The effect of slope gradient and length on the parameters of a sediment transport equation for sheetwash

Sheetwash sediment transport (Q s ) is often expressed by Q S =kQ m S N where S is slope gradient and Q water discharge. For practical reasons the length-rainfall intensity product (LI) is often used in this equation as a surrogate for discharge. The estimation of the exponents m and n is biased whenever complex hillslope shapes are used and when water discharge is not linearly related to LI. An experiment was designed to simultaneously measure water and sediment discharges on short straight hillslopes of similar material, sloping at 5°, 11° and 27°. Natural rainfalls were used throughout this study. The values obtained for the exponents m and n using all the available measurements are 1.5 and 0.9 respectively. The value of m lies between the boundaries proposed in literature and the exponent n is slightly under the lower limit. This experiment showed that water discharge is not linearly related to the length-rainfall intensity product and that the value of m calibrated with Q increases with slope gradient. This result is explained by the return flow occuring at the base of steeper slopes and by the contribution of rainsplash to particle detachment. Consequently, three points will be discussed in detail: (i) the relevancy of using LI rather than Q to estimate m and n or to facilitate measurement and mainipulation in hillslope simulation models; (ii) the implications on erosion processes and simulation of hillslope evolution of the systematic effect of gradient on water and sediment discharges; and (iii) the problem of scale in the calibration of sediment transport equations.