Influence of Sediment Supply Timing on Bedload Transport and Bed Surface Texture During a Single Experimental Hydrograph in Gravel Bed Rivers

Channel stability and sediment transport in gravel bed streams depend on temporally and spatially variable fluid forces, bed surface structures, armoring, and sediment supply/storage. Of particular interest here is the influence of sediment supply timing on bedload transport rate and grain size distribution, bed surface composition and channel morphology. We conducted flume experiments in a sediment feed flume with poorly sorted sediment. A symmetrical, identical stepped hydrograph was used with five different sediment feeding schemes: no feed, constant feed, rising‐limb only feed, falling‐limb only feed, and variable feed. The same sediment mass of 800 kg was fed during each experiment. Sediment transport rates ranged over five orders of magnitude regardless of feeding scheme. Clockwise hysteresis was observed for bedload transport rate and bedload grain size, that is, the transport rate was larger and coarser during the rising limb. Counterclockwise hysteresis was observed for the grain size distribution of the bed surface, that is, the bed surface was finest during the rising limb. In all experiments sediment yield during the rising was higher than during the falling limb, indicating that the rising limb is more capable to transport the supplied sediment. Our study provides insight on how timing of sediment supply influences sediment transport and bed surface during a single hydrograph, essential information for artificial sediment supply projects to restore and habilitate gravel bed streams.


Introduction
Bedload transport in gravel bed streams is controlled by water and sediment supply (including volume, timing, frequency, and grain size), bed surface structures, and channel morphology.However, how sediment supply and flow discharge variability impact channel morphology, bed surface texture, bedload transport rate and grain size has not been fully studied.In this paper, we explore how the timing of sediment supply over one hydrograph influences bedload transport and bed surface characteristics.Such information is essential for understanding gravel-bed streams morphodynamics, improving the effectiveness of sediment augmentation in streams, defining sediment management practices, and developing predictive tools to help the design and management of flood hazard mitigation and restoration of degraded streams.For example, information on the influence of sediment supply timing on channel dynamics will provide information on the best feeding scenario(s) that will likely meet the goals of research or restoration projects.
The importance of flow and sediment supply variability, as well as event history (sequencing) on gravel bed river morphology, bed surface texture, and structure has been long recognized (e.g., Beven, 2015;Wolman & • Sediment yield during a single hydrograph is dominated by sediment supply in the rising limb • Clockwise hysteresis characterizes sediment transport despite the sediment feed timing • Counterclockwise hysteresis was observed for bed surface grain size in most experiments

