Testing bedload transport equations with consideration of time scales
Evaluation des formules de transport solide
Abstract
Bedload transport is known to be a highly fluctuating temporal phenomenon, even under constant flow conditions, as a consequence of bedform migration, grain sorting, hysteresis, stochasticity 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 14 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, and (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. Because they predict zero transports, most threshold formulas are no longer valid when the Shields ratio θ84/θc84 (calculated for diameter D84) is lower than 2. When the calculated transport is non-zero, it is usually largely overestimated when D84 is high, which can result from increasing hiding effects with increasing grain size, not taken into account in these formulas. There is a need for new sediment data collected with highly reliable techniques such as bedload traps to complete this paper’s analysis.