Influence of the sediment supply texture on morphological adjustments in gravel-bed rivers

RESEARCH ARTICLE 10.1002/2013WR015117 Influence of the sediment supply texture on morphological adjustments in gravel-bed rivers Carles Ferrer-Boix 1 and Marwan A. Hassan 1 1 Department of Geography, University of British Columbia, Vancouver, British Columbia, Canada Abstract The role played by the texture of the sediment supply on channel bed adjustments in gravelbed rivers is poorly understood. To address this issue, an experimental campaign has been designed. Flume experiments lasting 96 h in a 9 m long, 0.60 m wide have been performed with different sand-gravel mixtures as feed textures. The response of the surface texture has been found to be highly dependent on the grain size distribution of the feed. When the feed texture included gravel, the finest fractions of the sediment supply infiltrate beneath the surface. Conversely, sand remains on the surface when the feed texture lacks gravel. This different textural response becomes obscured when water discharge increases. Further, the sediment transport rate approaches the feed rate differently depending on the content of gravel in the feed texture. When a small proportion of gravel is part of the feed texture, bed load transport rate asymptotically approaches the feed rate. However, when a significant fraction of gravel is part of the feed grain size distribution, bed load transport rate approaches the feed rate by following an oscillatory path. These findings have been verified in terms of a one-dimensional numerical model. This modeling reveals that the higher the differences in mobility among the grain sizes contained in the feed texture, the more evident is the nonasymptotic transient trend toward equilibrium. 1. Introduction Bed load transport and surface texture in gravel-bed rivers interact in a manner which obscures determination of the cause and effect relationships [Wilcock, 2001]: do changes in bed load transport cause adjustments in surface texture or, conversely, do bed load changes arise from surface texture modifications? How the bed surface adjusts to different sediment supplies and textures is still an open question. In a feed experiment, the surface composition and the bed slope adjust through time so that the bed load transport rate and its texture match the feeding values at equilibrium [Parker and Wilcock, 1993; Wilcock and DeTemple, 2005]. However, it is still unknown how this evolution proceeds. This investigation focusses on studying the transient adjustments of the bed surface, bed load transport rates, and their grain size distribution to different sediment feed textures in gravel-bed rivers. Gravel-bed rivers commonly have stable beds, with relatively little sediment mobilization even during high flows [Church et al., 1998; Church and Hassan, 2002; Hassan et al., 2008]. Under conditions of low sediment supply, it has been shown that gravel-bed streams commonly have a coarse armor which develops (i) as a result of horizontal sorting of fine material from the bed surface during small/intermediate flows that are incapable of mobilizing the coarser fractions [e.g., Gessler, 1970; Parker and Sutherland, 1990], or (ii) through vertical sorting during the movement of the coarse grains [e.g., Parker and Klingeman, 1982; Rosato et al., 1987]. In turn, it has been hypothesized that bed structures (e.g., clusters and imbrication) develop under below-competent flows [Haynes and Pender, 2007; Piedra et al., 2012]. Besides an impact on bed armoring, sediment supply plays a major role in bed stability and significantly impacts channel morphology. Frequency of sediment input events may temporally dominate channel processes and morphology, significantly changing sediment transport dynamics [Hassan et al., 2008; Madej et al., 2009; Pryor et al., 2011]. Patterns of the quasi-cyclic channel response by which channel first aggrades to later degrade, associated with rapid inputs of sediment from external sources, have been described in a number of field observations and some experimental studies [e.g., Hoffman and Gabet, 2007; Hassan et al., 2008; Sklar et al., 2009; Pryor et al., 2011; Podolak and Wilcock, 2013]. Changes in the magnitude of the sediment supply induce morphological responses in gravel-bed rivers. Particularly, a reduction of the sediment Key Points: Experiments on how feed texture affects bed adjustments are conducted Bed surface evolution is highly dependent on the feed texture Gravel fraction in the feed influences how bed load approaches the feed texture Supporting Information: Readme Detail of numerical code and figure and table captions Figure S1 Figure S2 Figure S3 Table S1 Correspondence to: C. Ferrer-Boix, [email protected] Citation: Ferrer-Boix, C., and M. A. Hassan (2014), Influence of the sediment supply texture on morphological adjustments in gravel-bed rivers, Water Resour. Res.,50, doi:10.1002/ 2013WR015117. Received 27 NOV 2013 Accepted 14 OCT 2014 Accepted article online 16 OCT 2014 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 1 Water Resources Research PUBLICATIONS supply leads to a narrow zone of active transport within the channel which can degrade [Dietrich et al., 1989, 2005; Nelson et al., 2009; Venditti et al., 2012] if the sediment availability is well below the sediment capacity. Sediment supply also plays a central role in the spatial arrangement of bed surface patches [Dietrich et al., 1989, 2005; Nelson et al., 2009; Venditti et al., 2012]. Channel morphology and sediment mobility are also influenced by the texture of the supplied sediment. Coarser sediment supply than what the flow is competent to move will likely result in the development of an upstream sediment wedge, changing bed surface slope, and reducing sediment mobility [Wilcock, 2001]. Of particular, interest for this study is the proportions of sand and gravel fractions present in the supply compared to those fractions present in the surface, especially with regards the coarse material. Sand-sized sediment delivered to channels fills pore spaces and reduces pivot angles for gravel-sized grains being transported over the bed surface, which then are more easily mobilized [Buffington et al., 1992; Wilcock, 1998; Curran and Wilcock, 2005]. Additionally, Venditti et al. [2010] observed that smoothing of the bed surface by interstitial filling of fine material enhanced the mobility of the coarse particles by increasing the drag force exerted on them by the flow. Researchers has also been conducted to study the effect of particle interactions on bed adjustments and temporal variations in bed load transport rates. Whereas Whiting