Supporting Information:
Supporting Information may be found in the online version of this article. 10.1029/2023WR035406 2 of 18 of time varying sediment supply on bedload transport rate, bedload transport grain size distribution, bed surface grain size, and channel morphology.Field (Hassan & Church, 2001;Hassan et al., 2014;Kuhnle, 1992;Moog & Whiting, 1998;I. Reid et al., 1985) and laboratory (Humphries et al., 2012;Lee et al., 2004;Mao, 2018;Mao et al., 2014;Wang et al., 2015Wang et al., , 2019Wang et al., , 2021) ) evidence shows that sediment transport during a flood is highly variable and the overall relation between flow and transport rate is nonlinear (Mao, 2018;Wang et al., 2021;Zuecco et al., 2016).However, we are not aware of any systematic study that examined the impact of time varying sediment supply on bedload transport rate and texture, bed surface grain size and channel morphology during a hydrograph.
Hysteresis in sediment transport, that is, the nonlinear relationship between water discharge and sediment transport rate (Figure 1), during a flood has been attributed to hydrograph shape (magnitude, duration), sediment supply (rate and grain size), bed state (grain size, armoring, bed surface structures), and channel morphology (Hassan et al., 2014;Humphries et al., 2012;Lee et al., 2004;Mao, 2018;Mao et al., 2014;I. Reid et al., 1985;Wang et al., 2021).Using a single hydrograph and no feed conditions, Guney et al. (2013) conducted flume experiment over armored and nonarmored bed surfaces.The experiments showed clockwise hysteresis (highest bedload transport rate during the rising limb) over nonarmored beds and counterclockwise over armored beds.Guney et al. (2013) attributed the differences in the hysteresis to sediment availability and bed surface conditions.Laboratory experiments also suggest that clockwise hysteresis in bedload transport rate is associated with sediment supply rate (Hassan et al., 2006;Humphries et al., 2012;Mao, 2012) and counterclockwise hysteresis is associated with bedform (e.g., dunes) passage or armor destruction at high flow (Bombar et al., 2011;Lee et al., 2004).Further, Martin and Jerolmack (2013) showed that the faster the rate of change in flow discharge, the greater is hysteresis in bedload transport rate, that is, the difference between bedload rate during rising and falling limbs of a hydrograph at the same flow discharge.
Variations in the relation between sediment transport rate and water discharge has been the focus of many field monitoring projects (e.g., Emmett, 1975;Hassan & Church, 2001;Moog & Whiting, 1998;Nanson, 1974;I. Reid et al., 1985).Working on mountain streams, Moog and Whiting (1998) observed clockwise hysteresis in bedload transport rate demonstrating the importance of sediment supply on sediment dynamics.Counterclockwise hysteresis in the sediment transport rate was linked to breakup of the armor layer and the bed mobilization after peak flow (e.g., Downs & Soar, 2021;I. Reid et al., 1985).Using high resolution bedload data collected during two high flows, Down and Soar (2021) reported a complex pattern of hysteresis: clockwise during the rising limbs and counterclockwise during the falling limbs.They linked the clockwise pattern to sediment supply and counterclockwise to the breakup of the bed surface.Roth et al. (2014) related hysteresis in sediment transport rate to the migration of sediment pulses downstream of a removed dam.Although statistics on the most common type of hysteresis is not available, it seems that clockwise is the most dominant one.For example, Hassan et al. ( 2014) ) no hysteresis where there is no difference between the rising and falling limbs and the peak sediment transport is coincident with the peak discharge, (c, d) a clockwise hysteresis where the peak sediment transport occurs before peak discharge, (e, f) a counterclockwise hysteresis where peak sediment transport occurs after peak discharge, and (g, h) combined.These trends can be combined in different orders and at different scales to create more complicated hysteresis trends.Q s is the sediment transport rate and Q is the flow discharge.Modified from Williams (1989). 10.1029/2023WR035406 3 of 18 reported clockwise hysteresis in bedload transport rate for all eight examined cases.Flume and field studies notwithstanding, physical processes that cause the hysteresis in bedload transport (both the rate and texture) and bed surface grain size remain poorly understood.More specifically, subtle differences in experimental design or forcing can result in opposing styles of hysteresis under the same bed condition.
In addition to the characteristics of an individual flood, flood history (defined as a sequence of floods of different magnitudes and duration) influences bedload transport capacity, sediment entrainment and transport, bed grain size distribution, bed surface armoring and surface structures (An et al., 2021;Curran et al., 2015;Frostick et al., 1984;Haynes & Pender, 2007;Mao, 2018;Piedra et al., 2012;I. Reid et al., 1985;Waters & Curran, 2015).Mao (2018) noticed that vertical sorting in flume experiment caused a 40% decrease in sediment transport rate when large flood follows an event of similar magnitude.When a low magnitude event proceeds large flood, Mao (2018) observed about 70% reduction in bedload transport rate due to bed surface structuring and armoring.In these experiments, Mao (2018) documented both clockwise and counter clockwise hysteresis in bedload transport rate.
Bedload size distribution, bed surface texture and bed topography adjust in response to changes in flow and sediment supply.Of particular interest here is the response of the bed surface grain size because of armor development, surface roughness, and bed stability.Under no sediment feed conditions and relatively long-duration floods, gravel beds tend to develop an armor surface (Hassan et al., 2006).Whereas, short hydrographs and above capacity sediment supply are likely to develop unarmored bed surfaces (Hassan et al., 2006).Wilcock and DeTemple (2005) demonstrated that the bed surface grain size distribution remained essentially the same at different flood flows and asserted that armoring persists even under relatively high flows.Laboratory experiments confirmed this finding showing that armoring persisted over a hydrograph but bed surface packing and surface arrangements changed during the hydrograph (Mao, 2012).Studies on the impact of sediment pulses on bed surface grain size and structure yielded similar results, the original armored bed become buried by the supplied sediment and got re-exposed shortly after the halting of the sediment feed (Hassan, Saletti, Zhang, et al., 2020) but research is needed to fully understand the complex adjustment of the bed (texture, structure, and topography) to changes in hydrograph characteristics and sediment supply regime.
The effects of cycled hydrographs and sediment pulses on sediment transport and bed evolution is another avenue of research that can improve understanding of how gravel beds adjust to different flow regimes, sediment supply rates and caliber with experimental and numerical modeling (e.g., An, Cui, et al., 2017;An, Fu, et al., 2017;Parker et al., 2007;Philipps et al., 2018;Viparelli et al., 2011;Wong & Parker, 2006).This approach is fundamentally different from single hydrograph studies discussed above in that it is based on how a channel subject to repeated hydrograph and/or sediment pulses reaches conditions of equilibrium (An, Cui, et al., 2017;An, Fu, et al., 2017).In presence of constant sediment supply, this equilibrium is reached downstream of a short reach called hydrograph boundary layer where bed elevation and surface size distribution cyclically vary over the hydrograph with erosion and bed surface coarsening during the rising limb and deposition and bed surface fining during the falling limb (An, Fu, et al., 2017;Parker et al., 2007;Viparelli et al., 2011).If the sediment supply is fed with the same time variability in rate and grain size distribution observed downstream of the hydrograph boundary layer, the boundary layer will disappear and the entire reach will be characterized by non-time varying bed levels and bed surface size distributions (Parker et al., 2007).Equilibrium conditions are not observed in single hydrograph studies, where the bed is remixed to set to initial conditions before each experiment, thus restricting the comparison with the cycled hydrograph studies.
Here, we present results of flume experiments specifically designed to study the effect of sediment feed timing during a single hydrograph.Experiments were run with identical symmetric hydrographs, sediment grain size distribution, sediment feed volume, but different timing and rate of sediment supply.We used the results to test three hypotheses.(a) Bedload transport rate over a hydrograph varies with the timing and magnitude of sediment supply.High supply on the rising limb leads to clockwise hysteresis (higher transport rates during the rising limb) whereas high supply on the falling limb results in counterclockwise hysteresis (higher transport during the falling limb).(b) Bedload grain size distribution coarsens at the end of the hydrograph in absence of sediment supply, as well as in case of constant sediment supply and the case of high sediment supply during the rising limb.This results in counterclockwise hysteresis of the bed surface and bedload grain sizes.Further, in the case of high supply rate during the falling limb, the transport and availability of fine sediment on the bed surface increases with time resulting in a clockwise hysteresis of grain sizes of the bed.(c) The characteristics of armor layers and surface structures depend on sediment supply rate during the falling limb.Increasing bedload transport rate during the rising limb inhibits the development of surface features and tends to destroy existing structures.In the absence of sediment supply over the falling limb, winnowing will coarsen the bed surface sediment and will help the formation of surface structures.

