[1] Vertical knickpoints (waterfalls) mark a prominent process transition zone whose governing mechanics is not represented by conventional stream power incision models. We examine the evolution of vertical knickpoints with resistant caprock utilizing numerical simulations that explicitly represent (1) face failure mechanisms, (2) flow acceleration and amplified erosion above a knickpoint lip, (3) deposition and removal of coarse debris below the knickpoint, and (4) base level lowering or tectonic uplift rates. Our model demonstrates that knickpoint retreat rate, where the subcaprock is weak or vertically jointed and base level fall rates are steady, is likely to become tied to downstream conditions and equal to the downstream incision rate divided by channel gradient. Mechanically, this coupling occurs where the subcaprock reaches a threshold height for failure in shear or buckling or where the weathering rate of the subcaprock is higher than the downstream incision wave velocity (V i_ds ). The height of the subcaprock face can influence its gravitational stability and the knickpoint lateral erosion rate and lead to a feedback between downstream incision and retreat rate. Retreat rate can be lower than V i_ds during transients, which could be long (>10 6 years) and set by the weathering rate of the subcaprock or influenced by lag debris evacuation. Key variables other than discharge can be important in setting retreat rates. These include base level lowering rate, the rock strength of stratigraphic units downstream of the knickpoint, and the size and flux of sediment contributed from above the knickpoint or from the canyon walls. Two types of oversteepened reaches can form in association with a vertical knickpoint: (1) an upstream, free fall-induced, oversteepened reach whose length is longer than the flow acceleration zone and (2) a downstream coarse debris-induced oversteepened reach. Although the model was constructed with caprock-type knickpoints in mind, some of its elements and insights are also relevant to homogenous substrates.

[1] 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, where E (x=L a ) 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 Cl-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.

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