Morphodynamics of Bedrock Rivers

Sediment size and supply exert a dominant control on channel structure. We review the role of sediment supply in channel structure, and how regional differences in sediment supply and land use affect stream restoration priorities. We show how stream restoration goals are best understood within a common fluvial geomorphology framework defined by sediment supply, storage, and transport. Land-use impacts in geologically young landscapes with high sediment yields (e.g., coastal British Columbia) typically result in loss of in-stream wood and accelerated sediment inputs from bank erosion, logging roads, hillslopes and gullies. In contrast, northern Sweden and Finland are landscapes with naturally low sediment yields caused by low relief, resistant bedrock, and abundant mainstem lakes that act as sediment traps. Land-use impacts involved extensive channel narrowing, removal of obstructions, and bank armouring with boulders to facilitate timber floating, thereby reducing sediment supply from bank erosion while increasing export through higher channel velocities. These contrasting land-use impacts have pushed stream channels in opposite directions (aggradation versus degradation) within a phase-space defined by sediment transport and supply. Restoration in coastal British Columbia has focused on reducing sediment supply (through bank and hillslope stabilization) and restoring wood inputs. In contrast, restoration in northern Fennoscandia (Sweden and Finland) has focused on channel widening and removal of bank-armouring boulders to increase sediment supply and retention. These contrasting restoration priorities illustrate the consequences of divergent regional land-use impacts on sediment supply, and the utility of planning restoration activities within a mechanistic sediment supply-transport framework.

Bedrock rivers carry large amounts of fine sediment in suspension. We developed a mechanistic model for erosion of bedrock channel banks by impacting bedload and suspended load particles that are advected laterally by turbulent eddies (advection‐abrasion model). The model predicts high lateral erosion rates near the bed, with rates decreasing up to the water surface. The model also predicts greater erosion within the suspended load layer than the bedload layer for many typical sediment supply and transport conditions explored. We compared the advection‐abrasion model with a previously derived model for lateral erosion of bedrock banks by bedload particles deflected by stationary bed alluvium (deflection‐abrasion model). Erosion rates predicted by the deflection‐abrasion model are lower, except within limited conditions where sediment is transported near the threshold of motion and the bed is near fully covered in sediment. Both processes occur in bedrock rivers at the same time, so we combined the advection‐abrasion and deflection‐abrasion models and found that the lateral erosion rate generally increases with increasing transport stage and relative sediment supply for a given grain size. Application of our combined‐abrasion model to a natural bedrock river with a wide distribution of discharge and supply events, and mixed grain sizes, indicates that finer sediment dominates the lateral erosion on channel banks in low sediment supply environments and can be as important as coarser sediment in high sediment supply environments.

Landscape scale bedrock erosion is the integration of bedrock erosion at the reach scale, which is driven by particle impacts from sediment transport caused by near‐bed hydraulics. Plunging flow hydraulics have been identified in bedrock canyons and cause velocity profile inversions, which enhance near‐bed velocities, sediment transport, and the potential for bedrock erosion. Observations of plunging flows are limited, and the frequency and statistical properties of this hydraulic phenomenon have not been investigated. Here, we define metrics to identify velocity inversions and use them to detect instances of plunging flows through a 375 km reach of the Fraser River where channel morphology is controlled by bedrock. Isolated plunging flows are identified as well as plunging flow complexes where a series of plunges cause the core of maximum velocity to remain depressed in the water column for a prolonged distance. A significant relationship between plunging flows and bedrock exposure is identified, and plunging flows occupy more than half of the bedrock confined reaches. Stronger plunging flows are correlated with deeper and narrower channels with higher maximum shear stresses. Plunging flows are also concentrated in steeper reaches, which likely represent knickzones in the river profile. We use particle abrasion‐based bedrock erosion models to show that plunging flows drive reach‐scale incisions in bedrock rivers, creating deep bedrock pools. These pools dominate the incision into the bedrock, which sets the base level for their drainage areas and in turn sets the pace of landscape evolution.