Experimental Design, Methodology, and Data
Experiments were conducted in the Mountain Channel Hydraulic Experimental Laboratory at the University of British Columbia in a 18 m long, 1 m wide, and 1 m deep tilting flume (Figure 2a).Our flume experiments were guided by field measurements conducted at East Creek, a small gravel-bed stream near Vancouver, British Columbia (Papangelakis & Hassan, 2016;Wlodarczyk et al., 2023).The initial bed slope was 0.022 m/m which is similar to the rapid reach of East Creek (Cienciala & Hassan, 2013;Papangelakis & Hassan, 2016).The sediment used in the experiments (parent material) was a mixture of sand and gravel with grain sizes ranging between 0.5 and 32 mm with a median diameter (D 50 ) of 7.8 mm (Figure 2b).The sediment mixture was scaled to the bed surface of East Creek (scale 1:4) with the maximum size in the flume (32 mm) approximating the largest grain size class of 128 mm observed in the field.Sediment finer than 0.5 mm was excluded to avoid material moving in suspension.The same mixture of sediment was used by Chartrand et al. (2018) and Hassan et al. (2022).The upstream 8 m long section consisted of a fixed and immobile flat bed made of particles with grain size equal to the D 90 of the parent material (D 90 being the diameter such that 90% of the parent material is finer).The observational reach extended over the downstream 10 m of the flume with a well-mixed mobile bed made of parent material and initial depth of 10 cm.Sediment was fed to the upstream end of the flume by a conveyor belt with adjustable speeds which can feed parent material at a specified rate (Figure 2a).For visualization, the parent material was sieved in half phi intervals and painted in different colors.The sediment transport capacity of each flow was estimated by running no feed tests and measuring the sediment collected at the downstream end of the test reach.
Flow discharge and the measurement frequency are presented in Figure 3 in blue and red, respectively.Water surface and bed elevation were measured at 0.5 m spacing along the center of the test reach using a mechanical point gauge with a precision of ±0.001 m at 10, 30-, and 50-min mark of each hour.Water depth and bed slope were computed from the elevation and the depth-slope product was used to calculate bed shear stress.
To determine the sediment transport rate and grain size at the flume outlet we used a light table (Figure 2a).The light table camera operates at 27-32 frames per second and allows for real time measurements of bedload transport rate (for details see An et al., 2021;Hassan, Saletti, Johnson, et al., 2020;Zimmermann et al., 2008).Sediment transport rates were collected at the resolution of 1 s and averaged over 5 min.The 5 min interval was selected to document the short-term variability in both bedload transport rate and grain size.To calculate sediment yield, we summed the 5 min bedload transport measurements over the rising limb, the falling limb and the entire hydrograph.Calibration measurements suggest that the light table overestimates the bedload transport rate by 4% on average (An et al., 2021).We compared  the light table measurements with the amount of sediment in the bedload trap.We found that 63% of the measurements were within 10% of one another and 84% were within 20%.
In addition to the sediment transport rate, the light table provided data on the grain size distribution of the bedload.The light table can detect grains as small as 1 mm.An et al. (2021) reported that the median bedload size (D 50L ) show that the light table overestimated D 50L by 3% on average (the subscript "L" denotes load).The light table underestimated D 10L by 20% on average and D 90L by 30% on average, with D 10L being the diameter such that 10% of the bedload sediment is finer.For further details on bedload transport measurements, we refer to Zimmermann et al. (2008) and An et al. (2021).Every 20 min, we calibrated the light table estimated mass and grain size against those measured in the bedload trap.By segmenting the experiment into 20 min sections, we avoid bias caused by sporadic transport of large grains which occur at the time scale of seconds.
Hysteresis in the relation between bedload transport rate and flow discharge can reveal information on sediment sources, interaction between bed composition (texture and structure) and flow, and sediment storage within the flume/channel.To calculate hysteresis in our experiments we used the method proposed by Langlois et al. (2005).
The method has been used to quantify hysteresis for both suspended and bedload in field and laboratory data (Hassan et al., 2014;Mao, 2018;D. A. Reid et al., 2016;Wang et al., 2021).The hysteresis ratio (H) is the ratio between the sediment yield during the rising limb and the sediment yield at the same flow discharge during the falling limb (Figure 1).Langlois et al. (2005) described events with H > 1 as displaying clockwise hysteresis, H < 1 displaying counterclockwise hysteresis, and H ∼ 1 as no hysteresis.In the calculation of H, the boundary between the rising and the falling limbs of the hydrograph was the middle point of the flow, that is, the 50% of the hydrograph of Figure 3, was considered.Given that fine sediment fractions might behave in a different way than coarse fractions, we performed the analyses for the total and the fractional load.
Bed surface GSD and topography were measured in a 2-m long observation reach between 4.5 and 6.5 m from the flume outlet.At the 20-and 40-min marks of each hour, the bed of the observational reach was scanned and photographed.At the end of each hour, the test reach was scanned and photographed from 1.25 to 9.25 m from the flume outlet to avoid the influence of the boundary conditions near flow inlet and outlet.A green laser mounted on motorized cart was used to measure bed surface elevation.The sampling resolution of the bed scans was 2 mm × 2 mm with a 1 mm vertical accuracy.A 5 cm wide buffer was set on each side of the flume to avoid measurement errors associated with the walls.
Digital elevation models (DEMs) of the bed were built from the laser scans.To determine the bed surface grain size distribution, we used cameras mounted on a motorized cart (An et al., 2021;Chartrand et al., 2018;Hassan, Saletti, Zhang, et al., 2020).Sediment grain sizes were detected from the photos with the GrainID image analyses software that was developed in our lab for the same material (Chen et al., 2022).The smallest detectable size using GrainID is 0.3 mm (Chen et al., 2022), which is smaller than the finest fraction in our experiment.The overall estimated error is about 8%: 6% for gravels and 13% for sand (see Table 3 in Chen et al., 2022).Both photos and laser scans were acquired after flow was stopped and the bed was allowed to dry.Bed surface data were used to examine changes in the bed surface texture between each scan.
The flume was run for over an hour before the start of each experiment with a fixed discharge of 50 l/s and no sediment supply.This created conditions representative of flow over a mix-sediment bed (conditioning stage).
After the conditioning stage, each experiment consisted of 7 hr of a symmetrical stepped hydrograph.Each step lasted for an hour, with the discharge sequence being 62, 75, 87, 100, 87, 75, and 62 l/s (Figure 3).Between steps, the flow changed between 12% and 17% (Figure 3; Table 1).The selected discharges were scaled to those observed in East Creek.The discharge of 87 l/s in our experiments is equivalent to the estimated bankfull flow in East Creek (2.54 m 3 /s) (for scaling see Yalin, 1971).The lowest flow (62 l/s) was chosen to mobilize most of the grain sizes in the flume.Depending on the flood magnitude and the climate conditions, the durations of competent events in East Creek can range from hours to up to more than a day (see Table 2 in Wlodarczyk et al., 2023).
For simplicity we maintained the same flow duration for all discharges.The one-hour duration of each flow step was chosen to facilitate interactions among sediment feed, sediment transport and bed material.
We considered five feed scenarios (Table 1) and we did not observe significant differences between the results.The flume bed was reset before every hydrograph, that is, the sediment collected at the flume outlet was returned to the flume, mixed with the sediment that remained in the flume, and the newly mixed material was leveled with a wooden board in order to bring the bed surface back to the starting elevation.The total feed was determined by running test hydrographs and collecting the material by the end of the hydrograph.A feed of 800 kg is equivalent to adding 4.4 cm sediment (∼5.6D50 of the mixture) into the flume, which is about 44% of the thickness of the original bed.In the case of the variable feed experiment, we estimated the amount of sediment yield for the 62 l/s during the two zero feed experiments.
Then we increase the feed by 31% for each higher flow making sure that the total feed for the hydrograph is 800 kg.The total feed rate in our experiments is well below the calculated sediment transport capacity of 2,800 kg (calculated using Wilcock & Crowe, 2003).Comparing our feed (800 kg) with the calculated capacity (2,800 kg), our experiments were conducted under the supply limited conditions.

