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Effects of episodic sediment supply on channel adjustment of an experimental gravel bed Elgueta Astaburuaga, Maria A. 2018

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Effects of episodic sediment supply on channel adjustment of anexperimental gravel bedbyMaria A. Elgueta AstaburuagaBA, Geography, Universidad de Chile, 2006MSc, Geography, The University of British Columbia, 2014A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Geography)The University of British Columbia(Vancouver)March 2018c©Maria A. Elgueta Astaburuaga, 2018AbstractA flume experiment was conducted to study channel adjustment of gravel beds to episodicsediment supply. The bed and sediment feed included grains 0.5–64 mm with geometric meansize 5.7 mm. Flow discharge was constant and every 40 h, 300 kg of sediment was suppliedthrough different feed regimes. Sediment transport and storage, bed slope, and bed surfacetexture responded to sediment supply regime. The preferential storage of grains > 8 mmcaused a cumulative increase in bed slope, which probably increased transport efficiency.Within a run, sediment transport rate qb and bed-surface texture were controlled by the magni-tude and frequency of sediment feed and not the total mass. Constant feed promoted gradualincreases in qb and small changes in bed surface texture, whereas large infrequent sedimentpulses caused pronounced increases in qb and strong surface fining, followed by monotonicdecreases in qb as surface re-coarsened. Pronounced trends caused stronger memory in bed-load time series for runs with episodic feed than in those for runs with constant feed, althoughwithin each run, the structure of memory varied. Long memory was observed for periodswhen bedload rate was nearly stable, which indicates that it could result from local changesin storage. Patterns of grain-size dependence were not affected by sediment feed and the limitfor full-mobility was stable around 8 mm. Scaling statistics for total bedload were similar tothose for fine gravel, which was fully-mobile and dominated bedload. A decrease in the fre-quency of movement with size for gravel fractions caused a reduction in the memory strengthof fractional bedload signals. Size-selective transport promoted the storage of coarse grainsupstream and downstream fining on the bed surface. Although fully-mobile, more than 60%of the sand fed got stored in the bed, probably because of its high potential to infiltrate and getcaught within larger grains. Memory was weaker for sand bedload rates than for fine gravel,which indicates that sand mobility was more influenced by short-term stochastic dynamics(e.g., clustering) and less affected by long-term processes like the evolution of large bedformsand sediment pulses.iiLay summarySediment supply is a first order control in channel morphology and sediment transport regimein mountain streams. Although streams usually receive sediment episodically through naturaland human induced mechanisms such as landslides, physical models have mostly used con-stant sediment feed to analyze the adjustments of gravel beds to changes in sediment supplyregime. Here, the importance of the magnitude and frequency of sediment supply regimes isassessed by comparing the adjustments of an experimental gravel-bed to changes in sedimentfeed under constant water discharge. The experiment included constant feed and differentepisodic feed regimes for comparisons. The limitations of assuming constant feed in experi-ments and the scales and situations for which the assumption would be correct are discussed.Experimental runs were conducted as a sequence, in which some feed regimes were run twiceto explore the effects of the initial bed on its adjustment.iiiPrefaceThe experiment was conducted in partnership with Claudia vonFlotow under the supervi-sion of Marwan Hassan. All the analyses and writing in this manuscript were conductedby the author while working toward a PhD. A version of Chapter 2 has been published asElgueta-Astaburuaga and Hassan (2017). For that paper, I conducted the analyses and wrote themanuscript, for both of which, Marwan Hassan provided guidance. A version of Chapter 3has been submitted as Elgueta-Astaburuaga et al. (2017). Here, I was again responsible for dataanalyses and writing. Marwan Hassan, Matteo Saletti, and Garry Clarke provided guidancefor methods, analyses, discussion, and writing. Chapter 4 was written as a paper to be submit-ted, in which I will be the first author and Marwan Hassan the second author. In this chapter,I completed the analyses and writing under M. Hassan’s supervision.ivTable of contentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of symbols and acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiAknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Experiment on temporal variation of bedload transport in response to changes insediment supply in streams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.1 Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.2 Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.3 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4.1 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4.2 Temporal patterns of variability in sediment transport rate under differ-ent supply regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.3 Statistical modelling of sediment transport rate series . . . . . . . . . . . 21v2.4.4 The effects of pulses of different sizes on sediment transport . . . . . . . 222.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.5.1 Hypothesis 1: The adjustment of a gravel bed to sediment supply is sig-nificantly affected by the magnitude and frequency of sediment feed . . 272.5.2 Hypothesis 2: If the time between sediment pulses is less than the timeneeded for the sediment transport rate to relax (Tp < Tr), the responsecan be similar to constant feed regimes . . . . . . . . . . . . . . . . . . . 282.5.3 Hypothesis 3: Large sediment pulses produce stronger responses in thetransport rate and require longer time for relaxation than small pulses . 282.5.4 Hypothesis 4: The temporal adjustment of sediment transport rates tochanges in the supply regime is conditioned by the initial bed slope, sur-face grain-size distribution, and sediment storage . . . . . . . . . . . . . 292.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 The effect of sediment supply regime on bedload scaling and sediment mobility . 313.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3.1 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3.2 Data analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.4.1 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.4.2 Memory and scaling statistics . . . . . . . . . . . . . . . . . . . . . . . . . 433.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.5.1 Controls on sediment mobility and the composition of large bursts inbedload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.5.2 Hypothesis 1: Bedload rate time series for runs with constant sedimentfeed have weaker memory than those for runs with large infrequent sed-iment pulses, which can cause pronounced trends in bedload transport 503.5.3 Hypothesis 2: The memory structure of total bedload reflects that offully-mobile grain sizes, which dominate sediment transport and exhibitstrong memory in their bedload signals . . . . . . . . . . . . . . . . . . . 513.5.4 Hypothesis 3: Grain-size dependence in bedload transport increases withsediment feed because the movement of fully-mobile sediment is moreresponsive to feed than that of partially-mobile grain sizes . . . . . . . . 523.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534 Temporal patterns of sediment storage and spatial variability on a gravel bed un-der changing sediment supply regimes . . . . . . . . . . . . . . . . . . . . . . . . . . 554.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55vi4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.3.1 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.3.2 Data analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.4.1 Temporal patterns of sediment storage . . . . . . . . . . . . . . . . . . . 614.4.2 Sediment transport–storage relations . . . . . . . . . . . . . . . . . . . . 634.4.3 Sediment storage and spatial variability over the channel bed . . . . . . 664.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.5.1 Hypothesis 1: Preferential deposition of coarse partially-mobile grav-els near the feed source promote increased storage upstream and down-stream fining on the bed surface . . . . . . . . . . . . . . . . . . . . . . . 714.5.2 Hypothesis 2: Constant feed, which makes sediment available more grad-ually, promotes larger sediment storage than sediment pulses because ofa greater probability for sediment being sequestered in the bed . . . . . 734.5.3 Hypothesis 3: Hysteresis in sediment transport-storage relations largelydepends on differences in bed surface texture and sediment availability 754.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.1 Which episodic sediment feed regimes could be represented by constant feedand at which time scales? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.2 How do bed history and bed state affect channel reponse to changes in sedimentfeed regime? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.3 What are the consequences of size-selective bedload transport on this response? 845.4 Limitations of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.5 Future research directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88viiList of tablesTable 2.1 Sediment feed characteristics and observations towards the end of each run 15Table 2.2 p-values from L-ratio tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Table 2.3 p-values from L-ratio tests using 5 different temporal resolutions . . . . . . . 22Table 2.4 Persistence and strength of pulse effects . . . . . . . . . . . . . . . . . . . . . 24Table 3.1 Summary of sediment feed regimes used in experimental runs . . . . . . . . 36Table 3.2 Bedload rate statistics and observations at the end of each run . . . . . . . . 40Table 3.3 Summary statistics for the percent of sediment bursts that included coarsematerial for all 10-h intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Table 3.4 Description of correlograms of bedload time series . . . . . . . . . . . . . . . 45Table 4.1 Mean flow characteristics, bed observations at the end of each run, and bed-load rate statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60viiiList of figuresFigure 1.1 Flume experiment in progress at the Mountain Channel Hydraulic Experi-mental Laboratory (UBC). Sediment was colored by grain size to facilitatethe identification of bed surface texture on photographs. The image wastaken after the first run. The flow had just started at a very low rate to wetthe bed after a scan and photographs (water flows from back to front). Sed-iment is prepared to be fed upstream during the second run. In subsequentruns, sediment was introduced manually. . . . . . . . . . . . . . . . . . . . . 4Figure 2.1 Grain size distribution of the bulk sediment that constituted bed and feedmaterial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Figure 2.2 Sequence of feed regimes followed during the experiment. Cumulative feedis plotted as a function of time for constant feed (blue) and three types ofepisodic feed regimes (red). The time at which bed surface photos, water-surface elevation (WSE), and bed scans were acquired are displayed withred bars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Figure 2.3 Time series of total bedload rate estimated by processing images recordedover a light table at the end of the flume. Red lines indicate sediment feedrates. The high resolution of the method allowed computing fractional massand number of grains that exited the flume at every second. Gaps in the dataare due to technical problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 2.4 (a) Shields number. (b) Thalweg slope (m/m). Grain size statistics of the bedsurface (red dots), bedload (blue dots) and bulk sediment that constitutedthe original bed and feed (horizontal dashed lines): (c) geometric mean par-ticle size, (d) D90, and (e) D16. Sediment pulses are indicated with verticaldashed lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Figure 2.5 Total sediment transport rate and fractional rate of four grain size classesduring R5. Red lines indicate sediment feed rate. . . . . . . . . . . . . . . . . 18ixFigure 2.6 Variation of sediment transport rate over each run. The mean transport rateof a run is subtracted from each observation for normalization, and the cu-mulative departure from the mean is plotted as a function of time. Sedimentinputs are represented with vertical dashed lines and major trend inflectionsare identified with black dots. . . . . . . . . . . . . . . . . . . . . . . . . . . 19Figure 2.7 Characteristics of cumulative departure from mean transport rate againstfeed regimes. (a) Range of cumulative departure. (b) Lag time betweenstarts of feed and associated inflections in the curve. (c) Slope of decreasesrelated to stops in feed. (c) The amount of feed received during the firsthour of each experiment is used to represent feed regime as a quantitativevariable in the x-axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Figure 2.8 Persistence and strength of the effects of supply episodes of different sizeon sediment transport. (a) Relaxation time Tr1 estimated with equation 2.2(exponential fit), and Tr2 estimated with equation 2.3 (log–linear fit). (b)Total sediment output until Tr2. (c) Estimation of total output until Tr forthe last small pulse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Figure 3.1 Bed adjustments for the entire 280-h experiment. Modified from Figures 3and 4 in Elgueta-Astaburuaga and Hassan (2017) (AGU Usage Permissions).(a) Total bedload transport rate and sediment feed rate (red lines and dots)in logarithmic scale. Gaps in the data are due to technical problems. (b)Geometric mean particle size Dg of the bed surface, bedload, and bulk bed.(c) Slope at the thalweg. Sediment pulses are indicated with vertical dashedlines in (b) and (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 3.2 Bedload transport intensity by grain size for each run. (a) Mean bedloadtransport rate. (b) Fraction of time immobile. Time immobile was estimatedas the time over which no grains of a specific size exited the flume. Grain-size fractions < 2 mm were grouped together as sand to avoid the effects ofmis-detection of grains < 1 mm. Coarse grains were observed to move forshort distances, but most of the time did not leave the flume. . . . . . . . . . 42Figure 3.3 Bedload transport rate qb and large bursts in qb (displayed in red) duringR3. The run was divided in four 10-h intervals (Interval 1–4) and, withineach interval, qb with probability of exceedance pe < 0.01 were selected aslarge bursts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 3.4 (a) Ratios between the proportion of sediment of each grain size class inlarge sediment bursts Pi[bursts] and the proportion of the same grain size classin bulk bedload Pi[bulk]. For large bursts, pe< 0.01. (b) Grain-size distributionof bedload rates with pe< 1, 0.1, and 0.01 over the first 10 h of R3. (c) Grain-size distributions over the last 10 h of R3. . . . . . . . . . . . . . . . . . . . . 43xFigure 3.5 Fractional bedload rate qbi of coarse grains against total bedload rate qb forthree 10-h time intervals. Only qb observations with pe< 0.01 are presented.Dashed line corresponds to qbi= qb. (a) Last 10 h of R1 when the intensityof sediment transport was low after 30 h of no feed. (b) Last 10 h of R2when the intensity of transport was moderate after 30 h of constant feed. (c)First 10 h of R3 when the intensity of transport was high because of a largesediment pulse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Figure 3.6 Sample autocorrelation ρτ against lag time τ. Examples for the three typesof correlograms described in Table 3.4. Note logarithmic ordinate. (a) R3displays persistently high ρτ due to strong trend. (b) For R2 ρτ is lower, butstill significant. (c) For the last 10 h of R1 ρτ is only significant at τ = 0, asfor white noise. The dashed horizontal line indicates 95% confidence limits. 45Figure 3.7 Scaled variance vs. aggregation time scale T. The variance σT at each T wasdivided by σT when T = 1 s. The number of observations N decreases as Tincreases. T at which N=50 is displayed with a vertical dashed line. (a) Re-sults for individual runs using total bedload rates. (b) Grain-size dependentresults for R2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Figure 3.8 Evolution of long-term memory. The Hurst exponent H was estimated foreach run over 5-h moving windows and in cumulative 1-h increments. . . . 47Figure 3.9 Hurst exponent H over 5-h moving window against mean bedload rate. . . 48Figure 3.10 (a) Range of H by run for five grain size fractions Di. (b) H for fractionalbedload against H for total bedload by grain size (run averages). . . . . . . 48Figure 3.11 Lag-one autocorrelation coefficient ρ1 against aggregation time scale T fortotal bedload and four grain size fractions. 95% confidence limits presentedin dashed lines. (a) Results for R2. (b) Results for R3. (c) Time scale T withhighest lag-one autocorrelation ρ1 for different grain sizes and runs. . . . . 49Figure 4.1 (a) Total and fractional sediment storage computed from mass balances overeach run. (b) Percent of sediment mass stored over mass fed for differentgrain size fractions and runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure 4.2 Cumulative sediment storage for bulk sediment (total) and four grain sizefractions. Mass balances were estimated every 15 min and the cumulativesum is plotted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Figure 4.3 Mean bedload transport rate against cumulative sediment storage over theexperiment. Seven runs (R1–R7) distinguished by color. Dashed lines indi-cate sediment feed rates used for constant and episodic feed regimes. . . . . 64Figure 4.4 Mean bedload transport rate against cumulative sediment storage over runswith constant feed (R2-R6). Dashed lines indicate feed rate. Small cycles ofaggradation–degradation occurred in R6 when mean bedload rate exceededfeed rate, which did not happen in R2. . . . . . . . . . . . . . . . . . . . . . . 65xiFigure 4.5 Mean change in bed elevation during the experiment. Mean change wasestimated by subtracting two consecutive DEMs and computing an average. 66Figure 4.6 Cumulative mean change in bed elevation over different bed sections. DEMswere divided in ten 1-m2 sections and cumulative changes in elevation werecomputed for each of them. The downstream end of the flume was at x = 0 m. 67Figure 4.7 Standard deviation for bed elevations ση for different bed sections. DEMswere divided in ten 1-m2 sections and ση was computed for each of them.The downstream end of the flume was at x = 0 m. . . . . . . . . . . . . . . . 68Figure 4.8 Digital elevation models (DEMs) at six different times. We chose these casesfrom the 34 DEMs collected to summarize the evolution of bed topographyat large and intermediate scales. Bed elevations η are relative to the floor ofthe flume. The downstream end of the flume was at x = 0 m. Lateral barsand upstream sediment wedge are delineated and examples of transversefeatures that intercalate with pools are indicated. . . . . . . . . . . . . . . . . 69Figure 4.9 Evolution of small-intermediate scale bedforms after the first small pulsein R4. (a) DEM of the bed one hour after the first small pulse in R4. (b)DEM ten hours after the pulse. Examples of bed features are presented withroman numbers: (i) transverse feature, (ii) stone cluster, (iii) stone line, and(iv) small arrangement of grains. The downstream end of the flume wasat x = 0 m. (c–f) Bed surface photographs showing the evolution of bedfeatures i–iv between 1–10 h after the pulse. . . . . . . . . . . . . . . . . . . 78Figure 4.10 Evolution of geometric mean particle size Dg on the bed surface for sevenbed sections along the flume. The downstream end of the flume was atx = 0 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Figure 4.11 Evolution of bed surface texture at∼6 m from downstream between the endof R1 and the end of R3. (a) The bed surface was coarse by the end of R1 thathad no feed. (b) After 40 h of constant feed in R2, there was no significantfining on the surface. (c) In contrast, one hour after the large pulse of R3,significant fining was observed. (d) Forty hours after the large pulse, thebed surface was coarse again. . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Figure 4.12 Downstream fining at the end of the experiment. Photos of the bed surfaceat three locations. The downstream end of the flume was at x = 0 m. . . . . 