Thresholds of erosion and sediment movement in bedrock channels

Geomorphology 118 (2010) 301–313

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Geomorphology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / g e o m o r p h

Thresholds of erosion and sediment movement in bedrock channels Ahmed Siddiqui, André Robert ⁎ Department of Geography, York University, 4700 Keele St, Toronto, ON, Canada M3J 1P3

a r t i c l e

i n f o

Article history: Received 5 October 2009 Received in revised form 15 January 2010 Accepted 18 January 2010 Available online 25 January 2010 Keywords: Bedrock river Sediment transport Shear stress Channel survey

a b s t r a c t This study examines the erosive resistance of the discontinuous, loose joint blocks of various sizes that comprise the bed material of the Etobicoke Creek, an incised bedrock channel found in an urbanized setting within the city of Toronto, Ontario, Canada. In order to accomplish this, both field and laboratory experiments were conducted on the bed material found in this channel. The field work involved repeated detailed surveying of the channel bed and estimations of distances of movement of various clasts during many sediment transport events. We found that rates of erosion and/or deposition can be significant during the snowmelt spring events and that there was a greater loss of bed material over the study reach than was gained in several spots, with bed lowering > 0.10 m in some locations. The field work also showed that the distances moved by the rock clasts scaled directly with shear stresses observed during rain events and that average distances of transport tend to be short. The frequency distributions of distance of transport scaled with particle size is log-normally distributed. Flume experiments demonstrated that the clasts offered different levels of resistance to movement, depending on their orientation. The platy nature of the rock fragments, clast orientation, and their imbrication significantly affect the threshold of erosion. The results have significant implications for the understanding of bedrock rivers from a management perspective, especially in the case of those rivers experiencing the effects of urban development in their drainage basins. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Bedrock channels include those reaches formed solely in bedrock, channels where bedrock is permanently exposed in the channel bed, and channels along which bedrock may be exposed during high flows. Generally, bedrock rivers can be differentiated from alluvial channels by a few main features. The morphology of these channels is influenced by the physical characteristics of the bedrock as well as the hydraulic and sediment transport characteristics of the river (Ashley et al., 1988). Here, sediment transport capacity often exceeds sediment supply in the long term, meaning that more sediment can be removed from these channels than is brought in. As a result, sediment storage in these channels is minimal (Ashley et al., 1988; Tinkler and Wohl, 1998a; Whipple, 2004). This implies that material removed from the bed may lower the base level of all points upstream. Similarly, the material removed from the walls is not replaced (Ashley et al., 1988). However, this does not mean that it is common to find long stretches of bare bedrock along the bed and banks of these channels, as these are in fact quite rare. Temporary sediment fills or patchy mantles of alluvium may be produced or persist, via the rapid delivery of sediment from hillslopes, as a result of landslides, land use changes, and other disturbances in the landscape.

⁎ Corresponding author. Tel.: + 1 416 736 5107; fax: + 1 416 736 5988. E-mail address: [email protected] (A. Robert). 0169-555X/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2010.01.011

Channel processes that contribute to bed erosion in bedrock rivers include plucking, abrasion, and cavitation. Some additional causes do exist, such as chemical and physical weathering, but these are more important in the preparation for erosion than the actual erosion itself (Baker, 1973; Wohl, 1993; Wohl et al., 1994; Baker and Kale, 1998; Hancock et al., 1998; Sklar and Dietrich, 1998; Whipple et al., 2000; Hartshorn et al., 2002; Whipple, 2004; Jansen, 2006). Several researchers (e.g., Hancock et al., 1998; Sklar and Dietrich, 1998; Whipple et al., 2000; Whipple, 2004) have discussed the mechanics and relative efficacy of these processes as well as bedforms sculpted in rock channels (Tinkler, 1993, 1997; Wende, 1999). These processes all include critical thresholds, which indicates that most work may be done by large floods (Baker, 1973; Vaughn, 1990; Wohl, 1993; Wohl et al., 1994; Baker and Kale, 1998; Tucker and Bras, 1998; Whipple et al., 2000; Hartshorn et al., 2002; Whipple, 2004). Lithology plays the strongest role in determining which of these is a dominant process (Hancock et al., 1998; Jansen, 2006). Indeed the river's sediment plays a significant role, by providing the tools for erosion and by protecting the bed when bedload is abundant (Sklar and Dietrich, 1998; Whipple et al., 2000; Whipple, 2004; Wobus et al., 2006). Bedrock channels are often seen as “fixed conduits.” The geometry of bedrock channels can therefore be viewed as fixed within the time frame of individual floods and, as a consequence, the flow must adjust to channel geometry (Carling, 2006). Bedrock reaches with high water surface slopes or a greater incidence of boulders in the channel also are characterized by high friction factor coefficients. These high values

