The effect of hydrographs on bed load transport and bed sediment spatial arrangement

Authors

  • Luca Mao

    Corresponding author
    1. Department of Ecosystems and Environment, Pontificia Universidad Católica de Chile, Santiago, Chile
    • Corresponding author: L. Mao, Department of Ecosystems and Environment, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Macul, Casilla 306-22, Santiago, Chile. (lmao@uc.cl)

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Abstract

[1] Field measurements of sediment transport in gravel bed rivers often reveal hysteretic effects due to differences in sediment availability between the rising and falling limbs of a flood hydrograph. However, only a small number of flume studies have analyzed the dynamics of sediment transport during hydrographs. Three types of stepped hydrographs with contrasting durations and magnitudes are simulated here under sediment recirculation conditions. Bed load transport rate and grain size have been measured continuously. The dynamic behavior of the surface armor layer has been explored by analyzing digital photographs and laser scanner surveys of the bed surface taken during hydrographs. The results indicate that sediment transport during the falling limb was lower than during the rising limb in all of the three types of hydrographs. This reduction is more evident for the low-magnitude hydrographs. The grain size of the bed remained virtually constant throughout the hydrographs but the grain size of transported sediments exhibited a counterclockwise hysteresis. Also, a significant increase in the reference shear stress for sediment entrainment was measured during the falling limb of hydrographs. Additionally, a detailed analysis of partial transport dynamics of the bed surface sediments reveals a reduction in sediment mobility during the falling limb of the hydrographs. The difference in sediment entrainment and transport before and after the peak of the hydrographs appears to be caused by a change in the organization of the surface sediments. An analysis of detailed laser scan bed surveys reveals a phase of bed restructuring (lower vertical roughness, clast rearrangement) during the falling limb of hydrographs. Consequently, changes in the degree of organization and complexity of the bed surface are likely the cause of the reduced mobility of sediments, and thus of the reduced sediment transport rate, during the falling limb of the hydrographs.

1. Introduction

[2] Bed load transport is the main driver of river morphodynamics, and its quantification is of the highest interest to fluvial geomorphologists, hydraulic engineers and ecologists. However, bed load is notoriously challenging to measure in the field [Vericat et al., 2006a; Bunte and Abt, 2005], and difficult to predict within one to two orders of magnitude using available formulas [Barry et al., 2004; Recking et al., 2012]. Bed load equations are usually derived from flume experiments [Ashida and Michiue, 1972; Fernandez Luque and van Beek, 1976; Meyer-Peter and Mueller, 1948; Parker et al., 1982; Wilcock and Crowe, 2003] and the latest formulas for sand-gravel mixtures use the surface grain-size distribution as an input parameter [e.g.,Wilcock and Crowe, 2003]. However, flume experiments are generally conducted under near-equilibrium, steady state conditions (i.e., with constant flow discharge over time), which do not approximate field conditions.

[3] Laboratory studies of bed load transport in sediment-recirculating flumes have shown that, while the grain size of the transported sediments changes systematically according to the shear stress and the transport rate, the grain size of the bed surface (armor) remains essentially the same, even under different flow conditions [Wilcock et al., 2001]. This has been recently integrated by the observation that mobile armor layers developed at higher discharges are rather constant in terms of grain size, but significantly different than static armor layers in terms of vertical roughness length scales and surface topographical complexity [Mao et al., 2011]. Assuming unlimited sediment supply from upstream reaches, Wilcock and DeTemple [2005]back-calculated surface sediment size from the bed load sediment rate and sizes of two sets of field data (Oak Creek, OR, [Milhous, 1973], and Goodwin Creek, MS, [Kuhnle, 1992b]), and showed that the predicted surface grain size during high flows corresponded to what was observed at low flows. However, the persistence of armor layers during flood events has rarely been observed in the field. Andrews and Erman [1986] reported that all sizes were transported over an unchanged surface armor layer during high flows in the Sagehen Creek (CA). Clayton and Pitlick [2008]reported on the remarkable case of a sudden channel avulsion during a high flow which left the previous channel as armored as it was before the event. They suggested that this was due to an unlimited supply of sediment of all sizes, thus implying the persistence of a mobile armor layer during high flow. The opposite case of an abrupt break-up of a static armor layer during a flood event has been reported byVericat et al. [2006b], but has been clearly related to the limited sediment supply conditions dominating in a highly regulated gravel bed river (the Ebro, Spain).

[4] Sediment transport during flood events often shows hysteretic effects due to temporal lags between flow and sediment transport [Reid et al., 1985]. The hysteretic pattern can be clockwise, implying that the peak of sediment transport occurs before the peak of flow discharge. This has been mostly related to an early rupture of the static armor layer [Kuhnle, 1992a], to time lags in sediment supply [Lisle and Madej, 1992; Habersack et al., 2001], to the loose surface bed material left by previous high-magnitude floods [Reid et al., 1985], or to disturbance of bed armor during storms and subsequent reformation during the waning stages [Hsu et al., 2011]. Counterclockwise hysteresis (bed load peak occurring after the peak flow) has also been observed [Humphries et al., 2012] and mainly related to bed form development lagging changes in flow [Lee et al., 2004], the time necessary to destroy a well-established armor layer [Kuhnle, 1992a], or the consolidation of grains in the bed during intraflood periods [Reid et al., 1985].

