Coarse Sediment Transport in a Bedrock Channel with Complex Bed Topography Jaime R

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WATER RESOURCES RESEARCH, VOL. 46, W11524, doi:10.1029/2009WR008135, 2010

Coarse sediment transport in a bedrock channel with complex bed topography Jaime R. Goode1 and Ellen Wohl2 Received 17 April 2009; revised 4 August 2010; accepted 18 August 2010; published 13 November 2010.

[1] Independent lithologic and structural controls in fluvial bedrock systems interact with coarse sediment transport processes to play a key role in bedrock incision processes such as abrasion. During a 3 year study on the Ocoee River in the Blue Ridge Province of the southern Appalachians, USA, we used painted tracer clasts to measure coarse sediment transport dynamics and address whether different scales of morphologic variability in bedrock channels lead to coarse sediment transport processes that differ from alluvial channels. At the reach scale, folded metasedimentary units are exposed in the channel bed and appear as linear bedrock ribs that vary in amplitude and orientation to flow. Under similar flow conditions for which size‐dependent transport has been observed in alluvial channels (dimensionless Shields stress within 1.5–2.0 times the dimensionless critical shear stress), transport distance was a significant function of grain size where bedrock ribs were longitudinal to flow (Reach 1 and Reach 2). However, transport distance was not size dependent where bedrock ribs were oblique to flow (Reach 3). At different intrareach scales, the variables characterizing the local bedrock topography and sediment architecture were the best predictors of transport distance in all three reaches. Therefore, bed load transport processes may be influenced by bed forms in bedrock streams (bedrock ribs) but at potentially smaller scales than bed forms in alluvial channels. The strong influence of bedrock ribs on coarse sediment transport suggested that coarse sediment transport processes are controlled by different factors in bedrock channels only when bedrock ribs cross the channel at a high angle to the flow. Citation: Goode, J. R., and E. Wohl (2010), Coarse sediment transport in a bedrock channel with complex bed topography, Water Resour. Res., 46, W11524, doi:10.1029/2009WR008135.

