Variable-Threshold Behavior in Rivers Arising From Hillslope-Derived Blocks

Geomorphologists often rely on simple models of river channel incision for predicting rates of landscape evolution and channel response to perturbations, as well as extracting climatic and tectonic signals from river longitudinal profiles. Recent work has shown that large, hillslope-derived blocks delivered to rivers may noticeably alter the form and evolution of river profiles from the behavior predicted by the most common models. Here we use a 1-D model of river reach erosion and hillslope block delivery to explore the conditions under which block delivery strongly influences channel evolution. We use global sensitivity analysis to understand which model parameters most strongly affect the channel longitudinal profile. We explore the effects of blocks on the relationship between erosion rate and channel gradient, and on the erosion rate-channel steepness exponent , and find that block effects result in highly variable slope and over the range of erosion rates and climatic conditions (discharge mean and variability) tested. The influence of blocks on erosion rate-slope scaling may be approximated by a piecewise model: The erosion threshold imposed by blocks scales linearly with erosion rate when blocks are infrequently mobile and remains constant when blocks are frequently mobile. We explore the implications of this variable-threshold model for the erosion rate-channel steepness relationship and find that erosion rate-dependent thresholds imposed by hillslope-derived blocks cause significant departures from previous models but may be consistent with existing field data sets. Our work has implications for landscape evolution modeling and the inversion of channel profiles for forcing information. Plain Language Summary Rivers control how quickly mountain ranges erode. The amount, size, and durability of sediment delivered to rivers determine the shape of their channels and control how rapidly those channels cut through bedrock. Studies of river erosion tend to focus on how rivers respond to the delivery of smaller sediment like sand or gravel. But steep mountain hillslopes often deliver larger sediment, including boulders and blocks of rock, into river valleys. In this study, we used a mathematical model of river erosion to explore river response to the delivery of these larger blocks to the channel. We found that the rate of block delivery, the durability of the blocks, and the block size strongly controlled the slope of rivers. We also found that block delivery to rivers fundamentally changed the relationship between how quickly a landscape was eroding and how steep that landscape was. Quantifying how block delivery affects river erosion will help mitigate natural hazards and aid prediction of future changes to Earth's surface.