Empirical Analysis of Slope and Runoff For Sediment Delivery from Interrill Areas

Slope steepness ( S ) and runoff discharge ( q w ) are two major factors in determining sediment delivery rates ( q s ) from interrill areas. Under the current interrill erosion model concept, these two factors are assumed to have independent effects on q s ; thus, each factor can be quantified individually if the other factor is kept constant. This study was conducted to show the effects of S and q w on q s and their interdependency. Sediment discharge rates, measured under different rainfall intensities and slope gradients, for eight soils from two laboratory studies were analyzed empirically with curve‐fitting procedures. Results showed that there was a pair of empirical equations for each soil: q s = A 1 q 2 w + A 2 q w + A 3 and q s = B 1 S 2 + B 2 S + B 3 , where A 1 , A 2 , and A 3 are functions of S and B 1 , B 2 , and B 3 are functions of q w . In other words, effects of slope steepness and runoff on sediment delivery are dependent on each other. When S and q w were combined together as stream power, Ω, and plotted against sediment concentration, q s / q w , a unique nonlinear relationship existed for each soil: q s / q q = D 1 Ω 2 + D 2 Ω + D 3 , where D 1 , D 2 , and D 3 are soil‐dependent coefficients. The stream power, which encompasses both slope and runoff effects, may provide improved estimates for interrill erosion. Although not based on theory, this result may be useful in process‐based erosion models.