<p>Sediment transport in rivers depends on interactions between sediment supply, topography, and flow characteristics. Erosion in bedrock rivers controls topography and is paramount in landscape evolution models. The riverbed cover indicates sediment transport processes: alluvial cover indicates low transport capacity or high sediment supply, and bedrock cover demonstrates high transport capacity or low sediment supply. This study aims to evaluate controls on the spatial distributions of bedrock and alluvial covers, by analysing scaling geometric relations between bedrock and alluvial channels. A Principal Component Analysis (PCA) was conducted to evaluate correlations between river slope, depth, width, and sediment size. The two principal components were used to implement a clustering analysis in order to identify differences in alluvial and bedrock sections. Spatial distributions of mixed bedrock-alluvial sections were investigated from two datasets - Scottish Highlands (Whitbread 2015) and the San Gabriel Mountains in the USA (Dibiase 2011)-, representing different environmental conditions, such as erosion rates, lithology, tectonics, and climate. The rock strength of both areas is high, and therefore it is excluded as a factor that explains the difference between the areas. The results of the cluster analysis were different in each environment. The main sources of variation among river sections identified by PCA were slope and width for the San Gabriel Mountains, and drainage area and depth for the Scottish Highlands. The rivers in the Scottish Highlands formed clusters that differentiate bedrock and alluvial patches, showing a clear geometric distinction between channels. However, the river analysis from the San Gabriel Mountains showed no clusters. Bedrock rivers are typically described as narrower and steeper than alluvial rivers, as demonstrated by rivers in the Scottish Highlands (e.g. slope was around 0.1 m/m for bedrock sections and 0.01 m/m for alluvial sections). However, this may not be always the case: both bedrock and alluvial sections in San Gabriel Mountains presented similar slope around 0.1 m/m. The inability to demonstrate significant geometry differences in bedrock and alluvial sections in the San Gabriel Mountains may be due to the frequency and magnitude of sediment supply of that region, which are influenced by tectonics and climate. A major difference in the supply of sediment in rivers of the San Gabriel Mountains is the frequent occurrence of debris flow. Non-linear interactions between hydraulic and sediment processes may constantly modify the geometry of bedrock-alluvial channels, increasing the complexity of analysis at larger temporal and spatial scales. This study is part of the i-CONN project, which links connectivity in different scientific disciplines. A sediment connectivity assessment in different environments and scales may be useful to evaluate the controls on the spatial distribution of bedrock and alluvial rivers.</p><p> </p><p>Dibiase, R.A. 2011. Tectonic Geomorphology of the San Gabriel Mountains, CA. PhD Thesis. Arizona State University, Phoenix, 247pp.</p><p>Whitbread, K. 2015. Channel geometry data set for the northwest Scottish Highlands. British Geological Survey Open Report, OR/15/040. 12pp.</p>

The width of bedrock rivers is set by the competition between vertical and lateral erosion in uplifting landscapes. Compared with vertical erosion rates, less is known about the lateral erosion rates that are thought to dominate when river beds are alluviated. Here, we derive an analytical model for lateral erosion by saltating bedload particle impacts that are deflected by alluvial cover. The analytical model is a simplification of the Li et al. (2020, https://doi.org/10.1029/2019jf005509) numerical model of the same process. The analytical model predicts a nonlinear dependence of lateral erosion rate on sediment supply, shear stress, and grain size, revealing the same behavior observed in the numerical model, but without tracking particle movements through time and space. The analytical model considers both uniformly distributed cover and patchy partial cover that are implemented with a fully alluviated patch along one bank and bare bedrock along the other. The model predicts that lateral erosion rate peaks when the bed is ∼70% covered for uniformly distributed alluvium, or when the bed is fully covered for patchy alluvium. Vertical erosion dominates over lateral erosion for ∼75% and >90% of sediment supply and transport stage conditions for uniformly distributed cover and patchy cover, respectively. We use the model to derive a phase diagram of channel responses (steepening, flattening, narrowing, and widening) for various combinations of transport stage and relative sediment supply. Application of our model to Boulder Creek, CA, captures the observed channel widening in response to increased sediment supply and steepening in response to larger grain size.

<p>Bedrock walls can be undercut by saltating bedload particle impacts that are deflected by alluvial cover. Continued undercutting of the lower wall creates an imbalance on the wall and may cause the upper part to collapse and to widen the whole channel. Compared with vertical erosion rates, less is known about lateral erosion (undercutting) rates that are thought to dominate when river beds are alluviated. Here, we derive an analytical model for lateral erosion by saltating bedload particle impacts. The analytical model is a simplification of the Li et al. (2020) numerical model of the same process. The analytical model predicts a nonlinear dependence of lateral erosion rate on sediment supply, shear stress and grain size, revealing the same behaviour observed in the numerical model, but without tracking particle movements through time and space. The analytical model considers both uniformly distributed cover and patchy partial cover that is implemented with a fully alluviated patch along one bank and a bare bedrock along the other. The model predicts that lateral erosion rate peaks when the bed is ~70% covered for uniformly distributed alluvium and when the bed is fully covered for patchy alluvium. Vertical erosion dominates over lateral erosion for ~75% and >90% of sediment supply and transport conditions for uniformly distributed cover and patchy cover, respectively. We use the model to derive a phase diagram of channel responses (steepening, flattening, narrowing, widening) for various combinations of transport stage and relative sediment supply. Application of our model to Boulder Creek, CA captures the observed channel widening in response to increased sediment supply and steepening in response to larger grain size.</p>