et al. [1988] suggest that the formation of bed load sheets (thin, downstream migrating mass of sediment, the front edge of which is formed by coarse particles) could be due either to the patchy nature of fine-sediment infilling or to the concentration of coarse grains, Nelson et al. [2009] found that the ratio of coarse to fine gravel could play an important role in the formation of bed load sheets, the dynamics of which are determined by the sediment supply. Iseya and Ikeda [1987] found that bed load fluctuations or pulses could be partly due to a changing availability of bed material (longitudinal sorting). Kuhnle and Southard [1988] reported bed load fluctuations related to bed load sheets and dunes passing. It is worth mentioning that the bed load fluctuations reported in the experiments by Iseya and Ikeda [1987], Kuhnle and Southard [1988], and Nelson et al. [2010] were observed under equilibrium conditions. These aforementioned bed load pulses, often referred to as periodic variations of bed load [Hoey, 1992], differ from sediment waves, which are longer variations of bed load associated with sediment storage [Gilbert, 1917]. Thus, coarse material temporarily stored as a sediment wedge [Wilcock, 2001] can be interpreted as a downstream traveling sediment wave. However, what remains uncertain is how the interactions of grains of different particle sizes affect bed surface texture and bed load adjustments during the transient stage to equilibrium. As mentioned above, it is well established what bed load transport (rate and texture) is at equilibrium in flume experiments in which water and sediment are both fed at a constant rate. However, the influence of the texture of the sediment supply on the adjustments of the texture of the surface and the bed load transport rates and their grain size distribution during the transient stages toward equilibrium deserves more research. In this sense, it has been recognized that river response to disturbances may not be monotonic [Hoey, 1992]. This research has direct bearing on gravel-bed streams in which large amounts of external sources of coarse material can enter the river [Benda and Dunne, 1997]. In these cases, not only the final equilibrium state is important but also the transient stages are relevant. Since a considerable time interval may be needed to achieve equilibrium [Hoey, 1992], frequent episodic inputs of sediment may preclude attainment of equilibrium. To study these issues, flume experiments and a numerical model have been designed. The numerical model was conceived to complement the flume experiments. Therefore, it provides supporting evidence and helps to explain some of the results obtained from the flume experiments. 2. Experiments and Numerical Model Description 2.1. Experimental Design A set of flume experiments, conducted in the Geography Department, Hebrew University, was designed to examine the influence of sediment supply texture on channel bed adjustment. Summary characteristics of the flow and sediment are provided in Table 1. The experiments were carried out in a 9 m long tilting flume, 0.60 m wide, and 0.50 m deep. The most upstream 1.0 m of the bed was fixed and immobile by using relatively large particles, equivalent to the D84 of the bed material. The experiments were carried out using a setup that had been well-verified in advance [Hassan et al., 2006]. A layer of 0.07 m deep loose material with specific gravity of 2.65 was placed along the last 8.0 m of the flume as the initial bed mixture (Figure 1). Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 2 Before starting each run, the bed was slowly saturated and then drained to aid sediment settlement. Thirteen experiments were conducted in feed mode: water and sediment discharge were supplied under steady conditions from the flume inlet. Sediment feed rate per unit width qb;f, ranged between 0.14 and 0.75 g/m/s. Two experiments were carried out under zero feed rate (Table 1). Runs were conducted using two water discharges which were chosen to be similar to water discharges at the beginning of the rising limb in a set of experiments with hydrographs [Hassan et al., 2006]. Four different textures were used as the feed material (Figure 1): moved-1, moved-2, coarse, and sand. All these textures are unimodal: whereas peak frequencies for sand in moved-1 and moved-2 textures are associated with a grain size of D51.41 mm, peak frequency for the coarse texture is associated with a particle size of D55.66 mm. The sand content in the three finest textures ranges between 60% and 70% (it declines to 41% for the coarse grain size distribution). The median grain diameter of the coarsest texture nearly doubles those of the other three grain size distributions and whereas the geometric standard deviation of these three latter textures ranges between 2.1 and 2.4, it reaches a value of 3.4 for the coarsest grain size distribution. The median grain size, r g , 16% and 84% percentiles (i.e., 16% and 84%, respectively, finer than) as well as the sand content are listed in the figure inset. The sand and the coarse feeds represent the extreme grain size distributions (the latter being the same as the initial bed). Moved-1 and moved-2 textures were the grain size distributions of the bed load collected between 8 and 16 h in the two runs without feed under low and high flow conditions, respectively (t516 h was considered as the time for the surface texture adjustment [Church et al., 1998] and t58 h was taken to have an intermediate measurement during the adjusting period). The duration of all runs was 96 h. The experimental procedures and the duration of the runs were the same as for the experiments of Church et al. [1998], Hassan and Church [2000], and Hassan et al. [2006]. The study follows previous research by Church et al. [1998] and Hassan and Church [2000]. They both modeled Harris Creek, British Columbia, Canada, under no feed conditions or feeding using moved textures. Harris Creek is a cobble-gravel-bed river and its hydrological regime is snowmelt-dominated; with a mean annual flow and maximum recorded flood of 19 and 35 m 3 /s, respectively [Church et al., 1998; Hassan and Church, 2000]. Channel width is of the order of 10 m, water surface slope ranges from 0.006 to 0.011, mean diameter of the subsurface material extends from 22 to 45 mm whereas mean surface material is 64 mm in pools and 76 mm in riffles. Harris Creek is an upland stream with little sediment supply and well developed armored surface. Experiments in these previous studies were scaled using Froude similarity at 1:20; for more details see Church et al. [1998] and Hassan and Church [2000]. The bulk