Re-examination of Bagnold's empirical bedload formulae

Bagnold developed his formula for bedload transport over several decades, with the final form of the relation given in his 1980 paper. In this formula, bedload transport rate is a function of stream power above some threshold value, depth and grain size. In 1986, he presented a graph which illustrated the strength of his relation. A double-log graph of bedload transport rate, adjusted for depth and grain size, versus excess stream power was shown to collapse along a line having a slope of 1.5. However, Bagnold based his analyses on limited data. In this paper, the formula is re-examined using a large data set in order to define the most consistent empirical representation, and dimensional analysis is performed to seek a rationalization of the formula. Functional analysis is performed for the final version of the equation defined by Bagnold to determine if the slope of 1.5 is preserved and to assess the strength of the relation. Finally, relations between excess stream power and bedload transport are examined for a fixed slope of 1.5 to assess the performance of various depth and grain size adjustment factors. The rational scaling is found to provide the best result. Copyright (C) 2000 John Wiley & Sons, Ltd.