Rebecca A. Hodge

Bed load transport in bedrock rivers: The role of sediment cover in grain entrainment, translation, and deposition

[1] Bedrock rivers exert a critical control over landscape evolution, yet little is known about the sediment transport processes that affect their incision. We present theoretical analyses and field data that demonstrate how grain entrainment, translation and deposition are affected by the degree of sediment cover in a bedrock channel. Theoretical considerations of grain entrainment mechanics and sediment continuity each demonstrate that areas of exposed bedrock and thin sediment depths cause sediment transport to be size-independent, albeit excluding extreme grain sizes. We report gravel and cobble magnetic tracer data from three rivers with contrasting sediment cover: the bedrock River Calder (20% cover), the bedrock South Fork Eel River (80%) and the alluvial Allt Dubhaig (100%). These data sets show that: 1) transport distances in the River Calder are controlled by sediment patch location, whereas in the other rivers transport distances are described by gamma distributions representing local dispersion; 2) River Calder transport distances are size-independent across all recorded shear stresses, whereas the other rivers display size-selectivity; 3) River Calder tracers are entrained at a dimensionless shear stress of 0.038, which is relatively low compared to alluvial rivers; and, 4) virtual grain velocities in the River Calder are higher than in a comparable reach of the Allt Dubhaig. These contrasts result from differences in the thicknesses and spatial distribution of sediment in the three rivers, and support the theoretical analysis. Sediment processes in bedrock rivers systematically vary along a continuum between bedrock and alluvial end-members. Citation: Hodge, R. A., T. B. Hoey, and L. S. Sklar (2011), Bed load transport in bedrock rivers: The role of sediment cover in grain entrainment, translation, and deposition, J. Geophys. Res., 116, F04028, doi:10.1029/2011JF002032.

Discrete-element modelling: methods and applications in the environmental sciences

This paper introduces a Theme Issue on discrete–element modelling, based on research presented at an interdisciplinary workshop on this topic organized by the National Institute of Environmental e–Science. The purpose of the workshop, and this collection of papers, is to highlight the opportunities for environmental scientists provided by (primarily) off–lattice methods in the discrete–element family, and to draw on the experiences of research communities in which the use of these methods is more advanced. Applications of these methods may be conceived in a wide range of situations where dynamic processes involve a series of fundamental entities (particles or elements) whose interaction results in emergent macroscale structures. Indeed, the capacity of these methods to reveal emergent properties at the meso– and macroscale, that reflect microscale interactions, is a significant part of their attraction. They assist with the definition of constitutive material properties at scales beyond those at which measurement and theory have been developed, and help us to understand self–organizing behaviours. The paper discusses technical issues including the contact models required to represent collision behaviour, computational aspects of particle tracking and collision detection, and scales at which experimental data are required and choices about modelling style must be made. It then illustrates the applicability of DEM and other forms of individual–based modelling in environmental and related fields as diverse as mineralogy, geomaterials, mass movement and fluvial sediment transport processes, as well as developments in ecology, zoology and the human sciences where the relationship between individual behaviour and group dynamics can be explored using a partially similar methodological framework.

A Froude-scaled model of a bedrock-alluvial channel reach: 1. Hydraulics

The controls on hydraulics in bedrock-alluvial rivers are relatively poorly understood, despite the importance of the flow in determining rates and patterns of sediment transport and consequent erosion. To measure hydraulics within a bedrock-alluvial channel, we developed a 1:10 Froude-scaled laboratory model of an 18 × 9 m bedrock-alluvial river reach using terrestrial laser scanning and 3-D printing. In the reported experiments, water depth and velocity were recorded at 18 locations within the channel at each of five different discharges. Additional data from runs with sediment cover in the flume were used to evaluate the hydraulic impact of sediment cover; the deposition and erosion of sediment patches in these runs are analyzed in the companion paper. In our data (1) spatial variation in both flow velocity and Froude number increases with discharge; (2) bulk flow resistance and Froude number become independent of discharge at higher discharges; (3) local flow velocity and Reynolds stress are correlated to the range of local bed topography at some, but not most, discharges; (4) at lower discharges, local topography induces vertical flow structures and slower velocities, but these effects decrease at higher discharges; and (5) there is a relationship between the linear combination of bed and sediment roughness and local flow velocity. These results demonstrate the control that bedrock topography exerts over both local and reach-scale flow conditions, but spatially distributed hydraulic data from bedrock-alluvial channels with different topographies are needed to generalize these findings.