1. Introduction Chatanantavet and Parker, 2008], and even more limited field examinations [Johnson et al., 2009]. These studies [2] In order to constrain parameters required for landscape document interactions and feedbacks among sediment supply, evolution models [e.g., Howard, 1994; Whipple and Tucker, localized transport, bedrock erosion rate, and channel 2002; Sklar and Dietrich, 2004; Turowski et al., 2007], recent morphology. Although it is reasonable to assume that alluvial studies have focused on reach scale processes involved in and bedrock channels have fundamentally different controls bedrock channel incision [Johnson and Whipple, 2007; on coarse sediment transport, the details of these different Finnegan et al., 2007; Chatanantavet and Parker, 2008; controls have not yet been explored and adequately quan- Johnson et al., 2009]. Particular attention has focused on the tified in the field. By examining the controls on coarse important role of bed load material in controlling incision via sediment transport in natural bedrock channels, we can abrasion in bedrock systems [Sklar and Dietrich, 1998, 2001; improve our understanding of the processes that control Hartshorn et al., 2002], illustrating the need to understand the bedrock incision by abrasion. dynamics of coarse sediment transport in bedrock channels. [3] In the process of abrasion, saltating bed load acts to While an extensive literature describes coarse sediment scour bedrock surfaces by fine‐scale removal of bedrock transport processes at the reach scale in alluvial channels material. Abrasion is distinguished from other physical ero- [e.g., Einstein,1950;Beschta,1987;Ferguson et al., 2002; sion processes such as plucking and macroabrasion, which Wilcock and Crowe, 2003; Parker, 2008], the reach scale remove cobble‐ and boulder‐sized blocks from the bedrock controls on coarse sediment transport in bedrock channels are channel substrate [Hancock et al., 1998; Whipple et al., 2000; poorly understood, except from a few experimental studies Chatanantavet and Parker, 2009]. Bedrock incision by [Johnson and Whipple, 2007, 2010; Finnegan et al., 2007; abrasion is conditioned on the interplay between bed load material either providing the tools that promote abrasion and 1Center for Ecohydraulics Research, University of Idaho, Boise, incision or being the cover that inhibits incision, depending Idaho, USA. on the ratio of sediment supply to transport capacity [Gilbert, 2Department of Geosciences, Colorado State University, Fort Collins, Colorado, USA. 1877; Sklar and Dietrich, 1998, 2001; Turowski et al., 2007]. The incision rate is maximized for intermediate sediment Copyright 2010 by the American Geophysical Union. supply relative to the transport capacity, such that a sufficient 0043‐1397/10/2009WR008135 amount of bed load tools are available for abrasion, and the W11524 1of14 W11524 GOODE AND WOHL: COARSE SEDIMENT TRANSPORT IN A BEDROCK CHANNEL W11524 bed is not fully covered by alluvium. Whereas this threshold 2002; Lenzi, 2004]. Results from these tracer studies indi- concept is simple, there are unconstrained details (e.g., cate that under moderate flow conditions, the structure of interactions between sediment transport and bedrock bed the bed sediment (i.e., variability in sediment size, sorting, forms) that arise upon experimental examination [Johnson and packing) is an important control on bed load transport, and Whipple, 2007; Finnegan et al., 2007; Chatanantavet whereas the flow characteristics are the dominant control on and Parker, 2008]. bed load transport at higher flows [Ferguson and Wathen, [4] The saltation‐abrasion model [Sklar and Dietrich, 1998; Lenzi, 2004]. Size selectivity in bed load transport 1998, 2004] incorporates the concepts of tools versus cover tends to occur in either of two scenarios: (1) over a range of effects quantitatively by considering bed load supply and flows for particles that are unconstrained by interparticle transport. This model assumes a planar bed surface, and packing and fully exposed to the fluid forces or (2) at mod- it does not incorporate channel morphology as a degree erate flows, when the shear stress is slightly above the of freedom. Natural bedrock channels, however, commonly threshold of motion for the median grain size, for particles display high spatial variability in bed topography as a result of that are constrained by interparticle contacts (i.e., imbri- sculpting and bedrock characteristics [Whipple, 2004; cated and incorporated into the armor layer) [Church and Richardson and Carling, 2005]. This variability has also been Hassan, 1992; Ferguson et al., 2002; Lenzi, 2004]. shown to control local erosion rates [Hancock et al., 1998; [8] Here we use painted tracer clasts in order to examine Johnson and Whipple, 2007] and promote feedbacks between the controls on coarse sediment transport in a bedrock incision and bed morphology [Finnegan et al., 2007; Johnson channel with a high degree of spatial variability in bed and Whipple, 2007, 2010]. It is well documented from allu- topography. We frame this study around a fundamental vial systems that variation in bed topography largely influ- question: Is coarse sediment transport in bedrock channels ences the local flow field [Furbish, 1993; Nelson et al., controlled by the same hydraulic conditions and sediment 1995; Papanicolaou et al., 2001], the dynamics of sedi- properties that control coarse sediment transport in gravel ment transport [Pyrce and Ashmore, 2003; Yager et al., 2007; bed streams? Specifically, we seek to understand what Thompson, 2007], and spatial variation in the surface texture conditions (flow or sediment architecture), if any, lead to of bed sediments [Dietrich et al., 1989]. size‐dependent transport. We address this question by testing [5] Sediment transport and deposition in bedrock chan- three specific alternative hypotheses. (H1) In all study nels are generally different from alluvial systems, in that reaches, transport distance is a significant function of grain (1) sediment loads are relatively low compared to transport size, D. (H2) Differences in coarse sediment transport dis- capacity, (2) highly turbulent flows are capable of trans- tance exist between study reaches can be explained by dif- porting up to boulder‐sized particles for large distances, and ferences in reach scale hydraulics and bedrock topography. (3) lateral hillslope connection directly supplies coarse sedi- This second hypothesis is designed to test the idea that, if ment through diffusive hillslope processes, landslides, rock- transport distance is not size dependent, then observed dif- falls, or debris flows [Wohl, 1999; Whipple, 2004]. Bedrock ferences in transport distance can be explained by reach scale characteristics (i.e., lithology and structure) also have a strong variations in bedrock channel bed morphology. (H3) The influence on channel geometry [Montgomery and Gran, local scale variability in bedrock channel topography and 2001; Whipple, 2004; Goode and Wohl, 2010], potentially sediment architecture is the dominant control on transport regulating bed load transport. distance. This hypothesis is based on the assumption that [6] In bedrock channels, sediment supply, grain size, and bedrock ribs in the channel examined here exert a strong bedrock detachment are all interrelated variables that tend to control on coarse sediment transport. We use the term coarse offset variation in one another [Sklar and Dietrich, 2008]. sediment transport rather than bed load transport because the Roughness supplied from sculpted forms in bedrock systems nature of this study precludes determination of the mode of increases form drag, which likely reduces the local shear transport. The focus is on coarse gravel, cobbles, and boulders stress [Shepherd and Schumm, 1974; Wohl and Ikeda, 1997; (32 mm < D < 362 mm). Wohl, 1998; Wohl et al., 1999; Johnson and Whipple, 2007; Finnegan et al., 2007; Turowski et al., 2007; Chatanantavet and Parker, 2008]. As a result, roughness may locally 2. Study Area reduce sediment transport capacity, such that the local bed- [9] The study area is located in the Ocoee River gorge, rock topography controls the spatial distribution of sediment Tennessee between the Tennessee Valley Authority (TVA) transport. In this study, we examine how spatial heterogeneity Ocoee No. 3 dam and the 1996 Olympic whitewater course at different scales controls the dynamics of coarse sediment (Figure 1). Here the Ocoee River flows through the Blue transport in a bedrock channel with bed morphology that is Ridge Province of the Southern Appalachians, with a drain- influenced by lithologic and structural variation. age area of approximately 1300 km2. Although the gorge is [7] In alluvial channels, strong spatial and temporal var- deeply incised, hillslopes exhibit limited bedrock exposure iability in bed load transport rates are explained by variability and are densely vegetated and mantled with thick soils typical in transport over bed forms [Schmidt and Gintz, 1995; of humid temperate landscapes. Homogenous denudation Thompson et al., 1996; Cudden and Hoey, 2003], temporal rates (25 ± 5 m/Myr) over 104–105 year time scales [Matmon variability in sediment supply [Beschta, 1987], variation in et al., 2005] characterize this tectonically quiescent region. armoring and sorting [Whiting et al., 1988], and burial and Bedrock in this region consists of slates and metasandstones vertical mixing [Ferguson and Hoey, 2002; Ferguson et al., contained within the Precambrian Ocoee Supergroup. Spe- 2002]. The spatial and temporal controls on bed load trans- cifically, bedrock exposures through the Ocoee River gorge port in gravel bed streams have been characterized by are the Precambrian‐age Sandsuck Formation in the western tracking the movement of individually marked gravels [e.g., gorge, which is composed of phyllites thinly interbedded Church and Hassan,1992;Wilcock, 1997; Ferguson et al., with arkosic and calcareous quartzites; the Dean Formation, 2of14 W11524 GOODE AND WOHL: COARSE SEDIMENT TRANSPORT IN A BEDROCK CHANNEL W11524

