 and low flow n values range from 0.057 to 0.96. Discussions of flow resistance mechanisms and quantitative prediction tools are also presented.

We collected high-resolution LiDAR-based spatial and reach-average flow resistance data at a range of flows in headwater stream channels of the Fraser Experimental Forest, Colorado, USA. Using these data, we implemented a random field approach for assessing the variability of detrended bed elevations and flow depths for both the entire channel width and the thalweg-centered 50% of the channel width (to exclude bank effects). The spatial characteristics of these channels, due to bedforms, large clasts and instream wood, were compared with Darcy-Weisbach f and stream type through the use of the first four probability density function moments (mean, variance, skewness, kurtosis). The standard deviation of the bed elevations (r z ) combined with depth (h), as relative bedform submergence (h/r z ), was well correlated with f (R 2 5 0.81) for the 50% of channel width. The explained variance decreased substantially (R 2 5 0.69) when accounting for the entire width, indicating lesser contribution of channel edges to flow resistance. The flow depth skew also explained a substantial amount of the variance in f (R 2 5 0.78). A spectrum of channel types is evident in depth plots of skew versus kurtosis, with channel types ranging from plane bed, transitional, step pool/cascade, to cascade. These results varied when bank effects were included or excluded, although definitive patterns were observed for both analyses. Random field analyses may be valuable for developing tools for predicting flow resistance, as well as for quantifying the spectrum of morphologic change in high-gradient channel types, from plane bed through cascade.