A Potential Link Between Waterfall Recession Rate and Bedrock Channel Concavity

Abstract

The incision of bedrock channels is typically modeled through the stream power or the shear stress applied on the channel bed. However, this approach is not valid for quasi-vertical knickpoints (hereafter waterfalls), where water and sediments do not apply direct force on the vertical face. As such, waterfall retreat rate is often modeled as a power function of drainage area (a surrogate for hydraulic processes, such as plunge-pool drilling and groundwater seepage, although a variety of non-hydraulic processes may also influence waterfall retreat). These different incision modes are associated with two measurable exponents: the channel concavity, θ, that is measured from the channel topography and is used to evaluate the exponents of drainage area and slope in the channel incision model, and p that is measured from the location of waterfalls within watersheds and evaluates the dependency of the waterfall recession rate on drainage area. To better understand the relations between channel incision and waterfall recession, we systematically compare between the exponents p and θ. These parameters were computed from digital elevation models (30-m Shuttle Radar Topography Mission) of 12 river basins with easily detectable waterfalls. We show that p and θ are (1) similar within uncertainty, (2) come from a similar distribution, and (3) covary for networks with a large number of waterfalls ((Formula presented.)). In the context of bedrock incision models this hints that the same processes govern waterfall retreat rate and the incision of nonvertical channel reaches in the analyzed basins and/or that downstream incision can dictate waterfall retreat rate.