[5] Bed load hysteresis observed in the field is thus most often due to different sediment availability conditions between the rising and falling limb of hydrographs [Hassan and Church, 2001]. The few examples of flume experiments in which hydrographs have been simulated seem to confirm larger sediment transport on the rising limb of hydrographs. Hassan et al. [2006] simulated stepped hydrographs of different magnitudes and duration in order to explore armoring processes in a range of hydrological environments. Sediment transport was always larger during the rising limbs, but this was due to the limitations in the sediment supply from the upstream end of the flume rather than the shape of the hydrographs. More recently, Humphries et al. [2012] simulated hydrographs over an armored bed in order to explore the effects of sudden sediment pulses, intended to replicate gravel augmentation procedures. The hydrographs showed significant clockwise hysteresis related to pool scour and fill. Because sediments fed from upstream were of the same grain size as the subsurface, during these experiments the bed surface became finer during the rising limb and coarser during the falling limb. As a consequence, the simulated conditions were different from the unlimited sediment supply conditions assumed by Wilcock and DeTemple [2005] when examining the persistence of an armor layer during flood events. Lee et al. [2004]explored bed load under unsteady flow conditions simulating triangular-shaped hydrographs over a sand bed, showing instead a counterclockwise hysteresis (i.e., peak of sediment transport occurring after the peak of hydrograph). This occurred even if no sediments were fed into the system, and has been explained by a delay in the passage of sand dunes. Similarly,Bombar et al. [2011] observed bed load counterclockwise hysteresis in flume runs simulating various triangular and trapezoidal shaped hydrographs. Wong and Parker [2006] and Parker et al. [2007] approached the issue of bed elevation adjustment, sediment transport, and both bed and bed load sediment size fluctuations during hydrographs by considering a system which receives a constant rate of sediment feed and is exposed repeatedly to the same hydrograph. Under these conditions, downstream of a short “boundary reach,” the channel bed maintained the same elevation while the transport rate fluctuated with the discharge. This model has recently been successfully applied to predict the effects of gravel augmentation strategies in the Trinity River [Viparelli et al., 2011].

[6] Overall, despite the fact that a complete understanding of sediment transport and channel bed evolution processes during floods is of crucial importance, there appears to be only limited field evidence of the persistence of armor layers during floods with no limit to sediment supply [Andrews and Erman, 1986; Clayton and Pitlick, 2008]. Although model results from Wilcock and DeTemple [2005]suggest that this could be explained by the presence of a mobile armor, which allows the sizes in transport to fluctuate with the discharge, to this date few flume experiments simulating hydrographs with no limit to sediment supply have been attempted. In this context, laboratory experiments have the potential of allowing the armor bed to be monitored continuously along with changes in transport rate and grain size. The present paper reports on a series of flume experiments simulating stepped hydrographs under sediment recirculating conditions. The main aim is to characterize dynamics of sediment transport, sediment mobility and surface sediment arrangement during floods. Three types of stepped hydrographs with contrasting durations and magnitudes are simulated in order to examine the response to disturbances ranging from the short/high-magnitude rainfall events to the long/low-magnitude snowmelt events. These data are then used to test the hypothesis that changes in sediment transport reflect changes in sediment mobility and entrainment, due to changes in the spatial organization of the sediment surface during hydrographs, and that the shear stress history has a role in determining sediment mobility and surface grain organization. In order to assess the deviation of sediment transport rate and grain size from equilibrium conditions, these experiments follow previous steady flow/sediment recirculation runs conducted at the same discharges used for the stepped hydrographs [Mao et al., 2011].

2. Materials and Methods

[7] A series of experiments were carried out in an 8 m-long, 0.3 m-wide tilting laboratory flume. To reduce inlet and backwater effects, 1 m-long artificially roughened bed sections were placed at both the upstream and downstream ends of the flume. Bed load traps (0.3 m-wide; 0.4 m-long) were used to collect sediments at the downstream end of the flume. The mesh on the bed load traps was fine enough to retain the smallest sand fraction of the mixture (0.5 mm). The capture efficiency of the bed load traps was greater than 95%, even at the highest transport rate.

[8] The sediment mixture used in the experiments had a bimodal grain-size distribution (20% sand - 80% gravel) withD16 = 1.7 mm, D50 = 6.2 mm, and D84 = 9.8 mm (Figure 1). Prior to running an experiment, the bed sediment was thoroughly mixed, then screeded flat to achieve a bed thickness of 0.13m and a constant bed slope of 0.01 m m−1 along the working length of the flume.

Figure 1.

Grain size distribution of the sediment mixture.

[9] Experiments were carried out with unit discharges ranging from 0.024 to 0.085 m2 s−1 (shear stresses ranging from 4 to 8.6 N m−2, respectively, Table 1). The flow was controlled by a signal inverter connected to the pump. The discharge was measured with a portable ultrasonic flowmeter (GE Panametrics PT878) within the inlet pipe. Water and bed surface elevations were measured approximately every 30 min with a point gauge at 11 positions along the flume. The downstream adjustable weir was laid flat to allow the flow depth to adjust naturally. Bed shear stress was calculated from measured slope and hydraulic radius, and corrected for sidewall effects [Vanoni and Brooks, 1957].

Table 1. Shear Stress and Sediment Transport at Long-Term Equilibrium Conditions for the Discharges Used to Design the Hydrographsa
Discharge (m2 s−1)Flow Depth (m)Shear Stress (N m−2)Dimensionless Shear StressTransport Rate (g m−1 s−1)Hydrographs
0.0240.0444.00.0370.05L
0.0310.0514.60.0420.30L
0.0380.0605.40.0460.79L; M
0.0440.0665.90.0502.08H; M; L
0.0490.0696.10.0512.80M
0.0540.0787.00.0604.96H; M
0.0640.0837.30.06120.87H
0.0850.1008.60.07752.57H

[10] Sediment was recirculated throughout the experiments. All of the sediment captured in the bed load traps was manually recirculated at intervals ranging from 1 to 10 min depending on the bed load transport rate; at least 200 g of sediment was collected prior to emptying the traps. This sediment was quickly weighed and manually fed into the fixed, rough-bed section located at the upstream end of the flume. During the experiments, the bed surface remained flat, with the appearance of small migrating sand sheets of negligible height only during the highest discharge runs. Because of the sediment recirculation conditions, there was no noticeable change of slope nor evident scour at the upstream end of the flume.

