Predicting fractional bed load transport rates: Application of the Wilcock‐Crowe equations to a regulated gravel bed river

Abstract

[1] Bed load samples from four locations in the Trinity River of northern California are analyzed to evaluate the performance of the Wilcock-Crowe bed load transport equations for predicting fractional bed load transport rates. Bed surface particles become smaller and the fraction of sand on the bed increases with distance downstream from Lewiston Dam. The dimensionless reference shear stress for the mean bed particle size (t* rm ) is largest near the dam, but varies relatively little between the more downstream locations. The relation between t* rm and the reference shear stresses for other size fractions is constant across all locations. Total bed load transport rates predicted with the Wilcock-Crowe equations are within a factor of 2 of sampled transport rates for 68% of all samples. The Wilcock-Crowe equations nonetheless consistently under-predict the transport of particles larger than 128 mm, frequently by more than an order of magnitude. Accurate prediction of the transport rates of the largest particles is important for models in which the evolution of the surface grain size distribution determines subsequent bed load transport rates. Values of t* rm estimated from bed load samples are up to 50% larger than those predicted with the Wilcock-Crowe equations, and sampled bed load transport approximates equal mobility across a wider range of grain sizes than is implied by the equations. Modifications to the Wilcock-Crowe equation for determining t* rm and the hiding function used to scale t* rm to other grain size fractions are proposed to achieve the best fit to observed bed load transport in the Trinity River.

Channel evolution on the dammed Elwha River, Washington, USA

“…Field studies demonstrate incision, narrowing, and bed armoring downstream of large dams (e.g., Leopold et al, 1964;Livesey, 1965;Galay, 1983;Simon et al, 2002;Grant et al, 2003;Rinaldi, 2003;Grams et al, 2007;Schmidt and Wilcock, 2008;Gaeuman et al, 2009). Bed armoring (winnowing) occurs as river flows evacuate fine sediment below dams, eroding sand from the main channel bed, in eddies, and along the channel margin (Laursen et al, 1976;Dietrich et al, 1989;Kearsley et al, 1994;Wright et al, 2005;Hazel et al, 2006).…”

An analysis of nonlinearity effects on bed load transport prediction

“…Similar results were obtained by Gaeuman et al . [] who compared the Wilcok and Crowe equation to bed load measurements of the Trinity river.…”

Multi-Fraction Bayesian Sediment Transport Model

“…We present a multi-fraction Bayesian sediment transport model developed using the Wilcock-Crowe equations and sediment transport data from mixed-size sediment transport experiments [8]. The Bayesian model was fitted to these transport observations and the resulting posterior distributions were analyzed and compared to transport model developed by Wilcock and Crowe [6].…”

“…For application with a new transport dataset, the fractional transport data (of an arbitrary number of size fractions) can be evaluated using Equation (8). In this capacity, the general form of the sediment transport curve would be the Wilcock-Crowe equation, which would essentially be calibrated for the new dataset.…”