A General Power Function for Predicting Bedload Transport Rates

A number of authors have illustrated the need to calibrate bedload transport equations with measured data to have confidence in the calculated rates of bedload flux at a site. Recent studies [Barry and Buffington, 2002] show that a simple power function relating bedload transport rate to discharge best described data from 13 long-term monitoring sites in Idaho, USA, when compared to the Meyer-Peter and Müller [1948], Parker et al. [1982] and calibrated Parker [Bakke et al., 1999] bedload transport equations. Here we identify channel and watershed characteristics that control the exponent and coefficient of observed bedload power functions, providing a simple generalized equation for predicting bedload transport in mountain rivers. We hypothesize that both the exponent and coefficient are principally factors of sediment supply limitations. Emmett and Wolman [2001] present two supply-limited situations in armored channels. First the amount of fine material present on the streambed limits the magnitude of Phase I transport (motion of finer particles over an immobile armor). Second, supply-limitation occurs when the coarse armor layer limits the rate of gravel transport until these large particles are mobilized (Phase II transport), thus exposing the finer subsurface material to the flow. We hypothesize that the greater the degree of channel armoring, or supply-limitation, the longer the delay in, and less sediment transport prior to, mobilization of the armor layer. Mobilization of the surface material in a well armored channel is followed by a relatively larger increase in bedload transport when compared to a similar channel with less surface armoring. Consequently, the greater the degree of channel armoring, or supply-limitation, the larger the difference in the bedload transport rates pre- and post-mobilization of the armor layer, resulting in a steeper bedload rating curve (i.e., larger exponent for the bedload power function). Data from 11 pool-riffle study sites within the Idaho batholith reveal an inverse relationship between the power-function exponent and the standard deviation of the bed surface grain-size distribution (σ = (d₈₄/d₁₆)^0.5). Smaller values of σ primarily resulted from relatively lower values of d₁₆ and a consequent decrease in the degree of channel armoring, or supply-limitation. As hypothesized, channels with finer surface material, (less supply-limited) were associated with lower-sloped bedload rating curves (smaller exponents of the power function). In contrast, the coefficient of the bedload power function determines the relative mass of gravel transported, rather than the rate of increase in gravel transport with discharge. We find that the coefficient is related to drainage area, which we interpret as a surrogate for upstream sediment supply, rather than in-channel supply as investigated with σ . Our results indicate that bedload power functions can be generalized as a function of drainage area and sediment sorting, surrogates for upstream and in-channel sediment supplies, respectively.