[11] The experiments were started by running a steady discharge of 0.031 m2 s−1for four hours to establish a water-worked surface with partially mobile grains. Discharges were then increased in steps to generate hydrographs. Three stepped hydrographs of different duration and magnitude were simulated (Figure 2 and Table 2); these are designated H, M and L to indicate high, medium and low discharges, respectively. Each hydrograph was symmetrical about the peak discharge and was composed of 7 steps. The peaks and durations of the hydrographs were adjusted to mimic hydrologic conditions ranging from high-magnitude short-duration rainfall events to low-magnitude long-duration snowmelt events. The duration and magnitude of the steps were adjusted accordingly (Table 2). The hydrographs were not precisely scaled from a specific prototype but were designed to represent processes occurring in a narrow gravel bed river. Considering an undistorted 1/30 Froude geometric scaling [Graf, 1971; Parker et al., 2003], the flume would represent a generalized moderate-slope (0.01 m m−1), 10 m-wide gravel bed stream with relatively coarse sediment (D50 = 200 mm, and D84 = 330 mm). Using the 1/30 reduction factor, the H hydrograph would scale to a flashy 9.5 m3 s−1flood lasting 10 h. The snowmelt-type L hydrograph represents a much longer flood (83 h) peaking at 4.9 m3 s−1, which is approximately half the discharge of hydrograph H.

Figure 2.

Shape and duration of the simulated hydrographs.

Table 2. Discharge and Duration of Flow Steps Used to Design the L, M, and H Hydrographs
Flow StepLMH
Discharge (m2 s−1)Duration (min)Discharge (m2 s−1)Duration (min)Discharge (m2 s−1)Duration (min)
Rising0.0241200.038600.04415
Rising0.0311200.044600.05415
Rising0.0381200.049600.06415
Peak0.0441200.054600.08515
Falling0.0381200.049600.06415
Falling0.0311200.044600.05415
Falling0.0241200.038600.04415

[12] The discharges used to generate the hydrographs discussed here were selected to match the discharges used in a previous set of experiments [Mao et al., 2011], where all runs involved steady flows (Table 1). In the previous experiments, the same range of discharges was used, but the discharge was held constant during the runs, and the run times were considerably longer, allowing the complete development of a mobile armor layer under conditions of equilibrium flow and sediment transport [Mao et al., 2011].

[13] During the hydrographs, the flow was stopped at the end of each step and the flume drained up to the sediment level in order to take pictures of the surface sediment and to empty the bed load traps to obtain the grain size distribution (at 0.5 φ) of the transported sediment. Eight detailed photographs (area: 0.20 m × 0.15 m) of the bed surface were taken along the downstream half of the flume at fixed positions with a 12 MP digital camera. The bed surface grain size distribution was derived using a point count technique, by digitizing the b-axes of 80 particles located at the intersection of a grid superimposed on each of the photographs (i.e., point spacing of 20 mm). The presence of fine and coarse sand (clearly distinguishable on the photographs) was counted but their diameter was not measured. The overall grain size distribution of the bed was obtained from an aggregate analysis of the eight photographs, thus counting at least 600 clasts. Grain size curves were truncated at 1.4 mm, thus sand grains up to 1 mm were not considered in the curves. Although this method is potentially biased by grain imbrication and partial hiding of some particles, the derived grain size distributions have been compared to a few area-by-weight samples collected using a standard clay sampling technique converted to bulk sample equivalents. This comparison revealed that difference in the obtained D50 and D84 are lower than 5%. An attempt to use automated methods for extracting grain size dimensions from images [e.g., Graham et al., 2005] proved unsuccessful due to the bimodality of the grain size distribution and the speckled nature of the coarsest particles, which led to overfragmentation during the automatic photograph analysis.

[14] In order to explore the mobility of surface sediments in a nonintrusive manner, a transparent plastic box was adjusted to the water surface in a fixed position within the last third of the flume length. A 12 MP camera was fixed above the box and was used to take photos of the bed surface at intervals ranging from 1 to 15 min depending on the transport rate and the mobility of sediments in the bed. Spot lights were used to illuminate the bed through the glass walls of the flume, and a polarized lens mounted on the camera avoided reflections on the Perspex board. The plastic box was controlled using a manual lifting system that allowed minimal disturbance on the water surface and allowed the exact distance from the camera to the Perspex board to be known. Assuming negligible vertical adjustment of the bed (confirmed by occasional measurements), the sizes of sediments in the photos were derived by projecting the dimension of fixed points drawn on the Perspex board onto the bed, using a simple trigonometric formula which considered water refraction and water depth at the exact time of the picture. The photos imaged a bed area of 0.2 m × 0.15 m and were used to digitize the b-axes of 80 particles located at the intersection of a grid superimposed on each of the photographs. A series of subsequent photos were used to note the presence or absence of grains lying on the bed at the time of the first photo, as previously done byWilcock and McArdell [1997] to assess the amount of active grains in the bed. A grain was considered removed if it moved entirely outside of its initial location, i.e., if it was displaced for a distance longer than its diameter. For each flow step, the number of grains of each class size transported from one photo to the following was measured. The proportion of particles entrained over time was measured with respect to the grains lying on the bed surface at the initial time, shortly after the beginning of a run.

[15] For three hydrograph runs, the bed surface was surveyed with a close range laser scanner (Scantron LMS6035S) to determine spatial variations in bed roughness and particle arrangement. Scans were taken at a 1 mm spatial resolution at the end of the first and last steps, and at the end of the peak step for one run of hydrographs L, M, and H. Using the same system and setup, Rumsby et al. [2008] demonstrated the high elevation accuracy (about 1 mm standard deviation) associated with the application of laser altimetry in the same context. The scans covered an area of 1.5 m × 0.2 m located in the downstream half of the flume. Repeat scans were taken each time, and these were aggregated to eliminate missing data points, which were always less than 5% of the total in a single scan. A kriging technique was used to interpolate the remaining missing points. Scans were detrended in both the stream-wise and lateral direction using a linear interpolation. The mean elevation was used as a false zero and all elevations are expressed relative to this value. Further details on the analysis process of laser scan data taken with the same device are given in Mao et al. [2011].

3. Results

3.1. Sediment Transport Rate and Grain Size of Transported Particles During Hydrographs

[16] Figure 3 shows sediment transport rates measured during the hydrograph experiments, including repetitions available for runs H and L. Because sediment was manually recirculated at intervals depending on the transport rate, more instantaneous measurements are available for the highest discharges. Figure 3 shows that sediment transport rates fluctuated considerably during the experiments), especially at the highest discharges. For instance, in run H, the standard deviation of bed load transport rates around the average is up to ten times larger at the highest discharge (0.085 m2 s−1) than in the lower discharge (0.044 m2 s−1). The same pattern of bed load fluctuations is evident in experiments M and L. The magnitude of bed load rate fluctuations tends to be larger in the rising than in the falling limb of hydrographs. In the H runs, standard deviation of bed load rates at the intermediate discharge of 0.054 m2 s−1 is 50 to 70% larger in the rising limb of hydrographs (Figure 3). In the runs of hydrographs L, the difference in bed load fluctuations between rising and falling limbs is weaker, but it is still 5 to 30% larger.

