Probability distributions for bed form-dominated bed load transport: The Hamamori distribution revisited

The Hamamori distribution is frequently used to describe the variability of bed load transport rates in bed form-dominated environments. However, the original derivation contains several incorrect steps. Here a corrected and generalized derivation is presented. It is shown that Hamamori's original distribution function arises if the underlying assumptions are adapted slightly. Two formalisms are presented to obtain probability distributions of instantaneous bed load transport rates from growth functions of ripples and from the distribution of ripple heights. Six distribution functions, among them the exponential distribution, the Hamamori distribution, and the gamma distribution, are compared to two laboratory data sets, one for gravel and one for sand transport, and to field data from a sand-bed river. For the gravel bed laboratory measurements, the Hamamori distribution gives a good description of the data for intermediate transport rates, while the gamma distribution performs best overall. For the sand-bed laboratory data, the exponential distribution shows the best performance. A distribution function derived from Rayleigh-distributed ripple heights performs best for the field data.