Flow Characteristics
Temporal variation of reach-averaged water surface slope, water depth, and bed shear stress are presented in Figure 4 and Table 1.Shear stress was calculated using average water depth and water surface slope in the streamwise direction.During experiment 1A, flow measurements were not recorded (saved) because of human error.As expected, mean water depth increased with discharge during the rising limb and declined during the falling limb (Figure 4a).For a given flow in experiments 2, 4A, and 5A, water depth during the falling limb was about the same as that measured during the rising limb at the same flow discharge.For example, the average water depth at the beginning and the end of hydrograph in 2A was 6.4 and 6.5 cm, respectively.In 1A, 1B, 3A, and 3B, average water depth during the falling limb was higher than that during the rising limb.Comparing the beginning and the end of experiment 3A, for example, the average water depth was 6.3 and 9.4 cm, respectively (Figure 4a).
Slight changes in water surface slope were observed for the no feed (1B) and constant feed (2A) experiments (Figure 4b).An increase in water surface slope was recorded for experiment 3B during the rising limb but little change was observed during the falling limb.Experiment 4A (falling limb feed) showed little water surface slope change during the rising limb but a declining trend during the falling limb.The lack of clear trends in water surface slope could be due to the low resolution of the data (measured every 0.5 m).The variation of the bed shear stress during the hydrograph follows the variation of water depth because of the small variability in bed slope over one hydrograph (Figure 4c).

Bed Topography
The laser scan data provide information on bed adjustment in response to changes in timing of sediment supply.Digital elevation models (DEMs) of bed elevation at the end of each hydrograph flow step are used to explore   feed experiments (3A and 3B) (Figure 5).A degradational trend was obtained for the variable feed experiment (5A) but less severe than that of experiments 1a, 1B, 3A, and 3B (Figure 5).Toward the end of the constant feed experiment (2A), the bed went through aggradation (see sediment balance below) during the falling limb and the bed profile straddled the conditioning profile (zero net change) (Figure 5).Finally, net aggradation along the flume was observed during the falling limb feed experiment (Figure 5).

