Hillslope-derived blocks and erosion rate-channel steepness scaling: Emergence of variable-threshold behavior

Abstract:

The combination of erosion thresholds and time-varying flow in stream channels has been shown to significantly influence channel form and evolution. Mathematical models that describe the relationship between stream channel gradient and erosion rate typically assume a time- and space-invariant erosion threshold, which is dictated either by the size of in-channel sediment or bedrock properties, and is constant across a range of erosion rates and stream gradients. This assumption becomes suspect in cases where the physical mechanisms that impose erosion thresholds may co-vary with erosion rate. For example, recent modeling and field efforts have suggested that large, hillslope-derived blocks of rock delivered to channels may significantly impede erosion and alter channel morphology and evolution. Given that rapid river erosion can lead to hillslope steepening and increased delivery of large grains to channels, it is reasonable to hypothesize that the erosion threshold in a channel may be correlated with its erosion rate. Using a 1-D fluvial erosion model that incorporates incision-rate-dependent delivery of large blocks, we explore the effects of block delivery on the relationship between erosion rate and channel steepness, and assess whether that relationship supports a fixed threshold or one that varies with erosion rate. Unsurprisingly, delivery of blocks to the channel results in steeper steady-state channel profiles than those obtained in the no-blocks case. The increase in steepness relative to the no-blocks case is greater with more rapid block delivery. Above a critical slope, channel steepness ceases to increase with increased block delivery, as blocks become mobile and no longer influence channel evolution. Modeled channel steepness values over a wide range of erosion rates are inconsistent with a single threshold value, but are instead well described by a threshold that increases with increasing erosion rate. The positive relationship between erosion rate and threshold arises as a result of increased erosion rates driving rapid block delivery from hillslopes, which increases the effective erosion threshold in the channel. Our results suggest that a variable-threshold incision model may be more appropriate than a single threshold in steep landscapes with tightly coupled channels and hillslopes.