as concave sculpted joint furrows and bedding plane furrows. Bedrock ribs differ from these features as opposing topographic features. Concave sculpted joint furrows and bedding plane furrows are long, narrow portions of bedrock that protrude above the surrounding bed, whereas bedrock ribs are asymmetrical in cross section, regardless of planform orientation, consistently oriented parallel to the metamorphic foliation in the rock, and occasionally follow dominant joints. The strike of the bedrock ribs varies as the trend of the sinuous channel changes downstream, which suggests that rib orientation is controlled by structural features in the underlying folded metasedimentary units. The occurrence of sculpted forms such as potholes (along the upstream and downstream faces of transverse bedrock ribs and in the troughs between longitudinal bedrock ribs) suggests that abrasion is the dominant mechanism of fluvial incision in this system. [11] Alluvial material in this system consists of sand‐ to boulder‐sized sediment, which covers roughly half of the channel bed area in three distinct areas: discontinuous patches, the intervening lows between bedrock ribs, and within potholes. In isolated locations of the channel bed, this alluvial material is armored by large cobbles and boulders. The wake zones of bedrock ribs tend to be associated with high con- centrations of well sorted, gravel‐sized material (Figure 2a). Sediment angularity ranges from very well‐rounded particles within potholes to slightly more angular particles across the channel bed. This difference in angularity appears to reflect not only the local hydraulic environment but also the lithologic origin (phyllite produces more angular particles, whereas the metagreywacke corresponds to well‐rounded particles) and fluvial transport distance. [12] After the closure of the Ocoee No. 3 dam in 1942, the natural‐channel flow was diverted through a bypass to the hydropower station downstream, beyond the study area. Since the 1996 Olympics, however, the TVA has guaranteed recreational flows in this section of roughly 45 m3/s for 6 h on both Saturday and Sunday, from the last weekend in May through the last weekend in August. Only exceptional winter stormflows that exceed the hydropower capacity Figure 1. Digital Orthophoto of the Ocoee River study are routed through the natural channel. Winter and spring area [U.S. Geological Survey, 1997]. Reach boundaries are storms produce flows for which the daily average releases from the dam range from 40 to 60 m3/s, and peak flows can indicated by the solid white lines. The downstream variation 3 of rib orientation can be seen in this areal photo of the dry reach 800 m /s. Infrequent flow releases and flow diversion channel bed, with black dashed lines indicating the rib has led to woody vegetation establishment in many loca- orientation. Reach boundaries are indicated with white lines. tions of the channel bed. We intentionally avoided these sections in this study. composed of thinly bedded quartzites and phyllites; and the Hothouse Formation, composed of metagreywacke and mica 3. Methods schist in the eastern gorge [Sutton, 1991]. Through the gorge, [13] Three study reaches within the study area were the rock units alternate between resistant ledges of meta- selected according to the dominant lithology and the orien- greywacke and quartzite and softer phyllite sequences. tation of the bedrock ribs to flow (Figure 1 and Table 1): Because the channel meanders across the folded metamor- Reach 1 (phyllite and longitudinal ribs), Reach 2 (meta- phic units at scales larger than the reach scale (Figure 1), the graywacke and longitudinal ribs), and Reach 3 (meta- orientation of flow relative to the dip and lithology of the greywacke and oblique ribs). A fourth reach, Reach 4 bedrock varies. (metagraywacke and transverse ribs), was initially included [10] This lithologic and structural heterogeneity appears in this study, but anthropogenic disruption of the experiments in the channel bed as undulating rib‐like bedrock forms that forced us to eliminate it [Goode, 2009]. Longitudinal ribs we refer to as bedrock ribs. These bed forms are not unique varied 0° ± 10° with respect to the main flow direction, to the Ocoee River [Goode and Wohl, 2010] but have not transverse ribs were oriented 180° ± 10° with respect to flow, received much attention in the literature. In their report on and oblique ribs occurred at all other angles to flow. The sculpted forms in bedrock channels, Richardson and Carling length of each surveyed reach was determined by the per- [2005] describe similar structurally influenced features such sistence of the rib morphology: reaches continued for as long 3of14 W11524 GOODE AND WOHL: COARSE SEDIMENT TRANSPORT IN A BEDROCK CHANNEL W11524

[15] For each tracer, we recorded the size (measured along the intermediate axis), applied a roughly 5 cm square patch of yellow concrete paint, and wrote the tracer number on the paint patch with a black permanent marker. Care was taken not to disrupt the bed material when clasts were tagged with paint. If the tracer was not incorporated in the armor layer, a paint patch and number were applied to a second side to increase the likelihood of finding the tracer if it flipped over after transport. A laser total station positioning system was used to map the initial tracer locations. During this survey, the area within one grain diameter was visually assessed for its potential influence on the transport of a given tracer (Figure 2b). Five categories defined this local scale: unconstrained (no surrounding particles or bedrock ribs protruded above the tracer), shielded (bedrock ribs protruded above the tracer, and likely interfered with transport), imbricated (surrounding particles constrained the movement), buried (required removing sediment in order to recover the tracer), or embedded (packed into the armor layer). Tracers that were both constrained by surrounding grains and bedrock ribs were assigned imbricated and shielded. [16] In addition to the local scale, we defined two other spatial scales within each reach: (1) cross‐section scale, with tracers linked to the nearest cross section, in the previous survey and (2) zone scale, with tracers linked to geomor- phically similar bed regions. The cross‐section scale was quantified by the cross‐sectional averaged hydraulic metrics, obtained from the modeling results of Goode and Wohl [2010], wherein we applied the U.S. Army Corps of Engineers (USACE) one‐dimensional flow model HEC‐RAS [U.S. Army Corps of Engineers (USACE), 2002] to iteratively determine the Manning’s roughness coefficients by matching the known discharges from the 2006 summer release flows (Q =45m3/s) and the surveyed water surface elevations at Figure 2. (a) Photograph illustrating the coarse sediment each cross section. Using these Manning’s roughness deposition in between bedrock ribs in Reach 3. (b) Tracer coefficients, we used HEC‐RAS to model each peak dis- clast (circled) downstream of a bedrock rib in a local charge between tracer resurveys. Without known water sur- hydraulic environment classified as shielded. Tape measure face elevations at the upstream and downstream reach for scale. Arrows indicate flow direction. Photos were taken boundaries for these peak flows, because we were not present between summer release flows when the channel was dry. in the field area during these flows, we set the downstream boundary condition to the normal flow depth. A sensitivity as the bedrock rib orientation and dominant lithology was analysis on the choice of the downstream boundary and maintained within a straight, single flow channel. response of the calculated hydraulic variables showed no [14] In each of the three study reaches, we used painted significant difference (P > 0.05) in the hydraulic variables, tracer clasts, which we selected from the existing alluvial especially in the upstream cross sections where the tracers patches. A total of 300 tracers were randomly selected using existed. This enhanced our confidence in the hydraulic a Wolman point count, where we paced the channel in a modeling results despite the uncertainty in the downstream conceptual grid. While it is argued that this method tends to boundary conditions. Although supercritical flow likely bias the sample toward the coarse grains [Kellerhals and occurs locally within each reach, model runs were performed Bray, 1971], our interest was focused on sediment that was larger than coarse gravel (>32mm), which supported the validity and practicality of this selection approach in this field study. The pattern that we followed for this selection Table 1. Summary of Differences in Reach Morphology, Lithology, procedure allowed us to span the channel width several Hydraulic Roughness, and Grain Size times and capture both a representative distribution of par- Reach 1 Reach 2 Reach 3 ticle sizes and a wide range of depositional zones associated with the highly variable bedrock channel bed topography Rib orientation to flow longitudinal longitudinal oblique (i.e., grains that were located upstream and downstream of Dominant lithology phyllite metagreywacke metagreywacke Mean rib amplitude (m) 0.44 0.57 0.79 bedrock ribs, in the thalweg, or in pools). If a selected Reach gradient 0.0075 0.0082 0.0106 particle was fully incorporated into the armor layer, such Manning’s n 0.059 0.075 0.094 that the particle boundaries could not be seen, it was not D16 (mm) 50 46 48 included in the sample. This occurred for less than five D50 (mm) 115 100 150 cobble‐ and boulder‐sizedgrainsineachreach. D84 (mm) 240 230 252 4of14 W11524 GOODE AND WOHL: COARSE SEDIMENT TRANSPORT IN A BEDROCK CHANNEL W11524