Bedrock rivers are the keystone to understanding landscape evolution as they control the rate of geomorphic responses to climatic and tectonic signals. Bedrock erosion is driven by channel hydraulics, which are not well understood for complex bedrock river morphologies. Some bedrock rivers exhibit a constriction-pool-widening morphology and associated plunging flow where the core of maximum velocity follows the bed into deep pools. Previous observations suggest that moderate discharges enhance the erosive potential of plunging flows, and that plunging flows are the dominant driver of morphology and downcutting in reaches where they are present. However, there are very few observations of plunging flows in natural environments, so their frequency and cumulative impact on landscape evolution is still unclear. Here we examine Acoustic Doppler Current Profiler and Multibeam Echosounder data collected in the Fraser Canyon of British Columbia, Canada to better understand the general properties and frequency of plunging flows. The entire 375 kms of the Fraser Canyon were analyzed for indicators of plunging flows to estimate their frequency. Results suggest that plunging flows appear to be abundant and are correlated with high shear stresses which are concentrated into deep bedrock pools. When examined using common erosion modelling techniques, observations suggest that reaches with plunging flows are incising at a much faster rate than non-plunging reaches. This work shows that considering reach scale hydraulics is critical for understanding the morphogenesis of large bedrock rivers and the mountainous landscapes that they drain. The abundance of plunging flows in large bedrock rivers suggests the importance of integrating complex flow patterns into bedrock erosion models, informs patterns of bedrock erosion at the reach scale, and begs for further investigation into the distribution of fluid shear stresses in complex bedrock channel morphologies.

Abstract. Rivers are dynamical systems that are thought to evolve towards a steady-state configuration. Then, geomorphic parameters, such as channel width and slope, are constant over time. In the mathematical description of the system, the steady state corresponds to a fixed point in the dynamic equations in which all time derivatives are equal to zero. In alluvial rivers, steady state is characterized by grade. This can be expressed as a so-called order principle: an alluvial river evolves to achieve a state in which sediment transport is constant along the river channel and is equal to transport capacity everywhere. In bedrock rivers, steady state is thought to be achieved with a balance between channel incision and uplift. The corresponding order principle is the following: a bedrock river evolves to achieve a vertical bedrock incision rate that is equal to the uplift rate or base-level lowering rate. In the present work, considerations of process physics and of the mass balance of a bedrock channel are used to argue that bedrock rivers evolve to achieve both grade and a balance between channel incision and uplift. As such, bedrock channels are governed by two order principles. As a consequence, the recognition of a steady state with respect to one of them does not necessarily imply an overall steady state. For further discussion of the bedrock channel evolution towards a steady state, expressions for adjustment timescales are sought. For this, a mechanistic model for lateral erosion of bedrock channels is developed, which allows one to obtain analytical solutions for the adjustment timescales for the morphological variables of channel width, channel bed slope, and alluvial bed cover. The adjustment timescale to achieve steady cover is of the order of minutes to days, while the adjustment timescales for width and slope are of the order of thousands of years. Thus, cover is adjusted quickly in response to a change in boundary conditions to achieve a graded state. The resulting change in vertical and lateral incision rates triggers a slow adjustment of width and slope, which in turn affects bed cover. As a result of these feedbacks, it can be expected that a bedrock channel is close to a graded state most of the time, even when it is transiently adjusting its bedrock channel morphology.

Gravel‐bed rivers that incise into bedrock are common worldwide. These systems have many similarities with other alluvial channels: they transport large amounts of sediment and adjust their forms in response to discharge and sediment supply. At the same time, the occurrence of bedrock incision implies behaviour that falls on a spectrum between fully detachment‐limited ‘bedrock channels’ and fully transport‐limited ‘alluvial channels’. Here, we present a mathematical model of river profile evolution that integrates bedrock erosion, gravel transport and the formation of channels whose hydraulic geometry is consistent with that of near‐threshold alluvial channels. We combine theory for five interrelated processes: bedload sediment transport in equilibrium gravel‐bed channels, channel width adjustment to flow and sediment characteristics, abrasion of bedrock by mobile sediment, plucking of bedrock and progressive loss of gravel‐sized sediment due to grain attrition. This model contributes to a growing class of models that seek to capture the dynamics of both bedrock incision and alluvial sediment transport. We demonstrate the model's ability to reproduce expected fluvial features such as inverse power law scaling between slope and area, and width and depth consistent with near‐threshold channel theory, and we discuss the role of sediment characteristics in influencing the mode of channel behaviour, erosional mechanism, channel steepness and profile concavity.

