Evolution of vertical knickpoints (waterfalls) with resistant caprock: Insights from numerical modeling

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.