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suggest that the flow is severely nonuniform and the resistance coefficients are being used to quantify the effects of energy dissipation from hydraulic jumps and internal distortions resulting from highly irregular planforms, boulders, constrictions and other disturbances (Carling and Tinkler, 1998; Carling et al., 2002; Heritage et al., 2004). This provides a reach-scale focus for investigations of bedrock channel hydraulics, flow routing, and sediment transfer mechanisms, which are of increasing relevance to land use and water resource development (Tinkler and Wohl, 1998a; Carling, 2006). Bedrock rivers may also comprise much of the headwater networks of some major rivers. A thorough understanding of the channel hydraulics and sediment transport processes, as well as the connectivity with other parts of the system, is therefore essential (Tinkler and Wohl, 1998a; Carling, 2006). The processes of fluvial incision and transport obviously play a significant role in controlling morphology and sediment flux. Therefore, an understanding of these processes is needed. However, no theory exists for incision and sediment transport by bedrock rivers. This is especially important when attempting to quantify erosion in channels composed of materials with low-erosion resistance. Similarly, a dearth of information is available on the bed lowering rates in rock-confined channels and recession rates of the channel margins (Carling, 2006).Whipple et al. (2000) showed through a simplified analysis of erosion by plucking that the rate of erosion would increase almost linearly with increasing bed shear stress over the critical threshold. However, the equations used apply to alluvial channels in general, and it is of interest to test whether they can be applied to such bedrock channels as Etobicoke Creek (see Section 2 below), which are dominated by discontinuous, angular joint blocks. Repeated surveys of the bed topography in a bedrock environment and monitoring of the transport distances of angular and platy rock clasts were undertaken in this study to better assess bedrock erosion and fluvial incision in an urbanized channel. Furthermore, complementary flume experiments were undertaken to assess thresholds of initial motion for sedimentary rock clasts originating from the field site. These experiments are complementary to the field measurements as they provide further information on the erosivity of the bed surface in bedrock environments, allowing us to specifically determine how the orientation and imbrication of sedimentary rock clasts affect thresholds of initial motion and, ultimately, distances of transport. The overall purpose of this study is therefore to examine the erosive resistance of angular rock clasts in a bedrock channel in the Toronto area of southern Ontario and add to the local knowledge about such streams. The specific research objectives are to (i) determine the intensity of bed erosion from field observations (surveys) and overall trends in bed topography (i.e., whether there is a net accumulation or loss of sediment or if the bed remains stable over time); (ii) examine the relations between the size of the clasts, distances moved by the rock fragments, and associated bed shear stresses; and (iii) estimate the thresholds necessary to initiate erosion using field and laboratory tests. Given the platy nature of the rock clasts, particular attention will be paid to the particle orientations and their role in either promoting or restricting initial movement. 2. Study site description The selection of an appropriate study site for in situ research on bedrock channels involved the consideration of several criteria: (i) the presence of channels with beds dominated by bedrock, where the necessary experiments could be carried out, was the foremost consideration; (ii) an actively eroding channel would be essential to study the conditions under which the thresholds for erosion are met; and (iii) proximity and accessibility of the study area.

Etobicoke Creek, a stream in the city of Toronto, was determined to be suitable for the purposes of this study, fulfilling the required criteria (Fig. 1). This particular channel originates in the rural area NW of Toronto, draining a total area of 211 km2 and ending into Lake Ontario in the south (Fig. 1). Bedrock is visible in a few places within the Etobicoke Creek watershed, most notably in the high valley walls of this creek south of Highway 401 (Toronto and Region Conservation Authority (TRCA), 1998; Fig. 1). This makes the Creek an ideal site for the study of the erosive resistance of bedrock clasts in such fluvial environments. The landscape in the region is underlain by a series of sedimentary rocks of early- and mid-Palaeozoic age. The bedrock in the Etobicoke Creek watershed consists primarily of Silurian and Ordovician shale (Coleman, 1913; Sharpe, 1980; Chapman and Putnam, 1984; Tinkler and Parish, 1998; Sharpe et al., 1999). Much of this bedrock is obscured by glacial deposits. Bedrock, however, is exposed in certain sections of the Etobicoke Creek (Toronto and Region Conservation Authority (TRCA), 1998; Singer et al., 2003), specifically in the study area. Presently, the land is largely urbanized with the current land use in the watershed characterized as industrial (22%), institutional (7%), commercial (2%), residential (22%), open space (22%), agricultural (21%), and the remaining 4% for future development (Toronto and Region Conservation Authority (TRCA), 1998). The creek has cut a well-defined valley through the landscape with valley walls 8–12 m high (Toronto and Region Conservation Authority (TRCA), 1998). Fig. 2 shows some photographs of the study area during a period of low flow. As mentioned earlier, the bedrock is primarily shale and interbedded siltstone and limestone. The bed consists predominantly of a large number of discontinuous loose joint blocks of various sizes of material derived from the bedrock and valley walls. The walls of the channel display clear examples of channelized bedding, suggesting a long-term trend of erosion and backfilling. From the characteristics of the bed material, we inferred that the dominant process of erosion in this channel is plucking and that the bedload consists of these locally derived angular joint blocks, a process illustrated by Hancock et al. (1998) and Whipple et al. (2000). A 283-m long section was selected in the Etobicoke Creek watershed to conduct the fieldwork. While the area around the creek is urbanized, the study area itself is relatively undisturbed, given its location in a park at the bottom of a ravine. The average bedslope in the study area was determined to be 0.0011 m/m, which is close to those found by other authors for nearby streams in the Greater Toronto Area (e.g., Lofthouse and Robert, 2008). 3. Methods 3.1. Field measurements The acquisition of data was spread over two seasons, 2006 and 2007, with the work divided into fieldwork conducted at the study site and laboratory work conducted in the flume laboratory facility at York University. The following section describes each aspect of the research conducted over the two field seasons. A standard tool used to record the changes in form and nature of the channel at discrete intervals in time is the topographic survey (Downward, 1995; Gurnell et al., 2003; Lofthouse and Robert, 2008). The estimation of change from topographic survey information involves the measurement of the differences in form between likeindices recorded at defined points in time. The rate of change is the net recorded change in a particular variable over the period separating the individual observations (Downward, 1995). Diachronic comparison of topographic records requires sets of comparable data (Gurnell et al., 2003). One widely adopted methodology in the analysis of river channel change from topographic information is to estimate change from planform information (Downward, 1995). Measurements of bed topography to determine changes in bed elevation were made three times over the two field seasons. These