Figure 3.

Sediment transport rates (qs) measured during simulated hydrographs (a) H, (b) M, and (c) L. Three repetitions are available for hydrographs H and L.

[17] Figure 4shows the averaged sediment transport rate at each flow step of the simulated hydrographs along with the grain size of transported sediment and of the bed surface. It shows that averaged transport rates of moderate to high discharges are consistently larger during the steps composing hydrographs than during long-term experiments where equilibrium conditions were attained. This is likely due to the fact that the duration of each step was not long enough to allow near-equilibrium conditions to be reached. Instead, the fact that sediment transport rate was lower than in equilibrium conditions for the lower discharges of hydrographs L (seeFigure 4e) is probably due to the fact that all experiments started from a bed water-worked with a discharge of 0.031 m2 s−1, which is larger or equal to the lower flow steps of hydrographs L (0.024 and 0.031 m2 s−1).

Figure 4.

Averaged transport rate (qs), grain size (D50 and D84) of the transported sediment (Dt, left hand side graphs) and of the surface sediment (Ds, right hand side graphs) at flow steps of hydrographs (a, b) H2, (c, d) M, and (e, f) L1. Rising limbs of hydrographs are identified by solid lines (and R notation) and falling limbs by dashed lines (and F notation). Stars in Figures 4a, 4c, and 4e represent the sediment transport rates under equilibrium conditions (from Mao et al. [2011]). Graphs referring to repetition experiments are not included for sake of clarity.

[18] Sediment transport rate is consistently lower during the falling limb in all of the three types of hydrographs (Figure 4). Differences between transport rates on the rising and falling limbs of hydrographs H range from 35 to 85% at the lower discharges (0.044 and 0.054 m2 s−1) and reducing to 2 to 10% at the highest discharge step (0.064 m2 s−1). Hydrograph M exhibits a difference ranging from 48 to 57%. Runs of hydrographs L showed the highest differences in transport rate, being up to 93% at the lowest discharge (0.024 m2 s−1) and reducing to 75% for the highest discharge (0.038 m2 s−1).

[19] Because sediment recirculation provided the same rate and size of sediment transported out of the flume, the difference in sediment transport rate between flow steps of the same discharge before and after the hydrograph peak should be related to changes in the bed load and/or the bed surface texture. Figure 4 (left) show that, in general, the grain size of the transported sediment, Dt, was lower on the rising limb of the hydrograph than on the falling limb. The right-hand panels inFigure 4 show that the grain size of the bed surface, Ds, changed little throughout the hydrographs. In fact, deviations in the average bed surface D50 and D84 throughout all hydrograph repetitions were less than 8% and 10%, respectively. Major changes in surface sediments size were mainly associated with the passage of long and low migrating sand sheets, and these were observed only during the highest discharge runs (similar to what was observed by Wilcock et al. [2001] at the highest discharges). Differences in the surface D50 between rising and falling limbs of the hydrographs were always less than 5%, and no consistent differences in surface sediment size were evident among the three different types of hydrographs. The grain sizes of transported sediments, Dt, are consistently higher on the falling limb than on the rising limb of all three types of hydrographs. In hydrographs H, the D50 and D84 of transported sediments are, on average, 10% and 7% coarser on the falling limbs, respectively, with larger differences at the lower discharge steps. During hydrograph M the difference is greater, being around 20% and 9% for the D50 and D84, respectively. In hydrographs L, differences between D50 and D84 on rising and falling limbs is even larger at the low discharge steps (up to 40% and 35%, respectively), but there is no substantial difference at the higher discharge steps (Figure 5).

Figure 5.

Bed surface (a) (Ds) and transport grain size (b) (Dt) at flow steps during hydrograph L1. Flow steps are identified by the discharge values (in m2 s−1). Flow steps on the rising limb of hydrograph are identified by solid lines (and R notation), falling limbs by dashed lines (and F notation), and the peak flow by a gray line (and P notation). The grain size of bulk sediment mixture is plotted as a gray line as well.

3.2. Sediment Incipient Motion During Hydrographs

[20] Rates and grain sizes of transported sediments were used to assess the incipient motion of sediment of various sizes during each flow step. Following Parker et al. [1982], incipient motion was defined as the dimensionless shear stress corresponding to a very low but measurable reference transport rate, Wr* = 0.002. As previously done by Wilcock and Crowe [2003], fractional dimensionless transport rates (Wi*) were calculated with reference to the size distribution of the bed surface rather than subsurface:

display math

where qb is the volumetric sediment transport rate per unit width, Pi is the mass fraction of material in the ith grain size range of the transported sediment mixture, Δ is the relative density of the sediments (ρs/ρρ), ρs is the density of sediment, ρ is the density of water, g is the acceleration due to gravity, and Fi is the mass fraction of sediment in the ith size range of the surface sediment. As commonly applied in bed load transport studies, fractional dimensionless transport rates (Wi*) are evaluated against the dimensionless shear stress (τi*), defined as:

display math

where τ is the shear stress acting on the bed, and Di is the grain size of the ith size fraction of the surface sediment.

[21] Figure 6 shows the dimensionless fractional transport rates versus the dimensionless shear stress plotted for grain sizes ranging from 1.4 to 22.6 mm. As expected, transport rates are larger during H than M and L runs, and dimensionless shear stresses are higher for the finer sediment fractions.

Figure 6.

Fractional dimensionless bed load transport rate (Wi*) plotted versus dimensionless shear stress (τi*) for each transported grain size. For sake of clarity, only one of the repetitions of hydrographs (a) H (H2) and (c) L (L1) are showed along with the graph of hydrograph (b) M. Reference value Wr* = 0.002 at which sediment transport is to be considered negligible [Parker et al., 1982] is also plotted.