texture (i.e., the one used as the initial bed surface and as feed in coarse-supplied runs) was selected such that the grain size distribution extended from coarse sand to coarse gravel forming a poorly sorted mixture as of gravel-bed streams. For these given texture, flow conditions (water discharges, initial bed slopes) were selected in such a way partial transport (as defined by Wilcock and McArdell [1993]) occurred. Slightly higher feed rates than in previous research in Harris Creek [Hassan and Church, 2000] were chosen. Unimodal feed texture for sand-supplied runs was chosen as of that transported at low flow in Harris Creek [Hassan Table 1. Experimental Hydraulic and Sediment Data a Experiment Qw(m 3 /s) qb;f(g/m/s) GSD Feed D50;f(mm) Sb0sb0(Pa) D50;sjt596 h (mm) qb;outjt596 h (g/m/s) D50;bjt596 h (mm) Wb;T (kg) G1 0.021 0.00 0.0080 5.1 5.6 0.024 1.2 49 G2 0.032 0.00 0.0080 6.2 6.4 0.042 1.1 150 G3 0.021 0.14 Moved-1 1.5 0.0081 5.1 6.3 0.14 1.2 60 G4 0.021 0.36 Moved-1 1.5 0.0081 5.1 5.9 0.36 1.2 89 G5 0.021 0.49 Moved-1 1.5 0.0080 5.1 5.9 0.47 1.2 130 H1 0.032 0.35 Moved-2 1.5 0.0085 6.2 4.0 0.37 1.4 200 H2 0.032 0.55 Moved-2 1.5 0.0085 6.2 6.4 0.56 1.7 260 H3 0.032 0.75 Moved-2 1.5 0.0080 6.2 6.1 0.76 1.3 280 H4 0.021 0.16 Coarse 2.8 0.0085 5.1 7.1 0.059 1.1 57 H5 0.032 0.29 Coarse 2.8 0.0085 6.2 6.0 0.14 1.2 160 H6 0.032 0.54 Coarse 2.8 0.0085 6.2 6.5 0.36 1.3 210 H7 0.032 0.73 Sand 1.4 0.0085 6.2 1.9 0.89 1.2 300 H8 0.032 0.38 Sand 1.4 0.0085 6.2 5.0 0.55 1.4 240 H9 0.021 0.25 Sand 1.4 0.0080 5.1 2.4 0.26 1.4 96 I1 0.021 0.48 Sand 1.4 0.0080 5.1 2.0 0.55 1.2 140 a Qw: water discharge, qb;f: sediment feed rate (per unit with), GSD: grain size distribution, D50;f: median grain size of the feeding texture, Sb0: initial bed slope, sb0: initial boundary shear stress; D50;sjt596 hand D50;bjt596 h: median grain size of the bed surface and the bed load at the end of the runs (i.e., after 96 h). qb;out jt596 hand Wb;T: unit bed load transport rate and total amount of sediment collected at the end the runs. Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 3 and Church, 2000]. Regardless of the experimental campaign was different in scope, it was conducted following as much as possible past research on East Creek so that results are still comparable. Although inspired by this past research, the experiments presented herein aimed to represent a general configuration of a gravelbed stream rather than a specific field case. Flow and sediment measurements were taken within a study reach between 4.75 and 5.25 m from the headbox. No water surface elevation was imposed at the outlet of the flume. Thus, a little acceleration of the flow was observed at the downstream end of the flume, which did not extend to the study reach. Sediment leaving the channel was collected in a trap at the end of the flume. At eight specified time intervals throughout the experiments, flow was lowered to a level below the initiation of motion of the particles for bed surface photography, bed surface sediment sampling, and sediment trap replacement. The volume of material collected at each specific time represents, thus, the mean bed load transport rate of the period of time during which the trap was filled. The bed surface was characterized based on two complementary methods: clay and color sampling [Hassan et al., 2006]. Clay samples were extracted using a piston device coated with clay [Fripp and Diplas, 1993] that was pressed onto the bed surface so that the bed material was embedded in the clay. The clay samples were taken downstream of the study reach. Bed load and clay samples were dried, weighted and sieved at 1/2 wintervals. The study reach was sampled by using an adaptation of the Wolman method based on color coded sediment at 1/2 wintervals, thus providing a noninvasive characterization of the bed surface in that area. Painting of each grain size was done manually by shaking a cylindrical receptacle containing the particles and the paint until it was visually observed that the paint uniformly covered the surface of the stones. Estimates of the initial boundary shear stress (Table 1) were obtained using the depth-slope method, taking the initial bed slope as the friction slope. It is assumed here that the depth-slope product is a reasonable proxy of the actual shear stress because the methodology yields an average value for the whole flume and the present investigation is focused on the overall adjustment of the channel in response to changes in the feed texture. 2.2. Numerical Model A one-dimensional morphodynamic numerical model was developed to simulate the feed experiments. For this study, the normal flow approximation (steady and uniform) has been used to reproduce the water flow. A detailed description of the numerical model can be found in supporting information. As the experimental effort was of limited scope, a set of numerical experiments have been performed to confirm the influence of the feed texture in the evolution of the bed surface and bed load transport rates by considering more discharges, feed rates, and feed textures than provided by the experiments. The main goals of the D50,f σg,f D84,f D16,f Fs,f (mm) (−) (mm) (mm) (%) 1.5 1.5 2.8 1.4 Moved–1 Moved–2 Coarse/bed Sand 2.2 2.4 3.4 2.1 3.0 3.5 9.1 2.8 0.50 0.57 0.70 0.54 66 62 41 68 −3−2−10123456 20 40 60 80 0.125 0.25 0.5 1 2 4 8 16 32 64 Grain size (mm) Grain size ( ) ψ % finer than 0 100 Moved−1 Moved−2 Coarse/bed Sand Figure 1. Particle size distribution of feed textures used in the experiments. Note that the sediment mixture, i.e., the texture of the bed before commencing the runs is the coarse distribution. D50;f: median grain size; rg;f: geometric standard deviation; D16;f: 16 percentile of the feed texture; D84;f: 84 percentile of the feed texture; and Fs;f: percentage of sand of the feed texture. Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 4 numerical tests are: (i) to confirm the observations of the textural and bed load responses to the feed grain size distribution and (ii) to broaden the range of feed textures, water discharges, and feed rates to obtain a more general picture of how the bed surface and the bed load transport rate adjust to those parameters. 