Testing bedload transport equations with consideration of time scales

Bedload transport is known to be a highly fluctuating temporal phenomenon, even under constant (mean) flow conditions, as a consequence of stochasticity, bedform migration, grain sorting, hysteresis, or sediment supply limitation. Because bedload transport formulas usually refer to a single mean transport value for a given flow condition, one can expect that prediction accuracy (when compared to measurements) will depend on the amplitude and duration of fluctuations, which in turn depend on the time scale used for observations. This paper aims to identify how the time scale considered can affect bedload prediction. This was done by testing 16 common bedload transport formulas with four data sets corresponding to different measurement period durations: (i) highly fluctuating (quasi-)instantaneous field measurements; (ii) volumes accumulated at the event scale on two small alpine gravel-bed rivers, potentially affected by seasonal fluctuations; (iii) volumes accumulated at the interannual scale in a meandering gravel bed river, thought to be weakly subject to fluctuations; (iv) time-integrated flume measurements with nearly uniform sediments. The tests confirmed that the longer the measurement period, the better the precision of the formula's prediction interval. They also demonstrate several consequential limitations. Most threshold formulas are no longer valid when the flow condition is below two times the threshold condition for the largest elements' motion on the bed surface (considering D84). In such conditions, equations either predict zero transport, or largely overestimate the real transport, especially when D84 is high. There is a need for new sediment data collected with highly reliable techniques such as recording slot bedload samplers to further investigate this topic. Copyright (C) 2012 John Wiley & Sons, Ltd.