Utilitarian Expressions for Bedload Transport: The Role of Particle Size

We demonstrate that empirical expressions relating measures of flow strength to the dimensionless bedload transport rate apply to a broad spectrum of sand- and gravel-bed rivers. The ability of the flow to transport sediment is expressed either 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. However, the key parameter is the median size of the hydrosedimentologically dominant textural facies in the local bed material, or a distanced upstream source from which the bedload is derived. In the former case, this representative size encodes information about the calibre and amount of sediment a river must transport to balance the environmentally controlled sediment supply. Thus, our expressions depict the transport rate, governed by the chosen measure of flow strength, realised for the long-term attributes of sediment entering and stored in a river channel. Higher(lower) transport rates are associated with a plentiful(limited) sediment supply; strong(weak) hillslope-to-channel and/or reach-to-reach coupling; the relaxation(imposition) of constraints on in-channel availability; and a live(static or armoured) bed. Departures from the fitted relations are indicative of an informed adaptation to an over(under) supply of sediment, an increase(decrease) in the availability of mobile in-channel sediment, or the strengthening(deterioration) of connectivity between upstream and/or riparian sources. Prediction limits for the 90% uncertainty range accommodate this natural variability. Transport rates modulated by the reflexive in-channel regulation of sediment availability by a static or armoured bed depart from but, nonetheless, are constrained by the fitted relations, because the environmentally controlled sediment supply also determines the range of particle sizes available on the bed surface. If, however, sediment supplied by mass wasting is neither filtered nor buffered by in-channel processes, the riverbed has no “memory” of this bedload material and no coherent trend emerges.