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Keywords:

  • bedrock river;
  • sediment cover;
  • sediment transport

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Theoretical Framework
  5. 3. Study Sites and Field Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Implications
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[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.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Theoretical Framework
  5. 3. Study Sites and Field Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Implications
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[2] Incision of bedrock rivers is a key process driving landscape development through setting the local base-level [Whipple, 2004; Stark et al., 2009]. A major control on bedrock erosion is the interplay between sediment cover and erosive mobile grains [Sklar and Dietrich, 2004; Finnegan et al., 2007; Johnson and Whipple, 2007; Turowski et al., 2007]. This interplay depends on processes operating over a range of scales, from single-event erosion and deposition through to long-term changes in sediment supply regimes and consequent morphological adjustment of the channel [Gasparini et al., 2004; Lague, 2010]. Process-based models of saltation-driven incision focus on the short-term dynamics of individual grains [Sklar and Dietrich, 2004, 2006; Turowski et al., 2007; Turowski, 2009]. A bedrock river is rarely entirely free from sediment cover; we use the term bedrock river to encompass the range of mixed alluvial-bedrock channel bed conditions [Turowski et al., 2008]. Consequently, mobile grains in a bedrock channel will typically be transported across both alluvial and bedrock surfaces. The extent of sediment cover is a result of the sediment flux supplied to the channel and the channel transport capacity, although the form of this relationship is debated [cf. Sklar and Dietrich, 2004; Johnson and Whipple, 2007; Turowski et al., 2007; Cowie et al., 2008]. Furthermore, the pattern of sediment cover can respond dynamically in response to both flow and sediment flux fluctuations [Chatanantavet and Parker, 2008; Johnson et al., 2009; Lague, 2010].

[3] During a single transport event, comprising grain entrainment, translation and deposition, a grain may interact with both bedrock and alluvial surfaces. The relative proportion of these surfaces depends on the quantity of sediment in the channel and on channel morphology; sediment cover can vary between zero and complete cover, as in Figure 1 [Howard and Kerby, 1983; Montgomery et al., 1996]. As sediment cover develops on a rock surface, dispersed patches and bars, which are typically one or two grains thick, form first. As sediment volume increases, sediment patches grow in both areal extent and depth [Chatanantavet and Parker, 2008], leading to bars forming that can be a meter or more thick [Tinkler and Wohl, 1998; Jansen, 2006]. With low sediment volumes, there is little reach-scale variation in grain size distribution whereas with higher volumes sediment thickness becomes sufficient for armoring and vertical size segregation to develop [e.g., Goode and Wohl, 2010a].

image

Figure 1. The continuum of channel types resulting from different degrees of sediment cover. (a) Cartoons illustrating different extents of alluvial cover along the continuum between fully bedrock and alluvial channels. (b) It is hypothesized that differences in size-selectivity are the result of the processes of grain entrainment (E), translation (T) and deposition (D) occurring from either bedrock or alluvial areas (e.g., Eb or Ea). The sequences show the combination of these processes that are expected to occur in each of the different channel types, as illustrated by the arrows in Figure 1a. The other possible combinations EaTaDb, EbTaDa and EbTaDb are considered to be unlikely to occur in any setting. (c) Study sites that represent each channel form.

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[4] Sediment transport is influenced by, among others, surface roughness and grain sheltering effects, the possibility for grain burial and the velocity profile of the overlying flow. Alluvial channel surface roughness is a function of the surface grain size distribution and, via grain sheltering effects, affects the relationship between grain size and critical entrainment shear stress [Kirchner et al., 1990; Buffington et al., 1992; Frey and Church, 2011]. Surface roughness also affects the probability of grain deposition, and hence the distance of grain translation [Einstein, 1950; Habersack, 2001; Wong et al., 2007]. The thick active layer (i.e., sediment that participates in bed load transport) in an alluvial channel enables grains to be deposited at depth in the bed, which can be a size-selective process and inhibits subsequent entrainment [Ferguson and Hoey, 2002; Pyrce and Ashmore, 2003a]. Surface roughness also affects the flow velocity profile and so influences entrainment via the force exerted on a grain [Grass, 1970; Papanicolaou et al., 2001; Schmeeckle and Nelson, 2003].

[5] In bedrock channels, the mosaic of bedrock and sediment cover means that the properties listed above can show large spatial variation. For example, the morphology of bedrock surfaces ranges from flat to complex 3D forms [Wohl and Ikeda, 1997; Whipple, 2004]. Complex topography can affect the local flow structure [Finnegan et al., 2007; Johnson and Whipple, 2007]. Areas of the channel without sediment or with thin sediment layers exclude the potential for grain burial. Laboratory data show that grain velocities and step length are greater over non-erodible beds than over mobile beds [Lajeunesse et al., 2010]. There are therefore several reasons to expect that the components of sediment transport will operate differently in alluvial and bedrock areas of the channel. Further, the proportion and distribution of alluvial and bedrock surfaces in a bedrock river will significantly affect the rate and grain-size specificity of sediment transport processes within that channel.

[6] To date, there are limited field data with which to constrain sediment transport processes in bedrock channels. Goode and Wohl [2010b] found that transport distances of sediment tracers were size dependent in a reach with bedrock ribs longitudinal to flow, but size-independent when the ribs were oblique to flow. The former result is consistent with much alluvial river data [e.g., Hassan et al., 1991; Wilcock 1997; Ferguson et al., 2002; Pyrce and Ashmore, 2003b], whereas the latter demonstrates the influence of the bedrock ribs on grain transport processes. Siddiqui and Robert [2010] also reported size-dependent transport lengths in a bedrock reach with high alluvial cover.

[7] The position of a channel along the continuum between zero and complete sediment cover is a key variable in bedrock incision models [Sklar and Dietrich, 2004, 2006; Turowski et al., 2007]. Consequently, there is a need to both theorize and quantify how the spatial extent of sediment cover in bedrock rivers affects sediment transport processes. We approach this task first by considering how the presence of a bedrock surface will affect the components of sediment transport. We do this both using Kirchner et al.'s [1990] model of grain entrainment and through analysis of sediment continuity. These theoretical considerations are then used to interpret sediment tracer data from three rivers with different sediment cover: the River Calder (20% sediment cover), the South Fork Eel River (80% sediment cover) and the Allt Dubhaig (100% sediment cover) [Ferguson et al., 2002]. Finally, we discuss the implications of the theoretical and field results for modeling bedrock incision.

2. Theoretical Framework

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Theoretical Framework
  5. 3. Study Sites and Field Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Implications
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

2.1. Sediment Cover Continuum

[8] The development of, and dynamic change in, sediment cover in a bedrock channel are driven by grain entrainment (E), translation (T) and deposition (D). These processes vary depending on whether a grain is on a bedrock or alluvial surface (e.g., entrainment from an alluvial surface, Ea, or a bedrock surface, Eb). A single grain movement, comprising entrainment, translation via saltation, and deposition, can therefore be described by one of eight possible combinations. The combination of ETD that a grain experiences depends on the extent of sediment cover in the channel, ranging from EaTaDa at the fully alluvial end-member to EbTbDb in the pure bedrock case (Figure 1). Given the proposed distributions of sediment cover, three of the eight combinations are unlikely to occur. To understand how the extent of sediment cover affects both the total flux and its grain size distribution in rivers across the spectrum in Figure 1, we extend established theory to predict how each of entrainment, translation, deposition and net mass continuity will vary between the bedrock and fully alluvial cases.

2.2. Grain Entrainment

[9] Except in the rare case of extremely low sediment cover, sediment forms patches on the bed of a bedrock river rather then being multiple isolated grains. Such grouping occurs because grains accumulate in areas of the channel where the bed roughness, hydraulics and the sheltering influence of other grains increase grain stability [Finnegan et al., 2007; Johnson and Whipple, 2007; Chatanantavet and Parker, 2008]. Consequently, initial grain entrainment primarily occurs from alluvial surfaces, i.e., Ea is far more probable than Eb, regardless of the extent of sediment cover. During a transporting event, a mobile grain may undertake multiple steps before being deposited in a stable position [Einstein 1950; Drake et al., 1988], where each step itself contains multiple saltation hops [Sklar and Dietrich, 2001; Attal and Lavé, 2009]. In a river with low alluvial cover, the initial step for a grain in an event is most likely to involve entrainment from an alluvial surface, but subsequent (and hence the majority of) entrainments are more likely to be from bedrock surfaces.

