Variable thresholds in mountain rivers imposed by hillslope-derived blocks

Abstract:

Recent field and modeling studies have shown that large, hillslope-derived blocks of rock delivered to channels may alter the course of river profile evolution in ways not accounted for by simple channel evolution models. Block delivery can set up a negative feedback in which blocks retard incision, which leads to a reduction in hillslope relief, and hence a reduction in block supply rate. Here we investigate the implications of these channel-hillslope feedbacks for the predicted relationships between erosion rate and channel slope. We use a 1-D model of fluvial erosion in the presence of hillslope-derived blocks to explore the influence of blocks on channel evolution across a wide range of erosion rates and block delivery scenarios. In general, hillslope block delivery causes increases in channel slope relative to the control (block free) case, and the magnitude of the increase in slope is proportional to the rate of block delivery. This behavior holds for channel slope gradients less than that required to mobilize blocks, beyond which point blocks are easily transported and block-influenced channels exhibit the same behavior as those in the control case. The behavior of the block-influenced channels is not well described by a shear stress/stream power type model with a constant erosion threshold. Instead, a shear stress/stream power model with an erosion threshold that depends on the imposed baselevel lowering rate successfully replicates the scaling of channel slope with baselevel lowering rate in block-influenced channels. We argue that the form of the function relating the erosion threshold to the baselevel lowering rate depends on the relationship between channel incision rate and hillslope block delivery. Our results indicate that the effects of hillslope-derived blocks may be easily incorporated into simple landscape evolution models. The use of a variable-threshold model has important implications for the relationship between erosion rate and channel steepness, showing lower steepness values at low erosion rates and higher steepness at higher erosion rates than equivalent constant-threshold models. The variable-threshold model that arises from considering block dynamics in fluvial erosion yields field-testable predictions for how channels might deviate from the predictions of simpler models.