Sediment Transport Rate and Yield
During conditioning flow, relatively large amounts of mostly fine sediment (sand and small gravel) were evacuated from the flume and probably some of the finest sand infiltered in between the large gravels or into the subsurface.
Figure 6 presents the time-series of total (i.e., summed over all grain sizes) sediment transport rates measured at the light table during the hydrographs (for visualization a log scale version of Figure 6 is presented in Figure S15 in Supporting Information S1).In Figure 6, we present the 1 s bedload transport data to demonstrate the large variability in our data and the 5 min average to show the general trend in the transport rate-flow relation.Experiments 1A and 1B are identical and represent a symmetrical hydrograph with no sediment feed (Figures 6a and 6b).During the rising limb of the hydrograph, the 1 s sediment transport rate ranged over five orders of magnitude for the lowest flow (62 l/s) and three orders of magnitude during the highest flow (100 l/s) (Figure 6a).Overall, in the runs with no sediment supply, the bedload transport rate increased during the rising limb.The highest 5-min averaged sediment transport rate was recorded during the 75 l/s (in 1A) and 87 l/s (in 1B) and then declined during the subsequent two high flows.During the falling limb, however, sediment transport showed a declining trend with lower transport rates than those of the rising limb.The variability in 1 s transport rate during the falling limb was smaller than that observed during the rising limb, suggesting that the most mobile particles had been eroded from the bed surface.The light table and the trap did not record any sediment transport during the last 20 min of the last flow step (i.e., 62 l/s; Figure 6a and Figure S15 in Supporting Information S1).Overall, similar results were obtained for Experiment 1B (Figure 6b).
Experiment 2A was conducted with constant feed rate through the hydrograph (Figure 6c).During the rising limb, 1 s sediment transport rate ranged over two orders of magnitude, suggesting that particles were being eroded and deposited in the mobile bed reach.Similar to Experiment 1A, a gradual increase in sediment transport rate was observed in association with increase in flow discharge with the maximum transport rate being recorded for 75 l/s in the rising limb.Overall, the mean transport rate was higher in Experiment 2A than 1A during the rising limb.A systematic decline in 5-min averaged transport rate was recorded during the falling limb of the hydrograph.This declining transport rate was associated with the largest variability in 1 s transport rate, which can be associated with coarsening of the bed surface sediment (Figure S15 in Supporting Information S1).
Experiments 3A and 3B are identical and were conducted with constant feed during the rising limb of the hydrograph (Figures 4d and 4e).Overall, the variation in sediment transport rate during these two experiments (3A and 3B) was similar to those observed in Experiment 2A (constant feed through the hydrograph).During the rising limb, three distinct spikes in the sediment transport rate were recorded (see Figure 6e).Each of these spikes was associated with an increase in flow discharge with the largest spike was associated with 75 l/s.As in the case of 2A, a gradual decline in the sediment transport rate was recorded for the falling limb of Experiment 3A and 3B.Overall, Experiment 3B yielded similar trends to those obtained for 3A (Figure 6e).Experiment 4A represents the falling limb feed scenario (Figure 6f).Sediment transport rates during the rising limb of Experiment 4A were similar to those obtained in the absence of sediment feed in Experiment 1A.The highest average sediment transport was recorded for the highest flow (100 l/s).Notwithstanding the sediment feed, sediment transport at the downstream end of the observational reach declined in time during the last two flow steps of the hydrograph.In comparison to the other experiments, the decline in transport rate was slow and transport rate by the end of the experiment was higher than in other experiments (e.g., 1, 2A, and 3A) because of the feeding (see Figure S15 in Supporting Information S1).Flow and sediment supply conditions during the rising limb of Experiment 4A were similar to those of Experiments 1A and 1B (no feed), but the rising limb of Experiment 4A yielded lower sediment transport rates than the rising limbs of Experiments 1A and 1B (See Figure 6 and Figure S15 in Supporting Information S1).This could be due to bed adjustment during the conditioning flow (given that the initial conditions of the three experiments are the same).According to our observation, during the conditioning flow of Experiment 4A, a relatively large amount of sediment was evacuated from the flume.Similar high variability in sediment transport rate under the same forcing conditions has been reported in the literature (e.g., Church et al. (1998) compared three identical experiments).
Comparing with Experiment 4A, Experiment 5A (variable feed) shows a similar pattern for the temporal variation of sediment transport rate.The magnitude of sediment transport was a little larger in Experiment 5A, but the sediment transport during the falling limb was very similar in the two experiments.In both cases, the highest transport rate was observed during the peak flow and the transport rate declined slowly but continuously during the falling limb (as in 4A) until the end of the experiment.

Sediment Transport Hysteresis
To determine the presence of hysteresis in our experiments, we considered the variation of the 5-min averaged sediment transport rates in terms of (a) total transport rate (Figure 7) and (b) fractional transport rates (Figures S16-S21 in Supporting Information S1).
Experiments 1A, 1B, 2A, 3A, 3B, and 5A yielded clockwise hysteresis of total transport rate whereas a weak counterclockwise hysteresis was obtained in 4A (Figure 7, Table 1).Overall, the differences in sediment transport rates between the rising and the falling are larger than the variability in the sediment transport rates implying that hysteresis is significant.Experiments 4A and 5A yielded a similar mixed pattern of hysteresis; rising and falling lines crossed each other and differences between them were small especially for flows larger than 87 l/s (Figure 7).While the rising limb for experiment 5A always had higher mean transport rates than the falling limb, the difference in transport rates between the rising and falling limbs during the 62 and 75 l/s steps was much larger than during the 87 and 100 l/s steps.Experiment 4A shows a relatively high transport rate toward the end of the last flow because of timing of the sediment feeding.Fractional analyses show a similar pattern of hysteresis (Figures S16-S21 in Supporting Information S1).

Sediment Balance and Yield
Sediment balance (sediment fed minus sediment delivered to the light table) was calculated for each step of the hydrograph and the whole event (Figure 8).The two nofeed experiments yielded net sediment lost; a fast decline in the balance during the rising limb while little changes during the falling part of the hydrograph.During the constant feed experiment (2A) a decline in sediment balance during the rising and the peak flows were recorded while an increasing trend and then balanced by the end of the experiment.During the first step of the rising limb feed experiments (3A and 3B), the bed aggraded and then net sediment lost during the rest of the hydrograph.The falling limb (4A) and variable feed (5A) yielded pattern similar to that of the constant feed.Overall, the falling feed is the only experiment that resulted by net positive balance (Figure 8).In Table 1, we compare event yield, yield during the rising and the falling parts of the hydrograph.Finally, event sediment yield (total amount of sediment evacuated from the flume during the experiment) was highest during the rising limb feed experiments, followed by the variable feed, while the lowest were obtained for the no feed and the falling limb feed (Table 1).For all cases, the yield during the rising limb was higher than that measured during the falling limb (Table 1).The hysteresis ratio (H) for the total transport rate is presented in Table 1.For 1A and 1B (no feed), the ratio was 4.50 and 5.93, respectively.A value of H > 1 indicates a clockwise hysteresis.The ratio is the largest for the constant feed experiment (2A), with a value of 7.93.The lowest ratio (0.84) was obtained for 4A (feeding during the falling limb).For 5A (the variable feed experiment) the ratio was 2.31 (Table 1).