3. Results The influence of the feed texture on bed adjustments is analyzed by selecting those representative experiments with the same water discharge and similar sediment feed rate, but with different feed textures (Table 1): runs G3 and H4, H2 and H6, and G5 and I1. The results of all other experiments are presented in Appendix A. 3.1. Experimental Observations 3.1.1. Sediment Transport Figure 2 presents the temporal evolution of the ratio between sediment transport at the outlet of theflumeandfeedratesatthe inlet for the six selected runs. Common trends during the first 20 h of the runs are observed in sediment transport rate for each pair of runs: the maximum difference between runs in each plot within this period of time is lower than 60%, except for runs I5 and G1 at t54 h. This common path can be interpreted as an influence of the initial bed surface and bed slope on the bed load adjustments. High bed load transport rates during the first 16 h occur because of the initial high content of fine material on the bed surface which enhances the mobility not only of fine grain particles but also of the coarse fractions [Curran and Wilcock, 2005]. From this time onward, bed load transport rate is affected by both the water discharge and the feed rate and its texture. As bed load inherently fluctuates, equilibrium is considered to be attained when consecutive measurements oscillate around the feed rate for an extended period of time. Except for the aforementioned bed load fluctuations, bed load transport rate in experiments fed with sand and moved material, regardless of the feed rate and the water discharge, asymptotically approaches the feed rate of each run, i.e., bed load transport gradually decreases until eventually reaching the feed rate within the 96 h of experiments. This is not the case in the coarse-fed runs in which an oscillatory (nonasymptotic) path is followed to reach the feed rate. This nonmonotonic trend toward the feed rate can be conventionally quantified by counting the number of points in the temporal evolution of the sediment transport rate in which the following conditions are satisfied: (i) bed load rate is below the feed (i.e., data points below 1 in Figure 2) and (ii) bed load still decreases. If these two simultaneous conditions are satisfied, bed load transport will have to rise in order to match the feed rate [Parker and Wilcock, 1993; Wilcock and DeTemple, 2005], and a nonasymptotic path will be followed to attain equilibrium. The average number of points that satisfy both conditions for coarse-fed runs equals 3 whereas a value close to 1 is obtained for the rest of the experiments, indicating a different bed load response toward equilibrium in coarse and fine (sand and moved) supplied runs. Sediment transport rate in fine-fed runs (i.e., supplied with sand and moved textures) starts to straddle equilibrium conditions after 16–24 h: the mean relative deviation of the bed load transport rate compared to the feed rate in these runs between t516 h and t596 h is 16%, which can be taken as a sign that these experiments had achieved 0.01 0.1 1 10 100 0.01 0.1 1 10 100 0.01 0.1 1 10 100 G3−Moved H4−Coarse H2−Moved H6−Coarse 1 10 100 Time (h) G5−Moved I1−Sand qb,out /qb,f (−) qb,f 0.15 g/m/s QW = 0.021 m3/s − ~ qb,f 0.55 g/m/s QW = 0.032 m3/s − ~ qb,f 0.49 g/m/s QW = 0.021 m3/s − ~ Figure 2. Evolution of the ratio between the bed load transport and the feed rates for runs G3 and H4, H2 and H6, and G5 and I1. The horizontal line: qb;out 5qb;f. Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 5 equilibrium at t596 h. Bed load transport approaches the feed rate differently in coarse-supplied runs (H4 and H6). Bed load transport rate rapidly declined with time, reaching values lower than the feed rate (e.g., out/feed <1) at t516 h. Bed load at the final stages of the experiments, mainly in run H4 but also in run H6, is below the feed rate (bed load at t596 h is 63% and 34% of the feed rate for each of these runs). Mean sediment transport rate for coarse-fed runs from t516 h to t596 h is 30% below the feed rate. The fact that the bed load transport at t596 h, along with the mean sediment transport rates after t516 h until the end of the runs are well below the feed rates mean that these runs were not at equilibrium at t596 h (although bed load transport rate for run H6 had almost matched the feed rate). Thus, if these runs had been longer, bed load would have had to rise in order to approach equilibrium. Comparing runs H5 and H6 (Figure A1), it is clear that with the higher feed rate (i) the earlier the sediment transport rate declines below the feed rate and (ii) the more rapidly it recovers toward equilibrium conditions. Bed load percentiles (D16;b,D50;b, and D84;b) for selected runs are presented in Figure 3. Despite the scatter, fine-supplied runs (moved and sand) illustrate that bed load statistics at the end of the runs are around those of the feed, confirming that these runs have achieved equilibrium: the median grain size of the bed load transport deviates 17% from that of the feed rate at t516 h to t596 h. The D50;fis rapidly attained regardless of the flow and the feed rates (some oscillations at high flow—run H2 and to a lesser extent in run G5—with respect to D84;bare noticed). Two-sample Kolmogorov-Smirnov goodness-of-fit tests have been carried out comparing each bed load sample with the feed texture in each run. These tests confirm that all bed load samples at t596 h of moved and sand-supplied runs (expect for that of run H2) are statistically the same at significance level of 0.05. However, since the null hypothesis (i.e., that the bed load sample is the same as the feed) is accepted in run H2 for all other bed load samples, particularly at t548 h and t572 h, achievement of equilibrium at the end of all fine-supplied runs is supported. The evolution of the bed load texture in coarse-supplied runs is completely different with respect to the fine feed experiments. Again, the bed load texture does not approach that of the feed monotonically (by coarsening or fining). Instead, bed load texture first fines to (eventually) coarsen later on depending on the 0 2 4 6 8 10 0 2 4 6 8 10 D (mm) 1 10 100 0 1 2 3 4 5 110100 Time (h) G3−Moved: QW = 0.021 m3/s qb,f = 0.14 g/m/s G5−Moved: QW = 0.021 m3/s qb,f = 0.49 g/m/s H2−Moved: QW = 0.032 m3/s qb,f = 0.55 g/m/s H4−Coarse: QW = 0.021 m3/s qb,f = 0.16 g/m/s I1−Sand: QW = 0.021 m3/s qb,f = 0.48 g/m/s H6−Coarse: QW = 0.032 m3/s qb,f = 0.54 g/m/s Figure 3. Bed load position statistics: D16;b(open squares), D50;b(filled squares), and D84;b(diamonds). Dashed lines illustrate the values of the percentiles for each feed texture. Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 6 experiment conditions. The grain size distribution of the bed load is finer than that of the feed at any time for all runs. Starting from a grain size distribution finer than the feed texture (D50;b=D50;f for runs H4 and H6 at t52 h are 0.62 and 0.72, respectively), bed load gets even finer (the average D50;b=D50;fratio for these two runs from t54htot516 h is 0.51 and 0.59, respectively) until occasionally it gradually starts coarsening (the same ratio for the entire period after t516 h is 0.51 and 0.74, respectively) depending on the run conditions (flow and feed rates). At t596 h, the ratio between the median bed load transport rate and the median of the feed rate ranges between 0.56 and 0.66 (the former corresponding to run H4, the latter to run H6). Bed load texture in run H6 reached its finest grain size distribution during the period from t54hto t524 h, suggesting an influence of the initial conditions [Haynes and Pender, 2007]: all fractions of the initial loose bed surface were evacuated during the process by which the bed surface was being worked by the flow [Hassan and Church,2000;Church and Hassan, 2002], and thus their mobility was gradually reduced. The coarse bed load fractions at t52 h and their subsequent fining until t524 h in coarse-supplied runs (Figures 3 and A3) respond to the evacuation of these fractions due to the increase of their mobility by the initial abundance of fine material on the surface [Curran and Wilcock,2005].Bedload texture in coarse-supplied runs coarsens from t524 h onward. The texture of the bed load in run H4 does not show any significant change after t54handbed load coarsening is clearly noticed after t58 h in run H6. The finer values of the bed load statistics of coarse-supplied runs compared to those of the feed in Figure 3 confirm that these runs were far from equilibrium at t596 h. Unlike finesupplied runs, results of two-sample Kolmogorov-Smirnov goodness of fit tests for coarse-supplied runs at significance level of 0.05 confirm that bed load transport at the end of the runs is statistically different from that of the feed. (pbi/Fi)H4(−) (pbi/Fi)G5(−) 11.3 5.66 2.83 1.41 0.707 0.354 0.177 (pbi/Fi)G3(−) (pbi/Fi)I1(−) D (mm) 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 t = 2 h t = 8 h t = 24 h t = 72 h t = 96 h t = 2 h t = 8 h t = 24 h t = 72 h t = 96 h Figure 4. Comparison of fractional transport rates pbi=Fi(pbi ,Fi:bedload and bed surface frequencies, respectively) evaluated at different times for runs H4 and G3 (left: qb;f0.14 g/m/s, Qw50.021 m 3 /s and coarse and moved feed textures, respectively) and runs G5 and I1 (right: qb;f 0.49 g/m/s, Qw50.021 m 3 /s and moved and sand feed textures, respectively). Solid line indicates the equal line between vertical and horizontal axes. Dashed lines highlight full mobility (pbi=Fi51). Histograms of bed load frequencies pbi for each grain size have been added to each plot (top right corresponding to run H4—left column—and G5—right column—and bottom left to runs G3—left column—and I1—right column). The upper bound of the vertical axis is 0.45. Each bar in the histogram represents the frequency of the bed load for each grain size (1 2wapart) in increasing order. Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 7 Figure 4 presents the fractional transport rates by plotting the ratio of the bed load transport rate pbi and surface fraction Fifor each grain size i. Since sediment available to be part of the bed load has its origin on the bed surface, pbi=Fiindicates how over or misrepresented a certain grain size is in the bed load compared to its availability on the bed surface: sizes with lower mobility (usually the coarsest ones) gradually increase their presence on the surface until the bed load transport reaches the feed rate at equilibrium [Wilcock and McArdell, 1993]. Full mobility is achieved when pbi=Fi1[Wilcock and McArdell, 1993]. Each plot depicts the comparison of the fractional transport rates (at 1 wintervals) at a given time for a pair of selected runs with equal water discharge and sediment feed rate. The fractional transport rates at a given time range over 2 or 3 orders of magnitude. The maximum grain size initially present in the bed (D545.3 mm) was never present in the bed load measurements. The largest mobile particle increases with water discharge. Particles of D522.6 mm were only found in run G4 at t52 h when the bed surface was not worked by the flow. The fractional transport of the grain sizes most present in the bed load (D51.41 mm and D52.83 mm) does not apparently depend on the feed rate and its texture. Experimental results show that grain size of D52.83 mm is the boundary between full and partial transport [Wilcock and McArdell, 1993] (note that these data fall in the upper right quadrant of each plot). All grain classes of the bed load finer than 5.66 mm are fully mobile at t52 h for run H4 (experimental results of the fractional transport of the two coarsest grain sizes for this run fall within an order of magnitude lower than pbi=Fi51, therefore being partially mobile). Fractional transport rates of the two coarsest grain sizes collected in the sediment trap in fine-supplied runs(G3, G5, and I1) are partially mobile 2pbi=Fiis between 1 and 2 orders of magnitude lower than 12at t52 h. From this time onward, particle mobility depends on the feed texture. Minor changes in relative mobility are observed in particles finer than 2.83 mm (fully mobile particles) in runs G5 and I1 at each time measurement (all data plot within a relatively narrow range above 1). However, the finest two grain classes in run I1 are systematically below 1. Mobility of partially mobile grain classes (D5.66 mm) in run G5 decreases from t52htot58 h, and gradually increases afterward until the end of the run. Mobility of these latter grain sizes in run I1 gradually and continuously declines from t52htot596 h. 0 3 6 9 12 15 0 3 6 9 12 15 D (mm) 1 10 100 0 3 6 9 12 15 Time (h) 110100 H4−Coarse: Qw= 0.021 m3/s, qb,f= 0.16 g/m/sG3−Moved: Qw= 0.021 m3/s, qb,f= 0.14 g/m/s H6−Coarse: Qw= 0.032 m3/s, qb,f= 0.54 g/m/sH2−Moved: Qw= 0.032 m3/s, qb,f= 0.55g/m/s I1−Sand: Qw= 0.021 m3/s, qb,f= 0.48 g/m/sG5−Moved: Qw= 0.021 m3/s, qb,f= 0.49g/m/s Figure 5. Surface position statistics: D16;s(open squares), D50;s(filled squares), and D84;s(diamonds). Dashed lines indicate the initial values of the respective percentiles. Each pair of plots in each row of the figure illustrates the results of two runs with the same water and sediment feed rate, but different feed texture. Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 8 The relative mobility of coarse and moved experiments (G3 and H4) is similar (data approximately plot along the equal line of each plot). Except for the two finest grain sizes of run G3 (for which the fractional transport fall within an order of magnitude lower than pbi=Fi51) grain sizes finer than D52.83 mm are fully mobile (pbi=Fi1); the mobility of the two partially mobile grain sizes (D5.66 mm) reduces gradually as time passes. 