Table 2. Hydraulic Variables From HEC‐RAS Modeling of Peak Discharges in Each Reach Between Each Recovery Summer 2006: Mean of Four Resurveys 2007 Resurvey 2008 Resurvey Variable Reach 1 Reach 2 Reach 3 Reach 1 Reach 2 Reach 3 Reach 1 Reach 2 Reach 3

3 Qpeak (m /s) 47 47 47 81 81 81 88 88 88 Manning’s n 0.06 0.08 0.09 0.06 0.08 0.09 0.06 0.08 0.09 Velocity (m/s) 1.5 1.1 1.0 1.8 1.4 1.2 1.9 1.4 1.2 Unit stream power (W/m2) 100 72 88 168 145 146 184 157 160 Total boundary shear stress (N/m2) 87 75 108 115 123 140 123 129 147 Shields parameter t*50 0.047 0.046 0.044 0.062 0.076 0.058 0.066 0.080 0.061 D50 (mm) 115 100 150 115 100 150 115 100 150 D50mobile (mm) 60 60 60 80 70 80 75 70 80 assuming subcritical flow and typical step‐backwater calcu- [18] The locations of the recovered tracers were resur- lations were performed. The substantial protrusion of the veyed after each of four summer recreational flow releases 3 bedrock ribs from the channel bed, which appear to exert a in 2006 (Qpeak =47m/s) and two annual hydrographs with 3 downstream hydraulic control, and the relatively shallow bed peak flows Qpeak in 2007 and 2008 of 81 and 88 m /s, slopes, support this assumption of subcritical flow. The fol- respectively (Figure 3). Tracers were recovered by walking lowing hydraulic variables were obtained from this modeling the channel in progression of the numbering sequence of the and used in both cross section and reach‐averaged scale initial installment. If a tracer was “missing” from its initial analysis (Table 2): streamwise velocity u, total boundary location, the surrounding channel was visually searched with- shear stress t, and unit stream power w. out disrupting the bed. We only searched for buried clasts in [17] To examine the effect of variable bed morphology on the well‐sorted patches associated with bedrock ribs, where coarse sediment transport within each reach, we divided we suspected vertical mixing. Transport distance was calcu- each reach into four to six zones (∼500 m2) of contiguous lated as the linear displacement of a tracer between each and internally consistent bed morphology (e.g., an alluvial resurvey. During each resurvey, we visually categorized the patch with limited bedrock rib exposure versus a zone with local grain scale for each tracer. The corresponding mor- substantial bedrock exposure and high amplitude bedrock phologic zone and nearest cross section were determined ribs). We visually defined these zones in the field and used from the surveyed coordinates of each tracer after each the surveyed boundaries to assign each tracer to a given resurvey. zone after plotting the tracer locations and morphological [19] Tracers were considered mobile if the calculated zones. These zones typically did not span the channel width. transport distance between surveys was greater than the Within each morphologic zone, we calculated the standard particle diameter. This accommodated for any error inherent deviation of the bed elevation Zstdev, from bed topography to repeat surveys. We minimized this type of error by con- points that were sampled at a 1 m resolution. We also sur- sistently reoccupying the setup location of the laser total veyed transects, orthogonal to the bedrock ribs, to calculate station, so that the backsight did not exceed 5 mm in distance the mean amplitude of the bedrock ribs A within each zone or elevation. Also, we consistently surveyed the patch of paint and reach. These values provided a quantitative metric for on the boulder‐sized tracers, which enhanced our confidence comparing the mesoscale variability in morphology. that repeat surveys reliably documented the same location on

Figure 3. Annual hydrograph for Ocoee No. 3 for 3 years of study. Note the systematic fluctuations in summer recreational release flows. Hourly discharge data were obtained from the TVA. 5of14 W11524 GOODE AND WOHL: COARSE SEDIMENT TRANSPORT IN A BEDROCK CHANNEL W11524

matched to the original number and included in the recovery. Despite these difficulties, recovery rates remained above 60% in all three reaches (61%, 63%, and 70%, respectively).

4.1. Grain Size‐Dependent Transport Distance [21] An examination of the transport distance of mobile tracers after each recovery indicated trends in transport distance and grain size were not consistent for all reaches, all recovery periods, or for all grain size classes (Figure 5). In 2006 and 2007, Reach 1 showed a decrease in transport distance with increasing grain size, only for the finer tail of the size distribution (D < 54 mm, in D < 108 mm, respectively). Reach 2 also showed a similar trend in 2007, only for D < 108 mm. In 2008, this trend occurred in all three reaches for D < 108 mm. Considering the cumulative transport distance over the study period, Reach 2 and Reach 3 showed a decrease in transport distance for D < 152 mm. These grain Figure 4. Size distribution of painted tracers, which were size threshold values, for which transport distance depends on sampled from the existing bed material in each reach. grain size, compare well to the size of the D50 within each reach (Table 1 and Figure 4). [22] Transport distance was a significant function of grain each tracer, and transport distances were not misrepresented size only in Reach 1 and Reach 2 in 2007 (P < 0.01) and by inconsistent survey points. Reach 1 in 2008 (P = 0.01), based on regression analyses of nonbinned, log‐transformed data in each reach. Although 4. Results this result in these two reaches supported the alternative hypothesis that transport distance is a function of grain size, [20] The size distributions of tracers in the three reaches inconsistency in these relationships among all three reaches were relatively similar (Figure 4), with median sizes D50 of resulted in a failure to reject the first null hypothesis that 115, 100, and 110 mm, respectively. This consistency allowed transport distance is not a function of grain size in all reaches. interreach comparisons of transport dynamics without adjust- Lack of a significant result in all three reaches led to the ing for differences in the bed material size distribution. In all second hypothesis, which investigated reach scale controls on three reaches during the recoveries between summer flows in transport distance. the first year (2006), the recovery rate was nearly 100% (Table 3). There were several cases in the 2007 and 2008 resurveys where the tracer number was indistinguishable. Renumbering and 4.2. Interreach Variability in Transport Distance measurement, along with spatial comparison to the previous [23] The size distributions of the tracers that were trans- year’s location, allowed for these tracers to be accurately ported during the entire study period were similar for all

