Variable thresholds in rivers: Causes and effects

Abstract:

River erosion thresholds strongly influence channel evolution and response to climate and tectonics, and erosion in most high-gradient channels may be dominated by the interplay between time-varying discharge and bed erosion thresholds. Most models assume spatially and temporally constant erosion thresholds, which are dictated in a given channel by bed load sediment size or bedrock properties. However, the constant-threshold assumption becomes suspect when we expand our view to account for feedbacks between channels and their adjacent hillslopes. Rapid river incision steepens adjacent hillslopes and increases the size of sediment delivered to the channel. We therefore hypothesize that erosion thresholds may co-vary with long-term erosion rates. We explore the origins and implications of variable thresholds imposed by hillslope sediment with a numerical modeling case study.

Recent work suggests that blocks of rock delivered from hillslopes to channels inhibit erosion and steepen river channels. We use a simple model of channel profile evolution and hillslope block delivery to test whether channel form and evolution outcomes are compatible with a hillslope-driven variable erosion threshold. Block delivery results in steeper steady-state channels relative to the no-blocks case, with greater slope increases tied to more rapid block delivery. We test whether the relationships between erosion rate and steady-state slope in modeled channels are compatible with a constant erosion threshold or require a variable threshold. Results indicate that channel steepening in response to erosion rate-dependent block delivery is inconsistent with a constant erosion threshold, but requires a threshold that varies with erosion rate. We test the effects of erosion rate-dependent thresholds in a standard stochastic-threshold model and find that relationships between erosion rate and channel steepness are much more linear under a variable threshold than a constant one. Variable erosion thresholds thus provide an alternative explanation to observed near-linear scaling between erosion rate and channel steepness. Increasingly realistic representations of stochastic climate are being applied to river erosion problems, but will only improve model predictive power if erosion thresholds are well-understood.