Performance of Bedload Transport Equations Relative to Geomorphic Significance

Bedload transport is a fundamental process for alluvial rivers, creating bedform topography that stabilizes channel form and provides diverse physical habitat for aquatic organisms. It also controls the storage and mobilization of heavy minerals and coarse-grained contaminants, and is an important aspect of channel migration that both revitalizes river floodplains and can threaten human infrastructure within river valleys. Numerous studies over the past two decades have assessed the performance of various equations for predicting bedload transport. However, these studies considered formula performance statistically based on paired observations of measured and predicted bedload transport, the majority of which were taken at low flows. Consequently, formula performance is weighted toward low discharges which may not have geomorphic significance. We define geomorphic significance in terms of both the effective discharge (that which transports the most sediment over time) and the total bedload yield (the product of discharge and bedload transport rate integrated over time). Accurate prediction of the effective discharge depends on how representative both the flow record and the flood frequency distribution are, and on the validity of the transport equation. The latter specifically depends on how well the transport equation represents the exponent of the observed bedload rating curve which is, in turn, a function of supply-related channel armoring (transport capacity relative to sediment supply). Poorly-armored, fine-grained channels exhibit lower thresholds for bedload transport and thus lower rating-curve exponents compared to well-armored, coarse-grained channels. In contrast, accurate prediction of the total bedload yield depends on the overall performance of the transport equation over the range of observed flows, and may be sensitive to a variety of factors, including performance of transport threshold functions embedded within the equation, roughness correction, and degree of equation calibration to site-specific conditions over the range of channel discharges. We consider the performance of 8 different formulations of 5 bedload transport equations at 41 gravel-bed rivers in mountain basins of the western United States. Performance is assessed in terms of the accuracy with which the equations are able to predict 1) the effective discharge, 2) the bedload transport rate for the effective discharge, and 3) the total bedload yield for a given discharge record.