An approximate analytic solution is given for the first time to previously published equations describing the characteristics of dynamic soil erosion caused by overland flow. The solution describes both the variation in time in total sediment concentration since the commencement of uniform overland flow, and also the dynamic change in the settling velocity characteristics (and size distribution) of eroding sediment. Following calibration for each of the three soils investigated in order to determine unknown but physically-defined model parameters, prediction based on this theory was found to provide good agreement with experimental data. Under steady-state conditions achieved at long time, the solution agrees with the exact solution for transport limiting conditions, and provides a simple expression for sediment concentration in other situations where soil strength affects the sediment concentration ultimately achieved.
Journal of Hydrology Vol. 333, Issue 39540, p. 449-458