Table 3. Summary of Transport Distances and Tracer Sizes Transporteda

3 Year Qpeak (m /s) nmobile % Recovered Lmean (m) Lmax (m) LD50 (m) D50mobile (mm) DLmax (mm) Reach 1 2006 (1) 48 81 99 0.38 ± 0.06 2.4 0.40 70 50 2006 (2) 47 166 99 0.27 ± 0.05 6.4 0.23 60 110 2006 (3) 48 129 99 0.16 ± 0.01 1.2 0.10 50 75 2006 (4) 46 110 99 0.22 ± 0.04 3.7 0.58 55 55 2006 (mean) 47 122 99 0.3 ± 0.04 3.4 0.33 59 73 2007 81 142 77 3.5 ± 0.39 27 2.7 80 50 2008 89 68 61 4.7 ± 0.71 29 4.2 75 45 Cumulative 266 4.2 ± 0.40 40 4.7 75 35 Reach 2 2006 (1) 48 117 99 0.2 ± 0.02 1.1 0.23 60 65 2006 (2) 47 86 99 0.27 ± 0.10 8.0 0.18 55 20 2006 (3) 48 73 99 0.2 ± 0.04 2.7 0.08 45 65 2006 (4) 46 94 99 0.16 ± 0.02 1.3 0.14 85 25 2006 (mean) 47 93 99 0.2 ± 0.04 3.3 0.16 61 44 2007 81 112 82 0.87 ± 0.13 7.4 0.81 70 25 2008 89 55 61 2.8 ± 0.81 26 2.5 70 105 Cumulative 232 2.5 ± 0.26 29 2.5 80 20 Reach 3 2006 (1) 48 127 99 0.45 ± 0.06 4.0 0.38 55 90 2006 (2) 47 105 99 0.35 ± 0.06 5.2 0.32 50 85 2006 (3) 48 179 99 0.34 ± 0.04 4.2 0.28 75 20 2006 (4) 46 168 99 0.36 ± 0.03 3.1 0.40 70 50 2006 (mean) 47 145 99 0.4 ± 0.05 4.1 0.34 63 61 2007 81 130 73 1.2 ± 0.16 12 0.36 80 30 2008 89 69 70 1.9 ± 0.32 14 2.6 80 30 Cumulative 227 2.3 ± 0.20 27 1.8 90 30

a Lmean, mean transport distance for all tracers in the reach; Lmax, maximum transport distance of an individual clast; LD50, transport distance of the median grain size; D50mobile, median grain size of mobile tracers only; DLmax, grain size of the farthest transported tracer. 6of14 W11524 GOODE AND WOHL: COARSE SEDIMENT TRANSPORT IN A BEDROCK CHANNEL W11524

Figure 5. Transport distance versus the tracer size. Tracers are binned into 0.5 size diametric classes ( = −log2D (mm)), and transport distances represent the mean for all tracers in that size class, with corresponding standard errors. Each plot shows results from that recovery period. The 2006 plot shows averages for all four resurveys during summer release flows. The cumulative plot represents the total transport over entire study period.

three reaches (Figure 6). Whereas the median grain size of parameters for the D50 in each reach ranged from 0.04 to all the transported tracers, D50mobile, did not vary greatly 0.05inthe2006flowsandfrom0.06to0.08forthe2007 among the three reaches, the corresponding transport dis- and2008peakflows. tance for tracers of that size, LD50, varied substantially, with [25] Comparison of the distribution of transport distance the largest LD50 in Reach 1 (Table 2). In the 2008 resurvey after the 2007 and 2008 recoveries indicated that more tra- after the largest peak flow (89 m3/s) and the longest duration cers were transported longer distances in Reach 1 (Figure 7). of flows (Figure 3), LD50 in Reach 1 was roughly 2 times the More tracers were transported shorter distances in Reach 3, distance in Reach 2 and Reach 3 (LD50 = 4.21, 2.45, and whereas Reach 2 yielded an intermediate distribution of 2.55 m, for D50mobile = 75, 70, and 80 mm, respectively). transport distances. In all reaches, more tracers were trans- Considering the sediment sizes and transport distances inte- ported longer distances during the 2008 flows, which were grated over the entire 3 year study period the median grain longest in duration and had the highest peak discharge in the size mobilized varied slightly between the three reaches study period. According to the Tukey HSD multiple com- (75, 80, and 90 mm, respectively). parison tests on the log‐transformed mean transport distance [24] Reach‐averaged hydraulic data from HEC‐RAS between reaches, Reach 1 was consistently associated with modeling of all peak flows are presented in Table 2. The significantly greater transport distances than the other two trends in total boundary shear stress in each reach were reaches (Figure 8). Transport distances in Reach 2 and Reach 3 consistent with the D50mobile in each reach. For example, were statistically similar after all resurveys. Hypothesis 2 was Reach 3 was associated with the largest D50mobile,aswell partly rejected because the mean transport distances were not as the greatest total boundary shear stress. The Shields significantly different in all three reaches: transport distances

