Modelling sediment transport from bare rilled hillslopes by areally averaged transport equations

Treating the dynamics of sediment transport as two-dimensional on interrill-areas and as one-dimensional in rill sections, areally averaged sheet sediment transport equations are developed. The two-dimensional sheet sediment transport equation is averaged over an individual interrill-area width and then along the interrill-area length to obtain local-scale areally averaged interrill-area sheet sediment transport equation (local-scale areal averaging). Similarly, the cross-sectionally-averaged rill sediment transport equation is averaged along an individual rill length to obtain local-scale areally averaged rill sediment transport equation (local-scale areal averaging). In order to minimize computational effort and economize on the number of model parameters, the local-scale areally averaged equations are then averaged over a whole hillslope section (large-scale areal averaging). These equations constitute the areally averaged model. The expectations of the terms containing more than one variable are obtained by the method of regular perturbation. In the large-scale areal averaging it is assumed that all the randomness in the state variable is due to the randomness in the parameters of the process. Comparison of the results obtained from the areally averaged model with those of the point-scale model indicates that the areally averaged model uses far less data and yet it performs as well as the point-scale model. The results of the developed model indicate that on a rilled-surface most of the sediment loads comes from rill sections. The developed model is successfully tested against experimental data obtained from a bare rilled hillslope. It predicted measured runoff and sediment rates with mean absolute errors of 11.07 l/min and 0.382 kg/s, respectively.