Stochastic bed load transport formulas for nonuniform sediment exist, but most of them do not account for the composition of surface material to predict fractional transport rate. This study transformed a surface-based bed-load transport predictor to a stochastic one by approximating the fluctuation of bed-shear stress with a standard log-normal distribution. The deterministic predictor underpredicts fractional transport rate at low values of bed-shear stress and Reynolds number. The modified stochastic predictor predicts fractional transport rate more accurately and converges to the deterministic one at high shear stresses.
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Duan et al. (2008) studied this question.
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