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the bed topography Zstdev were relatively low, which indicated that at the zone scale, these metrics were not a significant control on transport distance. Also, in Reach 3, pairwise comparison of all zones, using the Tukey HSD following ANOVA, indicated that the only zones with significantly different mean transport distances had similar mean rib amplitudes (A = 0.65 and 0.69 m, respectively) and standard deviations of the bed elevation (Zstdev = 0.33 and 0.36 m, respectively) within each zone. Within each reach, at the scale of morphologically similar zones, neither bedrock rib amplitude nor topographic variability controlled differences in transport distance. [28] In all three reaches and for both recovery periods, there was a strong relationship between transport distance and the local scale characteristics (unconstrained, shielded, imbricated, buried embedded; Table 4). In Reach 1, particles that were unconstrained by surrounding grains and unobstructed by bedrock ribs were transported the greatest dis- Figure 6. Size distribution of mobile tracers from each tances (Figure 11). In some cases, particles that were reach over the entire study period. Tracers were considered shielded by ribs were transported unexpectedly long dis- mobile if transport distances were greater than one particle tances, which may have been a result of local turbulence diameter in at least one resurvey period. fluctuations in the wake zones of ribs. Pairwise comparisons of all local scale categories, using the Tukey HSD following in Reach 1 were significantly different from the other two reaches, but transport distances were not significantly different in Reach 2 and Reach 3.

4.3. Intrareach Variability in Transport Distance [26] Transport distance according to the three spatial scales (cross section, zone, local) was considered for the 2007 and 2008 resurveys only, because these categorical variables from the four 2006 resurveys varied in each of the four resurveys. ANOVA of transport distance by cross‐sectional differences was not significant in either the 2007 or 2008 recovery period in any of the reaches (Table 4). Within each reach, transport distances did not differ significantly when the tracers were grouped according to the cross section for which they were nearest to in the proceeding survey. This suggested that differences in cross‐section averaged hydraulics cannot account for differences in coarse sediment transport. In Reach 1, despite a nearly twofold difference in unit stream power between two cross sections, mean transport distances of the groups of tracers referenced to those cross sections, were not significantly different between these groups (Figure 9). [27] Considering the morphologically similar zones, significant differences in mean transport distance were not consistently controlled by zone scale differences in bed topography (i.e., bedrock rib amplitude). In Reach 1, transport distance was significantly different in some of the zones, but not in the zones that we expected to correspond to these differences (Figure 10, 2007). For example, the mean transport distance in the zone where the bedrock rib amplitude was lowest (A = 0.42 m) was not significantly different than the mean transport distance of tracers in the zone where the bedrock rib amplitude was the highest (A = 0.65 m). For the 2007 tracer recovery, the significant ANOVA results indicated zone scale differences in transport distance in Reach 1 and Reach 3 (Table 4). Zone scale differences were not associated with significantly different mean transport distances in Reach 2 for 2007 or any reach for the 2008 recovery. Figure 7. Cumulative distributions of transport distances The mean transport distances were not greater in bed regions after the 2007 and 2008 resurveys for all three reaches. Cor- where the bedrock rib amplitude A and standard deviation of responding flows are reported in Table 2. 8of14 W11524 GOODE AND WOHL: COARSE SEDIMENT TRANSPORT IN A BEDROCK CHANNEL W11524

Figure 8. Reach scale variation in transport distances. Years indicate the resurvey period. The box plots indicate upper and lower quartiles as box ends, 10th and 90th percentiles as whiskers, and median values as the line within each box. Dots indicate values outside the 10th and 90th percentiles. Transport distances were log‐transformed for normality. Different mean transport distances are indicated by contrasting letters above each box (Tukey’s HSD following ANOVA on log‐transformed data, P < 0.05).

ANOVA, consistently showed that the transport distance of (P < 0.01 in both years; adjusted R2 = 0.48 and 0.32 for unconstrained tracers was significantly different (P < 0.05) 2007 and 2008, respectively). Both parameters in these models from imbricated, shielded, or buried particles, in all three were also significant at P < 0.01. reaches and for both years. The significant difference in [30] Recognizing that the local scale sediment character- transport distance according to local scale distinctions pro- istics had the strongest influence on transport distance, we vided support for hypothesis 3. This hypothesis was more reexamined the relationship between transport distance and rigorously tested in a multiple regression analysis. grain size by stratifying the data according to local catego- [29] Multiple linear regression with model selection, based ries (Figure 12). For the unconstrained tracers, transport on the minimum Akaike’s Information Criterion (AIC) distance was a significant power function of grain size (L = [Burnham and Anderson, 2002] and adjusted R2, further aDb) in Reach 1 and Reach 2 in 2007 (P < 0.01, R2 =0.54, supported that local scale characteristics explained the largest and P <0.01,R2 = 0.53). No other significant relationships proportion of the variability in transport distance (supporting were found for nonlinear regression analyses of grain size hypothesis 3). The parameters tested in these models and transport distance. included: tracer size D (mm), Reach (categorical), total t boundary shear stress , (at the nearest cross section), mean 5. Discussion rib amplitude within the morphologic zone, A, and the local scale (categorical). The best one‐parameter model included 5.1. Controls on Transport Distance only local scale classification (P < 0.01 in both years; adjusted [31] Transport distance was a significant function of grain R2 = 0.45 and 0.20 for 2007 and 2008, respectively). The size in Reach 1 and Reach 2, but not in Reach 3. As one best two‐parameter model included the reach and local scale possible explanation for this, bedrock ribs were oriented 9of14 W11524 GOODE AND WOHL: COARSE SEDIMENT TRANSPORT IN A BEDROCK CHANNEL W11524