81xiiList of symbols and acronymsRoman symbolsSymbol Definitiona intercept for log–linear relationAIC Akaike information criterionAR(1) autoregressive order 1b slope for log–linear relationb′ rate of decrease in sediment transport rate for Run 7b1−4 slopes for general least-squares modelcτ autocovariance at time lag τc0 autocovariance at time lag τ = 0Cumulative δηd cumulative mean change in bed elevationCumulative∆Tn cumulative mass balanced chronological order of DEMd f duration of sediment feedD total number of DEMs availableDEM digital elevation modelxiiiDg geometric mean grain sizeDg (bulk) geometric mean grain size for bedloadDg (bulk) geometric mean grain size for bulk sedimentDg (surface) geometric mean grain size for bed surfaceDi grain size iDmax maximum grain sizeD16 16th percentile of grain size distributionD75 75th percentile of grain size distributionD90 90th percentile of grain size distributionfi grain size distribution for bulk sedimentg acceleration of gravityH Hurst exponentL-ratio likelihood ration exponent for power law between variance σ2T andtime scale TN number of observationsp p-valuepe probability of exceedancePi[bursts] proportion of sediment with size i in large sedimentburstsxivPi[bulk] proportion of sediment with size i in bulk bedloadqb total sediment transport rate per unit channel widthqb mean sediment transport rate per unit channel widthqbi fractional transport rate for grain size i per unitchannel width[qb]i total sediment transport rate per unit channel widthat time instant iqre f reference transport rateq0 intercept for exponential fitQ f sediment feed rateQb mean sediment transport rateRh hydraulic radiusR1–R7 experimental runsR2 coefficient of determinationSDg geometric standard deviationS best fit slope on log-log scaleSw water surface slopet timeT aggregation time scaleTi time of first significant increase in sedimenttransport rate after a sediment pulsexvT max(ρ1) time scale with highest autocorrelation ρ for time lagτ = 1Tp time in between sediment pulsesTr relaxation timeTr1 relaxation time obtained from an exponential fitTr2 relaxation time obtained from a log–linear fit[x, y] DEM coordinatesY time seriesY mean for time seriesYt value for time series Y at time tYt−τ value for time series Y at time t minus time lag τGreek symbolsSymbol Definitionα level of statistical significanceδη[x,y] change in bed elevation for coordinates [x,y]δη mean change in bed elevation∆T mass balance for time period Tη bed elevationΛ rate of decay for exponential fitρs sediment densityρw water densityxviρτ autocorrelation coefficient for time lag τρ1 autocorrelation coefficient for time lag 1ρ1T autocorrelation coefficient for time lag 1 andaggregation time scale Tσqb standard deviation for bedloadσT standard deviation for aggregation time scale Tση standard deviation for bed elevationσ2T variance for aggregation time scale Tτ time lagτb mean boundary shear stressτci critical shear stress for grain size iτ∗ci critical Shields numberxviiAknowledgementsThe experiment was conducted in the Mountain Channel Hydraulic Experimental Laboratoryat the University of British Columbia and funded by NSERC. The studies of the first authorhave been funded by Becas Chile (Conicyt). Data was collected in partnership with ClaudiavonFlotow and Tobias Mu¨ller. I want to aknowledge the work of Marwan Hassan, GarryClarke, and Rob Millar in my supervisory committee. Marwan generously shared his knowl-edge on sediment transport and helped me come up with research questions and hypothesesof study. He supervised my work in a critical but very constructive way. Garry Clarke wasalways available for advice and his careful revisions of manuscripts improved them signif-icantly. He assisted me in time series analyses and instructed me on scientifc writing. RobMillar helped me to complete my comprehensive exam and provided me with useful sugges-tions for my research. The following people were supportive and their comments, advice,and questions helped me improve my research: Carles Ferrer, Matteo Saletti, Tobias Mu¨ller,Shawn Chartrand, Katie DeRego, Leonora King, Dave Reid, NianNian Fan, Eva Crego, andDan Moore. WRR Associate Editor, Jon Major, and an anonymous person reviewed the ver-sion of Chapter 2 published in WRR. Helena Trajic sieved some sediment samples and EricLeingerber assisted with some figures.xviiiDedicationThis manuscript is dedicated to my ancestors, who taught me the value of knowledge forknowledge’s sake.xixChapter 1IntroductionSediment transport and channel morphology in mountain streams are affected by unsteadyand non-uniform flow conditions (Hassan et al., 2006), the wide range of shapes and sizes ofgrains (Einstein, 1950; Wilcock, 1992), the arrangement of grains on the bed surface (Parker andKlingeman, 1982; Wilcock and Detemple, 2005), and changes in sediment supply regime, whichhas been proposed as a first order control (Hassan et al., 2006, 2008). At a reach scale, the chan-nel responds to imbalances between sediment supply and flow transport capacity by adjustingits width, slope, and the arrangement of grains on the bed surface. Channels for which trans-port capacity exceeds sediment supply are considered as supply-limited, whereas those forwhich sediment supply exceeds capacity are considered as transport-limited (Montgomery andBuffington, 1997). The intensity of transport in supply-limited streams is usually low becauseof the development of a coarse bed surface with structures that counteract bed degradation(Parker et al., 1982; Dietrich et al., 1989; Church et al., 1998; Venditti et al., 2008; Nelson et al.,2009). Instead, under the same slope and flow conditions, sediment transport is more intensein transport-limited streams, which develop a finer bed surface and an aggraded bed (Lisle andMadej, 1992; Madej et al., 2009; Pryor et al., 2011).Mountain streams are subjected to episodic sediment supply, which can cause them toshift between relatively high and low supply regimes. Sediment supply comes from multiplesources and enters the channel at discrete locations and through different mechanisms likedebris flows, landslides (Hovius and Stark, 2006), or the release of large wood jams (e.g. Hassanet al., 2005). The texture of sediment inputs and flow competence will dictate which grainsare potentially mobile and those that are not will likely be deposited in situ. Flow capacitywill dictate how much sediment can be transported and the channel bed will condition sedi-ment mobility by promoting efficient paths for sediment transport, as well as deposition fronts(Gaeuman et al., 2017). The sediment that gets deposited can entrain at later stages due to largerfloods or because of changes in the bed configuration (e.g., increase in bed slope, destruction ofbed structures). All of these processes and factors cause bedload transport to vary at multipletemporal and spatial scales.Data collection in the field is limited by technology, time, and accesibility, so flumes have1been used to study channel adjustment to changes in sediment supply under controled envi-ronments (e.g., Dietrich et al., 1989; Lisle and Church, 2002; Curran and Wilcock, 2005; Eaton andChurch, 2004, 2009; Madej et al., 2009; Nelson et al., 2009; Venditti et al., 2010; Pryor et al., 2011).Changes in the sediment supply regime are followed by adjustments of the channel and sed-iment transport–storage relations. Reductions in sediment supply have been linked to beddegradation, which can be counteracted by the expansion on the bed of coarse fixed patchesthat limit sediment transport (Dietrich et al., 1989; Nelson et al., 2009). Sediment transport–storage relations are also affected by changes in sediment supply (Lisle and Church, 2002) andcan exhibit complex patterns of hysteresis during aggradation–degradation cycles (Madej et al.,2009; Pryor et al., 2011; Luzi, 2014). The nature of stream boundaries influences channel adjust-ment to changes in sediment supply (Eaton and Church, 2004, 2009). Unconstrained channelsprimarily adjust channel sinuosity and slope, whereas constrained channels adjust particlesize and bed state. The content of sand (Curran and Wilcock, 2005) and texture of sediment feedrelative to bed texture (Venditti et al., 2010) affect critical conditions for gravel entrainment.Most experiments have used constant feed and only few have used episodic feed regimes likethose found in mountain streams (Cui et al., 2003; Sklar et al., 2009; Venditti et al., 2010; Johnsonet al., 2015).Experimental studies using episodic sediment feed have mostly analyzed the importanceof textural differences between the bed and feed for: pulse propagation (Cui et al., 2003; Sklaret al., 2009), pulse–bed interactions (Venditti et al., 2010), and bed surface texture (Johnson et al.,2015). Experiments indicated that sediment pulses transmit downstream by dispersion if thebed and feed material have similar texture, whereas pulse translation occurs if the feed mate-rial is considerably finer (Cui et al., 2003; Sklar et al., 2009). Field gravel augmentations (Gaeu-man et al., 2017) have revealed that pulses can propagate by fragmentation into smaller pulsesand that the time it takes to propagate depends on the state of intervening sediment reser-voirs. The interaction between sediment pulses and the bed can increase if sediment supplyhas a finer texture (Venditti et al., 2010). Beds have even been reported to become coarser androugher after fine sediment pulses (Johnson et al., 2015). Besides these studies, the roles of themagnitude and frequency of sediment pulses on channel adjustment remain as open ques-tions and the suitability of constant feed regimes for modeling mountain streams has not beenthoroughly discussed.Gravel-bed streams exhibit a wide range of grains sizes, which can sort in all directionsand at different scales as a result of sediment transport (Parker, 1992; Powell, 1998). Sedimentmixtures influence the mobility of specific grain sizes through the hiding effects of relativelylarge particles on smaller particles (Einstein, 1950), the relative exposure of large grains to theflow (Fenton and Abott, 1977), and the effects of sand on the entrainment of gravels (Wilcockand Crowe, 2003; Curran and Wilcock, 2005). Usually, part of the bed is transported duringbankfull flows capable of mobilizing a wide range of grain sizes, but with different intensi-ties. Finer material is fully mobile and its proportion in bedload is the same as in the bed,2whereas coarser material affected by size-selectivity is partially mobile and its proportion inbedload is less than in the bed (Wilcock and McArdell, 1993). Specific grain sizes are impor-tant at different scales and for different processes. Coarse material increases channel stability(Zimmermann, 2010; Waters and Curran, 2012; Mackenzie and Eaton, 2017), gravels provide fishspawning habitat (e.g., Kondolf and Wolman, 1993; Hassan et al., 2008), and fine sediment affectswater quality (e.g., Jones, 2012; Mathers et al., 2017). As different grain sizes move by differenttransport regimes, their temporal patterns of mobility are not the same and are not necessar-ily represented by those of total bedload transport (e.g., Saletti et al., 2015), which should alsoinfluence sediment storage. Whereas fully-mobile grains are frequently entrained and easilytransported downstream, coarser partially-mobile grains move occasionally and are preferen-tially stored when supplied.Here, the main objective is to study the effects of episodic sediment supply on channeladjustment of an experimental gravel bed (Figure 1.1). The research is guided by the followingquestions:1. Which episodic sediment feed regimes could be represented by constant feed and atwhich time scales?2. How do bed history and bed state affect channel response to changes in sediment feedregime?3. What are the consequences of size-selective bedload transport on this response?To isolate the effects of sediment feed, flow discharge was held constant throughout the ex-periment and 300 kg of sediment was introduced every 40 h using different feed regimes in asequence of seven runs. We included runs without feed and with constant feed as references,and three different episodic feed regimes to assess the roles of the magnitude and frequencyof sediment pulses. Many experiments start all their runs from flat well-mixed beds becauseit facilitates direct comparisons among them. This experiment was conducted as a sequenceof runs, which started one after the other, to develop a complex bed topography that resultedfrom a long history of flow and sediment supply. Runs with constant feed and without feedwere conducted twice within the sequence to explore the effects of initial bed conditions andbed history on channel adjustment to changes in supply. Although the importance of bed statefor transport–storage relations has been mentioned (e.g., Madej et al., 2009; Pryor et al., 2011),a meticulous assessment of the effects of bed characteristics and configuration in the responseof a channel to changes in sediment feed is still missing.The wide range of grain sizes in the bed and feed (0.5–64 mm) promoted sediment sortingand allowed the bed to armor, which influences sediment transport (Parker and Klingeman,1982; Parker et al., 1982). Given the flow and sediment texture, partial sediment transport wasexpected over the bed and the effects of sediment mixtures (Einstein, 1950; Fenton and Abott,1977; Curran and Wilcock, 2005) were expected to be strong. Fractional sediment transport data3Figure 1.1: Flume experiment in progress at the Mountain Channel Hydraulic Experimen-tal Laboratory (UBC). Sediment was colored by grain size to facilitate the identifi-cation of bed surface texture on photographs. The image was taken after the firstrun. The flow had just started at a very low rate to wet the bed after a scan and pho-tographs (water flows from back to front). Sediment is prepared to be fed upstreamduring the second run. In subsequent runs, sediment was introduced manually.was collected during the 280-h long experiment to study the effects of the wide range of sizesand size-selective entrainment on the temporal patterns for fractional bedload transport andstorage at multiple scales and how they relate to those for total bulk bedload.The study is organized around three main topics regarding the effects of sediment feedregime on channel adjustment and the influence of initial bed conditions. The first topic is theeffects of sediment feed on the temporal adjustments of total bedload transport, for which thefollowing hypotheses are proposed.• (T1-H1) Adjustment of a gravel bed to sediment supply is significantly affected by themagnitude and frequency of sediment feed.4• (T1-H2) If the time between sediment pulses is less than the time needed for the sedi-ment transport rate to relax to a low value after a pulse, the response could be similar toconstant feed regimes.• (T1-H3) Large pulses, which result in greater sediment availability, produce strongerresponses in the transport rate and have longer relaxation times than small pulses.• (T1-H4) The temporal adjustment of sediment transport rates to changes in the supplyregime is conditioned by the initial bed slope, surface grain-size distribution, and sedi-ment storage.The second topic is the patterns of grain-size dependence on bedload transport, and morespecifically, on the memory of bedload rate signals under changing sediment supply regimes.Under partial transport, as expected during the experiment, aggregated bedload patterns arenot representative of all grain sizes. Given that the relevance of grains of different sizes isvaried in river studies and projects (e.g., Hassan et al., 2008; Mackenzie and Eaton, 2017; Matherset al., 2017), it is interesting to evaluate the responses to sediment feed of specific grain sizesand how they relate to the response of total bulk bedload patterns. Three hypotheses areformulated.• (T2-H1) Bedload transort rate time series for runs with constant sediment feed haveweaker memory than those for runs with large infrequent sediment pulses which cancause pronounced trends in bedload transport.• (T2-H2) The memory structure of total bedload reflects that of fully-mobile grain sizes,which dominate sediment transport and exhibit strong memory in their bedload signals.• (T2-H3) Grain-size dependence in bedload transport increases with sediment feed be-cause the movement of fully-mobile sediment is more responsive to feed than that ofpartially-mobile grain sizes.The last topic is the effects of sediment feed regime and bed history on temporal and spatialpatterns of sediment storage, and how they relate to fractional bedload transport. As prefer-ential storage of coarse sediment is expected under partial transport, the following hypothesesare proposed.• (T3-H1) Preferential deposition of coarse partially-mobile gravels near the feed sourcepromote increased storage upstream and downstream fining on the bed surface.• (T3-H2) Constant feed, which makes sediment available more gradually, promotes largersediment storage than sediment pulses because of a greater probability for sedimentbeing sequestered in the bed.• (T3-H3) Hysteresis in sediment transport-storage relations largely depends on differ-ences in bed surface texture and sediment availability.5Chapter 2Experiment on temporal variation ofbedload transport in response tochanges in sediment supply in streams2.1 SummaryA flume experiment was conducted to study channel adjustment to episodic sediment supplyin mountain streams. The bulk sediment used for the bed and feed included grain sizes 0.5–64 mm with geometric mean Dg (bulk) of 5.7 mm. Water discharge was held constant for 40h, and 300 kg of sediment was supplied through a range of scenarios. Bed slope, sedimentstorage, sediment transport and bed surface texture responded to sediment supply. Duringthe first of seven runs, bed slope decreased from 0.022 m/m (flume slope) to 0.018 m/m dueto sediment starvation. Bed slope increased beginning in the second run as the bed aggradeddue to preferential storage of grains > 8 mm. Transport rate and bed-surface particle sizewere significantly affected by the magnitude and frequency of sediment feed. Under constantfeed, transport rate increased gradually and Dg (surface) ranged between 12–15 mm. Instead,sediment pulses caused a pronounced increase in sediment transport rate and surface fining,trends that were inverted as sediment evacuated. At the run-scale, sediment transport andstorage behaved as with constant feed if pulse relaxation time exceeded time between pulses.The increase in transport rate and surface fining were proportional to pulse size. After the300 kg pulse, transport rate reached 100 g m−1 s−1 and Dg (surface) was <10 mm. After 75 kgpulses transport rate reached ∼10 g m−1 s−1 and Dg (surface) was >12 mm. Textural differenceson the initial bed surface influenced the patterns of sediment transport. Channel adjustmentwas controlled by the magnitude and frequency of sediment feed and not by total feed.62.2. Introduction2.2 IntroductionMountain streams are commonly subjected to episodic inputs of sediment through bank col-lapse, landslides, debris flows, and other kinds of natural or anthropogenic disturbances (Madejand Ozaki, 1996; Benda and Dunne, 1997; Dadson et al., 2004; Hovius and Stark, 2006; Lancaster,2008). Depending on the amount and size composition of sediment, the introduced materialcan be transported downstream, or can remain in place and act as a persistent source of sedi-ment (Jackson and Beschta, 1982; Goff and Ashmore, 1994; Lane et al., 1995; Sutherland et al., 2002;Reid and Dunne, 2003). In the longer term, the supply regime for mountain streams is definedby the frequency and magnitude of the sediment inputs, which affect stream morphology.Mountain river channels exhibit a wide variety of morphologies that reflect variable sed-iment transport patterns. At the reach scale, stream morphology has been linked to magni-tude of transport capacity relative to sediment supply, distinguishing between supply-limitedand transport-limited conditions (Montgomery and Buffington, 1997). At slopes around 0.02m/m, rapids and riffle-pool channels can shift between supply-limited and transport-limitedconditions, which will be reflected in the degree of armoring and prevalence of bed struc-tures. Field evidence and experimental observations indicate supply-limited channels developcoarse, well-structured beds, with sediment transport rates below transport capacity (Parkeret al., 1982; Dietrich et al., 1989; Lisle et al., 1993; Church et al., 1998; Ryan, 2001; Venditti et al.,2008; Nelson et al., 2009). Under the same flow and slope conditions, transport-limited streamsaggrade, develop fine bed surfaces with little or no surface structure, and sediment transportrates near transport capacity due to greater sediment availability (Lisle and Madej, 1992; Madejet al., 2009). Given the difficulties of data collection in the field and advances in laboratoryinstrumentation, physical modeling commonly has been used to study the effects of distur-bances in streams (Yager et al., 2015).Flume experiments have been used to study the role of sediment supply, among othercontrols, on bedload transport and bed surface evolution. Observations indicate fine mobilepatches and coarse fixed patches coexist on gravel beds under high sediment supply. As sup-ply is reduced, coarse fixed patches expand and limit the areas of the bed where sedimenttransport occurs (Dietrich et al., 1989; Nelson et al., 2009). The content of sand in sediment feedaffects entrainment conditions over gravel beds (Wilcock and Crowe, 2003; Curran and Wilcock,2005). In systems that lack sand, sediment transport is affected by the size ratio between thefeed and bed material (Venditti et al., 2010). Sediment transport–storage relations respond toreductions in sediment supply (Lisle and Church, 2002), and the way in which this responseoccurs is strongly influenced by previous bed conditions (Pryor et al., 2011). An aggradedchannel responds with initial decrease in storage, followed by decline of transport rate as bedarmors. A channel at equilibrium with low supply rates instead does not adjust the storageand there is only decline of transport rate. The influence of the nature of stream boundarieson channel adjustment to changes in sediment supply has been tested in flumes as well (Eatonand Church, 2004, 2009). Results indicate unconstrained channels primarily adjust channel sin-72.2. Introductionuosity and slope, whereas constrained channels first adjust particle size and bed state (surfacetexture and structures, see Hassan et al. (2008)).For simplicity, most flume experiments have analyzed response of gravel bed streams tosediment supply using constant feed rates, and only a few studies have used episodic supplyrates typically observed in mountain streams (Cui et al., 2003; Sklar et al., 2009; Venditti et al.,2010; Johnson et al., 2015). Experiments using episodic feed rates show dispersion and trans-lation are the principal mechanisms of sediment pulse evolution, and the relation betweensediment feed particle size and bed particle size determines which mechanism dominates.When the bed and feed material have similar particle size dispersion dominates, but if thefeed material is considerably finer than the bed significant translation can occur (Cui et al.,2003; Sklar et al., 2009). The interaction between sediment pulses and bed sediment is influ-enced by the pulse grain size relative to the bed, and by the magnitude and frequency of pulseinputs (Venditti et al., 2010). More recently, flume studies of step-pool-like channel beds pointout that channel beds can become coarse and rougher in response to pulses of finer gravel(Johnson et al., 2015). These studies give insights on the effects of episodic sediment supply, butespecially on pulse propagation and the role of relative sediment texture.Here, we study channel adjustment under episodic sediment supply by introducing vari-ous volumes and frequencies of sediment over