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Fig. 1. Map showing field site location in southern Ontario, Canada.

measurements were made using a Leica TPS700 Performance Series Total Station. Three-dimensional coordinates at the origin of the survey were obtained using a hand-held GPS unit and were then programmed into the Total Station. The bed was surveyed at 1-m intervals across the channel and downstream (a 1 m grid), and at every point surveyed, water depth was also recorded. The first measurements were made in August 2006, followed by surveys in May and August of 2007. The field surveys allowed the estimation of how much the bed evolved over a relatively short timescale. The measurements made in May were considered to be the most important, as they were made soon after the spring snowmelt, which is generally the period with the highest flows in the stream and, therefore, the most erosive. The slope of the bed and water surface could also be determined from the measurements made by the Total Station survey. However, long profiles of the water surface at low flows are strongly influenced by river discharge at the time of survey (Gurnell et al., 2003) and, as such, would not be suitable for diachronic comparisons. Tracers have been commonly used to obtain information on the fluvial transport of sediment. Tracers are marked particles that are introduced into the channel for the purpose of monitoring sediment transport processes (e.g., Hassan and Ergenzinger, 2003). Naturally or artificially labelled sediment can be used for tracing the paths and timing of sediment movement. One hundred clasts of a variety of sizes determined to be representative of the bed material were randomly selected over the entire length of the study reach and were marked with a black indelible marker, with each clast identified by a number. This sample size, while arbitrary, fits within the range of numbers used in the studies listed by Church and Hassan (1992). Both sides of the clasts were marked to improve the chances of recovering them. These clasts were replaced in the same positions from which they were sampled.

After each storm event, the entire length of the study area was searched for these clasts, and the locations of the clasts along the bed were recorded before replacing the clasts on the bed surface for the next flow event in a method similar to that outlined by Hassan and Ergenzinger (2003). A hand-held GPS unit was used to assist in the recovery of the clasts and to determine the distance they had migrated during a rain event. The percentages of clasts recovered varied from one sediment transport event to another, ranging between 69 and 95% (with an average of 86.1%). Before the clasts were marked, however, the sediment size was determined for the bed material. There are several reasons for the sampling of bed material, for purposes such as input for equations to calculate bed mobilization, bedload transport rates, and likelihood of scour and as a measure of grain roughness in the channel (Kondolf et al., 2003). One of the most common surface sampling methods is the pebble count, described by Wolman (1954). This procedure was used for the sampling of 100 clasts on the river bed. All three axes of the clasts were measured in this exercise. Average flow measurements were made multiple times over the field season using a flow meter. The first measurements were made at low flows at the same time the survey work was being done. Additional measurements of velocity were made during storm events (see below). To enable calculation of shear stress, measurements of flow depth are required in addition to slope. Peak-flow data can be obtained in several ways. A simple and inexpensive procedure involves the placing of crest-stage gauges along the study reach (Simon and Castro, 2003). One such gauge suggested by Tinkler and Wohl (1998b) involved the marking of a horizontal scale of meters along the channel walls. The markings were made with an indelible marker and were made large enough to be visible from the opposite

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Fig. 2. Photographs of the section of Etobicoke Creek under study. Arrows indicate direction of water flow.

bank, allowing the peak water level to be recorded during the event. Peak flow was then easily estimated after a rain event even when the water level receded, based on the maximum limit along the valley wall that was wetted. 3.2. Flume experiments 3.2.1. Laboratory conditions This study incorporated a flume study of some aspects of sediment entrainment. The platy nature of the rock clasts favors the formation of depositional structures such as imbrications. These structures, in turn, enhance bed stability; and particle orientation within imbricated structures must significantly affect thresholds of initial motion and distances of transport. Flume experiments were therefore conducted to

assess thresholds of initial motion using various particle orientations and flow stages. Natural bedrock sediment distributions and structures were simulated and detailed flow measurements were made over these features using an Acoustic Doppler Velocimeter (ADV) in a laboratory sediment transport channel. The flume used for the study is 8 m long, 0.60 m wide, and 0.50 m deep. The sides and bottom are made of Plexiglas housed on an aluminium base. The bed of the channel can be raised and lowered by a hydraulic lift, which can adjust the slope of the channel. There is a tailgate at the downstream end that allows the user to adjust the flow depth as required. Water is transported through the flume using two large pumps, which are also used to control discharge in the flume. Lawless and Robert (2001a,b) have demonstrated how natural bed features in gravel-bed rivers can be recreated in the flume. A similar