[10] Differences between Ea and Eb reflect the effect of the underlying surface geometry on the grain position and hence critical entrainment shear stress (τc). We quantify this effect on τc by using a Monte Carlo application of the model of Kirchner et al. [1990], which calculates τc for a grain by solving the force balance at the threshold of motion:

  • display math

FD and FL are respectively drag and lift forces, FW is the immersed weight of the grain, Φ is the grain pivoting angle which describes pocket geometry, ρs is the density of sediment (taken as 2650 kg m−3), ρ is the density of water, g is acceleration due to gravity and d is the grain diameter. FD and FL are calculated assuming a logarithmic flow velocity profile and incorporate both grain exposure and elevation with respect to the local velocity profile. The boundary shear stress at the threshold of motion, τc, is calculated by expressing FD and FL in terms of τc and substituting into and rearranging equation (1); for the full derivation see Kirchner et al. [1990].

[11] In Kirchner et al.'s [1990] model, the underlying surface is assumed to be a granular material with grain size K (Figure 2), and its effect on τc is expressed through the values of Φ, FD and FL. By applying idealized geometrical relationships [Kirchner et al., 1990] and relationships derived from field data [Johnston et al., 1998], Φ, FD and FL can be expressed as functions of the relative sizes of the overlying grain (d) and the representative grain size of the underlying surface (K). When a grain is entrained from an alluvial surface (Ea), both d and K are drawn from the same grain size distribution (GSD) (Figure 2a). For illustration we use a measured lognormal sediment GSD from the River Calder (mean 5.56 ψ; standard deviation 0.69 ψ, where ψ = log2(d) and d is measured in mm).

image

Figure 2. Grain geometry in (a) alluvial and (b) bedrock cases. Bedrock is approximated by an alluvial surface with low surface roughness. Overlying grains (with diameter d) are black, underlying grains (with diameter K) are grey. (c) For each pair of d and K on an alluvial surface, Φ is calculated as Φ = 51.6(d/K)−0.30; coefficient values were calculated from field measurements by Johnston et al. [1998] in Sagehen Creek (steep mountain stream, d50 = 58 mm), which is the most similar of their study rivers to the River Calder. On a bedrock surface, Φ = tan−1(γ/ inline image), where γ = 1/√3, which represents pivoting from a pocket formed by three grains [Eagleson and Dean, 1961]. The former alluvial relationship for Φ incorporates the effect of surrounding grains on Φ, whereas the latter bedrock relationship better represents grains pivoting on a solid surface. Grain exposure e is measured from local upstream maximum elevation and calculated as e = 0.5[dK + (d + K) cos Φ]. Grain protrusion p is measured from local mean bed surface elevation as p = e + (π/12)K. When calculating p and e, all underlying grains are assumed to be the same size.

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[12] For entrainment from a bedrock surface (Eb), the local roughness of the bedrock surface is represented as an appropriate value of K. Bedrock surface roughness is very variable, from relatively smooth abraded surfaces to irregular plucked and jointed surfaces [e.g., Goode and Wohl, 2010b]. However, at the scale of an individual grain, most bedrock surfaces will be locally smooth so we omit the effect of macroscale roughness on local velocity profiles and represent these as a surface composed of roughness elements that are finer than the GSD of the overlying grains (Figure 2). To estimate the representative GSD of the roughness elements, bedrock roughness was calculated from high-resolution topographic profiles ∼3m long in total, measured in the River Calder. Roughness was quantified as the standard deviation of elevations (σz) within multiple 50 mm lengths of the profiles; 50 mm is the median alluvial grain size (d50), and so roughness is measured at a scale relevant to individual grains. Each value of σz was converted to an equivalent grain size. All together, these equivalent grain sizes follow a lognormal GSD with a mean of 4.42 ψ and standard deviation of 0.99 ψ. Trends in the model results are not sensitive to the particular values of these parameters.

[13] Our Monte Carlo application of Kirchner et al.'s [1990] model predicts τc for 1000 grains entrained from each of the alluvial (Figure 2a) and bedrock (Figure 2b) surfaces. In each case, 1000 pairs of an overlying and an underlying grain size are drawn at random from the respective distributions. d/K is used to calculate grain pivoting angle (Φ), exposure (e) and projection (p) (see Figure 2c) [see Kirchner et al., 1990]. τc and dimensionless τc (τc*) are subsequently calculated for each grain, and the results are shown in Figure 3.

image

Figure 3. Distributions of (a) τc and (b) τc* for 1000 grains in each of an alluvial and bedrock setting. Markers are shaded according to K, the size of the underlying grains. Values for K = K50 are shown in black. Note that in Figure 3a grain size is plotted relative to the median size of the overlying grains (d50), whereas in Figure 3b grain size is plotted relative to the median size of the underlying grains (K50). The line in Figure 3b shows equal mobility, i.e., τc* is proportional to 1/d; this line was fitted to theoretical and field data by Johnston et al. [1998]. Comparison between the gradients of the line and the model results are instructive; the difference in absolute values of τc* is less instructive because of the dependency of τc* on model components, e.g., the pivoting angle relationship.

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[14] τc for grains on a bedrock surface is about an order of magnitude lower than for the same size grains on an alluvial surface (Figure 3); when d = d50 and K = K50, τc = 2.5 and 21.9 Pa for the bedrock and alluvial cases, respectively. Dancey et al. [2002] also observed an order of magnitude increase in τc* when grain packing density increased from 3 to 91%, which is comparable to the difference between a bedrock and an alluvial surface. Re-entrainment during movement, Eb, therefore requires a significantly lower shear stress than the initial entrainment Ea. Consequently, for the same shear stress, excess shear stress (ττc) is greater for a grain in transport across a bedrock surface than for a grain on an alluvial surface.

[15] Entrainment from a bedrock surface shows a weak dependence of τc on grain size; fixing K at K50, τc decreases from 3.5 Pa for d = d05 to 2.1 Pa for d = d95. Model results are parallel to a line fitted by Johnston et al. [1998] to both theoretical and field data (Figure 3b). Along this line, τc* is proportional to 1/d, i.e., grains are equally mobile. The small dependence of τc on d is because changes in grain geometry as grain size increases mean that grains have lower pivoting angles, larger exposure and protrude higher into faster flow. Entrainment from a bedrock surface will therefore not be a major cause of size-selective transport. However, as entrainment is only one component of grain movement, other aspects may produce or inhibit size-selectivity.

[16] In a bedrock river, Ea may be affected by the shallow sediment depths associated with low sediment cover. In an alluvial channel, surface coarsening acts to equalize τc for different grain sizes because smaller grains having relatively less exposure and higher pivoting angles than larger grains [Wiberg and Smith, 1987; Kirchner et al., 1990; Parker and Sutherland 1990]. Thin sediment layers cannot develop surface coarsening thus reducing or eliminating this equalizing effect, such that entrainment shear stress is primarily a function of grain size. Consequently, the exact functioning of Ea in a bedrock river may vary according to sediment depth.

[17] Bedrock channels have slopes up to ten times greater than alluvial channels for a given drainage basin area [Howard and Kerby, 1983; Montgomery et al., 1996]. Critical entrainment shear stress is usually assumed to be independent of channel slope. However, Shvidchenko et al. [2001], Lamb et al. [2008] and Recking [2009] have demonstrated a significant effect of slope with the same size of grain being more stable on a steeper slope. This effect is due to slope dependence of the velocity profiles for a given discharge, and to the changes in the grain force balance due to relative roughness and partial grain emergence. Thus, the typically steeper nature of bedrock channels implies that grain mobility from alluvial patches in bedrock rivers will be reduced compared to alluvial cases.

2.3. Grain Translation

[18] As excess shear stress (ττc) is higher over bedrock surfaces than alluvial ones grain dynamics differ over the two surfaces (Ta and Tb). For example, saltation height, length and downstream velocity are each functions of (τ* − τc*/τc*)a, where a < 1 [Sklar and Dietrich, 2004]. Lajeunesse et al. [2010] showed that grain velocities and step lengths are larger over non-erodible (i.e., bedrock) surfaces than over mobile alluvial surfaces. The properties of a bedrock surface also affect saltation dynamics as there will be few, if any, particles to be entrained by an impacting grain. Further, grain rebound is affected by the coefficient of restitution and the distribution of angles of the bedrock surface impacted by mobile grains. Hence, grains moving over a bedrock surface will undergo longer, more frequent, translation steps than grains on an otherwise equivalent alluvial bed. Consequently, for the same shear stress, sediment transport capacity will be higher over bedrock surfaces.

2.4. Grain Deposition

[19] Grains are more likely to be deposited on an alluvial surface (Da) than on a bedrock surface (Db); the higher grain pivoting angles and lower exposures predicted by the Kirchner et al. [1990] model for the alluvial surface enhance deposition as well as impeding entrainment. In addition, grain roughness could also affect the local flow profile, decreasing shear stress and enhancing deposition. Consequently, in a bedrock channel with low sediment cover, deposition is mainly determined by sediment patch location. Deposition on a bedrock surface may occur as flow recedes, when translation is halted as shear stress falls before grains have reached an alluvial area.

