A model for predicting the sediment transport capacity of turbulent interrill flow on rough sur4faces is developed from 1295 flume experiments with flow depths ranging from 3.4 to 43.4 mm, flow velocities from 0.09 to 0.65 m s^{-1}, Reynolds numbers from 5000 to 26949, Froude numbers from 0.23 to 2.93, bed slopes from 2.7{\textdegree} to 10{\textdegree}, sediment diameters from 0.098 to 1.16 mm, volumetric sediment concentrations from 0.002 to 0.304, roughness concentrations from 0 to 0.57, roughness diameters from 1.0 to 91.3 mm, rainfall intensities from 0 to 159 mm h^{-1}, flow densities from 1002 to 1501 kg m^{-3}, and flow kinematic viscosities from 0.913 to 2.556 x 10^{-6} m^{2} s^{-1}. Stones, cylinders and miniature ornamental trees are used as roughness elements. Given the diverse shapes, sizes and concentrations of these elements, the transport model is likely to apply to a wide range of ground surface morphologies. Using dimensional analysis, a total-load transpot equation is developed for open-channel flows, and this equation is shown to apply to interrill flows both with and without rainfall. The euation indicates that the dimensionless sediment transport rate {\O} is a function of, and therefore can be predicted by, the dimensionless shear stress {\`e}, its critical value {\`e}_{c}, the resistance coefficient u/u_{*}, the inertial settling velocity of the sediment w_{i}, the roughness concentration C_{r}, and the roughness diameter D_{r}. Testing reveals that the model gives good unbiased predictions of {\O} in flows with sediment concentrations less than 0.20. FLows with higher concentrations appear to be hyperconcentrated and to have sediment transport rates higher than those predicted by the model. Copyright {\textcopyright} 2001 John Wiley \& Sons, Ltd.