3.1.2. Bed Surface Adjustments Temporal evolution of the D16;s,D50;s,andD84;sof the bed surface for selected runs is presented in Figure 5. Bed surface adjustments apparently do not depend on the feed rate in moved-supplied runs under low flow (runs G3–G5). D50;sincreasingly coarsens during the first 16 h of runs and reaches a constant value between 5.0 and 6.0 mm: the average D50;sfrom t516 h to t596 h in these two runs is 5.7 mm (the mean standard deviation is 0.56 mm). Less evident coarsening is observed with regard to D84;s: this grain size gradually coarsens until t516 h; from this time onward, whereas D84;sfor run G3 remains constant (despite the oscillations), it gets slightly finer for run G5 (this fining is clearly observed in the last two measurements). However, the mean value D84;sfor the last five measurements is between 24% and 11% coarser than the D84 of bulk material in runs G3 and G5, respectively. Mean coarsening of the finest percentile D16 is between 78% and 87% in both runs for the period after t516 h. The armor ratio at the end of the runs G3 and G5 ranges between 2.1 and 2.4 (Figure 6). The same trend is observed in high flow moved-supply runs in Figures 5, 6, and A3. The bed surface in coarse-supplied runs in Figure 5 (and also in Figure A3) generally coarsens with time until t516 h: starting from a median surface grain size at t52 h ranging between 2.2 mm (run H5) and 6.0 mm (run H6), it gradually increases up to a range between 6.4 mm (run H4) and 7.3 mm (run H5) at t516 h (D50;s57.2 mm for run H6). From this time onward, the median surface grain size is maintained constant or even gets finer: the average D50;sfrom t516 h to t596 h in runs H4 and H6 are 5.7 mm and 6.4 mm, respectively (the standard deviation is 1.2 and 0.72 mm, respectively). 110100 0 1 2 3 4 Time (h) 110100 0 1 2 3 4 D50,s/D50,s0(−) G3−Moved H4−Coarse G1−No feed H2−Moved H6−Coarse G2−No feed G5−Moved I1−Sand G1−No feed H3−Moved H7−Sand G2−No feed QW = 0.021 m3/s qb,f 0.15 g/m/s − ~ QW = 0.032 m3/s qb,f 0.54 g/m/s − ~ QW = 0.021 m3/s qb,f 0.49 g/m/s − ~ QW = 0.032 m3/s qb,f 0.74 g/m/s − ~ Figure 6. Ratio of the median surface diameter with respect to the initial one for selected runs. Surface coarsening data of no feed runs are included for comparison. The horizontal line defines no coarsening D50;s5D50;s0. Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 9 texture, the smaller the difference between the sand and coarse ratios (the smaller the amplitude of the bed load fractions), (ii) none of the curves follow an asymptotic trend toward 1 with time, i.e., peaks and troughs are evident in all plots, and (iii) the sand bed load fraction starts below the feed value only for the finest texture (moved 2, Figure 1). Sand and gravel fraction ratios oscillate through time as equilibrium are approached. Figure 13 shows the numerical results of the bed elevation in the channel at specific times for the four textures considered in Figure 12. For comparison, the initial bed elevation has been included in all 0.1 1 10 100 Time (h) 0.1 1 10 100 0.6 0.7 0.8 0.9 1.0 1.1 pb,c/pf,c qb/qb,f H5: Qw = 0.032 m3/s, qb,f = 0.29 g/m/s H6: Qw = 0.032 m3/s, qb,f = 0.54 g/m/s H5: Qw = 0.032 m3/s, qb,f = 0.29 g/m/s H6: Qw = 0.032 m3/s, qb,f = 0.54 g/m/s x = 0 m x = 8 m 0.1 1 10 100 1000 Figure 11. Results of the numerical model for runs H5 and H6. (top) Temporal evolution of the ratio between the gravel fraction of bed load and that fraction of the feed rate. (bottom) Temporal evolution of ratio between the sediment transport rate qbover the feed rate qb;f.Numerical simulations presented at eight cross sections of the flume 1 m apart: the darker the curve, the more upstream the cross section plotted. Sand Gravel 0.1 1 10 100 0 1 2 3 0 1 2 3 0.1 1 10 100 GSD−3: q*w = 4.48e+04 GSD−5: q*w = 8.17e+03 GSD−2: q*w = 9.47e+04 GSD−4: q*w = 2.17e+04 Time (h) pbi/pbi,f (−) Figure 12. Temporal evolution of the ratio between the sand and gravel bed load fractions at the outlet over the respective feed fractions when the feed rate is qb;f50.55 g/m/s and the water discharge Qw50.032 m 3 /s with the four coarsest textures of Figure 9. Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 16 top five plots. Figure 13 (bottom) illustrates the numerical results of the surface armor ratio at the same times. The five plots highlight the existing link between the differences in mobility illustrated in Figure 12 and the aggradation in the flume during the final stages of the runs, i.e., the formation of the upstream wedge of sediment: the stronger the difference in mobility among the grain sizes contained in the feed texture, the higher and the earlier the sediment wedge develops. Differences in mobility among the grain sizes are thought to be caused by the presence of sand on the bed surface, mainly driven by the sand content in the feed texture [Curran and Wilcock, 2005]. Figure 13 illustrates how this wedge travels along the flume. This bed elevation response can be interpreted as the passage of a slow wave of coarse sediment traveling downstream: the coarser the feed texture, the coarser the front of the sediment wedge. Slow kinematic waves of sediment were also observed by Reid et al. [1985] during bed load transport measurements. Recall that the coarsest fractions supplied (Figure 1) in coarse-fed runs are stored in the upper part of the channel, forming a sediment wedge (Figure 8). This sediment wedge causes a change in the availability of coarse material along the flume (provoked by longitudinal sediment sorting) which, as reported by Iseya and Ikeda [1987], is thought to be the cause of the bed load oscillations observed. Numerical results in Figure 13 also point out that the surface adjustments to the feed texture are produced faster than those of bed profile: whereas the wave of coarse material is clearly noticed at t58 h, bed profiles remain insensible to feed texture at this time; it is not until t516 h when a slight difference in bed profile is observed. Results of this research can be useful for river researchers and managers. Infiltration of fine material between the gravel interstices affects riverine ecosystems, alters sediment transport, and modifies channelbed adjustments. As demonstrated herein, the rate and the texture of the sediment supply influences the way by which equilibrium is attained. But more interestingly they also control the adjustment processes of a gravel-bed river in response to the grain size distribution of the feed: (i) by promoting infiltration of fine particles underneath the surface formed by a coarse framework or (ii) by enhancing the mobility of the coarse grain fractions on the bed surface due to the abundance of sand. Disturbances