[20] Sediment patch location is controlled by the interaction between local channel morphology and flow hydraulics. For example, patches may develop where the macroscale topography reduces local flow velocities, such as between bedrock ribs and within potholes [Goode and Wohl, 2010a, 2010b]. Sediment patches are therefore unlikely to exhibit the regular spacing of alluvial bed forms and bars. Once areas of sediment are established, the decreased probability of re-entrainment of grains from these areas provides positive feedback promoting their maintenance [Johnson and Whipple, 2007; Finnegan et al., 2007].

[21] Under low sediment cover, grains will mainly travel between areas of sediment, and so grain transport lengths will be determined by the inter-patch spacing. As sediment cover increases, the probability of deposition becomes more spatially uniform and the location of deposition is increasingly driven by processes identified in alluvial rivers [Pyrce and Ashmore, 2003b; Hassan et al., 1991]. The greater depth of sediment in alluvial rivers, and in bedrock rivers with higher sediment cover, also increases the potential for grains to be deposited at depth within the bed, thus reducing their probability of subsequent entrainment [Ferguson and Hoey, 2002].

2.5. Sediment Continuity

[22] All components of ETD show important differences between bedrock and alluvial surfaces, which will affect event-scale sediment movement. We now assess how these differences affect the long-term relative behavior of different size fractions and the long-term conditions under which a bedrock river could have steady state sediment cover. While our previous analysis treated sediment transport as a discrete process, we now turn to analysis of sediment continuity.

[23] The presence (or absence) of size selectivity in sediment transport is important because it links the volumes and GSDs of the incoming sediment, the sediment on the channel bed and the sediment transported out of the channel, and can result in aggradation or degradation. Size selectivity can occur in different components of sediment transport, including grain entrainment, velocities, frequency of motion and deposition. Here we focus on grain size dependence in grain travel distances, which is consistent with our use of gravel tracers.

[24] We extend the standard continuity (Exner) equation expressed for individual size fractions of bed sediment [Parker, 1991] to the case of a bedrock channel with fraction of bedrock exposure Fe, sediment cover 1 − Fe and uniform depth sediment deposits:

  • display math

where λ is sediment porosity, La is the thickness of the active (surface) layer, η is bed surface elevation above bedrock, qbT is the volumetric bed load transport rate per unit width (m2 s−1). Fi, εi, and pi are the fractional abundances of sediment in the ith size class in the surface layer, the sediment that is exchanged between the surface and sub-surface layer during aggradation or degradation and the bed load, respectively. Equation (2) is consistent with that given by Chatanantavet et al. [2010], although it assumes that abrasion and lateral sediment inputs are zero. Changes in sediment storage in a bedrock channel can arise via changes in La, sediment GSD and Fe. If the mean sediment thickness (z = 〈η〉) is greater than La, then a sub-surface layer and the potential for vertical variations in sediment GSD develop.

[25] We initially consider the maintenance of steady state in a bedrock river with very thin alluvial deposits, so that z is less than the active layer thickness, La, and there is no sub-surface layer. Averaging over several flood events to eliminate the impacts of stochastic upstream sediment supply, the following simplifications apply:

  • display math

Under steady state, the first three conditions maintain the sediment volume in the reach. While an increase in ηLa could be offset by a decrease in 1 − Fe, this is unlikely because ηLa and 1 − Fe will normally be positively correlated. Furthermore, in any reach the bedrock morphology is likely to dictate an optimum storage configuration (i.e., values of 1 − Fe and ηLa) for a given sediment volume. The second condition also applies because there is no subsurface layer if z < La. The final condition is satisfied if there is no change in the active layer GSD; La is generally assumed to scale with grain size, and in alluvial rivers is approximately 2d90 [e.g., Parker, 1991; DeVries, 2002].

[26] Under the limits from (3), (2) reduces trivially to

  • display math

[27] Any change in the stored sediment grain size (Fi) thus is achieved by a spatial gradient in pi, indicating the operation of size-selective entrainment and deposition. If a monotonic change in grain size persists for long time periods, Fi changes to produce coarsening (so reducing transport, inducing aggradation and development of full alluvial cover) or fining (increasing transport and transition to full bedrock exposure). To maintain steady state, both ∂Fi/∂t and ∂pi/∂x must tend to zero.

[28] The form of steady state in a bedrock river with z < La will depend on the relationship between Fi and pi. We envisage two possible forms. In the first, Fi is equal to pi for all i, and so all grain sizes have the same probability of entrainment and deposition. This is broadly consistent with the Kirchner et al. [1990] model predictions of τc for grains on a bedrock surface. In the second form, the stored sediment in the reach is coarse relative to bed load entering the reach, however bed load entering and leaving the reach have the same GSD. The typical lower probability of entrainment for larger grains is offset by their higher abundance in the active layer and vice versa, producing no aggradation. For larger grains therefore Fi > pi, with Fi < pi for smaller grains.

[29] In alluvial rivers, a coarse surface layer enables grain-size dependent probabilities of entrainment to exist under steady state [Parker and Sutherland, 1990; Allan and Frostick, 1999]. However, the development of such a layer requires z > La, which can only occur with relatively high sediment cover. Where sediment cover increases and Fe is low, a coarse surface layer may develop enabling grain-size dependent entrainment to operate in a bedrock river at steady state. If entrainment is correlated with grain size, over a given time period smaller grains will be entrained more frequently and will travel further than larger grains, subject to the relationship between grain size and translation distance.

[30] We consider total travel distance, rather than solely entrainment, as our measurements are of total travel distances. We hypothesize that size-selectivity of travel distances in a bedrock river is caused by sorting taking place in alluvial areas of the bed, and thus that the degree of size selectivity is a function of the sediment storage volume in the reach, and hence of sediment cover 1 − Fe. This hypothesis is illustrated in Figure 4, which shows the possible range of size-selectivity of sediment transport distances from a minimum value of 0 to a theoretical maximum for a fully alluvial river. As 1 − Fe increases, rivers are more likely to exhibit size-selectivity closer to the theoretical maximum, as shown by the increasing white area.

image

Figure 4. The dimensional space between proportional sediment cover and degree of size selectivity of sediment transport distances. Labeled points in this space are Oak Creek, an alluvial river with no size-selectivity [Parker et al., 1982] and the Allt Dubhaig, an alluvial river in which size-selectivity varies as a function of excess shear stress [Ferguson et al., 2002]. The difference in size selectivity between these two is because Oak Creek has no divergence in sediment transport (∇qbT) so is in steady state, whereas the Allt Dubhaig has divergence and is hence aggrading. It is hypothesized that bedrock rivers with low sediment cover cannot be size-selective, and thus no rivers should plot within the shaded area. However, little data have previously been collected from such rivers; the bounds of this area are therefore indicative with darker shading indicating a lower probability of rivers falling within this area.

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2.6. Use of Tracers

[31] Our theoretical analysis of the effect of sediment cover on transport dynamics in a bedrock river has considered both the short-term movement of individual grains and long-term, reach-averaged behavior. Both analyses suggest that the volume of sediment in a bedrock reach, which is correlated with 1 − Fe determines grain dynamics and size-selectivity. Two new sets of tracer data from bedrock rivers are used here to evaluate the theoretical analyses.

[32] Repeat mapping of magnetically tagged sediment grains quantifies sediment dynamics in alluvial rivers over the timescale of multiple events [Hassan et al., 1984; Ferguson et al., 2002]. Such data quantify locations and probability of entrainment and deposition, transport distances and the influence of grain size and flow magnitude; but within-event dynamics cannot be resolved. Tracer recovery rate affects data quality; in alluvial rivers recovery varies considerably due to the time intervals between searches and system scale. Low sediment volumes and low probabilities of deep tracer burial in small bedrock rivers facilitate tracer recovery [Goode and Wohl, 2010b].

[33] It is easier to use field data to test predictions of grain-scale dynamics than to test the longer-term predictions from the continuity analysis. Collecting longer-term data is more problematic, with a higher probability of changing boundary conditions. But, focusing on short-term data assumes that we do not need explicitly to consider stochastic forcing of discharge and sediment supply [e.g., Lague, 2010], and that extreme events, which are less likely in short-term data, do not contribute significantly to the long-term dynamics.

3. Study Sites and Field Methods

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Theoretical Framework
  5. 3. Study Sites and Field Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Implications
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[34] We present tracer data from three rivers of comparable size, slope and GSD along the bedrock-alluvial continuum (Table 1). All three rivers actively transport sediment, with regular flow events in the full mobility regime.