A Froude-scaled model of a bedrock-alluvial channel reach : 2. Sediment cover.

Previous research into sediment cover in bedrock-alluvial channels has focussed on total sediment cover, rather than the spatial distribution of cover within the channel. The latter is important because it determines the bedrock areas that are protected from erosion and the start and end of sediment transport pathways. We use a 1:10 Froude-scaled model of an 18 by 9 m reach of a bedrock-alluvial channel to study the production and erosion of sediment patches and hence the spatial relationships between flow, bed topography, and sediment dynamics. The hydraulic data from this bed are presented in the companion paper. In these experiments specified volumes of sediment were supplied at the upstream edge of the model reach as single inputs, at each of a range of discharges. This sediment formed patches, and once these stabilized, flow was steadily increased to erode the patches. In summary: (1) patches tend to initiate in the lowest areas of the bed, but areas of topographically induced high flow velocity can inhibit patch development; (2) at low sediment inputs the extent of sediment patches is determined by the bed topography and can be insensitive to the exact volume of sediment supplied; and (3) at higher sediment inputs more extensive patches are produced, stabilized by grain-grain and grain-flow interactions and less influenced by the bed topography. Bedrock topography can therefore be an important constraint on sediment patch dynamics, and topographic metrics are required that incorporate its within-reach variability. The magnitude and timing of sediment input events controls reach-scale sediment cover.

Bed load tracer mobility in a mixed bedrock/alluvial channel

The presence of bare or partially covered rock in an otherwise alluvial river implies a downstream change in transport capacity relative to supply. Field investigations of this change and what causes it are lacking. We used two sets of magnet-tagged tracer clasts to investigate bed load transport during the same sequence of floods in fully alluvial, bare rock, and partial-cover reaches of an upland stream. High-flow shear stresses in different reaches were calculated by using stage loggers. Tracers seeded in the upstream alluvial channel moved more slowly than elsewhere until the frontrunners reached bare rock and sped up. Tracers seeded on bare rock moved rapidly off it and accumulated just upstream from, and later in, a partial-cover zone with many boulders. The backwater effect of the boulder-rich zone is significant in reducing tracer mobility. Tracer movement over full or partial sediment cover was size selective but dispersion over bare rock was not. Along-channel changes in tracer mobility are interpreted in terms of measured differences in shear stress and estimated differences in threshold stress.

Flow resistance and hydraulic geometry in contrasting reaches of a bedrock channel

Assumptions about flow resistance in bedrock channels have to be made for mechanistic modeling of river incision, paleoflood estimation, flood routing, and river engineering. Field data on bedrock flow resistance are very limited and calculations generally use standard alluvial-river assumptions such as a fixed value of Mannings n. To help inform future work, we measured how depth, velocity, and flow resistance vary with discharge in four short reaches of a small bedrock channel, one with an entirely rock bed and the others with 20–70% sediment cover, and in the alluvial channel immediately upstream. As discharge and submergence increase in each of the partly or fully alluvial reaches there is a rapid increase in velocity and a strong decline in both n and the Darcy-Weisbach friction factor f. The bare-rock reach follows a similar trend from low to medium discharge but has increasing resistance at higher discharges because of the macroroughness of its rock walls. Flow resistance at a given discharge differs considerably between reaches and is highest where the partial sediment cover is coarsest and most extensive. Apart from the effect of rough rock walls, the flow resistance trends are qualitatively consistent with logarithmic and variable-power equations and with nondimensional hydraulic geometry, but quantitative agreement using sediment D84 as the roughness height is imperfect.

Calculating the explicit probability of entrainment based on inertial acceleration measurements.

A new method for the approximation of the explicit probability of entrainment for individual coarse particles is presented. The method is based on the derivation of inertial acceleration measurements, space-state approximation of the dynamics close to entrainment, and the probabilistic approximation of the threshold inertial acceleration that causes incipient motion. Results from flume experiments with a custom-made inertial measurement unit enclosed in an idealized spherical enclosure, under varied flow conditions (achieved through slope change) and two different arrangements (saddle and grain-top positions) are presented to demonstrate the application of the method. The analysis supports the modification of the existing flow velocity–based entrainment criteria so they respect the particle-frame realization of forces during incipient motion.