a poorly sorted gravel bed. The high resolutionof data systematically collected during the 280-hour long experiment allowed us to examinetemporal variation of bedload transport in a way that to our knowledge has not been donebefore. We were able to develop a bed that resembled those found in mountain streams, withcomplex topography and surface organization, as a result of the extended history of flow andsediment supply. The use of both constant feed and sediment pulses provided an opportunityto evaluate the use of constant feed for the study of sediment transport in mountain streams,and explore the temporal scales and cases for which it might be valid.The goal of this study is to test four hypotheses related to the impact of episodic sedimentsupply on channel adjustment and sediment mobility: (H1) adjustment of a gravel bed to sedi-ment supply is significantly affected by the magnitude and frequency of sediment feed; (H2) ifthe time between sediment pulses is less than the time needed for the sediment transport rateto relax to a low value after a pulse, the response could be similar to constant feed regimes;(H3) large pulses, which result in greater sediment availability, produce stronger responses inthe transport rate and have longer relaxation times than small pulses; and (H4) the temporaladjustment of sediment transport rates to changes in the supply regime is conditioned by theinitial bed slope, surface grain-size distribution, and sediment storage.82.3. Materials and methods2.3 Materials and methods2.3.1 Experimental designThe flume experiment was conducted in the Mountain Channel Hydraulic Experimental Lab-oratory at the University of British Columbia (UBC). The flume is 18 m long, 1 m wide and 1m deep, with a slope of 0.022 m/m. It is a generic model of riffle-pool reaches in East Creek,a mountain stream in the UBC Malcolm Knapp Research Forest. Flume dimensions and flowwere not scaled. Water discharge was kept constant at 65 L s−1, which was able to mobilizemost sediment size fractions and is similar to the scaled bankfull discharge in the prototypestream. The bed and feed were composed of poorly sorted sand and gravel (1:3 bed grain sizedistribution in East Creek), which ranged from 0.5 to 64 mm with geometric mean Dg (bulk) of5.7 mm (Figure 2.1). More details on experimental settings can be found in Elgueta (2014).Grain size (mm)% finer than10−1 100Dg101 102020406080100Figure 2.1: Grain size distribution of the bulk sediment that constituted bed and feed ma-terial.A sequence of seven runs was conducted with no feed, constant feed, and episodic feedregimes (Figure 2.2). Each run lasted 40 hours. The initial bed of the first run was well-mixedand flat, whereas subsequent runs inherited bed conditions from the previous runs. The se-quence of runs made direct comparisons more difficult, but gave time for the bed to evolveunder more realistic conditions and to develop complex channel morphology as observed innatural rivers. Run 1 (R1) was conducted under no feed to condition the bed. As a reference,in Run 2 (R2), 300 kg of sediment was introduced at a constant feed rate (2.1 g m−1 s−1) over40 h. To examine the response of the system to an abrupt supply, in Run 3 (R3) all the materialwas introduced during the first hour. Run 4 (R4) and Run 5 (R5) were designed to analyzethe role of size and frequency of episodic inputs, so the 300 kg was split in four pulses withduration = 0.25 h and two pulses with duration = 0.5 h respectively. Finally, to explore theimportance of the initial bed on the response to supply; Run 6 (R6) had the same constantfeed regime as R2, and Run 7 (R7) had no feed, as in R1. The feed rate used to supply allpulses was 83 g m−1 s−1, which is similar to the average transport capacity of the experiment(79 g m−1 s−1). The feed rate was established from several preliminary runs.92.3. Materials and methods40 80 120 160 200 240 28001000200300Time (h)Cumulative feedper run (kg)NoneFeedPhoto/WSEScanNoneConstant ConstantOne pulse Four pulses Two pulsesR1 R7R2 R6R3 R4 R5Figure 2.2: Sequence of feed regimes followed during the experiment. Cumulative feedis plotted as a function of time for constant feed (blue) and three types of episodicfeed regimes (red). The time at which bed surface photos, water-surface elevation(WSE), and bed scans were acquired are displayed with red bars.2.3.2 Data collectionDetailed information on flow properties, bed elevation, bed-surface particle-size organizationand sediment transport was collected systematically during the experiment (Figure 2.2). Waterdepth was estimated as the difference between the bed-surface and water-surface elevation,measured on the side of the flume every 0.5 m, and mean depth was 0.077 m over the ex-periment. Water depth measurements were used to compute water-surface slopes and shearstresses.Bed properties were measured from laser scans and photographs of the bed surface underno flow. Digital elevation models (DEMs) were obtained by scanning the bed with a videocamera that recorded the reflectance location of a green laser beam, with a resolution of 2mm in the longitudinal and horizontal direction and 1 mm in the vertical. Bed-surface grain-size distributions were obtained from point counts on four photos over 2 m2 in the center ofthe flume, 6 to 8 m upslope from the downstream end of the flume. A sample grid of 36×14points with a cell size of 65 mm (largest particle size) was superimposed on each photo. Grainssmaller than 2.8 mm were difficult to recognize and were grouped in one class.Sediment transport was estimated using video-based measurements with a light table. Themethod follows the same principles as Zimmermann et al. (2008), but we improved the designsignificantly by detecting grains as small as 1 mm. Grains that exited the flume were recordedusing a video camera (at frequency 27–32 frames per second) over a light table and imageswere post-processed in Labview Software to compute sediment transport information on aper second basis. The required conversion to weight based on measured projected particlearea and b-axis was calibrated by recording stones of known dimensions and weights, and ob-taining best fit linear regression relations (recorded minor axis against known b axis, recordedprojected particle area against known weight). To check the results sediment was collected ina trap placed at the downstream end of the flume.102.3. Materials and methods2.3.3 Data analysisSediment transport capacity was estimated using a modified version of Meyer-Peter and Mu¨ller(MPM) equation (Wong and Parker, 2006). Bed slope was estimated along the thalweg us-ing DEMs. Only data between 4–11.8 m were included to avoid upstream and downstreamboundary effects observed in flow profiles. Particle size data were used to calculate grain sizestatistics such as the geometric mean (Dg), geometric standard deviation (SDg), and the grainsize percentiles (e.g., D90 and D16). This was done for both the bedload and bed surface.To analyze the temporal variability of sediment transport rates over each run and the ef-fects of changes in the sediment feed, cumulative departures from the long-term mean werecomputed over each run usingN∑i=1([qb]i − qb); N = 1, 2, 3, ..., (2.1)where [qb]i is sediment transport rate at time instant i, qb is the mean sediment transport rateover a run, and N is the number of observations over a run. Data were averaged every 15min to reduce noise. The mean sediment transport rate of a run was subtracted from eachobservation for normalization, and the cumulative departure from the mean was evaluated asa function of time.To test our hypothesis regarding differences and similarities among sediment transportsignals of each run and the importance of the initial bed state, a statistical model of sedimenttransport rate was built using the R programming language. After trying different nestedversions, we used a general least-squares model (method of maximum likelihood), for whicha full version included: run as a factor, a time polynomial of degree 4 ( b1t + b2t2 + b3t3 +b4t4, where t is time and bi are the slopes of the model), interactions between run and timevariables, and an autoregressive order 1 (AR(1)) error term. Likelihood L-ratio tests wereused to compare goodness of fit among nested models. The Akaike information criterionAIC (Akaike, 1974) was used to penalize complexity (number of free parameters) in modelassessment. Including run as a factor allows changes in the intercept of the model (initialsediment transport rate) with run number. Adding the interactions between run and timevariables accounts for changes in the temporal trend of sediment transport rate (slopes of themodel) with run number. L-ratios were used to test the significance of the full model against:(1) a reduced version in which the intercept and slopes of the model are not allowed to changewith run, and (2) a partly reduced version in which only the intercept is allowed to adjustwith run. The significance level α was set to 0.05. Because the main interest was in long-termtrends, the data were averaged. Resolutions ranging from 5–60 min were used to explore thescales at which differences appeared. The 5 min resolution limit was selected to avoid randomfluctuation in the bedload transport, while early adjustments might be lost above 60 min. Theaveraged transport rates were log-transformed to approach normality.To assess the effects of pulses of different magnitudes, relaxation times were estimated us-112.4. Resultsing the relations obtained from an exponential fit and a log–linear fit to the sediment transportrate data (Tr1 and Tr2 respectively) asTr1 =ln(qre f /q0)−Λ (2.2)Tr2 = 10(log10(qre f )−a)/b (2.3)In equation (2.2), qre f is the low reference transport rate, q0 is the intercept, and Λ is the rateof decay. This type of function has been used to model changes in storage under degradation(Lisle and Church, 2002). In equation (2.3), a is the intercept and b is the slope of the linear rela-tion. The log–linear fit was used because it resembled more closely the decrease in sedimenttransport rate, especially after the large and medium-sized pulses.2.4 ResultsTo address the four hypotheses formulated in the introduction, we present our results as fol-lows:• Summary of the observations from each run, including sediment transport, hydraulics,bed-slope evolution, particle size adjustments, and sediment storage.• Assessment of temporal patterns of variability in sediment transport rate under the dif-ferent feed regimes.• Results of statistical tests for significant differences in the trend of sediment transportrate among runs at different temporal resolutions.• Relaxation times Tr and sediment output until Tr for pulses of different size.2.4.1 ObservationsTo assess the effects of feed regime on channel adjustment we comment on the evolution ofsediment transport rate (Figure 2.3), Shields number (Figure 2.4a), bed slope (Figure 2.4b), andgrain size statistics of the bed surface and bedload (Figure 2.4c–e). A summary of observationstowards the end of each run is presented in Table 2.1. To emphasize comparisons among andwithin the different supply regimes, observations over each run are presented by feed regimes.122.4. Results10510–510010510–510010510–510010510–510010510–510010510–510010510–5100(a) R1No feedFeed rate(b) R2(c) R3Sediment transport rate (gm-1s-1)(d) R4(e) R5(f) R60 5 10 15 20 25 30 35 40(g) R7Pulse 1Pulse 1Pulse 1 Pulse 2Pulse 2 Pulse 3 Pulse 4Time (h)Figure 2.3: Time series of total bedload rate estimated by processing images recorded overa light table at the end of the flume. Red lines indicate sediment feed rates. The highresolution of the method allowed computing fractional mass and number of grainsthat exited the flume at every second. Gaps in the data are due to technical problems.132.4. Results0 40 80 120 160 200 240 280010203040(d) D9002468 (e) D16(b)01020(c) Geometric mean Bed surfaceCritical (Wong & Parker, 2006)SedimentpulseBulk bedBedload(a)0.040.060.080.1Time (h)Grain size (mm)SlopeShields number0.0160.020.024R1no feedR7no feedR2constantR6constantR3one pulseR4four pulsesR5two pulsesFigure 2.4: (a) Shields number. (b) Thalweg slope (m/m). Grain size statistics of the bedsurface (red dots), bedload (blue dots) and bulk sediment that constituted the origi-nal bed and feed (horizontal dashed lines): (c) geometric mean particle size, (d) D90,and (e) D16. Sediment pulses are indicated with vertical dashed lines.142.4.ResultsTable 2.1: Sediment feed characteristics and observations towards the end of each runRun 1 2 3 4 4 6 7Feed type no feed constant episodic episodic episodic constant no feedFeed rate g m−1 s−1 0 2.1 83.3 83.3 83.3 2.1 0Number of pulses - - 1 4 2 - -Water discharge l s−1 65 65 65 65 65 65 65Mean water depth m - 0.073 0.08 0.083 0.072 0.075 0.073Water-surface slope m/m - 0.017 0.019 0.020 0.020 0.020 0.020Froude number - 1.11 0.84 0.75 1.15 1.02 1.11Reynolds number - 241564 294823 318700 260404 275292 264978Bed slope m/m 0.017 0.016 0.018 0.020 0.022 0.022 0.022Dg (surface) mm 14.5 15.3 14.4 14.3 14.4 13.8 15.7SDg (surface) 2.2 2.0 2.1 2.0 2.0 2.1 1.9D90 (surface) mm 34.1 33.7 31.5 31.6 31 31.7 31.5Roughness scale ks m 0.0716 0.0708 0.0662 0.0664 0.0651 0.0666 0.0662152.4. ResultsBoth R1 and R7 were conducted with no feed, but differed in their initial beds. R1 startedfrom a well-mixed plane bed that was not yet worked by water, had a slope of 0.022 m/m andDg (surface) = 4.7 mm. The transport rate was high initially, decreased two orders of magnitudeover the first five hours, and more gradually thereafter (Figure 2.3). No hydraulic data areavailable for this run. Bed slope changed subtantially during the first hour, but varied littlethereafter (Figure 2.4). Bedload fining was unclear, whereas bed surface coarsening was sig-nificant. Net degradation (157 kg) was equivalent to erosion of a 4.3 mm deep uniform layer.By the end of the run, a well-developed channel thalweg was present with no bedforms ap-parent. R7 was conducted on an armored bed that was the result of the six preceding runs.Its well-developed channel morphology included sediment wedge and riffle-pool sequencesupstream, and lateral bars toward the middle and lower parts of the flume. The transportrate was generally low and the decrease was less pronounced than in R1 (Figure 2.3). TheShields number was near the critical value of 0.05 (Wong and Parker, 2006), which can be asso-ciated with a low transport regime (Figure 2.4). There was slight variation in bed slope andmild adjustments of particle size. Overall, the bedload texture became finer as the bed surfacecoarsened. Net degradation of 59 kg corresponded to 1.6 mm of erosion.R2 and R6 received constant feed. R2 started from an armored bed with no bedforms, aslope of 0.017 m/m, and Dg (surface) = 14.5 mm. During the first seven hours sediment transportrate was well below the feed rate most of the time. Since then, transport rate showed anincrease. The rate of increase became milder with time as sediment transport rate approachedthe feed rate. By the end of the run, sediment transport rate fluctuated within two orders ofmagnitude. The largest values surpassed the feed rate, and the smallest rates were less than 0.1g m−1 s−1 (Figure 2.3). The Shields number was below the nominal critical at the beginning,but approached the threshold value toward the end of the run (Figure 2.4). The bed slopeincreased during the first 20 h, but decreased after that. Bedload grain size statistics variedwithout clear trends and the bed surface coarsened slightly. At the end of the run, alternatingbars were visible and net aggradation was 218.95 kg (5.7 mm deposition).The initial bed of R6 was armored and had a slope of 0.022 m/m. This run yielded trans-port patterns similar to those obtained for R2; transport rate was well below the feed rateduring the first hours, then increased markedly at around 8 h into the run (Figure 2.3). Shieldsnumber varied from near critical to twice this value, considerably larger than in R2 (Figure2.4). There was variability in bedload texture, which coarsened slightly during the run. Thesurface got finer during the first 10–20 h, and coarsened after that. Nonetheless, the bed slopewas relatively stable during this run. A mid-channel and a lateral bar disappeared by the end,while change in storage (122 kg) was only half the aggradation estimated during R2.At the beginning of R3, a 300 kg pulse entered the flume, producing an increase of twoorders of magnitude in the transport rate after 0.5 h (Figure 2.3). Thereafter, the rate decreasedmonotonically, but exhibited considerable variability. Another, albeit milder, rise in sedimenttransport rates was evident at around 7 h. Shields number exhibited a trend similar to trans-162.4. Resultsport rate, and by the end of the run it was slightly above the critical value (Figure 2.4). The bedslope first increased, but then decreased. A gradual fining in the bedload texture through theexperiment was evident. The bed surface exhibited significant fining one hour after the feed,followed by sharp coarsening within the next 7–10 h. Regardless of the large sediment outputduring this run, there was relatively little change in storage, and only 78 kg of aggradation (1.6mm deposition).With initial conditions inherited from R3, the sediment transport rate in R4 exhibited asimilar response after each sediment feed pulse, except after the third one (Figure 2.3). Shieldsnumber clearly increased following the first three pulses, but after the last pulse it remainedstable (Figure 2.4). Bed slope and grain size statistics clearly responded to all four pulses. Netaggradation was 160 kg (4.3 mm deposition). R5 began with a relatively coarse bed, a 0.020m/m slope, and lateral bars. Transport rate (Figure 2.3), Shields number, and bed surface andbedload texture adjusted to each pulse in a way similar to that described for R3 and R4. Bedslope increased after the first pulse, but changed little thereafter (Figure 2.4). By the end of therun, the bed aggraded 132 kg (3.5 mm deposition).The bulk sediment used for the original bed and feed included a wide range of sizes thatmoved at different rates (Figure 2.5). While sand and fine gravel exhibited nearly continuousmovement (Figure 2.5b–d), coarser gravel motion was sporadic (Figure 2.5e–f) as reflected inthe intermittency of the signal. Grains between 22–32 mm exhibited periods of no mobility thatlasted up to 5 h, coarser particles (not displayed here) were immobile even longer. Irrespectiveof the observed size selectivity on sediment transport, effects of sediment supply were evidentfor all fractions. The frequency of movement of all grain sizes increased with introductionof sediment pulses, bu s) exhibited temporal trends that resembled those of total transport(Figure 2.5a–d). The behavior observed during R5 is representative of all runs.All sediment pulses moved downstream by dispersion (no evidence of translation). Partof the feed was stored upstream in a wedge (especially coarser fractions that moved less fre-quently), acting as a source of sediment and dispersing during the experiment.2.4.2 Temporal patterns of variability in sediment transport rate under differentsupply regimesTo examine shifts in the sediment transport rate due to changes in the sediment supply regime,we performed cumulative departure analysis using equation (2.1). This analysis assumes thatinflections in the cumulative departure curve (Figure 2.6) indicate the timing and responseto changes in feed conditions. An increasing trend in the departure curve indicates a periodof high transport rate relative to the mean, whereas persistently negative departure representslow sediment-transport phases. A flat curve indicates a period when transport rate approachesthe mean. Our main interest is in long-term changes in transport rate, which are likely associ-ated with sediment pulses. Changes in feed conditions produce inflections in the slope of thecumulative departure trend. The start of sediment feed produces a shift from a negative slope,172.4. ResultsSediment transport rate (gm-1s-1)10210–210010210–210010210010210010210–210010210–2100(f) 22−32 mm(e) 11−16 mm(d) 5.6−8 mm(c) 2.8−4 mm(b) 1.4−2 mm(a) Total0 5 10 15 20 25 30 35 40Time (h)Pulse 1 Pulse 2Figure 2.5: Total sediment transport rate and fractional rate of four grain size classes dur-ing R5. Red lines indicate sediment feed rate.which represents low transport conditions previous to the feed, to a positive slope character-istic of more intense transport stages promoted by the feed. No feed produces an inflectionfrom a positive slope or a nearly horizontal curve, when sediment feed effects are still strong,to a negative slope when transport rate falls below average after sediment starvation.The two runs with no feed (R1 and R7) show cumulative departure curves with similarshape (Figure 2.6a and g). In both cases there is initial exponential increase, followed by con-tinuous decrease. The major inflection observed occurs earlier in R1 than in R7, which couldbe related to sediment storage during runs previous to R7. It could be associated with thehigh transport rates during the first hours of R1 which raise the mean over the run, causingobservations to fall below it earlier in the run.In comparison to no feed runs, different trends are obtained for constant feed. In both theseruns, transport rates initially fall below average values until 7–8 h into the run when there isa major inflection in the departure curve slope. Thereafter, the curve exhibits intermittent182.4. Results020406080100120Cumulative departure of sediment transport rate (gm-1s-1 )050100150−12−8−4048(c) R3 one pulse(d) R4 four pulses010203040Sediment pulseSediment pulseSediment pulse(e) R5 two pulses (f) R6 constant0 5 10 15 20 25 30 35 40−20−15−10−50Time (h)Time (h)50 10 15 20 25 30 35 4004812 (g) R7 no feed−12−10−8−6−4−20 (b) R2 constant(a) R1 no feedFigure 2.6: Variation of sediment transport rate over each run. The mean transport rateof a run is subtracted from each observation for normalization, and the cumulativedeparture from the mean is plotted as a function of time. Sediment inputs are rep-resented with vertical dashed lines and major trend inflections are identified withblack dots.192.4. Resultsperiods of flat, positive, or negative slopes, within an overall increasing trend.In multiple pulse runs, the departure curve varies as a function of the number of pulses. Itcan increase and decrease in sequences related to changes in the feed. The absence of a clearinflection in the curve after the third pulse in R4 is due to the weaker response observed inthe transport time series (Figure 2.3d). The span of total departure (Figure 2.7a) is greatestin runs with larger infrequent pulses such as R3 (or R1 in which the well-mixed initial bedcould be considered as a big isolated pulse as well). The range of departure decreases as thefeed magnitude during first hour becomes smaller and the range observed with 75 kg pulsesis similar to constant feed.10–1100101102−6−4−20R7R10 50 100 150 200 250 300060120180R7→→→R1R6R4R5R3R2Total feed during first hour (kg)Range of departure(gm-1s-1)SlopeLag time (h)(b)(c)(a)R2R6R4R4R5R3R5R3Figure 2.7: Characteristics of cumulative departure from mean transport rate against feedregimes. (a) Range of cumulative departure. (b) Lag time between starts of feed andassociated inflections in the curve. (c) Slope of decreases related to stops in feed.