Table 1. Properties of the Three Study Rivers
 River CalderSouth Fork Eel RiverAllt Dubhaiga
  • a

    Data are given for Allt Dubhaig reach T3 [Ferguson et al., 2002].

  • b

    Mean annual discharge. River Calder had insufficient flow data to quantify.

  • c

    Discharge with return interval of 1.5 years.

  • d

    Bankfull discharge, estimated assuming Manning's n = 0.05.

Sediment cover (%)2080100
Drainage area (km2)1911213
Channel slope (m/m)0.0090.0050.013
Width (m)8–131810
Grain size d50 (mm)506061
Reach length (m)8003000450
Discharge, Qmab (m3 s−1) 56
Discharge, Q1.5c (m3 s−1)10d1205–7
Depth, H1.5 (m)0.92.01.2
Shear stress, τ1.5 (Pa)4410073
Shields stress, τ*1.50.0540.1030.074

3.1. River Calder, Renfrewshire, Scotland (55°49′N, 4°41′W)

[35] The bedrock River Calder drains a peat moorland catchment. The study reach, described in Table 1, has no lateral sediment supply. Downstream of this reach alluvial cover varies from 0 to 100%, forming lateral bars and channel-wide patches (Figure 5). Bar location varies little between events, but their spatial extent changes. Measured sediment thickness ranges from one grain diameter up to ∼2 d90 (Figure 5), although visual estimates of sediment depth in one deep pool were up to 0.5 m.

image

Figure 5. The spatial distribution of tracers within the River Calder after four different sized events. Sediment cover was mapped on a single day. Inset figure shows distributions of sediment depths at two marked locations. Measurements were taken at ∼2 m spacing and d90 = 78 mm. Inset picture shows the upper part of the study reach. Picture taken from place indicated by the asterisk, looking downstream.

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[36] The 286 painted, numbered, magnetic tracers were created from River Calder gravel using 6 mm diameter neodymium magnets. The tracer sizes fall within five half psi size classes (b-axis (d) of 4.5 to 7 ψ, or 23 to 128 mm), which include 89% of the surface GSD measured in a predominantly alluvial reach 1 km upstream. This alluvial source supplies sediment to the study reach. Nine percent of the GSD is finer than 23 mm, and hence unsuitable for the magnetic tracer technique. Tracers will move as bed load.

[37] Throughout the 220 day study, flow depth was recorded at 10 min intervals by two pressure transducers 46 m apart in the upper part of the reach. Bed shear stress (τ) was calculated assuming uniform flow as τ = ρgRS, where R and S are respectively hydraulic radius and water surface slope calculated from the pressure transducer data.

[38] We installed tracers in the upstream end of the reach on three separate occasions: days 1 (16 February 2009), 88 and 110 of the study. The latter two installations were made to replenish tracers at the top of the study reach. The sequence of tracer emplacement and recovery and river shear stress (τ) are detailed in Figure 6. Of the 224 tracers emplaced on day 1, half of each size class were randomly placed as isolated grains along a single transect across the full channel width at the top of the reach, and the other half were used to replace grains of comparable size and shape in existing gravel bars. 50 tracers were placed in the upstream transect on day 88, with 64 tracers places in gravel patches on day 110 (see Figure 6 for tracer GSD). Different installation positions show the effect of grain position on entrainment probability.

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Figure 6. Time series of mean shear stress (τ), tracer installation and searches in the River Calder during the experimental period. Day 1 is 16 February 2009. Searches are numbered. Recovery rates are calculated as a percentage of the number of tracers in the river; this varies over time as a result of both tracer removal and emplacement. The recovery rate of search 1 is low because only a partial survey of visible tracers was undertaken. Histograms show the proportion of installed and found tracers in 5 half psi size classes from 22 to 128 mm. The horizontal line shows τc, the threshold shear stress for sediment transport.

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[39] Tracer positions were remapped at low flow on ten occasions up to day 220 (Figure 6). Between searches there generally were up to two flow events above the threshold for movement of tracer-sized material (defined later); one period contained seven events, and the last contained seventeen. Prior to day 212, tracers were only found as far downstream as a pool 95–120 m along the reach. In searches up to and including search 9 (day 155), we removed tracers found in this pool because our initial experimental aim was to investigate tracer movement only in the reach upstream of the pool. The large flow event between days 155 and 212 (Figure 6) transported tracers over 600 m through and downstream of this pool. Two searches (10a and 10b, days 212 and 220) were necessary to search this area adequately; search data from 10a and 10b are combined, and referred to as day 220.

[40] We visually located most tracers, used a magnetometer to search for buried tracers and mapped them using differential GPS (dGPS). Transport distances were calculated between all consecutive known locations as the downstream distance along the channel centerline, also mapped using dGPS. These distances are therefore the accumulation of an unknown number of individual steps. The tracer relocation error is up to 0.2 m due to both dGPS uncertainty and the location of the receiver relative to the grain; we use 0.2 m as the threshold for identification of tracer movement.

3.2. South Fork Eel River, California, USA (39°43′N, 123°39′W)

[41] Our second site was the reach of the South Fork of the Eel River in the University of California Angelo Coast Range Reserve [Seidl and Dietrich, 1992; Howard, 1998; Sklar and Dietrich, 2004, 2006]. Through this 4 km section, the active channel is confined within a meandering bedrock canyon, flanked by flights of terraces that are spatially coincident with a series of knickpoints [Seidl and Dietrich, 1992; Fuller et al., 2009]. The bed is predominantly covered by alluvial patches ranging in grain size from gravel to boulder; ∼20% of the bed area is broad bedrock exposures (see photograph in the work by Sklar and Dietrich [2004]). Through the study site, alluvial cover is typically complete immediately downstream of tributary junctions; further downstream of junctions bedrock exposure becomes more frequent and extensive. This pattern may reflect rapid breakdown of weak clasts supplied by tributaries. Study reach characteristics are in Table 1. The bedrock is dominantly mudstone with sandstone interbeds, and the coarse bed load material is primarily derived from upstream sandstone and conglomerate units.

[42] We installed a total of 330 tracers at the upstream end of the study reach in 1996 and 1997. The painted, numbered, magnetic tracers were made by implanting 9 mm diameter, 10 mm thick, cylindrical ceramic magnets into quartzite clasts collected on the Yuba River. We used the durable quartzite because drilling to implant magnets often fractured the weak local rock. Half the tracers were installed in an alluvial section, and the other half were installed as small artificial patches placed on bare bedrock just downstream. Tracer grain sizes were matched to the surface GSD of a bar with d50 = 90 mm. We recovered tracers using a Schoenstedt magnetic locator capable of detecting magnetic tracers up to ∼1 m burial depth. We searched for tracer grains during late summer low flow in 1997, 1998, and 1999 (Figure 7). Most recovered tracers were buried. We surveyed tracer recovery location to <1 m with a total station and reburied tracers to approximately the same depth. A hydrograph for the experimental period is in Figure 7.

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Figure 7. Hydrograph for the South Fork Eel River during the experimental period. Discharge has been calculated from data from Elder Creek, a tributary to the South Fork Eel River within the study reach because the South Fork Eel River was ungauged during the study. Correlation of daily flows from Elder Creek and South Fork Eel River during overlapping gauge records gave p < 0.0001. Number of tracers installed and found, and the percentage of found tracers that moved <1 m, are also given. Of the installed tracers, 148/86/62/34 tracers were found 0/1/2/3 times respectively.

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3.3. Allt Dubhaig, Scotland (56°51′N, 4°14′W)

[43] The Allt Dubhaig is a small fully alluvial stream (∼2.5 km long study reach) that has a strongly concave long profile with net aggradation that drives rapid downstream fining [Ferguson et al., 1996, 2002]. Ferguson et al. [1996, 2002] emplaced a total of 1220 magnetically tagged tracer particles in six reaches along the study section, each of which had different median grain size and shear stress. The GSD of tracers in each reach was based on the local bed GSD ensuring that statistically significant numbers of tracers were present in each half-psi size class. Tracers were emplaced in 1991, mapped regularly for two years (1991–1993) and remapped in 1999 [Ferguson et al., 2002]. High recovery rates were achieved using magnetometers and mapping to <1m precision used a network of monumented cross-sections and total station surveying. Of the six tracer sets used, set T3 [Ferguson et al., 2002] (Table 1) has the most similar conditions to the River Calder in terms of d50 and bankfull reach Shields stress, and so is used for direct comparison here. See Ferguson et al. [2002] for further information.

4. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Theoretical Framework
  5. 3. Study Sites and Field Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Implications
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[44] The tracer data are analyzed to quantify the effects of sediment cover, grain size and flow magnitude on the components of sediment transport. As the data record the total sum of grain movement between tracer searches, most analysis considers the sum of entrainment, translation and deposition, although individual components are also addressed. The three data sets were obtained using differing experimental designs, but they are compared wherever possible.

4.1. Tracer Entrainment

[45] Frequent remapping of tracers in the River Calder (Figure 6) shows most events entrained <100% of tracers, enabling analysis of how tracer and flow properties affected initial entrainment. The longer time periods and large number of events between re-mappings in the South Fork Eel River and the Allt Dubhaig mean that the population of immobile tracers is far smaller and initial entrainment cannot be analyzed.

[46] In the River Calder, the probability of initial entrainment of a tracer depends on the tracer substrate (bedrock or alluvial), tracer size (d) and the maximum event shear stress (τmax) (Figure 8a). For all tracers, logistic regression of whether or not a tracer was entrained (movement > 0.2 m) against d, τmax and a binary of starting position (bedrock, 0, or alluvial, 1) gave p-values (coefficients, which indicate the direction of the relationship) for: d 0.052 (−0.007); τmax < 0.001 (0.078); alluvial/bedrock < 0.001 (−1.022). The surface that a tracer starts on and shear stress are therefore significant at α = 0.05, whereas grain size is not.

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Figure 8. (a) The probability of tracer initial entrainment as a function of maximum event shear stress (τmax) and tracer starting position on bedrock or on sediment. (b) The probability of entrained tracers being deposited on an alluvial surface as a function of maximum event shear stress (τmax). Error bars show 95% confidence intervals for proportions. In both Figures 8a and 8b the lines show a logistic regression to all relevant tracer data.

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[47] Although grain size is not significant in the entire data set, probability of entrainment is proportional to grain size for tracers on alluvial surfaces, but not on bedrock surfaces. Logistic regression of entrainment against d just for grains starting on alluvial surfaces has p = 0.04; for just grains starting on bedrock, p = 0.81.

[48] Tracers on, or buried in, an alluvial substrate are less likely to be entrained than those on a bedrock surface (Figure 8a). Entrainment rates from both surfaces increase with shear stress; at higher shear stresses (90 Pa) tracers on both surfaces have comparable probabilities of entrainment.

4.2. Tracer Deposition

[49] In the River Calder, tracer deposition demonstrates the same variation between bedrock and alluvial surfaces as entrainment. For all events, the probability of entrained tracers (transport distance > 0.2 m) being deposited on an alluvial surface is at least 0.78 (Figure 8b). Logistic regression of deposition on an alluvial surface against d and τmax gave p-values (coefficients) for: d 0.971 (−0.0003); τmax < 0.001 (0.034). This regression indicates that at higher values of τmax, tracers are more likely to be deposited on an alluvial patch (seen in Figure 8b), and that tracer size does not influence deposition location.

4.3. Travel Distances

4.3.1. River Calder

[50] Although substrate affects the probability of initial entrainment, it does not affect subsequent travel distances. Paired comparisons (both parametric on log(L) and non-parametric on L) found for the majority of shear stresses no significant difference at experiment-wise confidence level p = 0.05 and comparison-wise confidence level p = 0.006. Non-significant differences were about 1 m, but the minimum detectable difference for 90% reliability is ∼4 m for these data. Where statistically significant differences were found (τmax = 34.7 and 35.0 Pa), the differences were less than 2.5 m, and unlikely to influence broader patterns in transport length. For the subsequent analysis, data from tracers starting from different substrates are amalgamated.

[51] We recorded 1416 individual transport distances. The number of individual transport distances measured for each tracer varies; of the 224 tracers installed on Day 1, all but two tracers were relocated at least once, with a median of seven and a maximum of ten times. Tracers were transported up to 650 m during the 220 day experimental period. The distribution of transport distance (L) for all 1416 measurements (i.e., all distances between consecutive relocations) is positively skewed and approximately lognormal. Of these values of L, 52% are under 0.2 m (the minimum distance necessary to identify transport), and a further 19% under 2 m.

[52] To assess L over longer time durations, while accounting for the large flow event in the final inter-search period and removal of tracers from the pool, we divided the tracer data into two sets. Set 1 contains the 222 tracers emplaced on day 1 and subsequently found up to Day 155 (i.e., including those that were removed from the pool). Set 2 contains the 74 tracers in the upstream end of the reach on Day 155 and thereafter found on Days 212 and 220.

[53] Of the 222 tracers in Set 1, 8% showed zero movement by day 155. A further 6% were no longer in situ by Day 155 and are assumed to have been entrained but not subsequently relocated. The distribution of L is bimodal (Figure 9a), with the main mode at 0 to 10 m, and a secondary mode in a channel-wide pool at 90 to 110 m. The largest event (τmax = 90 Pa) occurred on Day 180 and transported tracers from the top of the reach downstream through the pool (Figure 5). This event is reflected in the distribution of L for 74 tracers in Set 2 (Figure 9b), which is more disperse than for Set 1, although still contains dominant modes interspersed with empty bins.

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Figure 9. Distributions of tracer travel distances (L) from (a and b) the River Calder, (c–e) South Fork Eel River and (f and g) reach T3 of the Allt Dubhaig (grey bars). Data are only shown for tracers that moved. The distribution in Figure 9b for day 155–220 in the River Calder is only for tracers that were in the upstream section of the reach on day 155. All data cover a comparable range of travel distances, with the exception of Figure 9a, the River Calder day 1–155. A gamma distribution has been fitted to each data set (black line); bold values in the left hand table and solid lines indicate no significant difference between the gamma distribution and the field data. The number of tracers in each distribution is shown in the right hand table.

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[54] Gamma distributions have been fitted to alluvial sediment transport data and interpreted as representing local sediment dispersion [Hassan et al., 1991; Schmidt and Ergenzinger, 1992]. To test whether River Calder data are described by local dispersion, we fitted gamma distributions to both Set 1 and Set 2 (Figure 9), using the Matlab function gamfit. Gamma distributions provide poor fits to the tracer data; the Kolmogorov-Smirnov test shows a significant difference between the data and gamma distribution with p < 0.001.

4.3.2. South Fork Eel River

[55] Tracers in the South Fork River Eel were also installed on both alluvial and bedrock patches. However, there was no significant difference (p = 0.14) between distributions of log virtual velocity (see section 4.6) for tracers with the two contrasting starting conditions, and so the data are combined. We do, however, group tracer travel distances by year to account for annual variations in the hydrograph.

[56] Tracers traveled furthest in 1996–1997, with comparable distributions of smaller distances in 1997–1998 and 1998–1999 (Figures 9c9e). ANOVA of log(L) (where L > 0) for all three years shows a significant difference (p < 0.001). Tukey-Kramer analysis reveals a significant difference between 1996 and 1997 and each of the latter two years, whereas the latter two years are not significantly different from each other. For 1996–1997 and 1998–1999, the Kolmogorov-Smirnov test indicates no significant difference between the field data and a gamma distribution fitted to the data (p = 0.41 and 0.66 respectively), whereas for 1997–1998, p = 0.04.

4.3.3. Allt Dubhaig

[57] Figures 9f and 9g show distributions of L from reach T3 of the Allt Dubhaig over both two and eight years. Neither distribution of T3 travel distances is significantly different to a gamma distribution (two year data p = 0.26; eight year data p = 0.63).

4.4. Shear Stress Influence

4.4.1. River Calder

[58] Tracers traveled further under the higher shear stresses experienced after Day 155 (Figure 9). Using all 1416 measurements, L increases as function of τmax, which varies from 29 to 90 Pa; dimensionless shear stress, τ* = 0.036 to 0.111 (Figure 10). The relative effects of τmax and duration of flow above threshold (dt) cannot be separated because log(τmax) and log(dt) are highly correlated (R2 = 0.52, p = 0.017).

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Figure 10. Travel distance of each tracer (grey) and mean travel distances for all tracers in each size class (black) against maximum event shear stress. A power function (〈L〉 = 3.86 × 10−10 τmax6.03, R2 = 0.93) and a quadratic function (log (τmax) = 1.56 + 0.10 log (〈L〉) + 0.03(log (〈L〉)2), R2 = 0.97) are fitted to mean travel distances, represented by dashed and solid black lines, respectively. The value of τc is determined to be 31 Pa, which is identified by the vertical dashed line.

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[59] Motion is initiated at a threshold shear stress (τc) of between 29 and 34 Pa. To estimate τc, we fitted a quadratic to describe τmax as a function of mean L (〈L〉) (Figure 10); this is comparable to fitting a threshold power function to 〈L〉 as a function of τmax, but is better constrained. The quadratic tends to a minimum value of 30.7 Pa. We therefore determine τc to be 31 Pa with τc* = 0.038.