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approach was implemented in this study. Several clasts were brought back to the flume from Etobicoke Creek in numbers sufficient to line the entire length of the channel. All the clasts were marked for identification purposes, and the three axes of the clasts were measured. The clasts were then positioned along the flume bed, creating a bed surface similar to the natural setting. The slope was set to 0.2%, which was based on preliminary results from the topographical bed survey. Longitudinal profiles of the bed surface were surveyed using a digital depth gauge for each experiment. These measurements would primarily aid in determining the height of the flow above the bed surface. The middle section of the flume, located 3 m downstream of the headbox of the flume, was chosen as the study section. Any residual turbulence in the flow caused by the difference in cross-sectional areas would be negated at this distance downstream. The study reach was 2.1 m long, and with a width of 0.60 m, the area was 1.26 m2. Different sets of experiments were conducted in the flume by manipulating and reorienting the clasts. The first setup involved the placing of the clasts in no particular order, with some clasts leaning against the flow and others leaning toward the direction of the flow. Vertical velocity profiles were made at 15 different locations, each 15 cm apart. These profiles were made for two different flow conditions, with average flow depths of 10 and 20 cm, respectively. Each of the velocity profiles consisted of 13 vertical sampling points, with a greater number of sampling points near the boundary and fewer sampling points farther away. Velocity measurements were made for one minute (Buffin-Bélanger and Roy, 2005), with a sampling frequency of 20 Hz (i.e., 1200 measurements for a single sampling point). Linear regressions of velocity variation against the logarithm of the height above the bed in the near-bed region (e.g., Bergeron and Abrahams, 1992; Biron et al., 2004) provided estimates of roughness length that were subsequently used in the analysis of threshold of initial motion (as described below).

Fig. 3. (A) The arrangement of clasts, such that they leaned against the flow; (B) the arrangement of clasts, such that they leaned toward the direction of flow.

3.2.2. Experiment 1 In this experiment, the conditions under which entrainment began were quantified. For this part, both pumps were turned on to the maximum setting allowed, and the height of the tailgate was lowered

Fig. 4. Change in bed elevation for the study reach, showing the net change over the entire period of study.

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Fig. 5. Cumulative size distribution curves for the sampled bed material in the Etobicoke Creek study area, based on the measurements of 100 clasts.

gradually to a point where the clasts would begin to move along the bed. Under these conditions, the average velocity was recorded at each of the 15 points identified earlier. The shear stress could then be computed from the logarithmic relation between the shear velocity (U*) and the variation of velocity (U) with height above the bed, y (Wilcock, 1996; Biron et al., 2004):

We hypothesized that orienting the clasts in this way would offer the maximum amount of resistance to initial movement. As such, this setup also served as a control, only this time the maximum threshold shear stresses occurring in the channel would be encountered.

U = U* = 1 = κ ln ðy = y0 Þ

4.1. Topographic survey

ð1Þ

4. Results and discussion

where κ is von Karman's universal constant, generally assumed to be 0.41. U* can be determined by substituting the appropriate values and, in turn, can be used to estimate the local shear stress at the time the clasts were entrained. The average roughness length, y0, determined from the 15 velocity profiles and the two flow depths was used in this experiment and all subsequent ones. The average velocity measurement U (Eq. (1)) was read at a height (y) corresponding to 40% of the flow depth, using the ADV set to a frequency of 20 Hz for one minute for each of the 15 sampling points identified earlier and the overall average retained. Similarly, the average height y at which velocity measurements were taken was determined and subsequently used in Eq. (1) to determine shear velocity U* at the inception of motion. Once this was completed, the flow was slowed sufficiently to allow the replacement of the clasts that had moved, followed by replicate measurements to account for any differences in discharge or stage that may result. A total of three replicates were conducted.

The results of the topographic surveys and related comparisons are presented in Fig. 4. The figure shows the net change in elevation over the entire period of study. The data indicates there was a greater loss of bed material over the study reach than was gained in several spots, with a bed lowering of >0.10 m in some locations. However, some points surveyed showed little to no net change in bed elevation. While the bed surface showed a lowering trend overall, some areas experienced a filling in of sediment, which maintained the overall bed elevation at some locations or created a net increase in bed surface elevation. While comparing the rates of channel change over the two seasons, we observed that greater rates of bed erosion and deposition occurred between August 2006 and May 2007 than between May 2007 and August 2007. This is most likely because of the greatest flows occurring during the spring snowmelt season.

3.2.3. Experiments 2 and 3 The second setup (experiment 2) involved the positioning of the clasts in a way that they all leaned against the flow of water, as illustrated in Fig. 3A. We assumed that the positioning of the clasts in this way would offer the least amount of resistance to initial movement. Therefore, this experiment served as a control to estimate the lowest critical shear stresses that could potentially be observed in a channel. As in experiment 1, shear stress was estimated using the logarithmic relation between velocity and height above the bed (Eq. (1)). Three replicate observations were made for each of the techniques, as in experiment 1. The third setup was similar to experiment 2; however, this time the clasts were leaning in the same direction as the flow of water (Fig. 3B).

4.2.1. Bed material characteristics Immediately following the completion of the first topographic survey was the measurement of the bed material size. As described

4.2. Flow characteristics and bed material transport

Table 1 Summary of sediment size distribution for the bed material in the study area. Axis

D16 (mm)

D50 (mm)

D84 (mm)

a-axis b-axis c-axis

220 140 15

285 187 24

370 246 38

a-axis = long axis, b-axis = intermediate axis, c-axis = small axis, D16 = size for which 16% is finer, D50 = size for which 50% is finer, and D84 = size for which 84% is finer.