(c) The amount of feed received during the first hour of each experiment is used torepresent feed regime as a quantitative variable in the x-axis.To describe the strength of the effects of changes in sediment feed on the cumulative de-202.4. Resultsparture curve, the lag time between start of feed and associated slope inflection (Figure 2.7b),and the rate of decrease in the departure curve during periods of no feed (Figure 2.7c) arepresented as a function of total feed during first hour of experiment. The lag time in the re-sponse of the cumulative departure as a function of feed regime is related to the time that ittakes the sediment to move downstream. The lag time decreases with feed magnitude and isconsiderably longer under constant feed. The rate of decrease in the departure curve is usedto represent low sediment transport regimes during sediment starvation and was estimatedas the slope of the best fit line through the points between two inflections, or from one inflec-tion to the end of the run. Larger pulses exhibit steeper decreases, but there is considerablevariability within pulses of the same size that might be related to difference in pre-pulse bedconditions. The importance of bed conditions can be appreciated by the significant differencesin the slope of the cumulative departure curve for no feed runs. While in R7 the slope is gentle,R1 behaves in a manner similar to that of the single large pulse, R3.2.4.3 Statistical modelling of sediment transport rate seriesTo examine how sediment supply regime impacted the temporal variability of sediment trans-port, a least squares model was fit to the averaged sediment transport rate time series. Signif-icant differences in the evolution of sediment transport rate were detected among the sevenruns at 60 min resolution using likelihood L-ratio tests (p < 0.0001). To identify differencesbetween runs, the models were fit to include one pair of runs at a time. This was repeateduntil completing all possible pairs (21 in total). In most cases, L-ratio tests indicated modelslopes were significantly affected by run style (Table 2.2). Curiously, significant differencesappeared between R1 and R7, which had the same no feed regime. This is probably related totheir differing initial conditions as discussed subsequently.Changes in the slopes and intercept of the model were non-significant at 60 min averagingin only three pairs of runs. The first case corresponded to R1 and R3. The lack of differenceswhen using 60 min averages was not too surprising since both runs presented relatively hightransport rates during the first hours because one started with a well-mixed bed and the otherreceived the largest pulse (Figure 2.3). However, differences in slopes appeared when increas-ing the temporal resolution to 30 min averages (Table 2.3). Runs with constant feed were themost similar, exhibiting no significant changes in model parameters even when increasing theresolution to 5 min averages. Because sediment feed in R4 was better distributed over time infour small pulses, we expected to find similarities between this run and constant feed. Instead,significant differences were indicated between the four pulses (R4) and constant feed run R2;whereas between R4 and constant feed run R6, no significant differences were detected withaveraging periods larger than 15 min. As a group, no differences were found among R4 andconstant feed runs with 60 min averages; differences emerged only when the temporal resolu-tion was increased to 30 min.212.4. ResultsTable 2.2: p-values from L-ratio testsRun Test R2 R3 R4 R5 R6 R7R1F/R∗ <.0001 0.25 <.0001 0.0002 <.0001 <.0001F/PR∗∗ <.0001 - <.0001 0.0001 <.0001 <.0001R2F/R - <.0001 0.02 0.0002 0.8 <.0001F/PR - <.0001 0.008 0.0001 - <.0001R3F/R - - <.0001 0.01 <.0001 0.0001F/PR - - <.0001 0.004 <.0001 0.0001R4F/R - - - 0.002 0.19 0.03F/PR - - - 0.0006 - 0.02R5F/R - - - - 0.001 0.008F/PR - - - - 0.0005 0.004R6F/R - - - - - 0.001F/PR - - - - - 0.0005∗ L-ratios were estimated between the full and reduced model (F/R). ∗∗ L-ratios were esti-mated between the full and partly reduced model (F/PR). Initially, the 21 possible pairs ofruns were tested using 60 min averaged data. Statistically sgnificant differences indicatedwith bold font.Table 2.3: p-values from L-ratio tests using 5 different temporal resolutionsRuns Test Temporal Resolution60 min 30 min 15 min 10 min 5 minR1-R3F/R 0.25 0.003 - - -F/PR - 0.02 - - -R2-R6F/R 0.81 0.63 0.52 0.42 0.32F/PR - - - - -R4-R6F/R 0.19 0.07 0.027 - -F/PR - - 0.013 - -R2-R4-R6F/R 0.12 0.02 - - -F/PR - 0.006 - - -2.4.4 The effects of pulses of different sizes on sediment transportTo evaluate the persistence and strength of the effects of the different pulses on sediment trans-port rate, we estimated relaxation times Tr and total sediment output until Tr (Table 2.4). Therelaxation time Tr is the time required for the transport rate to adjust to a relatively stable lowmean value equivalent to no feed conditions. We used the mean transport rate over the last 20h of no feed in run R7 as a reference of low transport (0.27 g m−1 s−1). This period was chosenbecause time series plots (Figure 2.3) indicate the transport rate fluctuated around a nearlyconstant mean, which is supported by cumulative departures that display a nearly constantslope over this period (Figure 2.6). Such transport behavior is consistent with reported timesfor particle adjustment (Church et al., 1998; Hassan and Church, 2000; Hassan et al., 2006). Even222.4. Resultsthough it was expected that the system would have adjusted to even lower transport valuesif more time had been given, we assumed this would happen at very slow rates relative tothe run scale. Similar to the cumulative departure analysis, data were averaged every 15 minbecause of a good signal-to-noise relation.232.4.ResultsTable 2.4: Persistence and strength of pulse effectsRun-pulse ID Mass (kg) Exponential fit Log–linear fit Output to Tr2 (kg)q0 Λ R2 Tr1 (h) 10a b R2 Tr2 (h) raw adjustedR3p1 300 1.9 0.07 0.52 27.2 9.4 −1.11 0.74 24.9 208.5 195.7R5p1 150 2.1 0.11 0.45 18.4 5.4 −0.99 0.65 20.5 89.1 82.9R5p2 150 2.9 0.15 0.74 16.2 7.1 −1.13 0.84 17.6 76.6 73.2R4p1 75 1.8 0.15 0.43 12.6 2.4 −0.72 0.5 20.8 32.0 30.2R4p2 75 2.0 0.18 0.45 11.3 2.6 −0.79 0.45 17.6 33.5 27.5R4p3 75 0.8 0.03 0.03 30.8 1.4 −0.07 0.02 4.1× 1010 - -R4p4 75 3.1 0.23 0.63 10.7 4.3 −1.02 0.72 12.1 42.4 37.3242.4. ResultsThe relation between Tr of a pulse and the time between pulses (Tp) defined the dominanceof discrete or cumulative effects of episodic supply over a run and the recovery of ambienttransport rate. With the large pulse in R3 Tr < Tp, indicating relaxation occurred within therun (Table 2.4). With the pair of medium sized pulses (R5), Tr ≤ Tp. The experiment usingmultiple small pulses (R4) contrasts with Tr > Tp, indicating transport rate had not fullyrelaxed before a new input entered. There was no evident relation between pulse mass andrelaxation time (Figure 2.8a). The variability within pulses of the same size was as large asvariability among pulses of different size.The strength of the effects of a pulse on sediment transport rate was evaluated by comput-ing the total sediment output over the response time as followsTotal Output =Tp∑i=Ti[qb]i +Tr2∫Tp10aTb (2.4)Here, Ti is the time of the first significant increase in transport rate after a pulse, Tr2 is the re-laxation time estimated with (2.3), Tp is the time between sediment pulses, [qb]i is the observedsediment transport rate at time i, and a and b are the coefficients from (2.3). These coefficientsare used to predict the output beyond Tp, for those cases in which Tp < Tr2 (see Figure 2.8a).Tr2 was used instead of Tr1 because the log–linear fit better resembled the decrease in sedimenttransport rate, especially after small and medium sized pulses; and because it had higher co-efficients of determination R2 (Table 2.4).To account for differences in the transport rate previous to a pulse, we predicted the sedi-ment output under no feed conditions and subtracted it from the estimated output asAdjusted Output = Total Output−Tr2∫Ti10qb Tb′(2.5)Here qb is the mean sediment transport rate estimated over three hours before the input andb′ is the rate of decrease in sediment transport rate, estimated with equation (2.3) for R7. Ifqb ≤ qre f , the effects of the transport regime previous to the pulse were considered negligible.A positive trend was clear between the size of the pulse and the magnitude of the response(Figure 2.8b). There was variability in the total output within pulses of the same size, butit was considerably less than the variability observed among pulses of different sizes. Withsmall pulses the output varied between 30–45 kg, whereas with the medium-sized pulses theoutput was twice as much (between 70–90 kg). Finally, after the single large pulse ∼200 kg ofsediment had left the flume by the time transport rate relaxed to the no feed condition.252.4. Results0 5 10 15 20 25 30 35 4001234TrTpTime (h)Log-linear fitExtrapolationLimits for integration→→→Log-linear fitwith b from R7(a)(b)(c)  0Relaxation time (h)Sediment output untilrelaxation time (kg)Sediment transport rate (gm-1s-1)50 100 150 200 250 3002060100140180220Total feed per pulse (kg)RawTr1Tr2Adjusted to initialsediment transport rate10203040Time with no feed after 300 kg pulseAfter 150 kg pulsesAfter 75 kg pulsesFigure 2.8: Persistence and strength of the effects of supply episodes of different size onsediment transport. (a) Relaxation time Tr1 estimated with equation 2.2 (exponentialfit), and Tr2 estimated with equation 2.3 (log–linear fit). (b) Total sediment outputuntil Tr2. (c) Estimation of total output until Tr for the last small pulse.262.5. Discussion2.5 DiscussionIn the following section, we discuss the four hypotheses presented. Channel adjustment isevaluated in terms of sediment transport rate, bed surface and bedload particle size, sedimentstorage, and bed slope.2.5.1 Hypothesis 1: The adjustment of a gravel bed to sediment supply issignificantly affected by the magnitude and frequency of sediment feedThis hypothesis was verified after comparing the results under episodic and constant feed.All the runs with feed showed overall aggradation, which was considerably greater underconstant feed or with small frequent pulses than with larger rare pulses. The evolution ofsediment transport rate was consistent with particle size adjustments on the surface. As bedsurface coarsened, sediment transport rate decreased (see Figures 2.3 and 2.4c-e). As bed sur-face got finer, transport rate increased. Sediment feed caused surface fining and increasedtransport rate as described in previous studies (Dietrich et al., 1989; Venditti et al., 2008; Madejet al., 2009; Nelson et al., 2009); the intensity of change in transport was related to the supplyregime. Sediment pulses promoted stronger and faster, but more transient, responses than didconstant feed. In time the system behaved as if sediment starved after sediment pulses passed.Sharp increases in transport rate caused by one or few large pulses (R3, R5) can be explainedby surface fining that occurred initially, which provided great availability of fine sediment fortransport as well as a decrease of bed roughness at the grain scale. As the pulse dispersed andfine sediment was evacuated, the bed surface coarsened and reorganized, and transport ratedecreased. Our observations support the idea that dispersion is the dominant mechanism ofpulse evolution when the bed and feed material have similar particle size (Cui et al., 2003; Sklaret al., 2009). However, some adjustments cannot be explained simply by the supply regime.These include cumulative storage observed under episodic sediment supply, overall increasein bed slope, and little variability of bed slope following the last pulse fed in R5 until the endof the experiment.Cumulative storage and the general increase in bed slope over the experiment could be re-lated to the coarse grain-size distribution of the bulk sediment that constituted the original bedand feed material. Roughly 40% of the bulk sediment was coarser than 8 mm, which movedat lower intensities and more intermittently than the finer fractions. A significant fraction ofcoarse material was stored in a sediment wedge that developed near the upstream end of thebed. The wedge increased local slope and caused the bed slope to increase as the wedge grewand expanded. Such behavior could have promoted the mobilization of stored sediment atlater stages. With most sediment pulses, bed slope increased, but did not return to its pre-pulse value before more sediment was supplied. The cumulative increase in bed slope can beexplained by bed armoring and structuring, which could have counteracted degradation oncethe sediment feed was exhausted. This would explain as well the stability of channel slopeunder no feed during R7, and is consistent with previous observations that constrained chan-272.5. Discussionnels primarily respond to changes in flow or sediment supply by adjusting surface particlesize (Eaton and Church, 2009). Interestingly, by the middle of run R5 the slope became nearlyconstant at 0.02 m/m, which is similar to the flume slope. It is difficult to establish why theslope did not change with the second pulse in R5 or during R6 which had constant feed. Inthese cases, bed slope stability could be a result of bedforms or the fact that the upstream endof the bed was not included in bed slope estimations.In summary, the significance of the magnitude and frequency of sediment supply wasevident in particle size adjustments and the evolution of sediment transport rate. Cumulativestorage and changes in bed slope were conditioned by the grain-size distribution of the feed,which coarse fractions remained as partially mobile during the experiment.2.5.2 Hypothesis 2: If the time between sediment pulses is less than the timeneeded for the sediment transport rate to relax (Tp < Tr), the response canbe similar to constant feed regimesThis hypothesis is supported by similarities between constant feed regimes and run R4 whichintroduced multiple small sediment pulses. R4 had Tp = 10 h, with estimated Tr > Tp (Figure2.8). During R4 sediment storage was considerably greater than during the run that receivedthe large sediment pulse and more similar to the constant feed runs. The departure curve ofR4 was similar to that of constant feed runs. The span of cumulative variability in R4 was rela-tively small, similar to those for constant feed. That similarity may relate to a smaller increasein transport rate relative to those produced by larger pulses. Finally, L-ratio tests suggest sim-ilarities with constant feed regimes can emerge from high-frequency episodic inputs.But at time-scales shorter than 10 h, channel adjustments after the small pulses in R4 weresimilar to those following infrequent, large pulses. The timing with which the transport rateat the end of the flume responded to small pulses was similar to the response time for larger,less frequent pulses and much faster than the response under constant feed. The same wasnoted for particle size adjustments, for which responses following small pulses resembledthose following large pulses, but in a less pronounced way.2.5.3 Hypothesis 3: Large sediment pulses produce stronger responses in thetransport rate and require longer time for relaxation than small pulsesEstimated sediment outputs until Tr (Figure 2.8b) support the hypothesis that infrequent largepulses produce stronger effects in transport rate; however, there was no clear relation amongTr following different sized pulses (Figure 2.8a). The largest pulse delivered more than twicethe material delivered following medium-sized inputs, and more than five times the amountof sediment transported following multiple small pulses. Variability observed within pulsesof similar size was considerably less than differences among pulses of distinct magnitudes.Differences in bed configurations previous to a pulse, which affected mean sediment transportrates, defined how far from qre f (low reference sediment transport rate) the system deviated282.6. Conclusionsbefore the pulse and could have caused differences in Tr. In addition, differences in the degreeof armoring and slope of the bed could affect the value at which mean sediment transport ratewould become stable after a pulse. At lower bed slopes and coarser bed surfaces sedimenttransport rate could become stable at smaller values than with higher bed slopes and finer bedsurfaces. The steady state of sediment transport rate under no sediment feed in this study wasdefined as qre f , which was constant and added error to Tr estimations.2.5.4 Hypothesis 4: The temporal adjustment of sediment transport rates tochanges in the supply regime is conditioned by the initial bed slope, surfacegrain-size distribution, and sediment storageComparisons among results from runs with identical feed regimes are used to discuss theimportant influence of initial bed conditions in sediment transport rate. The L-ratios indicatethere were no significant differences in the intercept and slopes of the statistical model fit tosediment transport rates between runs with constant feed (even at 5 min resolution), whereassignificant differences were encountered at one hour averages between runs with no feed.These differences are explained by initial bed conditions. Because runs were sequentialand supply regimes varied, initial sediment storage was considerably different for runs withsimilar feed regimes. Constant feed runs (R2, R6) had different initial bed slopes but similarsurface-size compositions and degree of armoring. The initial beds of R1 and R7 (no feed)instead had similar slopes, but very different surface textures. In R1, the primary surface waswell-mixed and had the same grain-size distribution as the feed, whereas in R7 the bed wasarmored. Even though differences in the initial bed conditions were not tested statistically; wethink the different bed conditions between R1 and R7 were important for sediment transportbecause of a disparity in the availability of easily transportable fine material. The great avail-ability of fine sediment at the beginning of R1 made it more similar to the run with a largesediment pulse (R3) than to R7 which also received no feed. From the bedload transport ratetime series (Figure 2.3), we observe that despite an initial period of high transport in R1, sed-iment transport rate evolution in both runs without feed (R1, R3) was similar. In the case ofconstant feed regimes (R2, R6), differences in slope were less than 1% and relate to transportcapacity. The rather small effects produced by differences in bed slope could have been coun-teracted by surface armoring and structuring. In summary, only large textural differences inthe initial bed significantly affected the trend of sediment transport rates over runs.2.6 ConclusionsObservations on an experimental gravel bed under steady flow but variable feed conditionsindicate that the magnitude and frequency of sediment supply are important controls on bedsurface organization and temporal patterns of sediment transport rate. These results point outthat the assumption of constant feed might not be suitable to model streams that are subjectedto large, infrequent sediment pulses. Under these regimes, the channel changed significantly292.6. Conclusionsshortly after a pulse, but became relatively stable as sediment evacuated and the bed armored.Instead, the use of constant feed might be appropriate to study channels that receive morefrequent pulses (as in run R4), and over long time scales (i.e., > one event). In overall, tempo-ral patterns of sediment transport rate and sediment storage during the four frequent, smallpulses in R4 were like under constant feed.The use of poorly sorted sediment, which coarse fractions remained as partially mobileduring the experiment, promoted bed surface armoring and structuring between sedimentpulses and counteracted degradation, resulting in cumulative sediment storage. Infrequent,larger pulses caused stronger short-term (<10 h) effects on surface fining and sediment outputthan frequent smaller pulses, and caused less sediment storage over a run.The experimental design used helped to develop a realistic bed with different types ofchannel morphologies, which evolution reflected the history of flow and feed conditions. Thebed degraded during the first run, but then aggraded because of net storage during subse-quent runs, and developed complex topographies. Detailed analysis of bed topography andstructures (using DEMs and bed photos) would improve our understanding of bedform evo-lution under the different supply regimes.The initial bed surface texture and bed structures influenced significantly sediment trans-port rates during a run, whereas initial bed slope and cumulative storage played a minor role.Results were likely conditioned by the sequence of runs used and it would be interesting toexplore other experimental designs. Channel adjustment could have been different if eachrun had started from the same flat well-mixed bed or if the sequence of runs had followed adifferent order.30Chapter 3The effect of sediment supply regimeon bedload scaling and sedimentmobility3.1 SummaryThe effect of sediment supply regime on bedload scaling and mobility was analyzed for apoorly sorted (0.5–64 mm) experimental bed. Water discharge was held constant and, duringeach run, 300 kg of sediment was supplied in a different way. Total bedload transport rateand Dg of bed surface