4.4.2. South Fork Eel River and Allt Dubhaig

[60] In the South Fork Eel River, tracers traveled furthest in 1996–1997 (Figures 9c9e). Additional analysis indicated no appreciable difference in tracer movement between the first and second year after tracer installation; the increased travel distances in 1996–1997 are therefore attributed to the higher flows in this year (Figure 7). The large number of flow events between tracer mapping in South Fork Eel River means that it is difficult to quantify further the effect of shear stress on L, and that τc cannot be calculated from these data. In the Allt Dubhaig there were also multiple flow events between mappings. τc was estimated for the Allt Dubhaig by identifying a threshold flow that transported gravel > 16 mm (the size of the smallest tracer) into a bed load trap at the downstream end of the study reach.

4.5. Grain Size Influence

4.5.1. River Calder

[61] The analysis of deposition demonstrated that, once entrained, tracers of all sizes are transported across bedrock and are unlikely to be deposited until they reach an alluvial patch. This interpretation is consistent with the lower shear stress necessary for grain entrainment on a locally smooth bedrock surface calculated using the Kirchner et al. [1990] model and suggests that contrasts in deposition probability are more important than transport velocity. If the probability of deposition is itself not size-dependent, L will therefore be independent of grain size.

[62] The distributions of L for each of the five size classes are not significantly different (ANOVA of log(L) for the five size classes, where L > 0.2 m, gives p = 0.14). Regression analysis demonstrates that individual grain size is not significant; a regression of log(L) against log(d) (where L > 0.2 m) gives R2 = < 0.001 and p = 0.70. In both analyses, use of data only where L > 0.2 m excludes any effect of size-selectivity in initial entrainment.

[63] d is also not important within events; for each measurement period the relationship between 〈L〉 and τmax is independent of d (Figure 11; 〈L〉 is calculated from all values of L). Furthermore, results are reproduced between comparable events (e.g., three events at 35 Pa), suggesting generality of this trend. The distribution of log(L) for an event is also independent of grain size. ANOVA of the size-specific distributions of log(L) (where L > 0.2 m) for different τmax shows no significant difference between size classes for all events; in each case, p > 0.006 where 0.006 is the comparison-wise p needed for experiment-wise confidence level p = 0.05.

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Figure 11. Relationships between size class, travel distance and shear stress for the River Calder, South Fork Eel River and Allt Dubhaig. For the River Calder, data are plotted according to maximum shear stress. For the South Fork Eel River, data are plotted by year; shear stresses were higher in the first than in the latter two years. For the Allt Dubhaig, data are plotted by reach and are measured over two years. To aid comparison between the rivers, d is plotted as a multiple of reach d50. For all three plots, each symbol represents ≥10 tracers. Symbols are offset within each size class to aid clarity. For the River Calder, 0.2 m (dotted line) is the minimum resolvable travel distance. Error bars are the 95% confidence interval for the mean; error bars with values < 0 are not shown.

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4.5.2. South Fork Eel River

[64] In contrast to the River Calder, the South Fork Eel River shows a decrease in annual 〈L〉 with increasing grain size (Figure 11). Due to the uneven number of tracers in different half-phi size classes, tracers are instead divided into four size class quartiles. ANOVA of annual log(L) for the four different size classes shows that in 1996–1997 and 1997–1998, the distributions of log(L) are significantly different between the size classes (respectively p = 0.042 and 0.007). For 1998–1999, p = 0.060, indicating borderline similarity between the size classes.

4.5.3. Allt Dubhaig

[65] In the Allt Dubhaig over timescales of 2 and 8 years, mean travel distance decreased with increasing grain size across a range of excess shear stresses in each of six reaches [Ferguson et al., 2002] (Figure 11). The rate of decrease consistently varies as a function of d/d50, with a faster rate of decrease when d/d50 > 1.

4.6. Virtual Velocities

4.6.1. River Calder

[66] Tracer grains are stationary for large periods of time when flow is below threshold. Virtual velocities [Hassan et al., 1992] can be used to account for the intermittency of above threshold flows, allowing for easier comparison between different rivers and hence rates of transport across different surfaces. For the River Calder data, virtual velocities (V) were calculated by dividing the total transport distances for all 222 tracers emplaced on Day 1 by the duration of competent flow (τ > τc) (Figure 12). Transport distances were calculated between the tracer emplacement on Day 1 and their last known position.

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Figure 12. Relationships between (left) virtual velocity and grain size for all Calder tracers emplaced on Day 1, (middle) total velocity and grain size all South Fork Eel River tracers and (right) virtual velocity and grain size for all tracers in reach T3 of the Allt Dubhaig measured over two years. Virtual velocity and total velocity are respectively calculated using time when flow is above threshold and total experimental time. Mobile tracers are shown by grey closed circles. Grey open circles show the size of immobile tracers. Mean and 95% error bar for the mean for each size class are shown by the horizontal bars and vertical lines; River Calder and Allt Dubhaig data are grouped in half-phi size classes whereas South Fork River Eel data are grouped into four quantile size classes, with size classes being separated by dashed lines. Thick black lines show regressions fitted to the data, which are given by equations (5), (6) and (7) for Figures 12 (left), 12 (middle), and 12 (right), respectively.

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[67] In the River Calder, τc (31 Pa) is exceeded 3.6% of the time. The distributions of V for the data are similar across the five tracer size classes; ANOVA of distributions of V for the five size classes (where V > 0) gives p = 0.10. The relationship between d and V (where V > 0, d is in mm and V is in km yr−1) is:

  • display math

with R2 of 0.0006 and respective 95% confidence intervals for the coefficients of −1.4 to 17.6 and −0.23 to 0.34. It is noted that values of V are sensitive to the value of τc; for comparison, if τc = 32 Pa, mean V increases by 2.7 km yr−1 (31%).

4.6.2. South Fork Eel River

[68] Velocities were calculated for all tracers for the time between tracer installation and their last known position. In contrast to the River Calder, velocities show strong size dependence, larger grains traveling more slowly (Figure 12). The relationship is:

  • display math

with R2 = 0.17 and respective 95% confidence intervals for the coefficients of −3460 to 6900 and −2.7 to −1.3.

4.6.3. Allt Dubhaig

[69] Tracer velocities in the Allt Dubhaig are explained by a combination of τ* and d/d50 [Ferguson et al., 2002]. They also recorded a significant slowdown in tracer velocities between the initial survey period (1991–3) and the longer period (1991–9) that is attributed to diffusion processes [Ferguson and Hoey 2002]. Allt Dubhaig data from 1991 to 3 fit the relationship:

  • display math

with R2 = 0.02 and 95% confidence intervals for the coefficients of −0.73 to 22.1 and −0.50 to 0.04 respectively.

[70] Virtual velocities for the River Calder and Allt Dubhaig are compared using equations (5) and (7) to calculate V for the geometric mean of each of the five size classes present in both rivers. For the smallest size class (23–32 mm), V is 90% (4.5 km yr−1) faster in the River Calder than in the Allt Dubhaig. For the largest size class (91–128 mm) V is 180% (6.6 km yr−1) faster in the River Calder.

5. Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Theoretical Framework
  5. 3. Study Sites and Field Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Implications
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[71] Key differences have been identified between the River Calder, South Fork Eel River and Allt Dubhaig data sets, particularly in terms of the frequency distributions of L and the extent to which L is grain-size dependent. These contrasting behaviors reflect the position of the rivers along the bedrock-alluvial continuum (Figure 1), and result from the different ways in which ETD operate on alluvial and bedrock surfaces.

5.1. Tracer Transport Distances

[72] Values of L integrate grain entrainment, translation and deposition. Distributions of L can be described by gamma distributions in both the South Fork Eel River and reach T3 of the Allt Dubhaig, but not in the River Calder. Data from all three rivers (Figure 9) show a comparable range of travel distances (apart from days 1–155 in the River Calder), indicating that differences between the distributions are not because the River Calder tracers have not traveled as far and/or not experienced such high flows.

[73] In the River Calder, modal travel distances are comparable to the spacing of in-channel sediment stores, reflecting the morphological control on translation and deposition. Between days 1–155, L has two modal values; 0–10 m and 90–110 m. The first mode is from relatively immobile tracers that were mainly found along the channel edges, either on a bar or buried by gravel sheets. The second mode is from deposition in the channel-wide, predominantly alluvial, pool at the end of the reach (Figure 5). The irregular distribution of L between days 155–220 is also morphologically controlled; tracers are primarily deposited in the alluvial patches along the channel (Figures 5 and 8b). In summary, translation is mostly occurring as Tb, and Da is far more common that Db.

