Search

Theoretical approaches to magnitude-frequency analysis (MFA) of sediment transport in channels couple continuous flow probability density functions (PDFs) with power law flow-sediment transport relations (rating curves) to produce closed-form equations relating MFA metrics such as the effective discharge, Qeff, and fraction of sediment transported by discharges greater than Qeff, f+, to statistical moments of the flow PDF and rating curve parameters. These approaches have proven useful in understanding the theoretical drivers behind the magnitude and frequency of sediment transport. However, some of their basic assumptions and findings may not apply to natural rivers and streams with more complex flow-sediment transport relationships or management and design scenarios, which have finite time horizons. We use simple numerical experiments to test the validity of theoretical MFA approaches in predicting the magnitude and frequency of sediment transport. Median values of Qeff and f+ generated from repeated, synthetic, finite flow series diverge from those produced with theoretical approaches using the same underlying flow PDF. The closed-form relation for f+ is a monotonically increasing function of flow variance. However, using finite flow series, we find that f+ increases with flow variance to a threshold that increases with flow record length. By introducing a sediment entrainment threshold, we present a physical mechanism for the observed diverging relationship between Qeff and flow variance in fine and coarse-bed channels. Our work shows that through complex and threshold-driven relationships sediment transport mode, channel morphology, flow variance, and flow record length all interact to influence estimates of what flow frequencies are most responsible for transporting sediment in alluvial channels.

[1] Total flow resistance can be partitioned into its components of grain (ffgrain), form (ffstep), wood (ffwood), and spill (ffspill) 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 < S0 < 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/Dm) to ffgrain as well as using an additive drag approach. The drag approach was also used for calculating ffwood and ffstep. The ffgrain 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 D90 best represented ffgrain at high flows, whereas the Keulegan (1938) equation using D50 best characterized ffgrain at base flows, giving a lower bound for grain resistance. This suggests that ffgrain 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 ffspill 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 ffstep 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.

[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 (S0) and relative grain submergence (Rh/D84) individually explained a low proportion of the variability in f (R2 = 0.18), where Rh is hydraulic radius, D84 is the 84th percentile of the cumulative grain size distribution, and R2 is equal to the coefficient of determination. Because channel type, grain size, and S0 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-R2 = 0.74, 0.69, and 0.64) with S0, flow period, wood load (volume of wood/m2 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 S0. The regression analyses indicate that discharge explains the most variability in f, followed by S0 when discharge is similar among channel reaches, but that Rh/D84 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.

Received 28 April 2005; revised 6 January 2006; accepted 10 March 2006; published 20 June 2006. [1] Channel types found in mountain drainages occupy characteristic but intergrading ranges of bed slope that reflect a dynamic balance between erosive energy and channel boundary resistance. Using a classification and regression tree (CART) modeling approach, we demonstrate that drainage area scaling of channel slopes provides better discrimination of these forms than slope alone among supply- and capacity-limited sites. Analysis of 270 stream reaches in the western United States exhibiting four common mountain channel types reveals that these types exist within relatively discrete ranges of an index of specific stream power. We also demonstrate associations among regional interannual precipitation variability, discharge distribution skewness, and means of the specific stream power index of step-pool channels. Finally, we discuss a conceptual methodology for predicting ecologically relevant morphologic units from digital elevation models at the network scale based on the finding that channel types do not exhibit equal energy dissipation.