responded consistently to sediment feed. Constant feed caused grad-ual increases in bedload rate. In contrast, large sediment pulses caused pronounced increasesas the bed surface got finer, followed by monotonic declines as the surface coarsened. Pro-nounced trends caused stronger memory in bedload time series for runs with episodic feedthan in those for runs with constant feed. Autocorrelation coefficients ρτ were higher and theduration of a memory stage of fluctuation was larger. Over shorter periods of time (5-h) withineach run, memory (Hurst exponent H) exhibited considerable variation. Long-term memory(H ≈ 1) was observed during periods with strong decays in bedload rate and during periodswhen bedload rate was stable around a constant mean. This behavior indicates that memorycan result from bedform evolution at different scales and local changes in sediment storageand transport. Patterns of grain-size dependence persisted regardless of sediment feed. Mem-ory strength always decreased with grain size for gravels, as fractional transport became moreintermittent. The movement of sand exhibited more stochasticity than that of fine gravel (2–8mm), but not due to intermittency. Scaling statistics for total bedload were similar to those forfine gravel, which was fully-mobile and dominated bedload.313.2. Introduction3.2 IntroductionUnderstanding sediment transport patterns is important for river engineering design, habitatmaintenance, and river restoration projects (Parker, 2008). The movement of specific grainsizes is relevant for a variety of physical and biological processes in gravel-bed streams. Asexamples, coarse material is important for channel stability (e.g., Zimmermann, 2010; Watersand Curran, 2012; Mackenzie and Eaton, 2017), gravels are relevant for fish spawning habitat(e.g., Kondolf and Wolman, 1993; Hassan et al., 2008; Riebe et al., 2014; Hassan et al., 2015), andfine sediment can affect water quality and macroinvertebrates (e.g., Jones, 2012; Mathers et al.,2017).Sediment transport and channel stability in mountain streams are strongly affected by: un-steady and non-uniform flow conditions (Hassan et al., 2006), bed surface armor and structures(Parker and Klingeman, 1982; Wilcock and Detemple, 2005), the wide range of shapes and sizesof grains (Einstein, 1950; Wilcock, 1992), and changes in the texture and amount of sedimentsupply (Curran and Wilcock, 2005; Hassan et al., 2008). At the reach scale, stream morphologyresponds to imbalances between the magnitude of transport capacity and that of sedimentsupply, and streams can be classified as supply-limited if transport capacity exceeds sedimentsupply or transport-limited if sediment supply exceeds transport capacity (Montgomery andBuffington, 1997). Supply-limited channels commonly develop a coarse, well-structured bedsurface, with low intensity of sediment transport (e.g., Parker et al., 1982; Dietrich et al., 1989;Lisle et al., 1993; Church et al., 1998; Venditti et al., 2008; Nelson et al., 2009). Under the same flowand slope conditions, transport-limited streams aggrade and develop a fine, poorly-structuredbed surface, with sediment transport rates near transport capacity (e.g., Lisle and Madej, 1992;Madej et al., 2009; Pryor et al., 2011). Most experimental work on the effects of changes insediment supply on channel adjustment have used constant sediment feed and only a few ex-periments have introduced the sediment in isolated episodes as observed in mountain streams(Cui et al., 2003; Sklar et al., 2009; Venditti et al., 2010; Johnson et al., 2015). Flume studies that useepisodic sediment supply have primarily examined the mechanisms of sediment pulse propa-gation and the effects of relative sediment texture, but with few exceptions the role of the mag-nitude and frequency of sediment supply has received little attention (Elgueta-Astaburuaga andHassan, 2017).Field and flume observations indicate that sediment transport is a stochastic process thatvaries intermittently in space (Nelson et al., 2009; Heyman et al., 2014) and time (Heyman et al.,2013; Ghilardi et al., 2014). Variability appears at different scales, ranging from grain mobility tobedform evolution, even under steady flow and constant sediment feed. Studies that analyzethe effect of sediment supply regime on the scales of bedload variability are missing. Theuse of probabilities to account for the stochastic and intermittent nature of bedload transportstarted with Einstein (1937, 1950). In the past decade, numerous probabilistic approaches havebeen developed to describe fluctuations in bedload transport, which include: microstructuraldescriptions of bedload transport (Ancey et al., 2006) and their implications on larger scales323.2. Introduction(Ancey and Heyman, 2014), quantification of roughness and intermittency on bedload signals(Singh et al., 2009), deriving probability distribution functions for bedload transport (Turowski,2010; Furbish et al., 2012), and analyzing the dependence of bedload statistics on temporalscales (e.g., Ganti et al., 2009; Campagnol et al., 2012; Ma et al., 2014; Saletti et al., 2015), which isthe approach that we will use in this study.The scaling properties of bedload transport fluctuation are important for the design ofmeasurement programs, comparisons among data sets, testing bedload transport models, andconnecting the results from short-term studies to long-term evolution of stream morphology(Singh et al., 2009; Foufoula-Georgiou and Stark, 2010; Recking et al., 2012). One important aspectis the relationship between the variance of bedload flux σ2T and the aggregation time scaleT at which the signal is sampled. This relationship has been characterized as both a powerlaw (e.g., Einstein, 1937; Ancey et al., 2006) and a more complex relation (e.g., Campagnol et al.,2012). Using experimental data, Ma et al. (2014) proposed three stages of fluctuation in bedloadtransport rate: intermittent, invariant, and memoryless. The intermittent stage occurs at shortT with the variance σ2T decaying as a power law with exponent n=−1, indicating no memory.The invariant stage occurs at intermediate T with constant σ2T, indicating memory. At longT, σ2T decays with n=−1, the autocorrelation vanishes, and as for short T the process has nomemory. The authors suggest that to avoid underestimating σ2 (shorter T) or overestimating it(longer T) bedload statistics should be computed within the invariant stage. The classificationproposed by Ma et al. (2014) is based on three experiments under steady flow and constantsediment feed. Two of them used unisize particles (Ancey et al., 2006; Heyman et al., 2013)and the other used two separate groups of grain diameters (Singh et al., 2010). In this paper,we assess the effects of episodic feed regimes, as in natural rivers, on the stages of bedloadfluctuation. Unlike Ma et al. (2014), we used poorly sorted sediment in our experiment torecreate more realistic conditions like the development of bed armor and bed structures.The dependence of the current state on system history characterizes the system memory.If there is no dependence (e.g., white noise process), there is no memory. Short-term persis-tence occurs if the current state depends only upon the recent past (e.g., Markovian process).Long-term persistence occurs if the current state depends upon the entire history. The Hurstexponent H, describing the relationship between the standard deviation σT of a process andaggregation time scale T, has been used to quantify memory in time series of hydrologicalvariables (Hurst, 1951; Koutsoyiannis and Montanari, 2007), suspended sediment load (Shangand Kamae, 2005), and bedload sediment transport (Saletti et al., 2015). Using experimentaldata of step-pool morphologies under unsteady flow (Zimmermann, 2009, 2010), Saletti et al.(2015) found that, in the absence of feed, periods with intense transport exhibited strongermemory than periods with low transport. They also found that memory strength (sample au-tocorrelation ρτ and H) varied with grain size. Our experimental design allowed us to test theeffect of sediment feed regime on the memory of bedload time series and to assess the effectsof grain-size dependence over sand-sized fractions, which were not present in the experiments333.2. Introductionanalyzed by Saletti et al. (2015), and over longer time periods than the 1-h intervals used bythem. The bed morphologies developed over our experiment differed considerably from thosereported in Saletti et al. (2015), which could cause differences in the scales of the processes gov-erning sediment transport (e.g., step arrangement vs. armoring and cluster dynamics) thatwould show in the memory structure of bedload transport.Gravel-bed streams, composed of poorly sorted sediment, exhibit grain-size dependenceof their transport patterns under moderate (e.g., bankfull) flow conditions. Sediment entersa stream as episodic inputs through bank collapse, landslides, debris flows, and other distur-bances (Dadson et al., 2004; Hovius and Stark, 2006; Lancaster, 2008). The introduced material canbe immediately transported downstream or get deposited and become a source of sediment(Jackson and Beschta, 1982; Goff and Ashmore, 1994; Lane et al., 1995; Sutherland et al., 2002; Reidand Dunne, 2003). When mobilized, bed sediment can sort in the longitudinal, transverse, andvertical directions (e.g., Parker, 1992; Powell, 1998) with different grain sizes relating to specificprocesses of bed evolution. Despite studies that report on fractional bedload transport (e.g.,Wilcock and McArdell, 1993; Hassan and Church, 2000), our data provide an opportunity to as-sess the temporal variability of bedload transport at 1 s resolution for the multiple grains sizefractions in our experimental bed, which included sand between 0.5–2 mm and gravels in therange 2–64 mm.We examine the effect of sediment supply regime on bedload scaling and sediment mo-bility for a poorly sorted experimental gravel bed, which developed under steady flow butchanging sediment supply. Constant flow discharge allowed us to isolate the effects of changesin sediment feed. We used no feed and constant feed regimes as references, and three types ofepisodic supply regimes to evaluate the effects of the magnitude and frequency of occasionalsediment pulses. The same 300 kg was fed over each run to compare among them. The dataavailable allowed us to test if the three stages of bedload fluctuations proposed by Ma et al.(2014) hold under more realistic conditions (episodic sediment feed, wide grain-size distribu-tion) and if the memory structures described by Saletti et al. (2015) are also noticed for bedmorphologies that occur at milder slopes and have finer textures. Our experiment was con-ducted as a sequence of consecutive runs so that the bed had an extended history of flow andsediment supply as in natural streams. We repeated no feed and constant feed regimes twicewithin the sequence to assess the importance of bed history and initial bed conditions in theresults.The study aims to evaluate the following hypotheses related to the effects of sedimentfeed on the memory structure of bedload rates and the grain-size dependence of bedload pat-terns: (H1) bedload rate time series for runs with constant sediment feed have weaker mem-ory than those for runs with large infrequent sediment pulses, which can cause pronouncedtrends in bedload transport; (H2) the memory structure of total bedload reflects that of fully-mobile grain sizes, which dominate sediment transport and exhibit strong memory in theirbedload signals; (H3) grain-size dependence in bedload transport increases with sediment343.3. Methodsfeed because the movement of fully-mobile sediment is more responsive to feed than that ofpartially-mobile grain sizes.3.3 Methods3.3.1 ExperimentThe data were collected in a flume experiment conducted at the Mountain Channel HydraulicExperimental Laboratory, University of British Columbia (UBC). The flume was 18 m long,1 m wide, and 1 m deep, with a slope of 0.022 m/m (Elgueta-Astaburuaga and Hassan, 2017).The bed and feed sediment were poorly sorted and ranged from 0.5 to 64 mm, with ∼20%sand, geometric mean Dg = 5.7 mm, and percentiles D16 = 1.6 mm and D90 = 27 mm. Theexperiment consisted of a sequence of seven runs, denoted R1–R7, under constant flow dis-charge (65 L s−1), but combining multiple feed regimes. Except for the first run, which startedfrom a flat and well-mixed bed, the initial bed conditions for each run were inherited from theprevious runs. For R2–R6, 300 kg of sediment was introduced over 40 h. The magnitude andfrequency of sediment feed varied among runs (Table 3.1). R1 had no feed to condition the bedand R2, which served as a reference, received constant feed. In R3, a large sediment pulse wasintroduced at the beginning to test the bed response to large infrequent episodes. To assessthe roles of pulse magnitude and frequency, R4 and R5 received smaller, but more frequentsediment pulses than R3. Finally, to explore the importance of bed history, the constant feedregime of R2 was repeated in R6, and R7 was conducted under no feed as for R1.353.3.MethodsTable 3.1: Summary of sediment feed regimes used in experimental runsRun R1 R2 R3 R4 R5 R6 R7Sediment feed regime - constant episodic episodic episodic constant -Feed rate, g s−1 0 2 83 83 83 2 0Number of pulses - - 1 4 2 - -Pulse magnitude, kg - - 300 75 150 - -Pulse recurrence interval, h - - 40 10 20 - -363.3. MethodsDuring the experiment, flow properties, bed elevation, bed-surface particle size, and sed-iment transport were systematically measured. Water depth was measured along the side ofthe flume at an interval of 0.5 m and was used to estimate water-surface slope; the mean waterdepth was 0.077 m. Bed characteristics were measured under no flow. Digital elevation mod-els (DEMs) were obtained from bed scans using a video-camera and a green laser beam. DEMresolution was 2 mm × 2 mm in the horizontal and 1 mm in the vertical. Bed-surface grain-size distributions were obtained from point counts on bed surface photographs in the centerof the flume, 6–8 m upslope from the downstream end. The sample grid superimposed on thephotos had a cell size of 65 mm, which was equal to the largest particle size. Grains smallerthan 2.8 mm were difficult to recognize, and were grouped in one class. Fractional sedimenttransport data were generated using the video-based method explained in Zimmermann et al.(2008) supplemented by sampling of grains as small as 1 mm (Elgueta-Astaburuaga and Hassan,2017). Additionally, a sediment trap was placed at the downstream end of the flume to checkresults. Material < 1mm was under-detected by the video-based method, but no correctionwas applied because trap data had a considerably lower temporal resolution than that of thevideo-based data and because sediment < 1mm only corresponded to 2–3% of the sedimentmixture, so errors were small. More details on the experimental set up and data collection canbe found in Elgueta-Astaburuaga and Hassan (2017).3.3.2 Data analysesThe geometric mean diameter Dg was estimated for the bed surface from point counts andfor the bedload from video-based light table data. Bed slope was estimated along the thalwegusing DEMs. Only data between 4 and 11.8 m were included to avoid backwater effects down-stream and the effects of sediment feed upstream. As a reference, critical shear stress for eachgrain size τci was estimated rearrangingτ∗ci =τciDig(ρs − ρw) (3.1)where τ∗ci is the critical Shields number (Shields, 1936), Di is grain size, g is acceleration of grav-ity (9.8 m s−2), ρs is sediment density (2650 kg m−3), and ρw is water density (1000 kg m−3).We assumed τ∗ci = 0.047 (Meyer-Peter and Mu¨ller, 1948). The boundary shear stress τb wascomputed asτb = ρwgRhSw (3.2)where Rh is the hydraulic radius and Sw is the water-surface slope. Grains sizes for whichτb > τci were expected to be mobile during the experiment.Relative sediment mobility was analyzed by computing scaled sediment transport rates asin Wilcock and McArdell (1993). Fractional transport rates qbi were scaled by the grain-size dis-tribution of the bed bulk material fi. We used fi and not the bed surface to scale qbi for similarreasons to those argued in Church and Hassan (2002): differences in the temporal resolution of373.3. Methodssediment transport data (high) and bed photographs (low), difficulties linking transport mea-surements to specific bed surface conditions (temporally and spatially), and the truncationof bed surface grain-size distributions at 2.8 mm. We analyzed the grain-size composition oflarge bedload rates with probability of exceedence pe < 0.01 as in Saletti et al. (2015) to assessthe contribution of coarse partially-mobile grains and the effects that changes in sediment feedcould cause in this contribution.For bedload rate time series, the structure of memory for different grain sizes was analyzedto compare sediment transport patterns with those for total bedload. To assess short memoryand evaluate the presence of trends, the sample autocorrelation coefficients ρτ were estimatedas in Chatfield (1975)ρτ =cτc0=1NN−τ∑t=1(Yt −Y)(Yt−τ −Y)1NN∑t=1(Yt −Y)2(3.3)Here, cτ is the autocovariance at lag τ and c0 is the autocovariance at lag 0 for time series Y,Y is its mean, Yt and Yt−τ are values at time t and t minus lag τ respectively, and N is thenumber of observations. We assumed 95% confidence limits (±1.96/√N) as the threshold forsignificant autocorrelation.To detect multi-regime fluctuations in bedload, the relationship between variance σ2T andaggregation time scale T was evaluated on log-log scale plots as in Ma et al. (2014). We usedsediment mass for sediment flux instead of number of particles as in Ma et al. (2014) becauseof the wide range of grain sizes in our mixture. To compare results among different runswe divided the variance for each time scale σ2T by the variance for T = 1 s. To assess grain-size dependence, we grouped fractional data in four grain size classes: 0.5–2 mm (sand), 2–8mm (fine gravel), 8–16 mm (coarse gravel), and 16–64 mm (very coarse gravel). Sediment <2 mm was grouped together because we wanted to observe the behavior of sand, which wasexpected to be fully mobile and potentially sensitive to hiding effects and infiltration. Thelimit of 8 mm for fine gravel was near the limit for partial mobility during the experiment.Grains > 8 mm were grouped in two fractions to observe grain-size dependence on coarsepartially-mobile gravels. The limit of 16 mm corresponds to the D75 of the bulk sedimentand it is similar to the Dg observed for the bed surface when the bed was armored (Elgueta-Astaburuaga and Hassan, 2017).The Hurst exponent H was used to quantify long-term memory in time series (e.g., Hurst,1951; Shang and Kamae, 2005; Koutsoyiannis and Montanari, 2007; Saletti et al., 2015), and wasestimated asH = S + 1 (3.4)where S is the best fit slope on a log-log scale of the standard deviation σT against aggregation383.4. Resultstime scale T. The functional relation between σT and T is described asσT =σ0T1−H(3.5)Finally, to identify at which T different grain sizes exhibit the strongest memory, the sampleautocorrelation coefficient at τ = 1, ρ1, was computed at different T. Minimum T (1 s) used tocompute bedload rate statistics (σ2T, σT, ρ1T ) was limited by data resolution and maximum Twas taken as N/50.3.4 Results3.4.1 ObservationsBed adjustment and sediment mobilityTo summarize bed adjustments to changes in sediment supply regime, bedload transport rate(Figure 3.1a), Dg of the bed surface and bedload (Figure 3.1b), and bed slope (Figure 3.1c) arepresented as functions of time. Bedload rate statistics and observations at the end of each runcan be found in Table 3.2. As expected, bedload transport rate (Figure 3.1a) and Dg of thebed surface (Figure 3.1b) responded significantly to sediment feed. Without sediment feedas in R1 and R7, bedload rates decreased as the bed surface coarsened. With constant feedas in R2 and R6, bedload rate responded after 7 h with a gradual increase, but Dg of the bedsurface did not change significantly. Sediment pulses as in R3, R4, and R5, caused sharpincreases of bedload rate, which were related to a more pronounced fining of the bed surface.The increase in bedload was larger by orders of magnitude and much faster than with constantfeed. Once the feed stopped, there was a monotonic decrease in bedload rate as the bed surfacere-coarsened. The strength of the effects increased with pulse magnitude and the differenceswith constant feed were less evident in R4 that received smaller, but more frequent pulses. Therange of values for bedload rate was similar among the runs, with minimum values near zeroand maximum around 102 g m−1 s−1, although the mean bedload rate q¯b, standard deviationσqb , and 75th percentile were different (Table 3.2). Although, differences in q¯b were moderateamong runs (0.4–1.5 g m−1 s−1 range), differences in σqb were large (2–30 g m−1 s−1).The response of bed slope to sediment feed was not always consistent (Figure 3.1c). Bedslope decreased significantly during the first hour of R1 as a large amount of sediment exitedthe flume because of the well-mixed initial bed. During the rest of R1, bed slope remainedlow at ∼0.018 m/m and did not change much during R2. In R3, the slope increased signif-icantly with the pulse, but after the feed was stopped, it did not return to the same valuesprevious to the pulse, and remained considerably higher. A cumulative increase in bed slopewas observed through R3–R5, until it reached the flume slope (∼0.022 m/m) and remainednearly constant until the end of the experiment. The increased slope was coherent with a net393.4. ResultsTable 3.2: Bedload rate statistics and observations at the end of each runRun R1 R2 R3 R4 R5 R6 R7Bedload rate (gm−1s−1)Mean 1.29 0.65 1.56 0.98 1.19 1.25 0.42Standard deviation 27.06 5.12 7.64 3.17 10.32 31.32 1.5625th percentile 0.05 0.14 0.12 0.28 0.22 0.27 0.1350th percentile 0.14 0.37 0.24 0.50 0.41 0.54 0.2275th percentile 0.46 0.76 0.63 0.96 0.89 1.00 0.38Mean water depth (m) – 0.073 0.08 0.083 0.072 0.075 0.073Water-surface slope (m/m) – 0.017 0.019 0.020 0.020 0.020 0.020Bed slope (m/m) 0.017 0.016 0.018 0.020 0.022 0.022 0.022Dg surface (mm) 14.5 15.3 14.4 14.3 14.4 13.8 15.7sediment storage in the order of 102 kg, which consisted mainly of coarse grain sizes that wereless mobile.R1 - no feed R2 - constant R3 - one pulse R4 - four pulses R5 - two pulses R6 - constant R7 - no feedSediment pulseFeed rate(a)Bed surfaceBulkBedload(c)(b)10210–21001015200.0150.020.025Bed slope(m/m)D g (mm)Bedload rate(gm–1s–1 )054020 80 120 160 200 240 280Time (h)Sediment pulseFigure 3.1: Bed adjustments for the entire 280-h experiment. Modified from Figures 3and 4 in Elgueta-Astaburuaga and Hassan (2017) (AGU Usage Permissions). (a) Totalbedload transport rate and sediment feed rate (red lines and dots) in logarithmicscale. Gaps in the data are due to technical problems. (b) Geometric mean particlesize Dg of the bed surface, bedload, and bulk bed. (c) Slope at the thalweg. Sedimentpulses are indicated with vertical dashed lines in (b) and (c).Mean sediment transport rate varied with grain size over more than two orders of magni-tude (Figure 3.2a). Grains up to 45 mm exited the flume throughout the experiment, althoughτci > τb for grains > 20 mm under average flow conditions, which highlights the importanceof variability at small scales (e.g., arrangement of grains, flow turbulence) and that the criti-cal Shields stress for poorly sorted gravel is below the one we assumed from Meyer-Peter and403.4. ResultsMu¨ller (1948) already noted by Parker and Klingeman (1982). Transport rate increased with grainsize for sand fractions (< 2 mm), grains between 2 and 8 mm exhibited similar mean rate, butthis decreased with size for grains > 8 mm. The decrease in grains < 2 mm could be related tohiding effects limiting the fine material available for transport or to under-detection associatedwith the light table method (likely for grains < 1 mm). Relative mobility analysis (Wilcock andMcArdell, 1993) indicated that the limit between partial and full mobility was stable at ∼8 mmand was not significantly affected by changes in sediment feed.The frequency of fractional bedload transport was characterized by measuring the timeover which no grains of a given size exited the flume (Figure 3.2b). Even though, coarseparticles (> 16 mm) were seen moving through the flume during the experiment, they movedfor short distances and in most cases, did not leave the flume. Grain-size fractions < 2 mmwere grouped together as sand to avoid the effects of mis-detection noticed for grains< 1 mm.Time immobile was very low for sand and increased with grain size for particles > 2.8 mm.Over the entire 280-h experiment aggregated sand fractions (< 2 mm) exited the flume 97% ofthe time, fine gravel (2–8 mm) 98%, coarse gravel (8–16 mm) only 8%, and very coarse material(> 16 mm) less than 1%.Bursts in bedload ratesRegardless of their low frequency, occasional bursts in bedload rates mobilized large amountsof sediment, which in general exhibited a coarser composition than bulk bedload transport. Toassess the composition of such spikes in the transport rate, we divided each run into four 10-hintervals and then, within each interval, selected all observations for which bedload rates (in gm−1 s−1) had a low probability of exceedance pe < 0.01 as in Figure 3.3. 