[74] The gamma distributions of L in the South Fork Eel River and Allt Dubhaig are consistent with data from several alluvial rivers [e.g., Hassan et al., 1991; Schmidt and Ergenzinger, 1992], although other alluvial data have been approximated by different statistical distributions [e.g., Pyrce and Ashmore, 2003a; Bradley et al., 2010]. Pyrce and Ashmore [2003a] suggest that the appropriate statistical distribution depends on bed shear stress. However, the above distributions only reproduce the effect of local sediment dispersion, and assume that the processes of entrainment, translation and deposition operate in the same way across the channel, e.g., Ea, Ta and Da occur everywhere. Statistical distributions therefore do not account for morphological effects [Hassan et al., 1991; Frey and Church, 2011]. Consequently, the River Calder tracers are unlikely to approach a gamma distribution of travel distances over longer time periods and greater dispersion.

[75] In the River Calder, L is determined by the reach morphology affecting grain translation and deposition; this morphological influence is not observed in reach T3 of the Allt Dubhaig and is much weaker in the South Fork Eel River data which shows some secondary modes that may be associated with bar locations (Figure 9). Although the reach T3 data suggest that dispersion dominates over morphological effects, of the ten Allt Dubhaig data sets (five reaches, with data from two and eight years in each) [Ferguson et al., 2002], only four are not significantly different to a gamma distribution (p > 0.05). Differences to a gamma distribution occur because channel morphology controls L through deposition in bars and channel switching leading to some grains entering long-term storage [Ferguson and Hoey, 2002]. Pyrce and Ashmore [2003b] identified modes of L that were consistent with pool-bar spacing in several alluvial rivers, particularly at higher values of τ*, suggesting a morphological control on travel distances and the potential for spatial variation in Ea, Ta and Da. Morphological controls on grain transport processes are therefore important across the bedrock-alluvial spectrum, but there are likely to be significant differences in the factors influencing the morphology. In the River Calder and other bedrock rivers, the location of sediment stores is controlled by the interaction between the eroding river and reach geology [Goode and Wohl, 2010b]. In alluvial rivers, morphological controls are more likely to be autogenically produced.

5.2. Threshold Shear Stresses and Virtual Velocities

[76] In the River Calder, initial grain entrainment occurred at τc = 31 Pa (τc* = 0.038). This is within the range of values of τc* measured in alluvial rivers, from c. 0.025 to > 0.07, and is consistent with initial entrainment primarily occurring from alluvial patches (i.e., Ea), although care needs to be exercised in comparing results generated using different methods [Buffington and Montgomery 1997]. The relatively low value of τc* for the River Calder may reflect the sediment patches being more loosely packed than is usual for sediment in an alluvial channel; for loosely packed sediment, τc* can be as low as 0.01 [Fenton and Abbott, 1977; Dancey et al., 2002].

[77] Theoretical analysis of grain entrainment (Figure 3) predicts that grains on a bedrock surface will be entrained at τc* < 0.02. Consequently, if the flow is sufficiently high to entrain grains from alluvial patches in a bedrock channel (τc* > 0.038), these grains are very likely to be re-entrained if they are transported onto a bedrock surface. The differing values of τc* for alluvial and bedrock surfaces means that τ*/τc* will be higher over the bedrock surface, hence Tb will readily occur and Db is very unlikely.

[78] The difference in grain transport processes between bedrock and alluvial surfaces is reflected in the virtual velocities. Virtual velocities from the River Calder are significantly higher than those from a directly comparable reach of the Allt Dubhaig (Figure 12), suggesting different grain dynamics. The higher velocities in the River Calder could be because grains move for a greater proportion of the time when the flow is above threshold, or because they move further between initial entrainment and deposition. The low probability of Db and ready occurrence of Tb in the River Calder are consistent with these explanations, but full understanding requires within-event transport path and velocity data from individual grains [e.g., Lajeunesse et al., 2010].

5.3. Grain Size Effects

[79] The extent to which the components of grain movement are size-selective will also affect the sediment dynamics. In the River Calder, Ea is weakly size selective. Initial entrainment is mainly as Ea because grains are preferentially deposited on sediment surfaces. The size-selectivity of Ea is consistent with much data from alluvial rivers [Buffington and Montgomery, 1997]. In contrast, entrainment from a bedrock surface (Eb) is not size-selective, which is consistent with results from the Kirchner et al. [1990] model (Figure 3). The longer time scales of the Allt Dubhaig and South Fork Eel River data prohibit explicit analysis of initial entrainment.

[80] Distributions of L reflect the size-selectivity of translation and deposition. In the River Calder, 〈L〉 is independent of grain size across events with τmax from 0.94 to 2.9 τc (Figure 11a). In contrast, the South Fork Eel River and the Allt Dubhaig have an inverse relationship between 〈L〉 and tracer size (Figures 11b and 11c). All three rivers have a comparable range of relative grain size (d/d50), and so relative grain size is not responsible for the difference in the relationships. Differences in shear stress are also not responsible; τ* is higher in the South Fork Eel and the Allt Dubhaig than in the River Calder. As described below, this would predict the opposite pattern of size-selective transport to that observed. In the River Calder, the uniformity of L across grain sizes is consistent with the theoretical and field results that Eb, i.e., re-entrainment of grains in transport, is not size-selective (Figure 3). Although other components of grain transport, e.g., Tb, may be size selective the overriding control on travel distances is the relative ease of transport over bedrock surfaces and the contrast between Da and Db.

[81] The South Fork Eel River and Allt Dubhaig results are supported by tracer data from other alluvial rivers where multiple size classes spanning d50 have been tracked for multiple events [e.g., Church and Hassan, 1992]. Tracer travel distances in the Rio Cordon change from size-dependent to size-independent as a function of increasing discharge [Lenzi, 2004]. At low discharges L decreased rapidly with increasing grain size, but at a discharge 15 times threshold (τ/τc ≈ 4) L for all but the largest size class (d/d50 = 4.8) were size independent. Size independent bed load transport (i.e., bed load GSD is equal to the sediment surface GSD) has been recorded in other alluvial rivers when τ/τc is greater than 1.5 to 2 [Parker et al., 1982; Andrews, 1983; Wilcock and McArdell, 1993]; these rivers plot with Oak Creek in Figure 4. However, the hydraulic regime of most alluvial rivers means that typical flows are not substantially above threshold [Parker, 1978] and therefore the effect of multiple flow events is net size selectivity and divergence in bed load flux, plotting with the Allt Dubhaig in Figure 4 [Lisle, 1995]. The integrative nature of tracer data means that it is difficult to identify which component(s) of transport contribute most to the observed size-selectivity. The transition with increasing shear stress, however, suggests a change in the size-selectivity of Ea [Wilcock, 1997].

5.4. Distribution of Sediment Cover and Channel Morphology

[82] Our three data sets demonstrate how the volume of sediment within a channel affects the dynamics of entrainment, translation and deposition, and hence the reach-scale sediment flux. Both entrainment processes and depositional sorting are affected by surface sediment structure and vertical sorting, and so sediment depth becomes an important factor affecting sediment dynamics and may account for the differences in the size-selectivity of Ea between the rivers.

[83] At low sediment volumes, interactions between bedrock geometry and local hydraulics will control the locations of sediment cover [Johnson and Whipple, 2007; Chatanantavet and Parker, 2008; Goode and Wohl, 2010a, 2010b]. Bedrock geometry stems from the interaction between the river and the resistant bed, via the bed roughness, and is a function of the local geology. Consequently, sediment patches will tend to be irregularly spaced, as in the River Calder (Figure 5). At greater sediment volumes, sediment cover becomes more uniform and bed forms may develop. Regular bed forms could provide a new control on the locations of grain deposition and hence transport lengths [Pyrce and Ashmore, 2003a, 2003b]. Across the spectrum of sediment cover, lateral variations in shear stress may cause spatial variations in grain size that in turn produce size-selectivity in entrainment and transport [Paola and Seal, 1995].

[84] As the volume of sediment in a bedrock channel increases, sediment thickness will also increase. Sediment depth in the River Calder is generally less than 2d90 (Figure 5). The majority of sediment is therefore within the active layer and there is no longer-term storage at depth. In addition, surface coarsening, which controls size-selection in entrainment and bed load, cannot develop. Consequently, the volume of sediment stored in a bedrock reach and its spatial distribution together control long-term sorting processes. Surface coarsening is a dynamic response to the protrusion of large grains and the hiding of smaller ones and results, in part, from smaller grains being deposited in deep pores and effectively removed from the active layer [Allan and Frostick, 1999]. Kinematic sorting further enhances the selective removal of smaller grains [Parker and Sutherland, 1990; Frey and Church, 2011]. In beds with a coarse surface layer, Da and specifically deposition depth, may be size dependent, leading to smaller tracers being mixed more rapidly into the bed than larger ones [Ferguson and Hoey, 2002; Haschenburger, 2011].

