## 1. Introduction

[2] *Fang* [1998] remarked on the need for a critical evaluation and comparison of the plethora of sediment transport formulae currently available. In response, *Yang and Huang* [2001] evaluated the performance of 13 sediment transport formulae in terms of their ability to describe the observed sediment transport from 39 data sets (a total of 3391 transport observations). They concluded that sediment transport formulae based on energy dissipation rates or stream power concepts more accurately described the observed transport data and that the degree of formula complexity did not necessarily translate into increased model accuracy. Although the work of *Yang and Huang* [2001] is helpful in evaluating the applicability and accuracy of many popular sediment transport equations, it is necessary to extend their analysis to coarse-grained natural rivers. Of the 39 data sets used by *Yang and Huang* [2001], only 5 included observations from natural channels (166 transport observations) and these were limited to sites with a fairly uniform grain-size distribution (gradation coefficient ≤2).

[3] Prior to the extensive work of *Yang and Huang* [2001], *Gomez and Church* [1989] performed a similar analysis of 12 bed load transport formulae using 88 bed load transport observations from 4 natural gravel bed rivers and 45 bed load transport observations from 3 flumes. The authors concluded that none of the selected formulae performed consistently well, but they did find that formula calibration increases prediction accuracy. However, similar to *Yang and Huang* [2001], *Gomez and Church* [1989] had limited transport observations from natural gravel bed rivers.

[4] *Reid et al.* [1996] assessed the performance of several popular bed load formulae in the Negev Desert, Israel, and found that the *Meyer-Peter and Müller* [1948] and *Parker* [1990] equations performed best, but their analysis considered only one gravel bed river. Because of small sample sizes, these prior investigations leave the question unresolved as to the performance of bed load transport formulae in coarse-grained natural channels.

[5] Recent work by *Martin* [2003], *Bravo-Espinosa et al.* [2003] and *Almedeij and Diplas* [2003] has begun to address this deficiency. *Martin* [2003] took advantage of 10 years of sediment transport and morphologic surveys on the Vedder River, British Columbia, to test the performance of the *Meyer-Peter and Müller* [1948] equation and two variants of the *Bagnold* [1980] equation. The author concluded that the formulae generally underpredict gravel transport rates and suggested that this may be due to loosened bed structure or other disequilibria resulting from channel alterations associated with dredge mining within the watershed.

[6] *Bravo-Espinosa et al.* [2003] considered the performance of seven bed load transport formulae on 22 alluvial streams (including a subset of the data examined here) in relation to a site-specific “transport category” (i.e., transport limited, partially transport limited and supply limited). The authors found that certain formulae perform better under certain categories of transport and that, overall, the *Schoklitsch* [1950] equation performed well at eight of the 22 sites, while the *Bagnold* [1980] equation performed well at seven of the 22 sites.

[7] *Almedeij and Diplas* [2003] considered the performance of the *Meyer-Peter and Müller* [1948], H. A. Einstein and C. B. Brown (as discussed by *Brown* [1950]), *Parker* [1979], and *Parker et al.* [1982] bed load transport equations on three natural gravel bed streams, using a total of 174 transport observations. The authors found that formula performance varied between sites, in some cases overpredicting observed bed load transport rates by one to three orders of magnitude, while at others underpredicting by up to two orders of magnitude.

[8] Continuing these recent studies of bed load transport in gravel bed rivers, we examine 2104 bed load transport observations from 24 study sites in mountain basins of Idaho to assess the performance of four bed load transport equations. We also assess accuracy in relation to the degree of formula calibration and complexity.

[9] Unlike *Gomez and Church* [1989] and *Yang and Huang* [2001], we find no consistent relationship between formula performance and the degree of formula calibration and complexity. However, like *Whiting et al.* [1999], we find that the observed transport data are best fit by a simple power function of total discharge. We propose this power function as a new bed load transport equation and explore channel and watershed characteristics that control the exponent and coefficient of the observed bed load power functions. We hypothesize that the exponent is principally a function of supply-related channel armoring, such that mobilization of the surface material in a well armored channel is followed by a relatively larger increase in bed load transport rate (i.e., steeper rating curve) than that of a similar channel with less surface armoring [*Emmett and Wolman*, 2001]. We use *Dietrich et al.*'s [1989] dimensionless bed load transport ratio (*q**) to quantify channel armoring in terms of upstream sediment supply relative to transport capacity, and relate *q** values to the exponents of the observed bed load transport functions. We hypothesize that the power function coefficient depends on absolute sediment supply, which we parameterize in terms of drainage area.

[10] The purpose of this paper is fourfold: (1) assess the performance of four bed load transport formulae in mountain gravel bed rivers, (2) use channel and watershed characteristics to parameterize the coefficient and exponent of our bed load power function to make it a predictive equation, (3) test the parameterization equations, and (4) compare the performance of our proposed bed load transport function to that of the other equations in item 1.