25% of the total masstransported during the experiment can be attributed to bedload rates with low pe. Commonly,these large bedload rates had a greater proportion of sediment> 8 mm than the bulk bedload,but exceptions were noted during the first 10 h of R1 or R3 (Figure 3.4). For these exceptions,large spikes in the transport rate were caused by the large availability of fine mobile sedimentdue to an initial well-mixed bed in R1, and due to a large sediment pulse at the beginning ofR3 (Figure 3.3).Because of their large masses, a few coarse grains could significantly affect the composi-tion of large bursts in bedload rate under low–moderate transport conditions. The percent ofbedload observations with pe < 0.01 that involved coarse material was estimated over each10-h period (Table 3.3) to assess the frequency with which they occurred. Regardless of thevariability among analyzed periods, the percentage of large bedload bursts contributed bycoarse grains was large. Overall, 77% of the observations included grains > 8 mm, roughly53% contained material > 11 mm, and 24% included particles > 16 mm.To visualize variability in the grain-size composition of bedload observations with lowpe, bedload rate of coarse grain sizes (> 8 mm) was plotted against total bedload rate forthose cases over all the 10-h intervals. Three examples are presented in Figure 3.5 to describe413.4. Results1 2 4 8 16 32 64Grain size (mm)00.20.40.60.8110010–110–210–310–410–5Fraction of time immobileBedload rate (gs–1 )Sand Gravel(b)R1 - no feedR2 - constantR3 - 1 pulseR4 - 4 pulsesR5 - 2 pulsesR6 - constantR7 - no feedSand Gravel(a)Figure 3.2: Bedload transport intensity by grain size for each run. (a) Mean bedload trans-port rate. (b) Fraction of time immobile. Time immobile was estimated as the timeover which no grains of a specific size exited the flume. Grain-size fractions< 2 mmwere grouped together as sand to avoid the effects of mis-detection of grains < 1mm. Coarse grains were observed to move for short distances, but most of the timedid not leave the flume.observations under different transport intensities. In all three, there were cases that did notinclude any coarse grains, although a considerable number of them did. Grains coarser than 22mm contributed least frequently due to their sporadic movement. The range of grain sizes thatparticipated in observations with pe < 0.01 increased with sediment transport rate. Points thatfall on or near the 1:1 line represent cases that involved, almost exclusively a specific coarsegrain-size. These cases were common during low transport, as in the last 10 h of R1 (Figure3.5a). They became less abundant and coarser during moderate transport as in the last 10 h ofR2 (Figure 3.5b) when large bedload rates included a wider range of sizes. Finally, during veryintense transport as in the first 10 h of R3 or R1 (Figure 3.5c), fractional bedload was alwayssignificantly lower than total bedload and no points fall near the 1:1 line.423.4. Resultsq b (gm–1s–1 )10210–21000 5 10 15 20 25 30 35 40Time (h)R3 - 1 pulseInterval 1 Interval 2 Interval 4Interval 3Figure 3.3: Bedload transport rate qb and large bursts in qb (displayed in red) during R3.The run was divided in four 10-h intervals (Interval 1–4) and, within each interval,qb with probability of exceedance pe < 0.01 were selected as large bursts.0 40 80 120 160 200 240 280Time (h)P i [bursts] / P i [bulk]  R1 - no feed R2 - constant R3 - 1 pulse R4 - 4 pulses R5 - 2pulses R6 - constant R7 - no feed(a)< 2 mm2 - 8 m8 - 16 mm> 16mm(b) R3, first 10 h1 0.1 0.0100.20.40.60.81Cumulative proportion(c) R3, last 10 h1 0.1 0.01Exceedence probability pe > 16 mm8 - 16 mm2 - 8 mm< 2 mm10010–1101Figure 3.4: (a) Ratios between the proportion of sediment of each grain size class in largesediment bursts Pi[bursts] and the proportion of the same grain size class in bulk bed-load Pi[bulk]. For large bursts, pe< 0.01. (b) Grain-size distribution of bedload rateswith pe< 1, 0.1, and 0.01 over the first 10 h of R3. (c) Grain-size distributions overthe last 10 h of R3.3.4.2 Memory and scaling statisticsSample autocorrelation coefficientsThe sample autocorrelation coefficients ρτ were used to identify trends and evaluate short-term memory in sediment transport rate time series. In the presence of a trend, ρτ remains sig-nificant for large time lags τ. For a completely random process (e.g., white noise), ρτ vanishesexcept at τ = 0. Finally, for short-term correlation, ρτ vanishes except for small τ (Chatfield,433.4. ResultsTable 3.3: Summary statistics for the percent of sediment bursts that included coarse ma-terial for all 10-h intervalsStatistic % events with grains >16 mm 11 mm 8 mmMinimum 1.1 17.9 35.5Maximum 58.8 82.7 98.3Mean 23.7 53.2 76.6Standard deviation 15.2 18.2 15.5(a) R1, last 10 h (b) R2, last 10 h (c) R3, first 10 hq bi (gm–1s–1 )Total qb (gm–1s–1) Total qb (gm–1s–1)Total qb (gm–1s–1)0 2 4 6 8 10 12 0 2 4 6 8 10 1202468101202468101214 140 20 40 60 80 100 1200204060801001201408 - 11 mm11 - 16 mm16 - 22 mm22 - 32 mm> 32 mmno coarseFigure 3.5: Fractional bedload rate qbi of coarse grains against total bedload rate qb forthree 10-h time intervals. Only qb observations with pe< 0.01 are presented. Dashedline corresponds to qbi= qb. (a) Last 10 h of R1 when the intensity of sediment trans-port was low after 30 h of no feed. (b) Last 10 h of R2 when the intensity of transportwas moderate after 30 h of constant feed. (c) First 10 h of R3 when the intensity oftransport was high because of a large sediment pulse.1975).For each of the 40-h runs we computed ρτ over time periods that ranged from 10–40 h tocharacterize the effects of changes in feed on the strength and persistence of the bedload rateautocorrelation and found trends in most cases (Table 3.4). To represent the range of results, weprovide examples for the three types of correlograms observed: trend, low ρτ, and white noise(Figure 3.6). In some cases, strong trends caused ρτ to remain very high for large τ as in R3(Figure 3.6a). Cases where ρτ exceeded only slightly 95% confidence limits (< 10% as in Figure3.6b) are indicated as “low ρτ”. Seven of the 28 correlograms in Table 3.4 support a white noiseprocess (as in Figure 3.6c). In general, periods that included changes in feed conditions at thebeginning exhibited high ρτ whereas correlograms that resembled white noise only occurredover periods when sediment feed did not change and the system was more stable.443.4. ResultsTable 3.4: Description of correlograms of bedload time seriesRun Time period (h)0–40 10–40 20–40 30–40R1 trend∗ white noise white noise white noiseR2 trend (low ρτ)∗ trend (low ρτ) trend (low ρτ) trend (low ρτ)R3 trend∗ trend (low ρτ) white noise trend (low ρτ)R4 trend∗ trend∗ trend∗ trend∗R5 trend∗ trend (low ρτ) trend∗ trend (low ρτ)R6 trend (low ρτ)∗ trend (low ρτ) trend white noiseR7 trend∗ trend (low ρτ) white noise white noise∗ Changes in feed conditions at the beginning of these periods are thoughtto have influenced the trends.(a) R3 - one pulse(b) R2 - constant feed0 20 40 60 80 100 120 140 160 180 200Lag    (s) (c) R1 - no feed, last 10 h10010–410–2ρ τ10010–410–2ρ ττ10010–410–2ρ τFigure 3.6: Sample autocorrelation ρτ against lag time τ. Examples for the three typesof correlograms described in Table 3.4. Note logarithmic ordinate. (a) R3 displayspersistently high ρτ due to strong trend. (b) For R2 ρτ is lower, but still significant.(c) For the last 10 h of R1 ρτ is only significant at τ = 0, as for white noise. Thedashed horizontal line indicates 95% confidence limits.Variance scalingTo describe multi-regime fluctuation in bedload, the relationship between variance σ2T andtime scale T was plotted on a log-log graph (Figure 2.7). Ma et al. (2014) observed a decreaseof σ2T with −1 slope in the case of independent (non-correlated) fluctuations. This occurredat short T due to intermittency in the signal (intermittent stage) and at very long T, when453.4. Resultsautocorrelation vanished (memoryless stage). At intermediate T (invariant or memory stage),σ2T became more constant.In our experiment, only the runs with constant feed (R2, R6) exhibited the three stagesof fluctuation described by Ma et al. (2014). An intermittent stage was visible for T < 10 s,an invariant stage stretched over 10 s < T < 500 s, and a memoryless stage over longer T(Figure 3.7a). In all other runs, the invariant stage occurred over a wider range of T andshowed stronger fluctuations than with constant feed. The invariant and memoryless stageswere not always exhibited. The most extreme case was R3, for which the variance decreasedonly slightly with T and only the invariant stage was observed. This could be related to thestrength and persistence of the trends caused by the large sediment pulse introduced at thebeginning of the run.The decrease in variance σ2T with T was also analyzed for different grain sizes over each runand we found fine gravel (2–8 mm) to be the most representative of total bedload. Althoughthere was considerable variability in the results, total bedload and fine gravel displayed similarpatterns in most cases, in contrast to very coarse gravel or sand, which usually exhibited alonger intermittent stage and a more significant decrease in σ2T (for example, R2 in Figure2.7b).(b)Total< 2 mm2 - 8 mm8 - 16 mm> 16 mmIntermittentInvariantMemorylessSlope = –1(a)R1 - no feedR2 - constantR3 - 1 pulseR4 - 4 pulsesR5 - 2 pulsesR6 - constantR7 -  no feedPoisson process3 stages of fluctuation10010–110–3103102101100 10410–410–2Time scale T (s) 103102101100 104Time scale T (s) Scaled variance   σ 2 Tσ 2 T = 1/Figure 3.7: Scaled variance vs. aggregation time scale T. The variance σT at each T wasdivided by σT when T = 1 s. The number of observations N decreases as T increases.T at which N=50 is displayed with a vertical dashed line. (a) Results for individualruns using total bedload rates. (b) Grain-size dependent results for R2.Hurst exponent HThe Hurst exponent H, which is calculated from the relation between the standard deviationσT and time scale T, was used to quantify memory in bedload rate time series. For processes463.4. Resultswith memory, 0.5 6 H 6 1 with H = 0.5 corresponding to short-term persistence, character-istic of Markov processes, which only have memory of τ = 1. H = 1 indicates long-termmemory and is characteristic of series with trends, or of series in which observations at eachside of the mean cluster into prolonged periods (Koutsoyiannis and Montanari, 2007). To iden-tify changes in the memory structure of bedload rates within each run, H was estimated overa 5-h moving window that stepped forward at intervals of 1 h; cumulative H was computedin 1-h increments (Figure 3.8). T ranged between 1 s and 360 s.400 80 120 160 200 240 280Time (h)0.40.20.60.81.210HR1 - no feed R2 - constant R3 - 1 pulse R4 - 4 pulses R5 - 2 pulses R6 - constant R7 - no feedH = 0.5H every 5 hCumulative H Figure 3.8: Evolution of long-term memory. The Hurst exponent H was estimated foreach run over 5-h moving windows and in cumulative 1-h increments.Only part of the significant variability observed in H could be attributed to effects of sed-iment feed on sediment transport rates. The inconclusive relationship found between H andmean bedload rate (Figure 3.9) implies that long memory was not exclusively controled bybedload intensity. Large infrequent sediment pulses, as in R3 and R5, clearly influenced mem-ory. The strong trends in bedload rate due to these pulses caused H to approach 1 immediatelyafter the pulse and to decrease as bedload rate stabilized under no feed (Figure 3.8). Strongmemory observed over periods with relatively stable mean bedload rates (e.g., last 10 h ofmost runs) was unlikely to be a consequence of long-term trends caused by changes in sed-iment feed, but more likely a result of clustered observations that could be related to localchanges in bed conditions. Therefore, H ≈ 1 could result from the dispersion of large in-frequent sediment pulses or from significant releases of bed sediment (e.g., from a sedimentwedge created by sediment feed upstream).For each run, H was quantified for different grain size fractions and demonstrated a stronginfluence of grain size on memory. In general, memory strength decreased with grain size asindicated by a lower mean and shorter range of H (Figure 3.10a). Grains> 32 mm exhibited nolong-term memory because they moved very occasionally and only a small proportion of themexited the flume. These grain sizes corresponded to the coarsest 10% of the bed surface (meansurface D90 = 32 mm). Plots of H for five grain size fractions against H for total bedload arepresented in Figure 3.10b. H for fine gravel was very similar to H for total bedload (plot near1:1 line), which is consistent with our previous results on variance scaling (memory structureof total bedload rate was like that of fine gravel). Sand and coarse gravel had lower H than473.4. ResultsMean bedload rate (gs–1)0.40.50.60.70.80.911.1H total bedloadR1 - no feedR2 - constantR3 - 1 pulseR4 - 4 pulseR5 - 2 pulseR6 - constantR7 - no feed10–1 100 101Figure 3.9: Hurst exponent H over 5-h moving window against mean bedload rate.total bedload, and H was even lower for very coarse gravel.0.5 0.6 0.7 0.8 0.9 10.50.60.70.80.910.51H0.51H0.51H0.51H0.51HExperiment run H total bedloadH fractional  bedload< 2 mm2 - 8 mm8 - 16 mm16 - 32 mm> 32 mm(a) (b)Di = 16 - 32 mmDi = > 32 mmDi = 8 - 16 mmDi = 2 - 8 mmDi < 2 mmR1 R2 R3 R4 R5 R6 R71:1Figure 3.10: (a) Range of H by run for five grain size fractions Di. (b) H for fractionalbedload against H for total bedload by grain size (run averages).Effects of aggregation time scale T on memoryTo analyze the effects of the temporal aggregation scale T on the strength of short memoryin total and fractional transport rates, the lag-one autocorrelation coefficient ρ1 was estimatedusing T between 1–600 s. Results were very similar among runs, so only R2 (constant) and R3(one pulse) are presented as examples in Figure 3.11a–b. T with highest autocorrelation wasplotted against grain size for each run in Figure 3.11c.483.5. Discussion1 10 100Grain size (mm)Time scale T (s) Time scale T  with highest ρ1(s) 00.511 10 10000.51(c)R1 - no feedR2 - constantR3 - 1 pulseR4 - 4 pulsesR5 - 2 pulsesR6 - constantR7 -  no feed(a) R3All grain sizesAll grain sizes< 2 mmGrain sizes: 2 - 8 mm 8 - 16 mm > 16 mm(b) R6ρ 1ρ 1103102101Figure 3.11: Lag-one autocorrelation coefficient ρ1 against aggregation time scale T fortotal bedload and four grain size fractions. 95% confidence limits presented indashed lines. (a) Results for R2. (b) Results for R3. (c) Time scale T with highestlag-one autocorrelation ρ1 for different grain sizes and runs.Once more, total bedload follows a similar pattern to that observed for fine gravel: ρ1 in-creases rapidly with T for T < ∼20 s and decreases after it reaches a maximum. The decreasecan be gradual as in R1 or R3 (Figure 3.11a), or more pronounced as in R2, R4 or R6 (Figure3.11b). With coarse gravel (8–16 mm), ρ1 starts lower than for total bedload and peaks at longerT. The increase with T is more gradual and ρ1 reaches values similar to or higher than thatfor total bedload at long T. Grains > 16 mm show the lowest ρ1 and peak at longer T thantotal bedload. The case of sand is interesting because it does not fit the grain-size dependencepattern observed for gravels (> 2 mm). For sand, ρ1 usually falls among the coarse size classesand peaks at longer T than for fine gravel.3.5 Discussion3.5.1 Controls on sediment mobility and the composition of large bursts inbedloadSediment supply regime was a first order control on temporal adjustments of bedload rate andbed surface particle size. Constant feed made sediment gradually available, causing slowerand weaker responses than the occasional sediment pulses, which made a large amount ofsediment suddenly available. Differences among results from runs with the same sedimentsupply regime indicate that the initial bed conditions influenced the bed response to changesin sediment feed. Differences in the shape and statistics of bedload time series for R1 and R7(no feed) were mostly because of the contrast between the fine well-mixed bed at the begin-ning of R1 and the armored bed at the beginning of R7, although differences in bed slope and493.5. Discussioncumulative storage might had also been important. No textural differences were observedamong the initial bed surface of R2 and R6 (constant feed), so diversity among bedload statis-tics for these runs was likely because of cumulative sediment storage and the overall increasein bed slope that caused a steeper bed in R6 than in R2.The configuration of the bed surface conditioned the role of coarse grains in the occurrenceof large bursts in bedload rate. The role of coarse grains was significant during supply-limitedconditions when the bed was well-armored, but it became less relevant during transport-limited conditions when the bed had a less organized structure, as in the beginning of R1 orR3. Over most analyzed periods, the grain-size composition of large bedload rates with lowpe was coarser than the composition of bulk bedload. Most, but not all, large bedload ratesincluded coarse grains. It is important to consider that the role of coarse grains might not havebeen limited to their evacuation, but also to their interactions with the bed while moving. Forexample, a large grain that exits the flume might cause the movement of others by exposingfines, or by collisions, or any type of bed disruptions. Our observations are consistent withSaletti et al. (2015), although in their case large bedload bursts were even coarser because theywere associated with the collapse of steps in their step-pool morphologies. In our experiment,the bed exhibited riffle-pool morphologies, where the movement of coarse grains could be re-lated to the breakup of small bed features like clusters and the evolution of larger bedformssuch as bars.3.5.2 Hypothesis 1: Bedload rate time series for runs with constant sediment feedhave weaker memory than those for runs with large infrequent sedimentpulses, which can cause pronounced trends in bedload transportThe structure of memory in bedload rate signals was influenced by sediment feed regime,as proposed in our hypothesis, and by bed organization. Runs with episodic feed exhibitedhigher ρτ and more persistent memory than runs with constant feed. The three stages forbedload fluctuation (Ma et al., 2014) were only observed in the total bedload rate of runs withconstant feed, which had the same simplified feed regime as the experiments analyzed byMa et al. (2014). For runs that had episodic feed regimes as in mountain streams, the scal-ing regimes proposed by Ma et al. (2014) did not hold. Instability produced by episodic feedcaused the autocorrelation to persist over very long T and a longer duration of the invari-ant stage of fluctuations (memory stage). Without constant feed, a memoryless stage was notpresent. Constant feed caused a modest increase in bedload rate, a trend that could be ob-scured by bedload fluctuations caused by changes in bed elevation due to the building anddestruction of bed surface structures (e.g., pebble clusters). Episodic feed regimes producedmore persistent trends in the sediment transport rate as the system relaxed from the strongincrease caused by a sediment pulse. Long-term trends due to large sediment pulses (R3, R5)were pronounced and caused the invariant stage to extend over longer T than under constantfeed. For R3, the intermittent