to gravel-bed streams caused by episodic landslides or debris flows entail large amounts of sediment, the composition of which may be different than that of the bed. As seen, channel response to these disturbances depends on the magnitude and texture of the sediment inputs, as well as the time elapsed between these discrete pulses and on the antecedent channel conditions. Under these conditions, it becomes crucial to know whether the time elapsed between sediment pulses is such that the river can attain equilibrium or, on the contrary, it is not long enough for the river to recover to prepulse conditions. Our experiments were performed under steady flow and sediment supply. Thus, they cannot be used to inform about the critical times between successive episodic inputs of sediment for a channel to reach equilibrium. However, our research contributes reporting the required times to attain equilibrium depending on the texture of the sediment supply in gravel-bed streams with episodic pulses of sediment where (i) the frequency of these pulses is high enough to consider them as a constant supply of sediment and (ii) their 0 2 4 6 8 t = 2 h 0 2 4 6 8 1 2 3 4 5 t = 2 h t = 8 h 0 2 4 6 8 t = 8 h t = 16 h 0 2 4 6 8 t = 16 h x (m) t = 48 h 0 2 4 6 8 t = 48 h t = 96 h 0 2 4 6 8 t = 96 h GSD−5 GSD−2 Dg,S/Dg,s0 G S D − 4 G S D − 3 η b (cm) ηb0 Figure 13. (top) Numerical results of the bed elevation at five specific times (t52h,t58h,t516 h, t548 h, t596 h). Dashed line in each of the top plots is the initial bed elevation, common for all runs and feed textures. (bottom) Numerical results of the armour ratio (geometric mean diameter on the surface Dg;sover its initial value at the same four cross sections Dg;s0. Results are presented for the four coarsest grain sizes. Statistics of each texture are listed in the inset plot of Figure 9. Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 17 magnitude and texture are similar in time. Long-lasting numerical simulations have been carried out under steady flow and sediment feed rate (with a constant duration of 576 h, i.e., six times the duration of the experimental runs). The four coarsest textures of Figure 9 have been used under Qw50.032 m 3 /s and feed rate qb;f50.55 g/m/s. Under these conditions, the theoretical bed slope and the surface grain size distribution at equilibrium have been back-calculated using the Wilcock and Crowe [2003] equation and following the methodology proposed by Parker and Wilcock [1993] imposing that the bed load transport rate and its texture must match those the feed. The degree of equilibrium achievement is defined by the ratio of the surface grain size distribution, feed rate, and its texture at t5576 h over those values at equilibrium at the flume outlet (the last node in attaining equilibrium). Numerical results show that whereas run GSD-2 is nearly at equilibrium at t5576 h (qb50.99 qb;fand Dg;b50.99 Dg;f), run with GSD-5 is far from such conditions (the sediment transport rate and its geometric mean diameter are 81% lower and 81% finer, respectively, than those of the feed). The same trend is observed with respect to the geometric mean diameter of the bed surface: the ratios between Dg;sand those at equilibrium are 0.89 and 0.79 for GSD-2 and GSD-5, respectively. Results of numerical simulations with Qw50.021 m 3 /s and feed rate qb;f50.15 g/m/s point out to the same trends: qb51.06 qb;fand Dg;b50.98 Dg;ffor GSD-2 (i.e., nearly at equilibrium) whereas qb5 0.78 qb;fand Dg;b50.42 Dg;ffor GSD-5. It is worth noting that the slightly higher bed load transport rate obtained for run with GSD-2 compared to the feed rate confirms our findings with regards to the oscillations of bed load transport rate around the feed exposed in Figures 9, 11, and 12. From these results, it can be inferred that in rivers with frequent episodic inputs of sediments and given a flow discharge and a feed rate, the coarser the composition of the sediment supply, the longer to achieve equilibrium. Hence, given the results of Dg;s,qb, and Dg;bat the end of the 576 h long numerical tests compared to those at equilibrium, it can be stated that gravel-bed streams in valleys with frequent landslides or debris flows may not be ever in equilibrium conditions and may always be in a transient stage adjusting to successive discrete events. These long-term simulations point out that, at least for the conditions tested (flow and feed rates, feed textures, and bed slopes), large amounts of time are needed to achieve equilibrium. From the procedural point of view in laboratory studies, long-term measurements should be taken to properly assure that an experiment has reached equilibrium conditions. More research is needed, however, to better understand the role played by the texture of the sediment supply in the temporal adjustments to equilibrium. 5. Conclusions The influence of the texture of the sediment supply on adjustments in gravel-bed rivers has been experimentally studied. Numerical results confirm the experimental findings. Differences in the sand and gravel fractions in the feed texture result in distinct channel adjustments. Experiments demonstrate that the surface coarsening is controlled by the presence or absence of coarse gravel in the feed texture which can enhance the probability of kinematic sorting of the fine grain sizes by the increase of coarse particles on the surface. Fine sand continuously infiltrates underneath the surface in moved and coarse-supplied runs because of the gravel that is constantly being supplied. This results in increasing surface coarsening during the first 16 h of each run; from this time onward, bed load transport rates match the feed without substantial surface coarsening in moved-supplied runs whereas bed load transport rate and its texture are, respectively, below and much finer than those of the feed in coarse-supplied runs. On the other hand, whereas fine material in low flow sand-supplied runs infiltrates during the first 16 h, it remains on the bed surface once the near-surface pores are saturated. This causes the surface to coarsen in the first phase and to subsequently fine thereafter. It is worth noting that surface coarsening is observed, regardless of the feed texture, when flow strength increases. The experiments also demonstrate that when surface coarsening occurs, no persistent trends in the surface coarsening development are noticed after the first 16 h. Results of a one-dimensional numerical model demonstrate that longitudinal surface evolution proceeds differently when coarse partially mobile material constitutes a significant proportion of the feed texture (coarse-supplied runs): a wedge of sediment