Slide 23 of 66
Notes:
In two dimensions (z and x) linear diffusive mass wasting (left equation) can be solved for gradient, S (or ?z/?x), as a function of distance from the divide, x. Because of the steady state erosion, ?z/?t|m, the rate of erosion due to mass wasting, can be replaced by the constant -Es. On the other hand, for slopes that are close the the threshold conditions, the slope gradient is simply that threshold gradient, St. Note that the slope gradient is a linear function of erosion rate.
This analysis follows Howard (1997, op. Cit.), and Tucker and Bras (1998, op. cit.) offer a similar analysis)