stage was not observed. This could be explained by the larger503.5. Discussiontransport rates experienced after the pulse (first ∼10 h), which probably induced an increasedfrequency of sediment movement that could have reduced or erased the intermittency of totalbedload signal at T ≤ 1 s. These results support the idea that sediment supply and changes insediment storage are a first order control in channel response (e.g., Hassan et al., 2008).Long-term memory was observed after significant changes in sediment feed, but also dur-ing more stable periods. Changes in sediment feed caused trends which appeared as strongmemory in the signal (persistently significant ρτ, large H). When the processes governingtransport were related to bed evolution at small scales (e.g., grain sorting, arrangement ofsmall structures), bedload rate signals could become more stochastic over relatively stable pe-riods, as indicated by correlograms that resemble white noise and H ≈ 0.5. Over the same pe-riods, bedload signals could show long memory if the governing processes occurred at largerscales (i.e., evolution of bedforms) and caused bedload rate to shift between persistently highand persistently low values. In summary, memory was not exclusively determined by trans-port regime or sediment feed, but also by local changes in the bed configuration. The incon-clusive relationship found between mean transport rate and H supports this idea (Figure 3.9).3.5.3 Hypothesis 2: The memory structure of total bedload reflects that offully-mobile grain sizes, which dominate sediment transport and exhibitstrong memory in their bedload signalsThe memory structure of total bedload was similar to that of fine gravel (2–8 mm), whichcontributed the most to sediment transport, but was considerably different from those of othergrain sizes (Figures 3.10b and 3.11). The strength of memory decreased with grain size exceptfor sand, which exhibited weaker memory than fine gravel. In the gravel fractions, memoryweakened with grain size as mean bedload rate decreased (Figure 3.2a) because of the lessrecurrent entrainment of coarse gravel (Figure 3.2b). Total bedload rate displayed very similarmemory structure (H and ρ1T ) to that for fine gravel (Figure 3.10b and 3.11), which was themost mobile fraction during the experiment. As these grain sizes experienced full mobility,their response to sediment feed was expected to be strong, given that sediment feed increasedtheir availability on the bed surface. We found that H was a good proxy for relative sedimentmobility of gravel fractions. H ≈ 1 for fully-mobile gravels and H < 1 for coarse gravels underpartial mobility, which moved more sporadically and resulted in lower mean bedload rates.For gravels under incipient motion, H ≈ 0.5. The memory in bedload rate signals weakenedwith grain size, as the signals gained stochasticity and became more intermittent. Even thoughsediment transport processes are stochastic in nature, this was obscured by trends caused bychanges in sediment feed and by persistent autocorrelated patterns caused by bed evolution.On the other hand, sand was not affected by grain-size dependence in the same way asgravel fractions. Sand load signals exhibited greater stochasticity (e.g., longer intermittentstage) and weaker memory (decreased H and ρ1) than fine gravel, although there was consid-erable variability in their structures (e.g., wide range of H). The greater stochasticity of sand513.5. Discussionpatterns could not be due to increased intermittency because the signal was almost as contin-uous as for fine gravel (no movement 3% of the time) and very different from coarser fractions(> 90% time immobile). The sediment fed upstream and the bed itself were sources of sandduring the experiment. Flow conditions were well above critical for sand, so a considerableproportion of the sand supplied was expected to exit the flume. This could happen rapidlythrough pulse dispersion, but as the poorly sorted bed developed armor and bed structures,infiltration and hiding effects were expected to play a significant role in the availability ofsand for transport (sand < Dg of the bulk bed and Dg of the bed surface). Some of the sandinput could get stored in the bed and become available later during the experiment, whenthe movement of a coarser grain exposed hidden sand. The movement of sand might havebeen more influenced by these highly stochastic dynamics and less affected by longer scaleprocesses such as bedform evolution that reduced stochasticity in the system.Grain-size dependence in the statistics and memory structure of bedload rates needs tobe considered when studying sediment transport patterns of sediment mixtures under partialtransport. This is important because the most effective sampling durations and autocorrelatedtime scales also depended on grain size. The time scale T max(ρ1) with highest autocorrelationmax(ρ1) can be used as a reference. For T < T max(ρ1), the signal gains stochasticity possiblydue to intermittent sediment flux; for T = T max(ρ1), autocorrelation in the signal becomesstronger and better captures any trends that are lost at smaller T. If sampling duration isshorter than T max(ρ1) for a given grain size, the sample might not be representative of that sizebecause sampling duration is within the intermittency of the signal. On the other hand, thestochastic variability of the process is only observable at T < T max(ρ1).Our results are consistent with the observations of Saletti et al. (2015). As for these au-thors, we found a relationship between transport intensity and memory strength, togetherwith grain-size dependence in the memory structure of bedload signals that was reflected indifferences in H and ρ1. They used sediment coarser than 2 mm and did not find any inflec-tion of grain-size dependence patterns in their finest classes (2–5.6 mm) as we did for sand. Incontrast with our results, in their study coarser grain sizes (16–45 mm) exhibited a memorystructure closer to that for total bedload, which might be related to differences in boundaryconditions among the experiments (e.g., flow discharge, sediment feed) and the developmentof distinct bed morphologies: step-pool in their case, riffle-pool in ours.3.5.4 Hypothesis 3: Grain-size dependence in bedload transport increases withsediment feed because the movement of fully-mobile sediment is moreresponsive to feed than that of partially-mobile grain sizesThis hypothesis was not confirmed because the same patterns of grain-size dependence inbedload transport persisted during the experiment regardless of changes in sediment feed.Sediment feed increased the availability of fully-mobile sediment for transport and, as the bedsurface became finer and smoother, it increased the frequency of movement of partially-mobile523.6. Conclusionsgrains too. No matter what the intensity of movement, grain-size selectivity was always evi-dent in gravel bedload rates and the limit between partial and full mobility remained nearlyconstant. The largest grain size transported was the same in all runs, except for R1 when itwas slightly smaller. Grain-size dependence and relative sediment mobility could be moreaffected by changes in flow strength (e.g., Wilcock and McArdell, 1993) or sediment feed texture(e.g., Curran and Wilcock, 2005), which were constant through all the experiment.Sediment feed affected the duration of the invariant stage of bedload fluctuations and thestrength of memory, but the observed differences among the patterns of different grain sizeclasses remained the same. We expected grain-size dependence to be stronger in the presenceof sediment feed, which significantly increased the intensity of transport for fine gravels. Wealso expected that during long periods without feed when transport intensity was low, finegravel would exhibit a more stochastic behavior as for coarser fractions. The results did notsupport these hypotheses. Coarse gravel signals always had weaker memory and had thestrongest autocorrelation ρ1 at longer time scales T than those for fine gravel.Initial bed conditions might have influenced patterns of fractional bedload fluctuation inruns that had same sediment feed regime. Whereas patterns of multi-regime fluctuation intotal bedload rate were very similar over both runs with constant feed (R2, R6), memory struc-tures of fractional bedload rates exhibited differences in the range and mean of H (Figure3.10). T with highest ρ1 was the same for fine gravel in both runs, but differed for other grainsizes (Figure 3.11). Similar types of differences were noticed between the two runs withoutsediment feed (R1, R7).3.6 ConclusionsWe studied the effects of sediment feed regime on sediment mobility, long-term memory ofbedload transport, and grain-size dependence, over an experimental bed with a wide grain-size distribution and extended history. Sediment mobility was affected by sediment feedregime. Fully-mobile gravel (2–8 mm), which dominated sediment transport and stronglyinfluenced the memory structure of total bedload rate, was more significantly affected thanother grain sizes. The contribution of coarse material to large bedload rates with low pe wasmore important during periods with low sediment transport intensity.Episodic sediment feed caused more pronounced changes in the transport rate and strongermemory than constant feed, although memory was also controled by local changes in bed char-acteristics, such as bedform evolution and storage release. Sediment pulses caused differenttemporal scales of bedload fluctuations than constant feed. We think this relates to differencesbetween the time that it takes for the bed to armor and reach a stable mean bedload rate aftera pulse, and the temporal scale of fluctuations related to the largest bedforms present, whichprobably influenced the duration of memory in runs with constant feed.The three stages of bedload fluctuation proposed by Ma et al. (2014) only held under simpli-fied situations when we used constant feed as they did. The strong trends caused in bedload533.6. Conclusionsby occasional sediment pulses like those reported in mountain streams increased long-termmemory and the duration of the invariant stage. This caused the intermittent and memorylessstages to vanish.As expected under partial transport conditions, the patterns of fluctuation observed for to-tal bedload were not representative of all grain size fractions. We observed grain-size depen-dence in mean bedload rates and the memory structure of bedload signals. Our observationswere consistent with Saletti et al. (2015), although interesting differences were noticed. In ourcase, the memory structure for total bedload was like that for fine gravel (2–8 mm), whereas intheir case H for total bedload was closer to that for coarser grains (16–45 mm). This could berelated to substantial differences in bed morphologies: we developed a riffle-pool morphology,whereas they created step-pools.The patterns of grain-size dependence found in sediment transport were not significantlyaffected by sediment feed because we only changed the magnitude and frequency, but notthe texture of sediment feed, nor flow discharge. Changes in sediment texture could affectbed surface roughness and entrainment thresholds (Curran and Wilcock, 2005; Venditti et al.,2010), and changes in flow could affect the limit between partial and full mobility (Wilcockand McArdell, 1993; Church and Hassan, 2002). It would be interesting to analyze grain-sizedependence of bedload statistics under changing feed texture or flow discharge.The initial bed was different for each run because of cumulative sediment storage thatcaused an overall increase in bed slope with sediment feed and because of a different history.A detailed description of the bed morphology and patterns of sediment storage for differentgrain size fractions could help to relate our observations to processes of erosion and deposi-tion.54Chapter 4Temporal patterns of sediment storageand spatial variability on a gravel bedunder changing sediment supplyregimes4.1 SummaryPatterns of sediment storage and spatial variability on a gravel bed were analyzed using datafrom a sequence of experimental runs with steady flow discharge, but changing sedimentsupply regime. All grain sizes exhibited net storage, except for fine gravel, which had an over-all negative mass balance. Differences were observed among feed regimes, but also withinthe same feed regimes, which could be related to an increase in bed slope. The storage of finegravel (2–8 mm) responded the most to changes in sediment feed and bed conditions, whereasthe storage of coarser gravels and sand was nearly stable. More than 60% of the sand fed dur-ing each run got stored, probably due to its higher potential for infiltration and for gettingcaught within larger grains. Hysteresis in sediment transport-storage relations was observedbetween runs with constant feed and those without feed because of differences in bed state andsediment availability. Sediment pulses also caused hysteresis, although its direction was influ-enced by the lag time between sediment feed and downstream response in bedload rate. Smallcycles of hysteresis were observed during constant feed if the mean bedload rate approachedthe feed rate. Sediment transport processes and bed characteristics varied considerably inspace. The cumulative increase in mean bed elevation was larger upstream due to the prefer-ential storage of coarse material, which also promoted downstream fining on the bed surface.The evolution in the standard deviation of bed elevations ση was consistent with the develop-ment of bedforms at different scales. ση was more stable in the center of the flume, indicatingbed roughness was less affected by bedform evolution over that area. Instead, upstream and554.2. Introductiondownstream the development of lateral bars and larger scales bedforms caused more signif-icant changes in ση . The accumulation of sediment upstream due to size-selectivity createda sediment wedge that expanded downstream. The way in which the sediment entered dur-ing the first run probably dictated the development of lateral bars due to differences in flowconfiguration and erosion in the transverse direction. As sediment feed became better spreadlaterally, a longitudinal sequence of riffle-pool like morphologies developed downstream ofthe wedge.4.2 IntroductionSediment supply has been proposed as a first order control in mountain streams (e.g., Hassanet al., 2006, 2008). Well-armored and structured beds with low intensity of sediment trans-port have been reported for streams with low sediment supply regimes (sediment supply transport capacity). Instead, finer bed textures and more intense sediment transport have beennoticed for streams with high sediment supply regimes (sediment supply transport capacity).Transport capacity can be highly variable at intermedate time scales T (100 years < T <103 years) because of changes in sediment supply, storage, and bed surface composition (Lisleand Church, 2002). Mountain streams usually receive sediment episodically (e.g., mass move-ments, bank collapses, disintegration of large wood jams), which depending on its amount andtexture, will be either deposited or transported further downstream. For uniform sediment,the difference between sediment supply and transport capacity dictates sediment storage. Forpoorly sorted sediment, flow transport capacity and flow competence to entrain sediment ofspecific grain sizes will influence sediment storage significantly (if there is too much sedimentor if it is too coarse for the flow, it will be left behind). Under partial transport, gravel bedsusually exhibit size-selective mobility in the coarse fractions, which cause their preferentialdeposition. Even though, there are studies that report on size-selective transport (e.g., Wilcockand McArdell, 1993; Church and Hassan, 2002), there are still open questions regarding the effectsof particle size on sediment storage, sediment mobility, and channel morphology.Given the limitations for collecting detailed data in the field (e.g., technology, time, andaccesibility), flumes are a good alternative to study channel adjustment under controled envi-ronments (e.g., Dietrich et al., 1989; Lisle and Church, 2002; Eaton and Church, 2004; Curran andWilcock, 2005; Eaton and Church, 2009; Pryor et al., 2011). For simplicity, most experiments haveused constant sediment feed and in only a few of them, sediment was introduced in episodicpulses (Cui et al., 2003; Sklar et al., 2009; Venditti et al., 2010; Johnson et al., 2015). These studiesgive insights mostly on the importance of the grain-size distribution of sediment feed rela-tive to that of the bed, in terms of pulse–bed interactions (Venditti et al., 2010), mechanismsof pulse propagation (Cui et al., 2003; Sklar et al., 2009), and bed surface texture (Johnson et al.,2015). With the exception of Elgueta-Astaburuaga and Hassan (2017), there are still no thoroughdescriptions of the effects of episodic sediment supply on channel adjustments and the rolesof the magnitude and frequency of sediment supply are still an open question. In Elgueta-564.2. IntroductionAstaburuaga and Hassan (2017) we analyzed the effects on the temporal variability of bedloadtransport. Here, we use data from the same experiment to study temporal and spatial pat-terns of total and fractional sediment storage and how they relate to bedload transport andbed morphology.Lisle and Church (2002) pointed out the importance of understanding sediment transport–storage relations for sediment routing models. They proposed that each sediment reservoiris governed by a unique positive relation, which in degrading streams exhibit two phases. Inphase I there is significant degradation, whereas in phase II, transport rate decreases as ar-mor developes and counteracts degradation. Later, physical modeling of complete cycles ofaggradation–degradation revealed that the relation could become more complex (Madej et al.,2009; Pryor et al., 2011) and that hysteresis developed from differences in the bed state (i.e.,bed composition). In the light of these findings, Lisle (2012) described two possible scenariosfor transport–storage relations: a common relation that persists as the bed aggrades and de-grades (scenario I) or a more complex relation that changes as the bed evolves (scenario II).In the last case, bedload transport rates for a given sediment stage depend on bed conditionsand there is hysteresis during cycles of aggradation–degradation (as in Madej et al., 2009; Pryoret al., 2011). Lisle (2012) explained the occurrence of scenario II by changes in sediment supplythat cause variability in channel response and transport capacity. More recently, Luzi (2014)showed that hysteresis can also result from the variability of sediment transport rate underdynamic equilibrium when the mean transport rate approaches the feed rate. In this study, weanalyze transport–storage relations over a long experiment, in which the bed underwent muti-ple cycles of aggradation–degradation caused by changes in sediment feed under steady flowdischarge. Besides the complexity achieved in the bed due to the design and duration of theexperiment, we included no feed, constant feed, and episodic feed regimes for comparisons.Spatial variability of sediment transport and storage in a stream responds to the locationswhere sediment enters the stream and to variability in the channel bed (e.g., morphology,texture) and flow conditions. The wide range of grain sizes in gravel bed rivers promotessediment sorting processes at different scales and in different directions (vertical, across, anddownstream), which influence bed roughness and the availability of in-channel sediment fortransport. At small–intermediate scales, sediment sorting results in bed armor (e.g., Parker andKlingeman, 1982), bed structures (e.g., Hassan and Church, 2000), and the development of finesediment patches (e.g., Nelson et al., 2009) and sediment sheets (e.g., Iseya and Ikeda, 1987). Atlarger scales, sediment sorting can be appreciated over bars and riffle-pool sequences (e.g.,Chartrand et al., 2015) and along step-pools (e.g., Zimmermann, 2009). At the largest scale, sed-iment sorting can result in downstream fining (e.g., Seal and Paola, 1995). Channel morphol-ogy promotes distinct mechanisms and paths for bedload propagation downstream. Theseinclude, but are not limited to the migration of alternate bars (e.g., Ikeda, 1989) and discretejumps between riffles (e.g., Hassan et al., 1991).Sediment inputs propagate dowsntream by different mechanisms and at different rates,574.2. Introductionwhich largely depend on flow conditions, bed morphology, and the texture of sediment supplyrelative to bed texture. Grain arrangements and bedforms provide resistance to flow underbankfull conditions (e.g., Millar, 1999), affecting the spatial variability of transport capacity,which influences the distribution of bedload transport processes. Flume experiments havereported dispersion and translation as the main mechanisms for pulse propagation (Lisle et al.,2001; Cui et al., 2003; Sklar et al., 2009). Dispersion was reported if sediment supply had thesame texture as the bed, whereas translation occurred if supply was considerably finer. Morerecently and based on a field case of gravel augmentation, Gaeuman et al. (2017) proposed thatpulses propagated by fragmentation into smaller pulses at short-intermediate scales. Alsobased on field evidence, Brumer and Montgomery (2006) observed that poorly sorted sedimentdelivered to channels could form lag deposits that developed an armored layer, which wasdriven by size-selective sediment transport and counteracted incision. Our data provides anopportunity to analyze the response of spatial variability to changes in feed over a gravel bedunder partial transport. The dimensions of the flume together with a wide range of particlesizes allowed sediment sorting in all directions and the development of bedforms at differentscales, which ranged from pebble-clusters to lateral bars. The experiment was long enoughfor the bed to develop a complex topography as a result of an extended history of flow andsediment supply.Previously, we analyzed the effects of episodic sediment supply on temporal patterns ofbedload transport (Elgueta-Astaburuaga and Hassan, 2017) and their dependence on grain sizeand aggregation scale (Elgueta-Astaburuaga et al., 2017). The goal of this study is to assess theeffects