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Table 2 Some characteristics of the flow during each rainfall event. Storm #

Storm date

Amount of rainfall (mm)

τ0 (N/m2)

Fr

n

f

d (m)

U (m/s)

1 2 3 4 5 6 7 8 9 10

16 May 2007 8 June 2007 19 June 2007 19 July 2007 5 September 2007 11 September 2007 23 October 2007 12 November 2007 22 November 2007 29 November 2007

54.8 38.4 18.8 28.8 12.2 12.8 14.2 19.6 52.4 13.6

18.092 12.789 9.225 10.626 7.477 7.487 8.103 9.583 17.556 7.653

0.359 0.278 0.218 0.218 0.161 0.170 0.200 0.222 0.324 0.176

0.038 0.047 0.057 0.059 0.075 0.071 0.061 0.057 0.043 0.069

0.117 0.200 0.328 0.329 0.609 0.549 0.392 0.318 0.146 0.508

0.980 0.676 0.481 0.554 0.386 0.387 0.421 0.500 0.940 0.396

1.114 0.716 0.474 0.508 0.313 0.330 0.407 0.491 0.982 0.347

τ0 (N/m2) = mean bed shear stress, Fr = Froude number, n = Manning coefficient, f = Darcy–Weisbach coefficient, d = average flow depth, and U = average flow velocity.

earlier, the bed material consists of a large number of disjointed loose blocks. The particle size distributions of the three axes are presented in Fig. 5 as cumulative size distribution curves. Table 1 presents a summary of the sediment size distributions for the study area. 4.2.2. Flow characteristics The flow was sufficiently high to entrain a large amount of the marked clasts during 10 storms over the course of the study period. The flow characteristics of these storm events were recorded and are presented in Table 2, along with the dates they occurred. These include the mean shear stresses, the Froude number, Manning's roughness coefficient, the Darcy–Weisbach friction factor (Knighton, 1998), and the depths and velocities from which these were derived. The table also includes the amount of rainfall during each storm, obtained from Environment Canada. Trace amounts of snow were recorded during the storms in November. The Froude numbers indicate that the flow of water was subcritical during all the storms (Robert, 2003). The roughness values are slightly high, but comparable values have been reported for bedrock channels by other authors (e.g., Dingman, 1984; Heritage et al., 2004). These high values are likely a result of the irregular nature of the bed. In general, the storms resulting in the highest discharge were found to

have the lowest roughness values. This is similar to what Heritage et al. (2004) reported for the Sabie River in South Africa. They suggested that at low discharges the flow resistance coefficients are probably reflecting energy dissipations from hydraulic jumps and internal distortions. However, these are drowned out as discharge increases and are reflected in the decline observed in the flow resistance values. 4.2.3. Bed material transport The average distance moved by the clasts during each of the storms was compared with the mean shear stress during these rain events (Fig. 6). Although the average distances are overall short, a clear increase in the average distance of transport as a function of average bed shear stress is nonetheless observed. Frequency distribution curves were made for the distance/size ratios. Examples of such distribution curves, for the first two rain events, are presented in Fig. 7. The entire set of results (only the first two storm events are presented here) indicate a skew to the right, demonstrating a decline in the mean distance transported as the grain size increased and vice versa. The c-axis length is used in Fig. 7 (and the reasons for using the c-axis instead of the intermediate axis will be discussed in the next section).

Fig. 6. Relationship between the average distance moved by clasts and the mean bed shear stress during ten rain events in 2007.

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Fig. 7. Frequency distribution of the ratio of distance travelled by the clasts and their size.

The data were transformed by creating a log-normal distribution. The results of some of these transformations are presented in Fig. 8. The transformation showed that the data fit a simple log-normal model with statistically significant results (as determined from a Kolmogorov–Smirnov test). These log-normal distributions are representative of all storm events analysed. Some authors have studied sediment transport in gravel-bed rivers by dividing the distance moved by each tracer particle by the average distance of movement of the entire sample size (Hassan et al., 1991; Pyrce and Ashmore, 2003). An attempt was made to apply this procedure to the angular rock clasts of the study area. The results from the same two storms are presented in Fig. 9, but the findings from all 10 rain events show positively skewed distributions. This means that in almost all storms, the vast majority of clasts are only

transported a short distance. This is similar to the trend observed in gravel-bed rivers by other researchers (e.g., Hassan et al., 1991; Pyrce and Ashmore, 2003). The results of this study indicate that the distances of movement of rock clasts in bedrock channels appear to follow a trend similar to that found in gravel-bed streams, and models predicting particle movement in such streams can be applied to bedrock channels as well. Hassan et al. (1991) suggested that in coarse-grained channels shear stresses are often only slightly above the critical threshold of particle movement. This may explain why most particles in the study site are found to either move short distances or are trapped within depositional structures on the bed. The results of flume experiments (described below) will focus on detailed measurements of thresholds of initial motion and on the role played by particle imbrications