develops in the uppermost part of the channel. This bed aggradation reflects the passage of a slow wave of coarse sediment traveling downstream. This results in a change in the availability of coarse material in the lower sections of the flume which causes bed load oscillations. Results of the numerical tests provide evidence that under weak bed load transport conditions, the higher the differences in mobility among the finest and the coarsest fractions of the feed texture, the higher the amplitudes of the bed load oscillations toward equilibrium. Further, numerical results show that the Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 18 higher these differences, the more time is needed to achieve equilibrium. These results are significant for gravel-bed stream subjected to episodic sediment inputs, the frequency of which may prevent the river from recovering or achieving equilibrium. Appendix A This appendix presents the temporal evolution of the bed load transport rate (Figure A1), the evolution of the D16, D50 and D84 of the bed load transport (Figure A2) and the temporal evolution of the D16, D50 and D84 of the surface texture (Figure A3). 0.01 0.1 1 10 100 G1-No feed: Qw = 0.021 m3/s qb,f = 0 g/m/s G2-No feed: Qw = 0.032 m3/s qb,f = 0 g/m/s 0.01 0.1 1 10 100 G3-Moved: Qw = 0.021 m3/s qb,f = 0.14 g/m/s G4-Moved: Qw = 0.021 m3/s qb,f = 0.36 g/m/s G5-Moved: Qw = 0.021 m3/s qb,f = 0.49 g/m/s 0.01 0.1 1 10 100 H1-Moved: Qw = 0.032 m3/s qb,f = 0.35 g/m/s H2-Moved: Qw = 0.032 m3/s qb,f = 0.55 g/m/s H3-Moved: Qw = 0.032 m3/s qb,f = 0.75 g/m/s 0.01 0.1 1 10 100 H4-Coarse: Qw = 0.021 m3/s qb,f = 0.16 g/m/s H5-Coarse: Qw = 0.032 m3/s qb,f = 0.29 g/m/s H6-Coarse: Qw = 0.032 m3/s qb,f = 0.54 g/m/s 110100 0.01 0.1 1 10 100 0.01 0.1 1 10 100 H7-Sand: Qw = 0.032 m3/s qb,f = 0.73 g/m/s 110 100 Time (h) Time (h) H8-Sand: Qw = 0.032 m3/s qb,f = 0.38 g/m/s 110 100 H9-Sand: Qw = 0.021 m3/s qb,f = 0.25 g/m/s I1-Sand: Qw = 0.021 m3/s qb,f = 0.48 g/m/s qb,out (g/m/s) Figure A1. Temporal evolution of the bed load transport rates for all runs. Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 19 0 1 2 3 4 5 0 1 2 3 4 5 0 2 4 6 8 10 D (mm) 0 2 4 6 8 10 0 1 2 3 4 5 0 1 2 3 4 51 10 100 Time (h) Time (h) 1 10 100 1 10 100 G1-No feed: Q w = 0.021 m 3 /s q b,f = 0 g/m/s G2-No feed: Q w = 0.032 m 3 /s q b,f = 0 g/m/s G3-Moved: Q w = 0.021 m 3 /s q b,f = 0.14 g/m/s G4-Moved: Q w = 0.021 m 3 /s q b,f = 0.36 g/m/s G5-Moved: Q w = 0.021 m 3 /s q b,f = 0.49 g/m/s H1-Moved: Q w = 0.032 m 3 /s q b,f = 0.35 g/m/s H2-Moved: Q w = 0.032 m 3 /s q b,f = 0.55 g/m/s H3-Moved: Q w = 0.032 m 3 /s q b,f = 0.75 g/m/s H4-Coarse: Q w = 0.021 m 3 /s q b,f = 0.16 g/m/s H5-Coarse: Q w = 0.032 m 3 /s q b,f = 0.29 g/m/s H6-Coarse: Q w = 0.032 m 3 /s q b,f = 0.54 g/m/s H7-Sand: Q w = 0.032 m 3 /s q b,f = 0.73 g/m/s H8-Sand: Q w = 0.032 m 3 /s q b,f = 0.38 g/m/s H9-Sand: Q w = 0.021 m 3 /s q b,f = 0.25 g/m/s I1-Sand: Q w = 0.021 m 3 /s q b,f = 0.48 g/m/s Figure A2. Bed load position statistics for all runs: D16;b(open squares), D50;b(red squares), and D84;b(yellow squares). Dashed lines indicate the values of the respective percentiles of the feed texture. Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 20 Notation Dg;fgeometric mean diameter of the feed texture, L. Dg;sgeometric mean diameter of the surface texture, L. D16;b16% percentile of the bed load texture, L. D16;f16% percentile of the feed texture, L. D16;s16% percentile of the surface texture, L. D50;bmedian diameter of the bed load texture, L. D50;fmedian diameter of the feed texture, L. D50;smedian diameter of the bed surface texture, L. 0 6 12 18 0 6 12 18 0 6 12 18 0 6 12 18 0 6 12 18 0 6 12 18 1 10 100 1 10 100 1 10 100 D (mm) Time (h) Time (h) G1-No feed: Q w = 0.021 m 3 /s q b,f = 0 g/m/s G2-No feed: Q w = 0.032 m 3 /s q b,f = 0 g/m/s G3-Moved: Q w = 0.021 m 3 /s q b,f = 0.14 g/m/s G4-Moved: Q w = 0.021 m 3 /s q b,f = 0.36 g/m/s G5-Moved: Q w = 0.021 m 3 /s q b,f = 0.49 g/m/s H1-Moved: Q w = 0.032 m 3 /s q b,f = 0.35 g/m/s H2-Moved: Q w = 0.032 m 3 /s q b,f = 0.55 g/m/s H3-Moved: Q w = 0.032 m 3 /s q b,f = 0.75 g/m/s H4-Coarse: Q w = 0.021 m 3 /s q b,f = 0.16 g/m/s H5-Coarse: Q w = 0.032 m 3 /s q b,f = 0.29 g/m/s H6-Coarse: Q w = 0.032 m 3 /s q b,f = 0.54 g/m/s H7-Sand: Q w = 0.032 m 3 /s q b,f = 0.73 g/m/s H8-Sand: Q w = 0.032 m 3 /s q b,f = 0.38 g/m/s H9-Sand: Q w = 0.021 m 3 /s q b,f = 0.25 g/m/s I1-Sand: Q w = 0.021 m 3 /s q b,f = 0.48 g/m/s Figure A3. Surface position statistics for all runs: D16;s(open squares), D50;s(red squares), and D84;s(yellow squares). Dashed lines indicate the initial values of the respective percentiles. Water Resources Research 10.1002/2013WR015117 FERRER-BOIX AND HASSAN V C2014. American Geophysical Union. All Rights Reserved. 21 D84;b84% percentile of the bed load texture, L. D84;f84% percentile of the feed texture, L. D84;s84% percentile of the bed surface texture, L. D90;s90% percentile of the surface texture, L. Fii-th fraction of the surface. Fs;fsand content of the feed texture. gacceleration of gravity, LT 22 . pbi i-th fraction of the bed load transport rate. pbg gravel fraction of the bed load transport rate. pbs sand fraction of the feed rate. pb;ccoarse fraction of the bed load transport rate when the grain sizes are lumped into two grain classes. pb;fcoarse fraction of the feed rate when the grain sizes are lumped into two grain classes. pbg;fgravel fraction of the feed rate. pbs;fsand fraction of the bed load transport rate. Qwwater discharge, LT 23 . qbsediment transport rate per unit width, ML 21 T 21 . qb;fsediment feed rate per unit width, ML 21 T 21 . q wdimensionless water discharge. Rsubmerged specific gravity of the sediment 5qs2qðÞ=qwhere qand qsare water and sediment density respectively. ttime, T. gbbed elevation, L. qwater density, ML 23 . rg;fgeometric standard deviation of the feed texture. sbmean boundary shear stress, ML 21 T 22 . s gdimensionless shear stress associated with the geometric mean diameter the surface. s rs84 dimensionless reference shear stress of the 84% percentile of the surface texture. wgrain size on the psi scale; 5log 2 (D). References Benda, L., and T. Dunne (1997), Stochastic forcing of sediment routing and storage in channel networks, Water Resour. Res.,33(12), 2849– 2863, doi:10.1029/97WR02387. Buffington, J. M., W. E. Dietrich, and J. W. Kirchner (1992), Friction angle measurements on a naturally formed gravel streambed: Implications for critical boundary shear stress, Water Resour. Res.,28(2), 411–245, doi:10.1029/91WR02529. Church, M., and M. A. Hassan (2002), Mobility of bed material in Harris Creek, Water Resour. 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