Coupled two-dimensional modeling of bed evolution and bank erosion in the Upper JingJiang Reach of Middle Yangtze River

In bedrock rivers, bedload transport causes abrasion not only vertically but also laterally. Bank erosion causes sinuosity changes and lateral migration that influence terrace formation, hillslope base level and drainage divide evolution. We conducted laboratory experiments and developed equations to predict lateral bedrock abrasion rates, which are poorly understood compared to vertical incision rates. We systematically varied channel curvature, lateral (cross‐stream) bed slope, and the supply rate of bedload. Surprisingly, bank abrasion decreases with increasing channel curvature due to secondary circulation. Bank erosion increases with lateral bed slope because it increases sidewall sediment concentration. However, at higher sediment supply rates lateral erosion is ≈constant due to particle interactions and dynamic cover effects. We propose equations which capture the sensitivity of bank erosion rate to the experimental variables. Our model will be useful for predicting future lateral erosion and for constraining bedload transport rates from bedrock channel morphology.

<p>Gravel-bed rivers cross and sculpt Earth's upland regions. Field, flume, and theoretical studies together provide governing equations for these rivers. Building upon this rich background, we quantitatively link catchment-scale hydrology, sediment transport, and morphodynamics into a model of river long-profile change over time. We focus on the transport-limited case (i.e., alluvial rivers), as most rivers around the world expend the majority of their geomorphic work by moving sediment rather than eroding the underlying substrate. Morphologically, this "transport-limited" category includes all alluvial rivers as well as those bedrock rivers for which bedrock erosion is easy relative to sediment transport. This model provides predictions for how such systems respond to changes in water supply, sediment supply, and base level – which are often linked to climate, land use, and tectonics. After deriving the central equation for long-profile evolution, we demonstrate that river concavity is strongly determined by the attrition rate of gravel, which can occur by either hillslope weathering or downstream fining. This dependency creates the potential for significant feedbacks between climate, tectonics, lithology, and river morphology. Furthermore, the equation predicts that oscillations in sediment and water supply will lead to net river incision when compared to steady means of both quantities. If true, this theoretical prediction could help to explain the near-ubiquitous presence of river terraces around the world.</p>

Spatiotemporally varying inter-relationships between mainstem riverbed elevation and tributary sediment supply since the last interglacial in the upper Ara River, central Japan

Bedrock rivers are the pacesetters of landscape evolution in uplifting fluvial landscapes. Water discharge variability and sediment transport are important factors influencing bedrock river processes. However, little work has focused on the sensitivity of hillslope sediment supply to precipitation events and its implications on river evolution in tectonically active landscapes. We model the temporal variability of water discharge and the sensitivity of sediment supply to precipitation events as rivers evolve to equilibrium over 106 model years. We explore how coupling sediment supply sensitivity with discharge variability influences rates and timing of river incision across climate regimes. We find that sediment supply sensitivity strongly impacts which water discharge events are the most important in driving river incision and modulates channel morphology. High sediment supply sensitivity focuses sediment delivery into the largest river discharge events, decreasing rates of bedrock incision during floods by orders of magnitude as rivers are inundated with new sediment that buries bedrock. The results show that the use of river incision models in which incision rates increase monotonically with increasing river discharge may not accurately capture bedrock river dynamics in all landscapes, particularly in steep landslide prone landscapes. From our modeling results, we hypothesize the presence of an upper discharge threshold for river incision at which storms transition from being incisional to depositional. Our work illustrates that sediment supply sensitivity must be accounted for to predict river evolution in dynamic landscapes. Our results have important implications for interpreting and predicting climatic and tectonic controls on landscape morphology and evolution.

In this study, we present direct field measurements of modern lateral and vertical bedrock erosion during a 2‐year study period, and optically stimulated luminescence (OSL) ages of fluvial material capping a flat bedrock surface at Kings Creek located in northeast Kansas, USA. These data provide insight into rates and mechanisms of bedrock erosion and valley‐widening in a heterogeneously layered limestone‐shale landscape. Lateral bedrock erosion outpaced vertical incision during our 2‐year study period. Modern erosion rates, measured at erosion pins in limestone and shale bedrock reveal that shale erosion rate is a function of wetting and drying cycles, while limestone erosion rate is controlled by discharge and fracture spacing. Variability in fracture spacing amongst field sites controls the size of limestone block collapse into the stream, which either allowed continued lateral erosion following rapid detachment and transport of limestone blocks, or inhibited lateral erosion due to limestone blocks that protected the valley wall from further erosion. The OSL ages of fluvial material sourced from the strath terrace were older than any material previously dated at our study site and indicate that Kings Creek was actively aggrading and incising throughout the late Pleistocene. Coupling field measurements and observations with ages of fluvial terraces can be useful to investigate the timing and processes linked to how bedrock rivers erode laterally over time to form wide bedrock valleys.