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are presented in Fig. 10A, intermediate axis in Fig. 10B, and the small axis in Fig. 10C. The median grain size of the bed sediment, or the D50, was found to be 206 mm for the long axis, 147 mm for the intermediate axis, and 16 mm for the short axis. 4.3.1. Velocity profiles Velocity profiles were established under two flow depth conditions, as outlined in the previous section. A regression was performed on the profiles based on the “law of the wall,” which was used to describe the velocity gradient in the near-bed region (Robert, 2003). However, some of the profiles showed a clear break of slope with two very distinctive flow zones (as experienced by Lawless and Robert, 2001b, in their experiments downstream of pebble clusters in a flume). Lawless and Robert (2001a) devised a procedure to determine the appropriate division between the inner semilog-linear region and the outer semilog-linear region of the profiles. To do this, the break of slope between the two regions was visually determined. For each of the splits, regression was run on both the inner region and the outer region, and the near-bed flow region was used to estimate both y0 (roughness length) and τ0 (local bed shear stress). All these parameters are presented in Table 3. The linear regressions performed on the profiles were all significant at the 0.05 level. The log relation therefore does appear to perform well in the near-bed region, even in the presence of large roughness elements such as those used in our experiments. Estimates of shear stress are significantly higher under low flow conditions, as indicated by the higher averages. This implies that, in these experiments, bed shear stress does not scale with depth. As the discharge was kept constant, lowering the water elevation would increase the velocity of the flow over the bed. As a result, the greatest shear stresses are observed in these conditions. 4.3.2. Experiment 1 The conditions under which entrainment began were quantified under different experiments, as summarized in Section 3.2. For the first setup, the same orientation of clasts was used as for the measurement of velocity profiles. The water depth in the flume was lowered until the clasts began to be entrained by the flowing water. Velocity measurements were then made at a height corresponding to 40% of the flow depth. The estimates of shear stress made during this experiment are shown in Table 4 (showing the depth, y, at which measurements were taken; the corresponding average velocity reading (U); and the estimated shear velocity and shear stress values using the log-profile method of Eq. (1)). A value of y0 = 5.7 mm was used in Eq. (1) to determine shear velocity from single point measurements. This corresponds to the overall average roughness length observed in Table 3 from the two flow depth conditions.

Fig. 8. Kolmogorov–Smirnov analysis to test the normality of the data after transforming it through a log-normal distribution. A p-value >0.05 indicates the data fits a normal distribution.

and orientations (see Fig. 3) on the ease with which bed erosion takes place. 4.3. Flume experiments The particle size distributions of the clasts used for the flume experiments (and for the three axes) are presented in Fig. 10 as cumulative size distribution curves. The distributions of the long axis

4.3.3. Experiments 2 and 3 The second setup (experiment 2) involved positioning the clasts in such a way that they all leaned opposing the flow of water (Fig. 3A). The same procedures of estimating shear stress at the inception of motion (as in experiment 1) were implemented here, i.e., shear stresses were estimated at 15 locations along the entire length of the channel by measuring the velocity at 40% of the flow depth (and subsequently from Eq. (1)). Table 5 shows the estimates of shear stress made during this experiment. The final experiment (experiment 3) involved the positioning of the clasts in such a way that they all leaned in the direction of the flow (Fig. 3B). Table 6 contains estimates of shear stress made during this experiment. We found that in all three experiments the thinnest clasts (i.e., those with the shortest c-axis) were entrained first. From visual observations, the long and intermediate axes appeared to play no role in determining which particles were entrained by the flow. This is contrary to standard practice in studies of gravel-bed alluvial rivers

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Fig. 9. Particle path length distributions, with distance moved by each clast divided by the mean distance moved by all clasts.

where the threshold flow stress is usually based upon or estimated from the intermediate axis of the particles. Therefore, while the intermediate axis may place a limit on entrainment in gravel, in the case of these angular, plate-like rock clasts, the dimension of the short axis seems to dominate the entrainment process. As expected, the least resistance to movement was provided by the clasts that were oriented against the flow. This is evident from the low values of shear stress observed when entrainment began. Conversely, the highest values of shear stress were found when the clasts were oriented in the direction of the flow of water. When there was no apparent pattern in the orientation of clasts, the average critical shear stress is a value between those found under the other two conditions. There are some possible reasons for why this occurs. The area exposed to the flow is, in part, a function of the particle orientation, and this exposed area affects the drag force needed to initiate movement (Knighton, 1998). Moreover, when particles are oriented against the flow (as schematically illustrated in Fig. 3A), a significant lift force can be generated that could lead to lower estimated drag forces at the inception of motion (Knighton, 1998). Notably, the range of critical shear stress observed in the laboratory (Tables 4–6) is

similar to the range of estimated shear stress in the field when sediment transport took place (Table 2). The laboratory experiments provided useful results complementary to the fieldwork conducted in the Etobicoke Creek. The results of these experiments demonstrated the importance of velocity measurements when making local, small-scale estimates of bed shear stress. This study also allowed velocity profiles to be measured under controlled conditions in the flume to aid in the study of the friction exerted by the bed on flowing water. Finally, by examining the erosive resistance of the clasts in relation to their orientation on the bed, the study permitted a detailed understanding of the dynamics involved in the entrainment of the bed material. 5. Conclusion There has been an increased interest in bedrock channels in recent years. A thorough understanding of the channel hydraulics and sediment transport processes, as well as the connectivity with other parts of the fluvial system, is essential. The processes of fluvial incision and transport play a significant role in bedrock river morphology

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311

Fig. 10. Cumulative size distribution curves for the bed material placed in the flume, showing the size distributions for the (A) long axis, (B) intermediate axis, and (C) short axis.