[22] Data shown in Figure 6 were used to derive the reference dimensionless shear stress (τri*), defined as the value of τi* at which Wi* = Wr*. In doing that, all three repetitions were considered in the case of hydrographs H and L. Values of τri* were determined by eye as previously done in other studies [Wilcock and McArdell, 1993; Wilcock and Crowe, 2003]. For H and M hydrographs, observed values of Wi* were larger (usually within one order of magnitude) than Wr*, and required extrapolation.

[23] Values of the reference shear stress expressed in dimensional terms (τri) are plotted against grain size in Figure 7. Values of τri fluctuate considerably, especially those referring to H runs which required more extrapolation. However, it appears that, in general, the values of τriextrapolated from the rising-limb transport relations plot lower than those extrapolated from the falling limb relations. Furthermore, this is consistently verified in the three types of hydrographs (Figure 7). Lower values of τriduring the rising limbs of hydrographs imply that sediments are more easily entrained before than after the peak of hydrographs, which is well-matched by the observed reduction in sediment transport rates on the falling limbs. It is worth mentioning that, if fractional dimensionless transport rates are calculated using the subsurface (fi) rather than the surface (Fi) grain size, the overall pattern of Figure 6 is maintained, with only lower values of Wi* for the finer fractions and higher values for the coarsest. Using subsurface rather than surface referenced fractional transport rate makes no difference in the calculation of τri, and differences between rising and falling limbs of the three hydrographs are maintained.

Figure 7.

Reference shear stress for each grain size fraction derived from sediment transport measurements taken during rising and falling limbs (solid and dashed black lines, respectively), and peaks (solid gray line) of hydrographs. All measurements taken during repetitions were included in deriving reference shear stress for hydrographs (a) H and (c) L. Because only one repetition was available, reference shear stress was not calculated for the peak flow of hydrograph (b) M.

[24] If the reference shear stress is computed for the surface D50 and D84 and plotted against flow discharges representative of the rising, peak, and falling limbs of hydrographs, a counterclockwise hysteresis pattern is depicted (Figure 8). The reference shear stresses for the surface D50 and D84 were 9.8% and 7.7% higher on the falling limb of hydrograph L, respectively. These percentages increased to 12.8% and 17.6% for hydrograph M. The largest difference between the reference shear stress on rising and falling limbs was observed for hydrograph H, with differences around 41% and 54% for the D50 and D84, respectively.

Figure 8.

Counterclockwise hysteresis of reference shear stress as calculated for the D50 and D84 of the surface sediments for hydrographs (a) H and (b) L. The flow step on the rising limb of hydrograph is identified by a solid line (and R notation), while falling limb by a dashed line (and F notation). Because no reference values are available for peak flow of hydrograph M, this graph is not showed.

3.3. Partial Transport During Hydrographs

[25] The term partial transport was first used by Wilcock and McArdell [1997] to describe conditions in which only a portion of the surface layer grains are mobile during a transport event. Wilcock and McArdell [1997]observed the extent of partial transport in near-equilibrium/long-run experiments under sediment recirculation conditions. In the present study, flow steps were relatively short and were not necessarily representative of equilibrium conditions. However, quantifying the extent of partial transport can shed further light on sediment mobility differences between flow steps during the rising and falling limbs of the hydrographs.

[26] The percentage of active grains of each size entrained from the bed (yi) increased over time, approaching or reaching 100% toward the end of the runs for the finer sizes (Figure 9). Exponential regression curves of the percentage of grains entrained, yi = exp (−k t) were fit for each grain size, as previously done by Wilcock and McArdell [1997]. This procedure was applied to calculate the extent of partial transport at the end of the flow step (Yi) which represents the percentage of surface grains in a certain size class that were transported during the period of observation, i.e., the duration of each hydrograph flow step.

Figure 9.

Percentage of active grains of different size entrained overt time. Exponential regression curves fitted for each grain size are showed as well. The values of yi at the end of each flow step represent the limiting value Yi, thus the extent of partial transport for that grain size. The graph represents the last 100 min of a 120 min 0.038 m2 s−1 flow step of a L hydrograph falling limb.

[27] Figure 10 shows the percentages of active grains Yi of different sizes during each flow step of the three different hydrographs. These results show that Yitends to decrease for coarser grain fractions and smaller discharges. Comparisons between same flows of different hydrographs are not possible because of the difference in the durations of each step. However, even if derived at non-equilibrium conditions, differences in values ofYi for the same flow steps on rising and falling limbs of the same hydrographs highlight interesting differences in sediment mobility processes. Figure 10 shows that a systematic difference in Yi occurs between the rising and falling limbs of the hydrographs: Yi is larger during the rising limbs and sediments are thus more easily mobilized before the peak of hydrographs. In other words, on the falling limbs partial transport is maintained but grains are less mobile, while bed slope and flow depth remain unchanged. This difference is consistent for all flow steps of the three types of hydrographs. For example, the extent of active grains of the 16 mm class was 0.8 and 0.5 at 0.054 m2 s−1 during the rising and falling limb of hydrograph H, respectively. Consistently, Yi for 16 mm was 0.5 and 0.25 at 0.044 m2 s−1 during the rising and falling limb of hydrograph M, respectively. At flow steps of 0.031 m2 s−1 during the rising and falling limb of hydrograph L, Yi was 0.65 and 0.37 for the grain size class of 8 mm (Figure 10).

Figure 10.

Extent of active sediments in the bed (Yi) at each flow step during hydrographs. Flow steps are identified by the discharge values (in m2 s−1). Flow steps on the rising limb of hydrograph are identified by solid lines (and R notation), falling limbs by dashed lines (and F notation), and the peak flow by a gray line (and P notation). For clarity, the representative repetitions of hydrographs (a) H (H2) and (c) L (L1) are showed along with the graph of hydrograph (b) M.

