## 1. Introduction

[2] River engineers and scientists have been studying the nature of bed load transport and working to develop reliable equations for calculating sediment transport rates for more than a century [e.g., *du Boys*, 1879]. Important applications of sediment transport predictions include estimating rates of reservoir sedimentation [*Morris and Fan*, 1998], stream restoration design [*Skidmore et al.*, 2001], assessing aggradation and flood risks [*Klaassen*, 2006], and prescribing in-stream flow requirements [*Andrews and Nankervis*, 1995]. At their most fundamental levels, these applications require predictions of total sediment transport rates only. Efforts to achieve even this relatively modest goal, however, have met with only limited success. The poor performance of many bed load transport equations has been widely noted [*Wilcock*, 2001; *Barry et al.*, 2004; *Duan and Scott*, 2008]. Under optimum conditions, the best performing bed load functions predict transport rates within a factor of 2 of the actual value about two thirds of the time [*Ackers and White*, 1973; *Gomez and Church*, 1989].

[3] A more ambitious application of predictive sediment transport equations is to support numerical models that aim to simulate geomorphic evolution. Models of this sort have been developed to investigate geomorphic dynamics in a variety of settings, including alluvial fans [*Parker et al.*, 1998], deltas [*Sun et al.*, 2002; *Swenson et al.*, 2005], and river channels [*Ferguson et al.*, 2001; *Lisle et al.*, 2001; *Cui*, 2007]. In gravel bed rivers with mixed sediment particle sizes, differences in the transport rates of different particles size classes are likely to influence geomorphic evolution through processes such as longitudinal sediment sorting [*Knighton*, 1980; *Fedele and Paola*, 2007] and bed surface coarsening [*Dietrich et al.*, 1989]. Simulation of these geomorphic processes requires bed material transport equations capable of predicting fractional transport rates, as well as total transport.

[4] At present, the *Wilcock and Crowe* [2003] equations are among the more widely used formulae for predicting fractional bed load transport rates in gravel bed streams. The Wilcock-Crowe equations (hereinafter referred to as WC) were developed using bed load transport information obtained in laboratory flume experiments with bed material sediments ranging in particle size from sand to coarse gravel [*Wilcock and Crowe*, 2003]. This paper presents a comparison between fractional transport rates predicted with the WC equations and fractional transport rates determined by intensive sampling of bed load transport during periods of sustained high flow in the Trinity River, a regulated gravel bed stream in northern California. Our objectives for this comparison are (1) to evaluate the accuracy of the WC equations for predicting total and fractional bed load transport rates in a relatively large gravel bed stream, (2) to calibrate the equations for optimal performance in the Trinity River, and (3) to consider the extent to which the calibration results may represent a general, rather than site-specific, improvement.

[5] The WC equations are shown to yield reasonable estimates of total bed load transport in the Trinity River. These equations, however, systematically under-predict the transport of the coarsest fractions in the bed load. Numerical experiments summarized later demonstrate that differences in the predicted mobility of the largest grains in the bed load can have a disproportionately large influence on the output of morphodynamic models. Thus it is critical that the transport equations used in these types of models predict the fractional transport characteristics of the larger size classes as accurately as possible.