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Table 3 Bed shear stress and roughness length determined for the 15 locations. Distance down a study section (cm)

b

y0 (mm) R2

a. Low flow (mean flow depth = 10 cm) conditions 0 15.08 9.96 2.2 15 − 32.60 28.68 31.2 30 − 44.13 34.54 35.9 45 10.13 5.15 1.4 60 19.28 5.05 0.2 75 20.87 4.54 0.1 90 17.38 10.42 1.9 105 25.35 3.31 0.0 120 19.08 6.88 0.6 135 25.58 4.10 0.0 150 6.13 22.27 7.6 165 11.29 11.07 3.6 180 11.63 12.12 3.8 195 11.97 8.93 2.6 210 21.35 3.82 0.0 averages 6.1 b. High flow (mean flow depth = 20 cm) 0 8.68 4.25 15 − 3.04 8.46 30 − 14.28 12.83 45 4.61 2.08 60 9.12 2.05 75 4.84 8.56 90 6.15 4.45 105 8.85 3.79 120 7.20 4.50 135 9.18 3.87 150 4.62 5.79 165 10.33 3.81 180 6.87 4.95 195 − 1.94 7.82 210 9.52 1.29 averages

conditions 1.3 14.3 30.4 1.1 0.1 5.7 2.5 1.0 2.0 0.9 4.5 0.7 2.5 12.8 0.0 5.3

τ0 (dyn/cm2) U⁎ (cm/s)

0.98 15.86 0.92 131.62 0.89 190.86 1.00 4.25 0.89 4.09 0.90 3.30 0.99 17.36 0.94 1.75 0.97 7.58 0.96 2.69 0.99 79.35 0.96 19.60 0.98 23.50 0.93 12.77 0.75 2.34 34.46

0.93 1.00 0.96 0.99 0.97 0.88 0.93 0.89 0.95 0.96 0.98 0.95 0.98 0.93 0.82

2.89 11.45 26.33 0.69 0.67 11.71 3.17 2.30 3.23 2.40 5.37 2.32 3.92 9.78 0.27 5.77

3.98 11.47 13.82 2.06 2.02 1.82 4.17 1.32 2.75 1.64 8.91 4.43 4.85 3.57 1.53 4.56

1.70 3.38 5.13 0.83 0.82 3.42 1.78 1.52 1.80 1.55 2.32 1.52 1.98 3.13 0.52 2.09

Table 5 Shear stress and corresponding flow parameters measured during experiment 2; measurements made at 40% of flow depth. Distance down study section (cm)

U (cm/s)

y (cm)

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210

54.93 62.59 62.67 63.43 58.01 62.66 60.72 63.53 66.41 66.77 65.20 66.24 69.10 65.75 66.34

8.5 8.6 7.7 8.5 8.0 9.0 8.1 8.5 9.3 7.9 8.3 8.4 8.6 8.3 8.8

U⁎ (cm/s) 8.13 9.23 9.63 9.39 8.78 9.08 9.15 9.41 9.51 10.16 9.74 9.85 10.18 9.82 9.70 average

τ0 (dyn/cm2) 66.11 85.10 92.72 88.16 77.15 82.50 83.76 88.45 90.51 103.22 94.82 96.99 103.72 96.41 94.02 89.58

and related sediment fluxes. Therefore, an understanding of these processes is needed. The Greater Toronto Area is a highly urbanized and densely populated area that has experienced growth in recent years. As a result, rivers that flow through the city and surrounding areas are heavily affected by urbanization. The Etobicoke Creek is one such river that flows through the municipalities of Toronto, Mississauga, and

Brampton. Bedrock is visible in a few places in the Etobicoke Creek watershed. The results of a series of topographic surveys suggested that changes were occurring on the channel bed and that the river bed was found to show a lowering trend overall. However, in several locations, sediment is filling in, which helps to maintain bed elevations. Most of the change was found to occur following the spring snow melt where higher flows would result in the greatest amount of sediment transport. Examination of flow characteristics during 10 rain events showed high roughness values that can be attributed to the irregular nature of the bed. However, the highest roughness values were found in storms with the lowest discharges. This was probably a result of energy dissipation at these low discharges from hydraulic jumps and internal distortions; while at higher discharges, these are drowned out. A distinct relationship was observed between the average distance moved and the average shear stress during each of the storms. The highest shear stresses resulted in the largest distances travelled by the clasts during these storms. This was supported by a comparison of dimensionless ratios of distance travelled by the clasts and the size of each. Larger clasts were found to move smaller distances, while smaller clasts moved larger distances. We also found that the vast majority of clasts are only transported a short distance or are trapped within depositional features on the bed. This was similar to results observed in gravel-bed rivers found by other researchers (e.g., Hassan et al., 1991; Pyrce and Ashmore, 2003), despite the completely different

Table 4 Shear stress and other flow parameters measured during experiment 1; measurements made at 40% of flow depth.

Table 6 Shear stress and other flow parameters measured during experiment 3; measurements made at 40% of the flow depth.

a = regression coefficient, b = regression slope, y0 = roughness length, R2 = coefficient of determination, τ0 = shear stress, and U⁎ = shear velocity.