[28] If Yi is computed for the surface D50 and D84 and plotted against flow discharges representative of the rising, peak, and falling limbs of hydrographs, a clockwise hysteresis is observed (Figure 11); this is consistent with the counterclockwise pattern recognized for the transport grain size and the reference shear stress, and with the clockwise pattern of sediment transport rate. The active proportion of surface sediments at 0.044 m2 s−1 was 14% and 31% lower on the falling limb of hydrograph L for the D50 and D84, respectively. These percentages reduced to 2% and 10% for a larger discharge (0.064 m2 s−1) of the same hydrograph L. If hydrograph L is considered, the active proportion of surface sediments at 0.024 m2 s−1 was 50% and 92% lower on the falling limb for the D50 and D84, respectively. These percentages reduced to 3% and 22% for a larger flow step (0.038 m2 s−1) of the same hydrograph L (Figure 11).

Figure 11.

Clockwise hysteresis of proportion of active sediments as calculated for the D50 and D84 of the surface sediments for hydrographs (a) H, (b) M, and (c) L. The flow steps on the rising limb of hydrographs are identified by solid lines (and R notation), while falling limb by dashed lines (and F notation).

3.4. Organization of Surface Sediment During Hydrographs

[29] Laser scan surveys of the bed taken at the end of the first and last steps, and at the end of the peak step, are available for three hydrographs (H2, M, and L1). The probability density function (PDFs) of the bed elevations reveals that the curves are narrower and higher at the beginning and the end of the hydrographs, and that the peak flows tend to produce broader curves with greater deviations away from the mean (zero) value (Figure 12). It is worth noting that, for the H and M hydrographs, the rising and falling limbs change the PDF in a similar manner but by a different degree, larger in the rising limbs. Also, the PDFs before the rising limb of the three hydrographs are almost identical in shape and distribution, showing that the initial water-worked bed was very similar at the beginning of hydrograph runs, so the results from each hydrograph are comparable.

Figure 12.

Probability density functions of the bed elevations at the end of the first and last flow step (solid and dashed black lines, respectively) and at the end of the peak step (gray line) for the hydrographs (a) H2, (b) M, and (c) L1.

[30] The standard deviation of the bed surface elevation (σ), which can be considered the vertical roughness length scale of water-worked gravel beds [Nikora et al., 1998; Aberle and Smart, 2003; Aberle and Nikora, 2006] shows that the bed was smoother before and after the peak of hydrographs (Figure 13a), even if differences are relatively small in absolute terms. After the peak flows, σincreased proportionally to the magnitude of the hydrograph, being 26%, 21%, and 7% larger than the beginning of hydrographs for experiments H, M, and L, respectively. It seems reasonable to relate this to the fact that coarse grains are entrained and actively transported during larger peak flows, and that they continue to protrude into the flow, increasing the vertical roughness scale relative to lower flow steps. Because the grain size of the bed sediments remains virtually unchanged during the hydrographs, this change in roughness needs to be related to a change in surface organization of those grains which are responsible for the change in roughness. During the falling limb of the hydrographs the bed surface tends to become smoother, likely because the sediment forming the surface becomes more structured and imbricated and coarser clasts protrude less above the surrounding bed. The duration of the falling limb seems to have played a central role in the degree of roughness reduction after the peak. In fact, roughness returned to the pre-hydrograph value for the long experiment L, but reached a final value 13% higher than before the peak flow for experiments M and H (Figure 13a).

Figure 13.

The counterclockwise hysteresis of standard deviation of bed elevations (a) (σ) and scaling exponent derived for the stream-wise direction (b) (Hx), and the dominant clockwise hysteresis of correlation length scales of the bed surface elevations in the stream-wise direction (c) (Lx). The flow steps on the rising limb of hydrographs are identified by solid lines (and R notation), while falling limb by dashed lines (and F notation).

[31] In order to provide further insight into the dynamics of the bed surface organization due to hydrograph peak flows, a 2-D second-order structure function was applied to the bed surface elevations. Comprehensive details on previous applications of semivariograms to analyze gravel bed surfaces are provided byGoring et al. [1999], Marion et al. [2003], Smart et al. [2004], Aberle and Nikora [2006], and Cooper and Tait [2009] among others. Briefly, structure functions D(lx, ly) are used to assess the correlation between elevations zb(x, y) at various spatial scales and in different directions:

display math

where lx = x and ly = y are spatial lags, n and m are multiplying coefficients for the spatial lags, δx and δy are the sampling intervals, and N and Mare the total number of measured bed elevations in the stream-wise x and cross-stream y directions, respectively. For a globally homogeneous random field, the second-order structure function has the following relationship with the correlation functionR(lx, ly):

display math

Equation (4) indicates that at large spatial lags when R(lx, ly) → 0 and D → 2σ2 the data are spatially uncorrelated and the lags at which D → 2σ2can be used to derive characteristic stream-wise and cross-stream length scales [Nikora et al., 1998; Aberle and Nikora, 2006]. The 2-D structure functions are then plotted against the spatial lags in the stream-wise (lx) direction. At small spatial lags the curves can be described with a power function between D(lx = 0)/2σ2 and lx2Hx [Nikora et al., 1998; Aberle and Nikora, 2006]. At this limited spatial scale the scaling region is identified and Hxis called the scaling exponent in the stream-wise direction. At larger spatial lags the structure functions eventually approach the saturation region whereD/2σ2 reach unity [Nikora et al., 1998; Nikora and Walsh, 2004; Aberle and Nikora, 2006].

[32] The scaling region (Hx) can be considered a measure of the complexity of bed elevations, with topographical complexity varying inversely with Hx [Bergeron, 1996]. The scaling exponent increases very little (1 to 2%) from low flow to the peak flow in hydrographs M and L, and after the peak flow the Hx exponent is reduced but reaches larger values than before the peaks (Figure 13b). In the case of hydrograph H, after the peak the scaling dimension increased by up to 12%, and maintained very high values after the falling limb. Overall, the scaling exponent showed a counterclockwise hysteresis pattern during floods, apparently suggesting that larger flows shape the channel bed to a less complex surface.

