Amplified erosion above waterfalls and oversteepened bedrock reaches

None of the conventional bedrock erosion laws can predict incision immediately upslope of a waterfall lip where the flow is accelerating toward a freefall. Considering the expected increase in flow velocity and shear stress at the lip of a waterfall, we determine erosion amplification at a waterfall lip as E_lip/E_(x=La) = ( 1 + 0.4/Fr_(x=La)²)³ⁿ, where E_(x=La) is the erosion rate at the upstream end of the flow acceleration zone above a waterfall, Fr is the Froude number at this setting, and n ranges between 0.5-1.7. This amplification expression suggests that erosion at the lip could be as much as 2-5 times higher relative to erosion at a normal setting with identical hydraulic geometry. Utilizing this erosion amplification expression in numerical simulations, we demonstrate its impact on reach-scale morphology above waterfalls. Amplified erosion at the lip of a waterfall can trigger the formation of an oversteepened reach whose length is longer than the flow acceleration zone, provided incision wave velocity (V_i) at the upstream edge of the flow acceleration zone is higher than the retreat velocity of the waterfall face. Such an oversteepened reach is expected to be more pronounced when V_i increases with increasing slope. The simulations also suggest that oversteepening can eventually lead to steady state gradients adjacent to a waterfall lip provided V_i decreases with increasing slope. Flow acceleration above waterfalls can thus account, at least partially, for prevalent oversteepened bedrock reaches above waterfalls. Using the cosmogenic isotope C1-36, we demonstrate that incision wave velocity upstream of a waterfall at the Dead Sea western escarpment is probably high enough for freefall-induced oversteepening to be feasible.