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Variable‐Threshold Behavior in Rivers Arising From Hillslope‐Derived Blocks
Author(s) -
Shobe Charles M.,
Tucker Gregory E.,
Rossi Matthew W.
Publication year - 2018
Publication title -
journal of geophysical research: earth surface
Language(s) - English
Resource type - Journals
eISSN - 2169-9011
pISSN - 2169-9003
DOI - 10.1029/2017jf004575
Subject(s) - channel (broadcasting) , erosion , scaling , geology , bank erosion , soil science , hydrology (agriculture) , variable (mathematics) , environmental science , geomorphology , geometry , mathematics , geotechnical engineering , computer science , computer network , mathematical analysis
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 ϕ , and find that block effects result in highly variable slope and ϕ 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.