Utilitarian Expressions for Equilibrium Bedload Transport

Heterogeneous field and laboratory measurements of equilibrium bedload transport can be collapsed to coherent relations by: expressing flow strength (x) as the ratio of the Shields number to the critical Shields number, or the ratio of dimensionless specific stream power to a reference dimensionless specific stream power; adjusting the dimensionless transport rate (y) to accommodate temporal variations in flow depth and bedload size; and treating the threshold shear stress as a variable parameter. The generalised form of the empirical functions we elaborate is: $y=c_1{x}^{e_1}{\left(1+c_2{x}^{e_2}\right)}^{e_3}$; and uncertainty surrounding estimates of y is accounted for by specifying prediction intervals for a confidence level of 90%. Their effectiveness is demonstrated by independent applications to analogous cases; and we anticipate these functions will afford a practical approach for estimating cross-section average bedload transport rates in a wide range of fluvial systems where similar conditions can be assumed to exist. Our analysis also suggests that, although it has been appreciated that data obtained in the laboratory may not be directly comparable to measurements made in the field for more than seven decades, the inveterate use of a constant value to represent the threshold shear stress has unwittingly served to obscure the disparity between rivers and flumes.