Grain Size of Bedload and Bed Surface
Temporal patterns of bedload grain size distribution at the light table is represented by D 50L (median size of the 5-min average transport rate) in Figure 9.A clear fining trend of bedload transport was recorded for the no feed experiments (1A and 1B).Similar trends were obtained in experiments 3A and 3B.A slight decrease in bedload median grain size was observed in the constant feed experiments (2A).For both the falling and variable feed experiments, no clear trend was observed during the rising limb whereas a coarsening trend during the falling limb of the hydrograph (Figure 9).
In Figure 10, we present the D 50s (median size with subscript s indicating bed surface) in different experiments.Given the error range in the estimation of the grain size, the median grain size of the bed surface fluctuated with no trend during the rising limb of experiments 1A and 1B.The median grain size coarsened during the falling limb in experiment 1A (Figure 10).The no feed experiment 1B had similar results, with a notable difference being that the grain size of the bed surface fined during the last two stages of the falling limb.An overall coarsening trend of the bed surface material was observed during the constant feed experiment (A2).Experiment 3A showed bed surface coarsening during the rising limb, fining at the highest flow stages, and then coarsening during the last stage of the falling limb.In contrast, few changes in bed surface grain size were observed for experiment 3B.No trend was observed for experiments 4A (feed during the falling limb) and 5A (variable feed).
In Figure 11, we present hysteresis in the median grain size of the bedload as calculated using the light table data.Overall, clockwise hysteresis was observed for experiments 1A, 1B, and 3A.No clear trend was observed for the other experiments.For these experiments, the estimated error range on the grain size of the bedload was large and made it difficult to identify a particular trend in hysteresis patterns (Figure 11).Based on median values (used to calculate the hysteresis index in Table 1), in all experiments except the variable feed (5A), a clockwise hysteresis was obtained for the D 50L .In the case of experiment 4A, the H value was 1.04 (Table 1) indicating weak clockwise hysteresis.Taking into consideration the estimated error, we conclude that there is no hysteresis in experiment 4A (Figure 11).Similar results were obtained for experiment 5A, the calculated H value yielded a weak counterclockwise hysteresis but no hysteresis if we take into consideration the estimated errors (Figure 11).In experiments 1A, 1B, 3A, and 3B, differences in D 50L values between the rising and the falling limbs were high during low flows and shrank (declined) as the flow increases.Overall, relatively high H index was obtained for the no feed and the feed during the rising limb experiments.For the constant, feed during the falling and variable feed, the difference in D 50L value between the rising and falling were relatively low.Interestingly, the hysteresis analyses yielded a weak counterclockwise hysteresis (coarser bed surface in the falling limb) for D 50s (Figure 12).Overall, larger hysteresis ratio values and higher variability were obtained for D 50L than D 50s.

Discussion
We explored the influence of sediment feed timing on bedload transport rate, sediment yield, bedload texture, bed surface texture, and bed elevation adjustment using a set of flume experiments.Five sediment feed scenarios were implemented: no feed, constant feed, feed during the rising limb, feed during the falling limb and variable feed (Table 1).In all experiments, we used a symmetrical hydrograph with identical flow rates and total volume of sediment feed except for the scenario with no feed.To facilitate the comparison between experiments, the initial condition of all experiments was the same (i.e., well mixed sediment with a conditioning flow).

Sediment Transport and Feeding Time (Hypothesis 1-Bedload Transport Rate Over the Hydrograph Varies With Timing and Magnitude of Sediment Supply)
Overall, the 5 min average sediment transport rate during the rising limb of the hydrograph was larger than that of the falling limb (Figures 5 and 6).In no feed experiments (1A and 1B), the sediment transport rate during the rising limb was more than three orders of magnitude larger that of the falling limb.Similar results were obtained for the constant feed Experiment 2A, the transport rate was two orders of magnitude higher during the rising limb than the falling limb.Experiments 3A and 3B yielded similar results.For experiments 4A and 5A (feed during the falling limb and variable feed), differences in transport rate between the two limbs of the hydrograph were relatively small.In the absence of feed, this could be attributed to larger sediment availability from the bed during the rising limb of the hydrograph.In the case of the feeding experiments (constant and rising limb), the fed sediment is an additional source of sediment during the rising limb of the hydrograph.Feeding during the falling limb and variable feed just reduced the differences in the sediment transport between the two limbs (Figures 4 and 5).
Differences in transport rate between rising and falling limbs are well illustrated in the sediment yield that was evacuated during each limb.Higher sediment supply during the rising limb resulted in higher transport rate, sediment yield and reduced net sediment loss by the bed.Degradation was reduced as the flow accommodated extra sediment from the feed.Indeed, the highest degradation rates were measured during the no feed experiments followed by feed during the rising limb and variable feed.On the other hand, feed during the falling limb resulted in net aggradation by the end of the experiment.For all experiments sediment yield during the rising limb was higher by up to 5 times than that during the falling limb, indicating that the rising limb is more capable to transport the sediment that is supplied in the channel (Table 1).
The relation between sediment transport rate and flow discharge is highly nonlinear.Hysteresis in the relation between sediment transport and flow is determined by hydrograph characteristics (magnitude, duration, shape, event sequencing), sediment supply regime (amounts, timing, and texture), bed state (texture and structure) and bed morphology.A clockwise hysteresis (higher sediment transport rate during the rising limb of the hydrograph) was observed for no feed (1A and 1B), constant feed (2A), rising limb feed (3A and 3B) and variable feed (5A) experiments.For the falling limb feed experiment, the H value was slightly below one indicating no hysteresis between sediment transport rate and water discharge.In previous studies, clockwise hysteresis has been reported for experiments without (e.g., Hassan et al., 2006) and with (Humphries et al., 2012;Mao, 2012) sediment supply; counterclockwise hysteresis is associated with destruction of armoring or bedform passage (e.g., Bombar et al., 2011;Lee et al., 2004) and; mixed (clockwise, counterclockwise and mixed) hysteresis is observed from no feed experiments (Wang et al., 2021).Experiments 1A and 1B were conducted under the no feed conditions yet a clockwise hysteresis was obtained for both.It seems that the 10 m long reach served as an adequate source of sediment during the rising limb.However, the feed timing influences the magnitude of the hysteresis, the largest was recorded for the no feed and constant feed while the smallest for the variable and falling limb feed.Comparing the magnitude of the hysteresis obtained from our experiments with those published in the literature (e.g., Mao, 2018;Wang et al., 2021), our values are relatively high.