[33] As proposed by Nikora et al. [1998], the correlation length scale (Lx) of the bed surface elevations have been determined as the spatial lags the stream-wise (lx) direction at which D/2σ2 approaches unity. The correlation length scales were larger before the peak flow steps for hydrographs H (12%) and L (1%), suggesting that the bed evolved during the rising limbs of the hydrographs by reducing the longitudinal dimension of bed features and particle structures (Figure 13c). Unexpectedly, the correlation length scale decreased even more during the falling limb of the hydrographs H (14%) and L (10%), meaning the bed was unable to restructure large particle structures and features likely due to the very low duration of hydrograph H and to the lack of mobility of large particles in the case of hydrograph L. In contrast to hydrographs L and H, which feature a clockwise cycle of Lx, run M features a counterclockwise pattern, with Lx being 31% larger at the flow peak than at the low flow, and experiencing a later reduction (19%) during the falling limb of the hydrograph (Figure 13c).

4. Discussion

4.1. Changes in Sediment Transport, Sediment Mobility and Surface Particle Arrangement During Hydrographs

[34] Several cases of hysteresis between fluid and sediment discharges during floods have been reported for gravel bed rivers. The observed pattern tends to be counterclockwise when sediment transport is larger after the flood peak, and this has been related to the break-out of the well-structured static armor layer [Kuhnle, 1992a], delay in sediment supply [Habersack et al., 2001], consolidation of grains in the bed during intraflood periods [Reid et al., 1985], and passages of bed forms [Bell and Sutherland, 1983], none of which can be related to a condition of mobile armor layer and unlimited sediment supply. Both clockwise [Hassan et al., 2006; Humphries et al., 2012] and counterclockwise hysteresis [Lee et al., 2004] have been observed in flume experiments, but in all cases these patterns seem to be due to temporal variation of sediment availability from upstream or to the passage of bed forms or sediment pulses. In fact, there are no flume observations on bed load hysteresis under unlimited sediment supply conditions, and no attempts have been made to explain processes of sediment entrainment and transport during hydrographs under these conditions.

[35] In the present experiments, consistent hysteresis patterns of variables directly related to the processes of sediment entrainment and transport and to the bed surface organization, have been observed (Figure 14). Bed load exhibits a marked clockwise pattern in the three types of hydrographs, which cannot be related to changes in sediment availability from upstream. This is because sediment was recirculated continuously and thus the sediment rate and size furnished at the upstream end of the flume depends only on the previous conditions of the bed and the flow rate [Parker and Wilcock, 1993]. Under these conditions, the sediment size of the bed appears relatively invariant during the experiments. This would support the field observation of Andrews and Erman [1986] and Clayton and Pitlick [2008] and the inverse calculation results of Wilcock and DeTemple [2005]that the bed and the bed load adjust to produce a variable transport grain size and a persistent bed surface grain size over floods. In the present experiments, grain size distribution of the bed has been manually derived from close-range photos. Even if no clear evidence of a reduction of sand percentage (>1.4 mm) from the bed surface has been detected, vertical winnowing of finer fractions from the surface to the subsurface layer cannot be excluded, and may represent an important process during longer hydrographs with a coarser gravel matrix. In fact, vertical infiltration has been previously claimed to represent an important process in gravel bed rivers [Frostick et al., 2006; Wooster et al., 2008; Gibson et al., 2009], and certainly a decrease in sand percentage from the surface would contribute to a reduction in the sediment transport rate [Wilcock et al., 2001; Curran and Wilcock, 2005].

Figure 14.

Conceptual scheme of hysteresis cycles of sediment sizes, transport rate, incipient motion, sediment mobility and bed surface nature during hydrographs under sediment recirculating conditions.

[36] Assuming that vertical winnowing of sand was a negligible process in the short experiments, and having verified the invariance of surface grain size throughout the hydrographs, changes in bed load transport at similar flow steps before and after hydrograph peaks have to be related to the different grain size of transported sediments or different process of sediment entrainment from the bed. In fact, being coarser during the falling limbs of hydrographs, the grain size of transported sediments exhibited a counterclockwise hysteresis (Figure 14). This could be potentially due to a reduced availability of fine sediment from the surface because of vertical winnowing of sand through the gravel framework, which was not experienced to a measurable degree during the experiments or to a lower mobility of sediment from the bed. Indeed, the degree of partial transport consistently reduced after the peak of hydrographs (clockwise hysteresis), and the reference shear stress for sediment entrainment increased in the falling limbs of hydrographs (counterclockwise hysteresis). In a recent analysis of bed load measurements taken in the Trinity River (CA) during floods, Gaeuman [2010] observed a marked clockwise hysteresis over individual events. Interestingly, he claimed that this pattern was due to changes in sediment entrainment after the peak. Reference shear stresses for the median size remained constant, but smaller fractions were less mobile in the falling limb (higher τri), in which transport conditions were closer to equal mobility after the flood peak. This represents a remarkable insight into the dynamics of bed load during flood events. As pointed out by Gaeuman [2010], the following potential mechanisms can lead to a clockwise hysteresis of bed load in gravel bed rivers: a coarsening of the bed, an increase in reference shear stress, or a change in the bed surface texture. In the laboratory conditions, the first and the second mechanism have been verified, corroborated by clear evidences of a reduction of sediment mobility in the falling limbs of hydrographs.

[37] Regarding the change in bed surface texture, the results clearly show a counterclockwise hysteresis of standard deviation of the bed surface elevations (σ in Figure 14). It is worth stressing that the standard deviation increases whereas the grain size of the bed remains relatively invariant at higher discharge. This has been previously reported by Wong et al. [2007] and Mao et al. [2011], and is due to the fact that mobile armor layers are composed of coarse grains which are actively transported. The fact that the vertical roughness is higher during the falling limb of hydrographs suggests that the bed has changed the geometrical organization of the coarsest grains (also because transported sediments are coarser) in a manner which is proportional to the magnitude and duration of the hydrographs.

[38] During these experiments, no detailed flow field measurements have been taken. However, it is likely that, even if the grain size remained invariant, the different arrangement of surface grains influenced the flow field. For instance, Cooper et al. [2008] demonstrated that surface grain-size and roughness height cannot accurately account for the resistance imposed by a water-worked gravel bed on the flow, stressing the importance of grain orientation. Even ignoring the changes in the flow field in the present experiments, if the grain size of the bed remains invariant but there is a change in surface organization, then the change in sediment entrainment thresholds should be related to changes in surface topography. Indeed, using a numerical model, Measures and Tait [2008] showed that remote sheltering due to surface sediment organization has a very strong influence on grain entrainment.