Distance down study section (cm)

U (cm/s)

y (cm)

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210

47.11 46.27 58.84 56.78 60.05 71.71 66.97 58.15 63.38 70.88 77.18 83.89 78.07 62.30 52.19

6.3 6.1 5.8 5.9 5.0 5.2 5.4 5.4 5.1 5.3 5.5 5.1 5.6 5.3 5.7

U⁎ (cm/s) 7.84 7.81 10.14 9.72 11.06 12.98 11.91 10.35 11.57 12.71 13.62 15.31 13.67 11.18 9.07 average

τ0 (dyn/cm2)

Distance down study section (cm)

U (cm/s)

y (cm)

61.51 60.97 102.91 94.44 122.34 168.36 141.93 107.01 133.84 161.65 185.45 234.50 186.78 124.89 82.19 131.25

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210

70.63 78.61 78.49 74.55 76.74 74.97 77.07 78.66 77.26 77.04 77.19 78.13 77.80 78.23 78.32

6.7 6.8 5.8 6.7 6.5 7.2 6.3 6.6 7.4 6.1 6.4 6.6 6.9 6.5 6.9

U⁎ (cm/s) 11.46 12.68 13.53 12.10 12.61 11.82 12.83 12.85 12.05 13.00 12.77 12.76 12.48 12.86 12.56 average

τ0 (dyn/cm2) 131.43 160.89 183.14 146.43 159.05 139.81 164.61 165.02 145.31 168.99 163.01 162.80 155.74 165.31 157.83 157.96

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environments. Our observations suggest that imbrication structures possibly play a dominant role in tapping rock clasts while in motion and potentially control to a large extent thresholds of initial motion, range of particles in motion, and related distances of transport. Velocity profiles were made under two flow conditions: at water elevations of 20 and 10 cm, respectively. The results showed that shear stresses were generally higher under the lower flow depth, which was a result of an increased velocity under these conditions in the flume, when discharge is kept constant. Three sets of experiments were conducted in the flume, where clasts from Etobicoke Creek were oriented against the flow of water, with the flow, and in no particular pattern of orientation. We found that, as expected, the least amount of resistance to movement was offered by the clasts that were oriented against the flow, as evidenced by the low shear stresses observed when entrainment began. Conversely, the greatest amount of resistance was offered by the clasts that were oriented in the direction of the flow. When the orientation of the clasts shows no pattern, the shear stress is a value in between those found under the other two conditions. This study may have implications in many fields. Bedrock rivers have been known to have extreme flow patterns and are capable of moving large-sized debris during such flood events; these can cause problems to structures built on these rivers. Similarly, processes of erosion that impact the bedrock could have similar effects on structures in these rivers. Increased understanding of the geomorphic processes in these channels can assist, from a management perspective, in reducing damages to such structures caused by erosion in these channels. Acknowledgements Financial assistance from the Natural Sciences and Engineering Research Council of Canada (Discovery Grant to AR) is gratefully acknowledged. Thanks also to Richard Sunichura and Stanley Yee for their field assistance. Comments from two anonymous referees were most helpful in reviewing the manuscript. References Ashley, G.M., Renwick, W.H., Haag, G.H., 1988. Channel form and processes in bedrock and alluvial reaches of the Raritan River, New Jersey. Geology 16, 436–439. Baker, V., 1973. Erosional forms and processes from the catastrophic Pleistocene Missoula floods in eastern Washington. In: Morisawa, M. (Ed.), Fluvial Geomorphology. SUNY Publications, Binghampton, NY, pp. 123–148. Baker, V.R., Kale, V.S., 1998. The role of extreme floods in shaping bedrock channels. In: Tinkler, K.J., Wohl, E.E. (Eds.), Rivers over Rock: Fluvial Studies in Bedrock Channels. American Geophysical Union, Washington, DC, pp. 153–162. Bergeron, N.E., Abrahams, A.D., 1992. Estimating shear velocity and roughness length from velocity profiles. Water Resources Research 28, 2155–2158. Biron, P.M., Robson, C., Lapointe, M.F., Gaskin, S.J., 2004. Comparing different methods of shear stress estimates in simple and complex flow fields. Earth Surface Processes and Landforms 29, 1403–1415. Buffin-Bélanger, T., Roy, A.G., 2005. 1 min in the life of a river: selecting the optimal length of the measurement of turbulence in fluvial boundary layers. Geomorphology 68, 77–94. Carling, P.A., 2006. Editorial. The hydrology and geomorphology of bedrock rivers. Geomorphology 82, 1–3. Carling, P.A., Tinkler, K., 1998. Conditions for the entrainment of cuboid boulders in bedrock streams: an historical review of literature with respect to recent investigations. In: Tinkler, K.J., Wohl, E.E. (Eds.), Rivers over Rock: Fluvial Studies in Bedrock Channels. American Geophysical Union, Washington, DC, pp. 19–34. Carling, P.A., Hoffamnn, A.S., Baltter, A.S., Dittrich, A., 2002. Drag of emergent and submerged rectangular obstacles in turbulent flow above bedrock surface. In: Schleiss, A.J., Bollaert, E. (Eds.), Rock Scour due to Falling High-velocity Jets. Swets and Zeitlingger/Balkema, Lausanne, Switzerland, pp. 83–94. Chapman, L.J., Putnam, D.F., 1984. The Physiography of Southern Ontario, 3rd Ed. Ministry of Natural Resources, Toronto, Ontario, Canada. Church, M., Hassan, M.A., 1992. Size and distance of travel of unconstrained clasts on a streambed. Water Resources Research 28, 299–303. Coleman, A.P., 1913. Geology of the Toronto region. In: Faull, J.H. (Ed.), The Natural History of the Toronto Region, Ontario, Canada. Canadian Institute, Toronto, pp. 51–80. Dingman, S.L., 1984. Fluvial Hydrology. Freeman, New York. Downward, S.R., 1995. Information from topographic survey. In: Gurnell, A., Petts, G. (Eds.), Changing River Channels. Wiley, Chichester, UK, pp. 303–323.

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