Reliable field data obtained by directly measuring bed-load transport of fine- to coarse-grained bed material are extremely scarce, mainly because of the difficulty of sampling accurately. Therefore, the verification of bed-load transport formulae is largely based on flume experiments, which refer to unrealistic shallow-water conditions. In this study, some bed-load transport formulae were tested against data from natural environments. As an alternative to ascertaining the bed-load transport rate by sampling the bed-load, the transport rate was deduced from data on bedform height and bedform celerity. For this purpose, 43 sets of data from rivers, representing a wide range of bed material, bedform dimensions and hydraulic conditions were collected as were some sets of data from tidal settings. Two formulae were used for the prediction of the bed-load transport: the formula of Van Rijn (1981) and the Kalinske (1947) formula as approximated by Elzerman & Frijlink (1951) (and, in the present study, slightly modified for application to tidal waters). Both the bed-load function of Van Rijn and the modified formula of Kalinske-Frijlink require data which are easily obtained and that can be measured accurately.

At those stages of the flow when bed-load transport was high the Van Rijn function tended to overestimate that transport. For flow stages when bed-load transport was low the opposite was true. The modified Kalinske-Frijlink function gave consistently good results: 86% of the transport rates predicted using the river data were within 0·5–2·0 times the values actually measured.