[39] The scaling exponent Hxof 2-D structure functions derived from the PDFs of the beds exhibits a counterclockwise pattern when its variation with discharge is analyzed, indicating that the bed becomes less complex after the falling limb of hydrographs. This would contrast with the evidence of a higher surface roughness after the peak of hydrographs. In fact, the trends are not entirely straightforward to interpret and might be biased by the very marked change in H exponent during hydrograph H, because during hydrographs M and L the scaling exponent remains relatively unchanged. Similarly, the apparent clockwise cycle of correlation length scales of the bed elevations (Lx) is to be considered carefully because it is not entirely obvious for all hydrographs. However, a decrease in Lx during the falling limbs of hydrographs would entail that grain structures are smaller, probably due to the fact that coarse grains are less mobile and have thus less chance of becoming organized in larger structures. Intriguingly, this is in agreement with the recent results of Piedra et al. [2012], who showed that sediments in the bed are more resistant to entrainment where coarse-grain clusters are less developed and coarse grains are distributed more widely over the bed surface. This would also help explaining the higher dimensional reference shear stress during peak flows of hydrographs.

4.2. Effects of the Rate and Duration of Antecedent Flows Effects on Bed Load Transport and Bed Surface Structures

[40] To date, a still almost neglected factor which has a strong influence on incipient motion and bed load transport is the “history” of flows over a mobile bed, with very few studies being carried out on this issue. However, there is increasing evidence that even flows lower than the critical threshold for grain incipient motion can strongly affect sediment transport. Frostick et al. [1984] and Reid et al. [1985]indicated that long inter-flood period stabilizes the gravel framework increasing the shear stresses needed to entrain sediment.Paphitis and Collins [2005] and Monteith and Pender [2005]showed that larger critical shear stresses are required to move grains from a bed previously exposed to longer and larger under-threshold flows.Haynes and Pender [2007] also added that higher antecedent shear stresses reduce bed stability due to the selective entrainment of the fine matrix within the bed, but that a longer duration of the antecedent shear stress increases bed stability due to local particle rearrangement.

[41] Over-threshold flows are even more important in structuring bed surface structures and thus in determining sediment transport. The low-magnitude peak flow of hydrograph L caused a moderate increase of bed roughness and complexity, and its long duration allowed the surface clasts to rearrange as to the point that bed roughness returned to pre-disturbance values but with different arrangement. As a result, sediment transport in the falling limb is much lower (up to one order of magnitude) than in the rising limb of L hydrograph. The opposite occurred during the short/high-magnitude hydrograph H, which left a rougher and looser bed surface.

[42] Clearly, the composition and stability of the bed surface layer is time-dependent. Long/low-magnitude floods or even long periods of under-threshold flows promote the consolidation of the bed, and lower sediment transport until a larger magnitude flood rearranges the bed, loosening it. It is worth stressing that this dynamics appear over mobile armor layers under sediment recirculation conditions. This would imply that the antecedent flow conditioning sequence could be reduced to a correction factor for bed load transport formulas. This factor should represent the flow duration curve from the previous high-magnitude event able to restructure the bed (e.g., mobilizing even theD84 as fully mobile conditions in the sense of Wilcock and McArdell [1997]). Also, because timings and temporal sequences of flood events can have a strong influence on bed load transport [Cohen et al., 2010; Recking et al., 2012] this correction factor for bed load transport formulas should also include a term characterizing the temporal sequence of disturbance of different magnitude. The present study reveals that differences between rising and falling limb of hydrographs, mainly due to changes in the degree of grain organization in the mobile armor layer, could be quantified by analyzing simple statistical moments and second-order structure functions. Although this needs to be further explored both in flume and in the field, it highlights the potential of using relatively rapid terrestrial laser scanning to unveil dominant sediment transport processes. In fact, differences in roughness, imbrication and orientation at the grain- and cluster-scales correspond to significant differences in sediment transport dynamics, supply conditions, transport rate, and armor ratio [Hodge et al., 2009; Mao et al., 2011], and could be used to assess the degree of sediment transport overestimation by sediment transport capacity formulas.

5. Summary

[43] Flume simulations of stepped hydrographs conducted under sediment recirculation conditions indicate that sediment transport during the falling limb is lower than during the rising limb of three hydrographs (clockwise hysteresis), different in terms of duration and peak magnitude. This reduction is more evident for the long/low-magnitude hydrograph. The grain size of the bed remains virtually constant during hydrographs, and the grain size of the transported sediments increased after the peaks of hydrographs, revealing a counterclockwise hysteresis pattern. During the falling limb of hydrographs, sediments are also more difficult to entrain (larger reference shear stress), and are actually less mobile. An analysis of detailed laser scan bed surveys reveals that, even if the grain size of the bed remain invariant, significant changes occurs in terms of vertical roughness and rearrangement of particles and sediment structures. The bed roughness increased proportionally to the magnitude of the hydrograph, and then reduced during the falling limb of hydrographs because sediment surface becomes organized in structures. Only the long hydrographs allows the bed to reach the initial roughness, whereas the short/high-magnitude disturbance left a rougher and less organize bed surface. The paper emphasizes the need of considering the antecedent flow history (duration and sequences of disturbances) in assessing sediment entrainment and transport even under unlimited sediment supply conditions. Finally, it provides preliminary evidence that detailed survey of gravel bed rivers could allow inference of the sediment supply and transport conditions.

Acknowledgments

[44] This research was supported by a Marie Curie Intra European Fellowship (219294, FLOODSETS) within the 7th European Community Framework Program while the author was based at the Department of Geography of the University of Hull (UK). Diego Ravazzolo, Matteo Dalla Costa, and Elena Biasetto helped in digitizing grains on the photos. Lynne Frostick is thanked for providing useful suggestions during the experiments. The author is indebted to James Cooper for performing the laser scanner analysis and for continuous constructive discussion during the experiments. James Cooper and David Gaeuman are thanked for providing detailed comments on an earlier draft of the paper. The author also thanks three anonymous reviewers, the Editor, and the Associate Editor (John Pitlick) for their careful reading and useful comments on the paper.

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