Bedload Grain Size (Hypothesis 2-Bedload Will Coarsen at the End of the Hydrograph in the Absence of Sediment Supply, As Well As in Case of Constant Sediment Supply and High Sediment Supply During the Rising Limb)
We used the light table data to explore changes in bedload grain size distribution.These data provided a detailed information (every 5 min) on how the bedload texture responded to feed timing and changes in the flow magnitude.In the literature the median grain size values (i.e., no consideration for errors) has been used.Median values in our experiments except 5A show a clockwise hysteresis in the texture of the bedload sediment and therefore reject our hypothesis (Figures 7 and 9).For no feed and feed in rising limb (Exp.1A, 1B, 3A, and 3B), our results show a clear fining trend in the median size of the bedload.For the rest of the experiments, the median bedload size did not show a particular trend.It has been suggested that the rising limb (e.g., Mao, 2018) transports higher rates but finer material whereas during the falling limb the transport is lower but the sediment texture is coarser.In our experiments, the median grain size of the bedload either displayed a fining trend or remained approximately constant, indicating that fine material remained available for the flow even in the case of no feed.This implies that even under no feed conditions, the flow was high enough to scour and mobilize fine material from the bed.Another possible explanation is that the formation of bed surface structures shelters small grains, limiting the availability of fine sediment to be transported.Whereas, a weak counterclockwise hysteresis of bedload texture was observed for the variable feed experiments.Again, these results indicate that fine sediment was available for transport throughout the experiment.Given the large errors in the estimation of the grain size, caution should be applied in the interpretation of the results.

Bed Surface Grain Size (Hypothesis 3-Characteristics of Armor Layers and Surface Structures Depend on the Sediment Supply During the Falling Limb)
Our experiments were conducted under different feeding timing using a symmetrical hydrograph.Vertical sorting and surface winnowing of fines will likely tend to develop a coarse bed surface and hence armoring.Regardless of feeding timing, during the rising limb of the hydrograph, we hypothesized that the bed will keep adjusting for an increasing flow.Feeding during the rising limb will likely limit or reduce the armoring process because of continuous increase in the flow and the addition of sediment fed into the flume.For no feed, constant feed, and feed during the rising limb, an armor layer developed during the falling limb of the hydrograph.Overall, hypothesis 3 was thus accepted.Indeed, experiments 1, 2A, and 3A yielded an overall coarsening of the grain size of the bed surface during the hydrograph.However, similar experiments (1B and 3B) yielded no particular trend, emphasising the large variability in our experiments.Variable feed and falling limb feed either show a fining trend during the falling limb or no trend which can be attributed to the high amounts of sediment feed during the waning part of the hydrograph (Figure 11).
Examining the hysteresis of the median size of the bed surface yielded a counterclockwise pattern in all experiments (Figure 12 and Table 1).Overall, the weakest H values were obtained for the variable feed and feed during the falling limb while the strongest during the no feed experiments.In comparison to the bedload transport rate and bedload grain size distribution, our grain size of the bed surface was measured every 20 min.A more detailed sampling (i.e., every 5 min) program might provide more insights on how the bed surface respond to changes in sediment supply and flow regimes.

Implications and Limitations
Sediment supply (volume, caliber, location and timing) is one of the governing conditions of the fluvial systems.It affects bed composition (texture and structure), channel stability, sediment transport, water quality, habitat and aquatic communities.Knowledge of the sediment regime of a river is prerequisite for ecosystem conservation, channel restoration, and effective management of the fluvial system.To address sediment related issues in streams, sediment augmentation or nourishments are commonly used methods to artificially supply sediment in sediment starved streams (Czapiga et al., 2022;Mörtl & De Cesare, 2021;Viparelli et al., 2011;Wohl et al., 2015).The results of our study provide insight on how the timing of the sediment supply throughout hydrograph will influence bed surface texture, bed topography and sediment transport regimes.The scenario should be selected based on the study objectives.Feeding during the falling limb, for example, will likely result in sediment storage in the channel and well mixed sediment in the bed.No feed or feed during the rising limb will result in degradation, clockwise hysteresis and some bed surface coarsening.
Our reported experiments shed light on the role of feeding timing during a symmetrical hydrograph on sediment transport rate, bed surface sorting, and bed surface topography.For simplification, we used a symmetrical hydrograph in our experiments, the shape of which is likely rare in nature.Hydrograph shape is likely to have an influence on the sediment transport rate, hysteresis in the transport rate, and the texture of the bedload and bed surface (e.g., Hassan et al., 2006).Conducting experiments using asymmetrical (e.g., flashy) hydrographs to explore the fluvial system to changes in the sediment supply regime will expand our understanding of the processes and facilities comparison with our current experiments.Another avenue of future research is conducting a sequence of experiments (similar to those conducted by Mao, 2018) to explore the influence of the feeding history on the channel response.In this paper, we discuss the effect of sediment feed timing on the morphological process during a single hydrograph.However, at longer timescales, when repeated hydrographs and sediment supply are considered, the river might reach a mobile bed equilibrium under which the sediment feed timing might play a different role than that under the event timescale (An, Fu, et al., 2017;Parker et al., 2007;Wong & Parker, 2006).In nature, sediment supply regime in terms of supply rate, texture and timing vary over time and are mostly episodic.Exploring the influence of changes in the sediment supply timing, magnitude and grain size is another research direction worth pursuing.