Table 4. Summary of ANOVA Analysis of Transport Distance by grain size. Also, grain size did not appear as a significant Intrareach Spatial Scalea explanatory variable in any of the models, which further indicates that in this bedrock river, bedrock rib character- 2007 istics at the reach scale, and variations in morphology and XS ZONE LOCAL sediment architecture at the local scale, are the most FPFPF Pimportant controls on sediment transport. Reach 1 1.77 0.14 3.46 0.005 19.2 <0.0001 Reach 2 0.52 0.47 0.76 0.47 8.9 <0.0001 5.2. Different Controls on Coarse Sediment Transport Reach 3 1.44 0.23 3.79 0.006 36.1 <0.0001 in Alluvial and Bedrock Channels 2008 [34] It is well established that bed load transport is an event XS ZONE LOCAL dependent process and, whether or not transport distance is FPFPF Psize dependent, is controlled by the flow conditions and sediment structure [e.g., Parker, 2008]. If size‐dependent Reach 1 1.15 0.34 1.56 0.19 26.3 <0.0001 Reach 2 0.22 0.64 0.93 0.40 19.3 <0.0001 transport is governed by similar processes in alluvial and Reach 3 0.48 0.70 1.59 0.21 6.8 <0.0001 bedrock channels, then we would expect transport distance to be size dependent when the Shields stresses t* are 1.5– a 50 Bolded values indicate significance (P < 0.05). XS, cross‐section scale; 2.0 times the dimensionless critical shear stress of the ZONE, scale of morphologically similar bed zones; LOCAL, local scale characteristics. parallel to flow in both of these reaches, leaving down- streamflow and sediment transport generally unobstructed (Figure 2a). In Reach 3, where bedrock ribs were oblique to flow and of greater amplitude (Table 1), transport distance was not a significant function of grain size after any recovery period (Figures 5 and 12). Because the trend in transport distance and grain size was not similar in Reach 3, where the bedrock rib characteristics were the most different from the other two reaches, it is likely that bedrock ribs influence sediment transport when they are oriented oblique to flow. In Reach 3, the Manning’s roughness was substantially larger than in Reach 1 and Reach 2, suggesting that bedrock ribs account for a large proportion of the total roughness. Hence, less of the total boundary shear stress is available for sediment transport in Reach 3. This may also explain why Reach 3 did not show a trend in transport distance with grain size in any of the recovery periods. As a result, where bedrock ribs are larger in amplitude and oriented in a direction that obstructs flow and sediment transport, these bedrock bed forms exert the greatest control on sediment transport. [32] The central finding from this field study (variable bedrock topography (bedrock ribs) influences sediment transport distance) corresponds well with experimental observa- tions of sediment transport patterns in bedrock channels with spatial variation in bed topography [Johnson and Whipple, 2007, 2010; Finnegan et al., 2007; Chatanantavet and Parker, 2008]. In the field, the additional boundary roughness supplied by bedrock ribs most likely limits the amount of boundary shear stress required to transport coarse sediment. This was apparent from the lower transport distances Figure 9. Box plot comparing the transport distance of in Reach 3 (oblique ribs and largest hydraulic roughness, n). tracers linked to the nearest cross sections in Reach 1. Similarly, experimental studies have shown that erosional bed (a) Transport distance (2007) by cross section (ANOVA, forms act to dissipate energy and reduce the sediment trans- F = 1.77, P = 0.14). (b) Transport distance (2008) by cross port capacity [Johnson and Whipple, 2007; Finnegan et al., section (ANOVA, F =1.15;P = 0.34), so comparison of 2007; Chatanantavet and Parker, 2008]. means was not appropriate. The box plots indicate upper [33] In a comparison of variables thought to control and lower quartiles as box ends, 10th and 90th percentiles transport distance at different spatial scales, none of the as whiskers, and median values as the line within each box. models selected in the multiple regression analysis explained Dots indicate values outside the 10th and 90th percentiles. more than 50% of the variability in transport distance. Hydraulic variables at each cross section: streamwise velocity However, more variability was explained by the local scale u, total boundary shear stress t, and unit stream power w, bedrock topography and sediment architecture than the were obtained from HEC‐RAS modeling of the peak dis- relationships of transport distance as a power function of charge between recoveries [Goode and Wohl, 2010]. 10 of 14 W11524 GOODE AND WOHL: COARSE SEDIMENT TRANSPORT IN A BEDROCK CHANNEL W11524

forms that intersect and obstruct the flow (oblique ribs), processes that control coarse sediment transport are not similar to alluvial channels. Furthermore, the transport distance of unconstrained clasts in Reach 3 (oblique ribs) was not dependent on tracer size as has been reported in alluvial studies [Church and Hassan, 1992]. [35] Similar to alluvial channels, where variations in channel morphology and sediment structure at different scales are an important control on variations in transport distance [Ferguson et al.,2002;Lisle et al., 2000; Wilcock and Crowe, 2003], the variations in bedrock topography also control bed load transport differences, but at scales potentially smaller than bed form scales of alluvial channels [Schmidt and Gintz, 1995; Thompson et al., 1996; Cudden and Hoey, 2003]. In alluvial channels, long‐term storage can occur through deposition in bars, zones of reduced velocity, or clast burial [Ferguson and Hoey, 2002; Ferguson et al., 2002]. The bedrock reaches examined here behave similar to these alluvial systems, but it is the variation in

Figure 10. Box plot comparing tracer transport distance by zone topographic metrics in Reach 1. (a) Transport distance (2007) by zone (ANOVA, F = 3.46, P < 0.01). Signif- icant pairwise differences in means (P < 0.05) are indicated by contrasting letters above each box (Tukey’s HSD following ANOVA on log transformed data). (b) Transport distance (2008) by zone was not significant (ANOVA, F = 1.56; P = 0.19), so comparison of means was not appropriate. The box plots indicate upper and lower quartiles as box ends, 10th and 90th percentiles as whiskers, and median values as the line within each box. Dots indicate values outside the 10th and 90th percentiles. Zstdev is the standard deviation of the bed elevation within the bed zone, and A is the mean amplitude of bedrock ribs within that area. Boxes are in order of increasing A from left to right.

D50 t*c50, as demonstrated in gravel bed streams by Ferguson and Wathen [1998], Wilcock and Crowe [2003], and Parker [2008]. When the dimensionless Shields stresses were within this range for the 2007 and 2008 peak flows (t*50 = Figure 11. Box plot comparing tracer transport distance 0.06–0.08, compared to for bedrock rivers tc50* = 0.03) by local hydraulic environment classification in Reach 1. [Sklar and Dietrich, 2004], transport distance was size (a) Transport distance (2007) by local classification (ANOVA, dependent in Reach 1 (2007 and 2008) and Reach 2 (2007 F =19.2;P < 0.01). (b) Transport distance (2008) by local only), both of which have longitudinal ribs. Although the classification (ANOVA, F = 26.3; P < 0.01). Significant pair- dimensionless Shields stress was also within this range in wise differences in means (P < 0.05) are indicated by contrast- Reach 3 for both years, size‐dependent transport did not ing letters above each box (Tukey’s HSD following ANOVA occur. This suggests that, in bedrock channels with bed on log transformed data). The box plots indicate upper and forms that do not intersect the flow (longitudinal ribs) ,the lower quartiles as box ends, 10th and 90th percentiles as whis- processes controlling coarse sediment transport are similar kers, and median values as the line within each box. Dots indi- to alluvial channels. However, in bedrock channels with bed cate values outside the 10th and 90th percentiles.