[85] The development of a coarse surface layer alters the surface GSD and the geometry of grains in the bed, and hence changes the grain-size specific τc. Initial entrainment from alluvial patches in the River Calder is weakly size-selective; although entrainment is a function of grain weight, size-selectivity is weak due to the effects of surrounding grains on grain exposure and pivoting angles. Surface coarsening over-represents large grains in the surface, so that at high relative shear stresses the bed load GSD is equal to the sub-surface GSD. However, at lower relative shear stresses, entrainment is still biased toward smaller grains [Wilcock and McArdell, 1993; Powell et al., 2001]. Over a range of flows, entrainment from beds with coarse surface layers is somewhat size-dependent leading to size-selective tracer movement distances as observed in the South Fork Eel River and the Allt Dubhaig. Such size-selective entrainment may produce aggradation; if so, unless large floods periodically clear the channel [e.g., Lague, 2010], the river will eventually become alluvial.

[86] The field results show that sediment cover extent can affect channel transport capacity. Bedrock channels with lower sediment cover and otherwise equal characteristics could have a higher transport capacity because of bedrock surfaces facilitating grain transport. The low probability of deposition means that once exposed a bedrock surface will tend to stay exposed. Transport capacity is hence limited by the alluvial patches, and so fractional exposure is a first-order control on transport capacity. Net sediment flux, however, will be limited by supply rather than transport. The role of sediment cover means that supply can affect transport distances; if lower supply reduces sediment cover, then transport velocities will increase. However, the above may only apply if the bedrock is relatively smooth; on a rough bed increased sediment cover could reduce the mesoscale roughness, reducing form drag and increasing sediment transport capacity. Equally, at higher sediment cover, velocities may increase through increased sediment supply because deposition niches in the bed get filled [Lisle and Church, 2002].

6. Implications

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Theoretical Framework
  5. 3. Study Sites and Field Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Implications
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[87] The idea that sediment processes vary as a function of the amount of sediment in a bedrock channel has implications for understanding and modeling bedrock river evolution. Predicting the distribution of sediment flux and sediment cover throughout a channel network is significant for understanding landscape evolution and has management applications. Rivers with bedrock reaches are widespread and effective management of such rivers, for example in managing the effects of hydropower schemes on in-stream biota, requires prediction of how sediment flux and cover will vary under given conditions.

[88] A common approach to modeling bedrock rivers is to assume that all sediment can be represented by a single grain size [e.g., Lague, 2010] and/or is equally mobile [e.g., Sklar et al., 2006; Stark et al., 2009]. Although these assumptions are broadly consistent with the River Calder data and the sediment continuity analysis, the South Fork Eel River data show that this assumption is invalid when the river contains significant sediment cover. Bedrock river models therefore need to allow for a continuum of sediment processes, as in Figure 1. The location of a reach along this continuum will depend on both the spatial extent and depth of sediment cover. Further research is necessary to identify whether the transition between bedrock and alluvial styles is linear along this continuum. There is also a need to consider the role of pebble abrasion, which has been discounted in this study but which is significant in many bedrock rivers; abrasion can produce downstream fining in a bedrock river where transport is not size-selective [Attal and Lavé, 2009]. The rate of downstream fining also depends on the interaction between abrasion and longitudinal variation in the GSD of local sediment supply [Sklar et al., 2006; Chatanantavet et al., 2010].

[89] Over the timescales of relevance to landscape evolution, the rate of sediment supply to a river varies considerably [Stark et al., 2009]. Such variations will alter the amount of sediment in the channel and therefore the location of reaches along the alluvial-bedrock continuum [Sklar and Dietrich, 2008]. River reaches could thus switch between alluvial and bedrock-style behavior [Lague, 2010]. The possibility for size selective transport in bedrock rivers questions the extent to which such rivers are in long-term equilibrium, given that size-selective transport could mean that larger sediment is accumulating in the river. However, the accumulation rate may be sufficiently slow such that the channel is in a quasi-stable equilibrium, or accumulation may be offset by abrasion. A complete understanding also needs to consider the distributions of discharge, sediment supply and GSD entering these rivers [Lague, 2010].

7. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Theoretical Framework
  5. 3. Study Sites and Field Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Implications
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[90] Processes of grain entrainment, translation and deposition vary according to position of a bedrock river along the bedrock-alluvial continuum (Figure 1 and Table 1). We predict that, with the exception of rivers with extremely low sediment cover, grains are primarily entrained from alluvial patches. Once in transport, subsequent re-entrainment from a bedrock surface is likely because the necessary shear stresses are an order of magnitude smaller than for entrainment from an alluvial surface (Figure 3). Grains are correspondingly more likely to be deposited on alluvial surfaces. Both grain entrainment and sediment continuity considerations predict that sediment transport in a predominantly bedrock channel should not, in the absence of abrasion, be significantly size-selective.

[91] Gravel tracer data from three rivers across the spectrum of bedrock and alluvial channels have been used to test these theoretical predictions: the River Calder (20% sediment cover), the South Fork Eel River (80%) and the alluvial Allt Dubhaig (100%). Key differences were identified between the three sets of tracer data, namely: 1) in the South Fork Eel River and Allt Dubhaig, distributions of tracer travel distances are adequately described by gamma distributions, whereas the River Calder tracers show multimodal transport distances; 2) transport distances in the River Calder were size independent across shear stresses up to 2.9 τ/τc, whereas both the South Fork Eel River and the Allt Dubhaig demonstrated size selectivity; 3) grains in the River Calder had higher virtual velocities than grains in a directly comparable reach of the Allt Dubhaig; and 4) grains in the River Calder were entrained at a lower value of τc* than is typically observed in alluvial rivers.

[92] The empirical findings concur with the theoretical predictions, and are explained by the effect of sediment cover and depth on the components of sediment transport. Despite entrainment primarily occurring from alluvial surfaces in all rivers, entrainment occurs at a lower dimensionless shear stress in the River Calder. This is hypothesized to be because the sparse sediment patches are loosely packed; shallow sediment depths mean that all sediment is frequently mobilized and that surface coarsening is inhibited. The loose packing also means that entrainment is more weakly size selective than in the fully alluvial case.

[93] In the River Calder, sediment is mainly translated across bedrock surfaces. As predicted by the theoretical modeling, grains are not deposited on bedrock surfaces but instead are transported between, and deposited on, sediment patches producing the irregular distribution of transport lengths. The minimal variation in entrainment shear stress with grain size predicted by the theoretical grain model means that there is no significant difference in transport lengths as a function of grain size. The relative ease of transport across bedrock surfaces also results in the higher virtual velocities identified in the River Calder. In contrast, the more complete sediment cover in the South Fork Eel River and Allt Dubhaig means that sediment step lengths are more directly a function of diffusion processes although the scale of bed forms constrains these. The deeper sediment deposits enable surface coarsening to develop, which affects the size-selectivity of grain entrainment and deposition.

[94] The theoretical and field results identify a continuum in sediment processes between alluvial and bedrock rivers. This continuum indicates that models of bedrock rivers can neither assume that all transport is size independent, nor unquestioningly apply formulas developed from alluvial data. Instead, there is a need to consider how the spatial extent and depth of sediment cover affect sediment processes. The data presented in this paper have been used to identify these key controls; these data however only represent three points along the continuum. Further empirical and modeling work is needed to quantify sediment processes along this continuum.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Theoretical Framework
  5. 3. Study Sites and Field Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Implications
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[95] Funding was provided by the John Robertson Bequest, University of Glasgow. For the River Calder, thanks to the Clyde Muirshiel Regional Park for access and flow information, to Kenny Roberts for field support, and to Florenz Hollebrandse for previous data. Allt Dubhaig data was collected in projects funded by NERC led by Rob Ferguson, who provided valuable comments on an earlier draft of this paper. For the South Fork Eel River, thanks to Bill Dietrich, Mary Power, Peter Steele, Martin Trso, Leslie Ferguson, Douglas Allen, and many others. Funding was provided by the U.C. Natural Reserve System Mildred E. Mathias Research Grant. Reviews and comments from Jens Turowski, Gary Parker, an anonymous reviewer, the Associate Editor, and the Editor improved an earlier version of this paper.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Theoretical Framework
  5. 3. Study Sites and Field Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Implications
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Theoretical Framework
  5. 3. Study Sites and Field Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Implications
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information
FilenameFormatSizeDescription
jgrf871-sup-0001-tab01.txtplain text document1KTab-delimited Table 1.

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