Conclusions
We conducted a flume study using a symmetrical stepped hydrograph to study the impact of sediment feeding timing on sediment transport rate, bedload grain size, bed surface grain size and topography.Five different feed scenarios were conducted: no feed, constant feed, rising-limb only feed, falling-limb only feed, and variable feed.Each scenario with feed produced different bedload transport behaviors despite having the same total feed mass.Feeding on the rising limb strongly controlled sediment transport rates, overall bedload yield of the hydrograph, and bed scouring severity.For all experiments, except feed during the falling limb (4A) yielded clockwise hysteresis in the sediment transport rate.In terms of magnitude, hysteresis trends in the sediment transport rates were high during no feed and constant feed experiments, moderate during rising-limb feed experiment, and the lowest during variable feed and falling-limb feed experiment.Overall, a fining trend in the grain size of the bedload was observed during no feed, constant feed and feed during the rising limb experiments, whereas no clear trend was obtained for the variable and feed during the falling limb experiments.As a result, analyses of the grain size of the bedload yielded clockwise hysteresis.Counterclockwise hysteresis was observed for grain size of the bed surface for most of the experiments.Given that the sediment supply in natural streams can vary in both magnitude and timing during a flood hydrograph, these experiments show that it is incorrect to assume that a constant feed will accurately represent bedload transport in natural settings.

Figure 1 .
Figure 1.Patterns of hysteresis in the relation between sediment transport rate and water discharge.Four typical cases are shown(a, b)  no hysteresis where there is no difference between the rising and falling limbs and the peak sediment transport is coincident with the peak discharge, (c, d) a clockwise hysteresis where the peak sediment transport occurs before peak discharge, (e, f) a counterclockwise hysteresis where peak sediment transport occurs after peak discharge, and (g, h) combined.These trends can be combined in different orders and at different scales to create more complicated hysteresis trends.Q s is the sediment transport rate and Q is the flow discharge.Modified fromWilliams (1989).

Figure 2 .
Figure 2. (a) Experimental setup showing the fixed bed, mobile bed, feeder, measurement cart, light table, and sediment trap (catch basket).(b) Grain size distribution of the sediment used in the experiments.

Figure 3 .
Figure3.Experimental design, including flow hydrograph, measurement timing of WSE (water depth, water surface slope, bed surface slope, photos), Scan (DEM), and sediment Trap.Sediment transport was measured continuously using the light table and on regular intervals using a trap at the flume outlet (shown in Figure2a).
: (a) no feed (experiments 1A and 1B); (b) constant feed through the hydrograph (experiment 2A); (c) feed only during the rising limb (experiment 3A and 3B); (d) feed only during the falling limb (experiment 4A); and (e) variable feed (experiment 5A).A total of 800 kg of parent material was fed in experiments (b)-(e) during the seven-hour hydrograph.Feed scenarios (a) and (c) were repeated twice temporal and spatial patterns of bed elevation adjustments during the experiments.In Figure5, we present the final bed DEM of difference (DoD) of each experiment.Also, the DEMs and DoDs of all experiments are in Figures S1-S14 in Supporting Information S1.The no feed experiments 1A and 1B show a net erosional pattern near the upper part of the flume.This pattern continues and migrated to the middle part of the flume by the peak flow (Figures S1-S14 in Supporting Information S1).A significant decline in the erosion rate occurred during the falling limb of the hydrograph.In fact, little changes in the bed elevation were observed during the last flow steps the experiment (Figures S1-S14 in Supporting Information S1).A similar pattern was obtained for the rising limb

Figure 5 .
Figure 5. Cross-section averaged difference of DEM (DoD) along the flume at the end of each experiment (between 1.25 and 9.25 m).The mean DEM values were calculated relative to the conditioning elevations prior to each experiment.Feeding scenarios: no feed (1A and 1B); constant through the hydrograph (2A); feed only during the rising limb (3A and 3B); feed only during the falling limb (4A); and variable feed (5A).For detailed information, see Figures S1-S14 in Supporting Information S1.

Figure 6 .
Figure6.Sediment transport rate versus time.Sediment transport rates were measured every second and they are plotted as gray points.Red line is a 5-min average, blue line is the flow discharge.Feeding rates values are presented in Table1.Note no sediment movement was recorded by the light table or the trap during the last 20 min of experiments 1A, 3B, and 4A.For visualization, a log scale version of this figure is presented in FigureS15in Supporting Information S1.

Figure 7 .
Figure 7. Sediment transport rates versus discharge during the different experiments.The sediment transport rate is the 5 min average data collected by the light table at the flume outlet.The 1-s sediment transport rate data were used to calculate the standard deviation (error range) around the 5 min mean transport rate.

Figure 8 .
Figure 8. Mass balance of the bedload transport as calculated for each flow step (sediment input -sediment output).Bedload rates are based on the light table data presented in Figures 6 and 7.

Figure 9 .
Figure9.Temporal changes in the median grain size of bedload sediment including the estimated error range.The bedload grain size is 5 min average estimated from the light table data.The 20-s sediment transport rate data were used to calculate the standard deviation around of the 5 min median bedload grain size.For comparison, we plot the median size (D 50 ) of the original mixture.

Figure 10 .
Figure10.Temporal median grain size of bed surface material and estimated error range as calculated from the bed surface images.The data were collected every 20 min along the control area in the middle of the flume.For comparison, we plot the median size (D 50 ) of the original mixture.

Figure 11 .
Figure 11.Median grain size of the bedload sediment versus discharge during the different experiments.The bedload grain size is 5 min average estimated from the light table data.The 20-s sediment transport rate data were used to calculate the standard deviation around of the 5 min median bedload grain size.

Figure 12 .
Figure 12.Median grain size of the bed surface versus discharge during the different experiments.The data were collected every 20 min along the control area in the middle of the flume.
Note.The highest flow (100 l/s) was split in half between the rising and the falling limbs; No bed slope, water surface and water depth data available for experiment 1A.D 50s is the median grain size of bed surface as measured from images, and D 50L is the median grain size of bedload as measured by the light table.The feed for 62, 75, 87, and 100 l/s is 1,075, 1,600, 2,325, and 3,350 g/min/m, respectively.Summary of Hydraulics and Sediment Data a As measured by the end of the experiment.b

Table 1 .
Note no sediment movement was recorded by the light table or the trap during the last 20 min of experiments 1A, 3B, and 4A.For visualization, a log scale version of this figure is presented in FigureS15in Supporting Information S1.