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Figure 12. Transport distance versus the tracer size segregated by local scale categories for each reach in 2007 and 2008. Transport distance is significantly (P < 0.05) correlated with grain size only for unconstrained tracers in Reach 1 in both years and Reach 2 in 2007. bedrock morphology (bedrock rib geometry) that controls transport may be influenced by factors that are similar to variability in transport distance. Because the unconstrained alluvial systems, only in bedrock rivers with relatively tracers showed some size dependence in transport distance in homogenous bed topography. On the other hand, if the Reach 1 and Reach 2, but not in Reach 3, coarse sediment underlying bedrock lithology and structure create strong 12 of 14 W11524 GOODE AND WOHL: COARSE SEDIMENT TRANSPORT IN A BEDROCK CHANNEL W11524 heterogeneity in bed forms and channel morphology, then ronment, here, variations in bedrock morphology set up the local scale factors are the dominant control on sediment conditions for burial and vertical mixing. transport. The key difference is that bed forms in bedrock channels can be partly controlled by independent processes (structure and lithology), whereas bed forms in alluvial 6. Conclusions channels are directly related to the flow and sediment prop- [40] This study demonstrates that lithologic and structural erties. The bedrock ribs examined here exert a strong control controls on bedrock channel topography (bedrock ribs) exert on transport patterns at the reach scale. Also, the finest spatial a major control on the transport dynamics of coarse material resolution of intrareach variability, which captures local over time scales up to 3 year and spatial scales up to 102 m. variation in bedrock ribs, was the best predictor of coarse A comparison of three reaches with different bedrock rib sediment transport distance. orientations and amplitudes indicated that where bedrock ribs were longitudinal to flow and of lower amplitude, transport was less obstructed, which led to greater transport distances 5.3. Temporal Scales and Resolution than in reaches where the bedrock ribs were oblique to flow [36] Although transport distance was not consistently and of larger amplitude. Under similar flow conditions for related to grain size over the study period, it is possible that which size‐dependent transport has been observed in alluvial at longer time scales transport distance varies more closely channels (dimensionless Shields stress within 1.5–2.0 times with grain size. This is because local scale controls that the dimensionless critical shear stress), transport distance was influence transport distance during single flows might a significant function of grain size where bedrock ribs were become less important when averaged over longer time longitudinal to flow. Where bedrock ribs were oriented at a spans that include multiple transport events. high angle to flow however, greater reach scale roughness and [37] The D50 of the unrecovered tracers was similar to the lower reach‐averaged velocity corresponded to lower trans- D50 of the mobile tracers in the last resurvey. This suggests port distances with no relation to tracer size. Because local that unrecovered particles were transported, despite unknown scale bedrock topography and sediment architecture corre- transport distances. It is uncertain whether these particles lated most strongly with tracer transport distance, channel bed were transported beyond the reach or moved to locations properties at this scale (100–101 m) likely play a dominant within the highly variable alluvial deposits and bedrock role in the transport of coarse sediment. The importance of channel bed topography (i.e., within potholes or between local scale variables and the lack of size dependence on coarse bedrock ribs). Although the recovery rates were relatively sediment transport distance where bedrock ribs are oriented large between surveys, there are inherent difficulties in using oblique to flow may limit the use of reach scale sediment visually identified tracers. For example, it was necessary to transport formulas, developed for gravel bed streams, in repaint and number most tracers each year because Sun bedrock channels with similar morphologic variability. bleaching and algal growth obscured the tracer number. [38] The shorter transport distances recorded after the four 3 summer 2006 flows (47 m /s) may reflect the shorter tem- [41] Acknowledgments. This study was funded by the National poral resolution, which facilitates documenting transport Science Foundation grant EAR‐0507098. We thank William Stubblefield, distances that may be closer to the hop length of single William Lyons, and Roy Syrmanske for their valuable field assistance. Dmitri Hawk and the Tennessee Valley Authority supplied discharge records transport events. However, these flows were also half the for the Ocoee No. 3 dam. The manuscript benefited greatly from insightful magnitude of the yearly peak, after which larger transport and thorough reviews by Phairot Chatanantavet and two anonymous distances were measured. It is not clear how the magnitude reviewers. Kristen Jaeger and Kyle Nichols provided helpful reviews of an of individual flow peaks affects the integration of all flow earlier draft. events. Complexity in coarse sediment transport in this system is also demonstrated by some clasts being transported References ∼ upstream ( 5 m). These few upstream transport events always Beschta, R. L. (1987), Conceptual models of sediment transport in streams, occurred in sites with substantial bedrock rib exposure, which in Sediment Transport in Gravel Bed Rivers,editedbyC.R.Thorne, suggests complex flow patterns in these areas. The turbulent J. C. Bathurst, and R. D. Hey, pp. 387–419, John Wiley, Chichester. flow structure that is typically associated with bed forms Burnham, K. P., and D. R. Anderson (2002), Model Selection and Multi- ‐ [Nelson et al., 1995; Papanicolaou et al., 2001] is likely to model Inference: A Practical Information Theoretic Approach,2nded., Springer, New York. play an important role in determining sediment transport Chatanantavet, P., and G. Parker (2008), Experimental study of bedrock dynamics. channel alluviation under varied sediment supply and hydraulic condi- [39] Spatial variations in turbulence structure and thereby tions, Water Resour. Res., 44, W12446, doi:10.1029/2007WR006581. sediment flux, which are not describable in terms of local Chatanantavet, P., and G. Parker (2009), Physically based modeling of bedrock incision by abrasion, plucking, and macroabrasion, J. Geophys. bed shear stress, are important aspects of coarse sediment Res., 114, F04018, doi:10.1029/2008JF001044. transport [Nelson et al., 1995; Papanicolaou et al., 2001]. Church, M., and M. A. 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