of episodic sediment inputs on sediment storage and bed evolution. Fractional trans-port data provided an opportunity to study the effects of size-selective transport on sedimentstorage. We used constant flow discharge to isolate the effects of sediment feed and followeda sequence of seven consecutive runs with different supply regimes to test the effects of feedmagnitude and frequency. We were able to assess transport–storage relations over multiplecycles of aggradation–degradation, which exhibited different durations depending on feedregime. These cycles included the intercalation between runs without feed and runs with con-stant feed, as well as short periods of intensive aggradation caused by sediment pulses thatwere followed by longer periods of degradation. Systematic measurements of bed propertiesalong and across the flume allowed us to assess spatial variability on bed topography and bedsurface texture, which were used to explain patterns of aggradation–degradation along theflume and the propagation of sediment feed downstream.We propose the following hypotheses. (H1) Preferential deposition of coarse partially-mobile gravels near the feed source promotes increased storage upstream and downstreamfining on the bed surface. (H2) Constant feed, which makes sediment available more gradu-ally, promotes larger sediment storage than sediment pulses because of a greater probabilityfor sediment being sequestered in the bed. (H3) Hysteresis in sediment transport–storage re-lations largely depends on differences in bed surface texture and sediment availability.584.3. Methods4.3 Methods4.3.1 ExperimentThe data were collected at the Mountain Channel Hydraulic Experimental Laboratory, Uni-versity of British Columbia (Elgueta-Astaburuaga and Hassan, 2017) in an 18 m long, 1 m wideflume, with a 14 m long working bed and a slope of 0.022 m/m. The bed and feed were com-posed of poorly sorted sediment (0.5–64 mm), with∼20% sand, geometric mean Dg = 5.7 mm,and percentiles D16 = 1.6 mm and D90 = 27 mm. The experiment consisted of a sequence ofseven 40-h runs, denoted R1–R7, under constant flow discharge (65 L s−1), but changing sed-iment feed regimes. Only R1 started from a flat and well-mixed bed; all other runs inheritedtheir initial beds from previous runs. For R2–R6, 300 kg of sediment was introduced over eachrun, but the magnitude and frequency of sediment feed varied. R1 had no feed to conditionthe bed and R2 received constant feed. R3 received the 300 kg of sediment during the firsthour to assess channel adjustments to large infrequent inputs of sediment. R4 and R5 received75 kg of sediment every 10 h (four pulses) and 150 kg of sediment every 20 h (two pulses)respectively, to test the importance of the magnitude and frequency of sediment inputs. Toexplore the importance of bed history, the constant feed regime of R2 was repeated in R6, andno feed like in R1 was repeated in R7. All sediment pulses were introduced at the same rate(83 g m−1 s−1), but feed duration d f differed with pulse size (d f = 1 h for 300 kg, 0.5 h for 150kg, and 0.25 h for 75 kg).Flow properties, bed elevation, bed-surface particle size, and sediment transport were sys-tematically measured. Water-surface elevation and depth were measured along the side of theflume at an interval of 0.5 m. Bed elevation was measured under no flow, by video-recordingthe reflectance of a green-beam laser with a resolution of 2 mm × 2 mm in the horizontaland 1 mm in the vertical. Bed-surface texture was assessed from photographs of the bed sur-face along the flume. A grid with cell size = Dmax was superimposed on the photographs forpoint counts to compute grain-size distributions. Grains smaller than 2.8 mm were groupedin one class because of difficulties in their identification. Fractional sediment transport datawere generated using the video-based method explained in Zimmermann et al. (2008), which inour case was improved by sampling grains as small as 1 mm (Elgueta-Astaburuaga and Hassan,2017). A sediment trap was placed at the downstream end of the flume to confirm results. Adescription of the experimental set up and data collection can be found in Elgueta-Astaburuagaand Hassan (2017). A summary for each run with mean flow properties, bed characteristics atthe end, and bedload transport statistics is presented in Table 4.1.4.3.2 Data analysesWe analyzed temporal and spatial patterns of sediment storage by computing mass balancesusing video-based sediment transport data and also by estimating changes in digital elevationmodels (DEMs) built from laser scans on the bed. Time series of sediment storage ∆T from594.3. MethodsTable 4.1: Mean flow characteristics, bed observations at the end of each run, and bedloadrate statisticsRun R1 R2 R3 R4 R5 R6 R7Mean water depth (cm) – 7.3 8.0 8.3 7.2 7.5 7.3Water-surface slope (m/m) – 0.017 0.019 0.02 0.02 0.02 0.02Bed slope (m/m) 0.017 0.016 0.018 0.02 0.022 0.022 0.022Bed surface (mm) Dg 14.5 15.3 14.4 14.3 14.4 13.8 15.7D16 6.7 7.7 7.0 7.4 7.2 6.3 7.8D90 34.1 33.7 31.5 31.6 31.0 31.7 31.5SDg 2.2 2.0 2.1 2.0 2.0 2.1 1.9Bedload rate (g s−1) Mean 1.29 0.65 1.56 0.98 1.19 1.25 0.42Standard deviation 27.06 5.12 7.64 3.17 10.32 31.32 1.5625th percentile 0.05 0.14 0.12 0.28 0.22 0.27 0.1350th percentile 0.14 0.37 0.24 0.50 0.41 0.54 0.2275th percentile 0.46 0.76 0.63 0.96 0.89 1.00 0.38mass balances were computed by subtracting output mass estimates (video-based transportdata) from the known mass of sediment fed over a specific time interval T as∆T = T ×Q f − T ×Qb (4.1)where Q f and Qb are the sediment feed rate and mean bedload transport rate. Cumulativesediment storage was estimated asCumulative∆Tn =n∑1∆T; for n = 1 : N (4.2)where N is the total number of observations in ∆T time series. We used T = 15 min to reducenoise caused by stochastic variability of bedload transport in the short term, without loosingthe responses caused by sediment pulses.We analyzed sediment storage from mass balances for the bulk sediment and for fourgrain-size classes: 0.5–2 mm (sand), 2–8 mm (fine gravel), 8–16 mm (coarse gravel), and 16–64mm (very coarse gravel). Sand was grouped together because it behaved in a distinct way; 8mm was the limit between partial and full mobility; 16 mm was the D75 of the bulk sedimentand similar to the Dg on the surface of an armored bed (Elgueta-Astaburuaga and Hassan, 2017).Sediment transport–storage relations for bulk sediment were assessed in plots of cumulative∆Tn vs. Qb (Pryor et al., 2011; Madej et al., 2009; Luzi, 2014).Sediment storage was also analyzed by computing changes in bed elevation δη betweentwo consecutive DEMs asδη[x,y] = η[x,y]d − η[x,y]d−1 ; for d = 1 : D− 1 (4.3)where [x, y] are DEM coordinates, η is bed elevation, d is the DEM chronological order, and D604.4. Resultsis the total number of DEMs available. Mean change in bed elevation δη between two DEMswas computed asδη =∑N1 δηN(4.4)where N is the number of observations for η in a DEM (columns × rows). Cumulative meanchange in elevation was estimated asCumulative δηd =d∑1δη; for d = 1 : D (4.5)To assess spatial variability over the bed, we estimated cumulative δη for 1-m2 sectionsalong the flume. To evaluate differences in bed roughness, we computed the standard devia-tion of bed elevation ση for the same 1-m2 sections. Elevation data were relative to the floorof the flume. We used DEMs to identify bedforms like bars, sediment wedges, and riffle-poolsequences (i.e., mesoforms and macroforms in Hassan et al. (2008)). No objective method forbedform delineation was available (e.g., bars are usually delineated relative to base flow in thefield), so we used slope inflections in longitudinal and transverse profiles to guide the delin-eation of boundaries. To assess textural differences on the bed surface, we estimated grain-sizestatistics from point counts on seven bed sections between 1–10.5 m from downstream. Eachbed section included two bed surface photos (an area of 1.3–1.4 m2).4.4 Results4.4.1 Temporal patterns of sediment storageAll runs with sediment feed had net positive mass balances between sediment feed and sed-iment outputs from video-based transport data. Significant differences were mainly causedby variability in storage of fine gravel (2–8 mm) because storage of sand and coarse gravelwas more stable (Figure 4.1). Within each run, stored sediment was primarily composed ofvery coarse gravel (> 16 mm), followed by sand. Coarse gravel (8–16 mm) contributed moresignificantly to storage than fine gravel, except over R2. R3, which received one 300 kg sedi-ment pulse, stored considerably less sediment than all the other runs with sediment feed. Itexhibited a negative mass balance for fine gravel of ∼60 kg, which is equivalent to ∼50% ofthe mass of fine gravel fed (Figure 4.1b). In R5, which received a 150 kg pulse every 20 h, finegravel also had negative balance, but five times smaller than in R3. In R4, which received a 75kg pulse every 10 h, fine gravel had a positive mass balance of 10 kg (∼10% mass fed).Runs with same feed regimes exhibited differences in sediment storage. Runs R2 and R6received constant feed, but R2 stored a significant amount of fine gravel (37 kg), whereas R6stored almost none. R2 also stored two times more coarse gravel (8–16 mm) than R6. Thesedifferences could relate to the increased bed slope in R6 relative to R2, as a result of cumulative614.4. Resultsno feed constant 1 pulse 4 pulses 2 pulses constant no feed(a)R1 R2 R3 R4 R5 R6 R7Run-300-200-1000100200300Sediment storage (kg)<2 mm2-8 mm8-16 mm>16 mmtotal100 101 102Grain size (mm)-80-60-40-20020406080100Mass stored over mass fed (%)(b)0.5-2 mm2-8 mm8-16 mm16-64 mmR2 - constantR3 - 1 pulseR4 - 4 pulsesR5 - 2 pulsesR6 - constantFigure 4.1: (a) Total and fractional sediment storage computed from mass balances overeach run. (b) Percent of sediment mass stored over mass fed for different grain sizefractions and runs.sediment storage. Runs R1 and R7 had negative mass balances because of no sediment feed,but the mass of sediment degraded in R1 was three times the mass degraded in R7. Both runsstarted from the same initial bed slope (0.022 m/m), but the bed surface was considerablycoarser at the beginning of R7 with a Dg 2.5 times the Dg at the beginning of R1. The timetaken for the bed to armor over each run influenced the strength of bed degradation duringno feed. As the initial bed of R1 was well mixed, a lot of sediment exited the flume during thefirst few hours as the bed armored. Instead, the initial bed of R7 was already armored to somedegree, which prevented degradation earlier than in R1.Except for fine gravel, all grain size fractions exhibited cumulative increase in sediment624.4. Resultsstorage over the experiment (Figure 4.2). The cumulative storage of all grain sizes increasedwith sediment feed, but only that of fine gravel exhibited pronounced decreases without sed-iment feed as bed armor counteracted degradation. Instead, the cumulative storage of othergrain sizes remained nearly constant under no feed. With constant feed, increases in cumu-lative storage were gradual and persistent, whereas with episodic feed, increases were sharpand followed by gradual decreases as sediment pulses propagated downstream. Overall theexperiment, there was a negative mass balance of ∼200 kg of fine gravel, whereas all othersize fractions exhibited positive mass balances: > 200 kg for sand, ∼100 kg for grains 8–16mm, and > 300 kg for grains 16–64 mm. The pattern observed for total mass combined thecumulative increase in storage of most grain sizes with fluctuations in storage of fine gravel asa response to changes in sediment feed.40 80 120 160 200 240 280Time (h)-400-300-200-1000100200300400500600Cumulative storage (kg)R1 - no feed R2 - constant R3 - one pulse R4 - four pulses R5 - two pulses R6 - constant R7 - no feed2-8 mm8-16 mm< 2 mm>16 mmtotalFigure 4.2: Cumulative sediment storage for bulk sediment (total) and four grain sizefractions. Mass balances were estimated every 15 min and the cumulative sum isplotted.4.4.2 Sediment transport–storage relationsTo assess sediment transport–storage relations we plot mean total bedload transport rate vs.cumulative sediment storage for the entire 280-h experiment (Figure 4.3). There was consid-erable variability in mean bedload rate for the same stages of sediment storage (hysteresis)because of differences in sediment availability and bed surface texture. The direction of hys-teresis observed within cycles of aggradation–degradation changed over the experiment anddepended on bed state. In runs with episodic feed, it also depended on the duration of theaggrading phase relative to the time that it took for bedload rate in the downstream end to634.4. Resultsrespond to sediment feed. In R1, the transport–storage relation was steep because the ini-tial well-mixed bed caused large bedload rates, which decreased as the bed armored slowingdown bed degradation. The relation was milder during persistent aggradation caused by con-stant sediment feed in R2 and for the same levels of cumulative storage, bedload rates weresignificantly smaller than during degradation in R1 (counter-clockwise hysteresis). The con-trast between a well-mixed initial bed in R1 and a conditioned armored bed at the beginningof R2 explains the observed pattern.-100 0 100 200 300 400 500Cumulative sediment storage (kg)10-210-1100101102103Mean bedload rate (gs-1)constant feed ratepulse feed rateR1R2R3R4R5R6R7Figure 4.3: Mean bedload transport rate against cumulative sediment storage over theexperiment. Seven runs (R1–R7) distinguished by color. Dashed lines indicate sedi-ment feed rates used for constant and episodic feed regimes.R6, which also received constant sediment feed, exhibited a pattern similar in shape tothat of R2, but with larger levels of cumulative sediment storage and a higher range of meanbedload rate (Figure 4.3). In R6, transport rates occasionally exceeded the feed rate, causingcumulative storage to decrease and the development of small aggradation–degradation cycles(Figure 4.4) with larger transport rates during the degrading phase (counter-clockwise hys-teresis). These cycles were not present in R2 because mean bedload rate was always belowthe feed rate. Differences in the intensity of sediment transport among R2 and R6 could berelated to cumulative increases in sediment storage and bed slope, but not likely to the initialbed surface Dg, which did not change significantly among them.R7 had no feed like R1 and exhibited a similar shape for transport-storage relations, butwith greater levels of cumulative storage and a narrower range of mean bedload rates (Figure4.3). Bedload rates were not as large at the beginning of R7 as in R1 because in R7 the bed wasarmored to some degree, whereas in R1 it was well-mixed. Bedload rates were not as low at the644.4. Results0 20 40 60 80 100 120 140 16010-210-1100101102Mean bedload rate (gs-1 ) R2feed rate0 20 40 60 80 100 120 140Cumulative storage (kg)10-210-1100101102Mean bedload rate (gs-1 )1 23small cyclesR6feed rateFigure 4.4: Mean bedload transport rate against cumulative sediment storage over runswith constant feed (R2-R6). Dashed lines indicate feed rate. Small cycles ofaggradation–degradation occurred in R6 when mean bedload rate exceeded feedrate, which did not happen in R2.end of R7 as in R1 because R7 started at a greater level of cumulative storage, which implieda steeper bed slope upstream and more sediment available. For same levels of cumulativestorage, bedload rates were greater during aggradation in R6 than during degradation in R7(clock-wise hysteresis), which differs from what we observed between runs R1–R2. Differencesin the initial beds of the degrading runs influenced the patterns observed. The initial well-mixed bed in R1 caused intense bedload during degradation, whereas the armored bed in R7exhibited considerably lower bedload intensity.Cycles of aggradation and degradation were also observed within runs with episodic sedi-ment supply (Figure 4.3). These runs received large amounts of sediment during short periodsof time that alternated with longer periods of no sediment feed. There was a time delay τ of0.5–1 h between the start of the feed and the response of bedload rate at the downstream endwhere sediment output was measured. The difference between the delay τ and feed durationd f influenced the direction of hysteresis found in aggradation–degradation cycles. If τ < d f ,as in R3, bedload rates were larger during aggradation as expected. If τ ≤ d f , as in R4 or R5,transport rates could become larger during degradation. The size of pulses affected the degreeof hysteresis. Differences in bedload rate for the same levels of storage were stronger with thelarger pulses in R3 and R5 than they were with the small pulses in R4, for which hysteresiswas not always clear.654.4. Results4.4.3 Sediment storage and spatial variability over the channel bedMean changes in bed elevation obtained from DEM subtractions were consistent with resultsof storage computed from mass balances. Despite differences in the temporal resolution, cu-mulative mean change in bed elevation (Figure 4.5) displayed similar temporal trends to totalcumulative sediment storage presented in Figure 4.2. Sediment feed caused positive changesin bed elevation, which were more pronounced with sediment pulses than with constant feed.Instead, the absence of feed first caused slight negative changes in bed elevation and then amore stable behavior as the bed armored. As a DEM for the initial bed in R1 was not available,the strong degradation that occurred during the first hours is not visible in Figure 4.5.0 40 80 120 160 200 240 280Time (h)-10010203040Bed elevation (mm)R1 - no feed R2 - constant R3 - 1 pulse R4 - 4 pulses R5 - 2 pulses R6 - constant R7 - no feedmean changecumulative changeFigure 4.5: Mean change in bed elevation during the experiment. Mean change was esti-mated by subtracting two consecutive DEMs and computing an average.To assess differences along the channel, we estimated cumulative mean change in elevationfor ten bed sections (Figure 4.6). In all sections, the response to sediment feed consisted ofan increase in bed elevation, which occurred faster and was larger towards the upstream endwhere sediment entered the channel. In sections located more than 10 m from the downstreamend, the cumulative change in elevation started to increase after 1–10 h of feed in R2. Instead,in sections located less than 7 m from the downstream end, cumulative change in elevationdid not increase until the end of R2. At the end of the experiment, the farthest upstreamsection exhibited the largest cumulative change in elevation (40 mm at x = 11.5 m), which wasprobably related to cumulative storage of coarse gravels and sand as shown in Figures 4.1 and4.2. Near the downstream end (at x = 2.5 m), the increase in elevation with feed was verysmall and the cumulative mean change curve plots near zero. Stability over this area couldbe because it was far from the feed source or due to the influence of downstream boundaryconditions.To evaluate bed rugosity and roughness due to the presence of bedforms, we computedstandard deviation of bed elevation ση for each bed section. We expected to find higher ση inthe presence of larger bedforms (i.e., bars) and the lowest values in the absence of bedformswhen differences in η only occur at the grain scale. The temporal evolution of ση varied alongthe flume (Figure 4.7). In the center of the flume (5–8 m from downstream end), ση changedvery little. Downstream, short-term changes were not pronounced, but ση at the end of the664.4. ResultsFigure 4.6: Cumulative mean change in bed elevation over different bed sections. DEMswere divided in ten 1-m2 sections and cumulative changes in elevation were com-puted for each of them. The downstream end of the flume was at x = 0 m.experiment was considerably larger than ση at the beginning. Upstream, the most dramaticchanges occurred between R2–R4 (pulses in R3 and R4 had clear responses) and for sectionsat x > 10 m, an increase in ση was also noticed towards the end.To link changes in ση (Figure 4.7) to the development of bedforms, we summarize the evo-lution of bed morphology using DEMs for the channel bed at six different times as examples(Figure 4.8). Degradation during no feed in R1 resulted in a straight channel with no large-scale bedforms, but small bed structures (Figure 4.8a). The feed in R2 (constant) entered fromthe side of the flume and it obstructed the flow causing marked differences in flow and trans-port patterns in the transverse direction (Figure 4.8b). Upstream, this caused deposition of a674.4. ResultsFigure 4.7: Standard deviation for bed elevations ση for different bed sections. DEMs weredivided in ten 1-m2 sections and ση was computed for each of them. The down-stream end of the flume was at x = 0 m.sediment bar towards one side of the flume and erosion towards the other. The pattern wasinverted downstream, which indicated a shift in the thalweg with distance downstream andmaybe in the paths of sediment transport. After R3 (large pulse), the main changes in bed mor-phology occurred upstream where sediment deposited mostly over previously eroded areas(Figure 4.8c). Transverse features developed and pools got excavated, which were evident bythe first 10 h of R4 (Figure 4.8d). By the end of R4, the bed had gained considerable elevation,the upstream bar disappeared, transverse features were identified further downstream, and alateral bar developed downstream (Figure 4.8e). After R5, the upstream bed was undulatedand sequences of transverse features and depressions were evident and persisted until the end684.4. Resultsof the experiment (Figure 4.8f). The bed gained elevation in R6, but channel morphology re-mained almost unchanged at a large scale, except for the lateral bar downstream that reducedits area but became more prominent. A significant amount of the sediment fed into the channelwas not immediately transported and formed a sediment wedge near the upstream end of thebed, which expanded downstream and could have acted as a persistent in-channel source ofsediment for transport. Although the wedge started to develop early in R2, it was only evidentin DEMs of late runs (Figure 4.8e-f).Elevation(mm)Flowwedgewedgebarbarbarbarbarbartransverse featureFigure 4.8: Digital elevation models (DEMs) at six different times. We chose these casesfrom the 34 DEMs collected to summarize the evolution of bed topography at largeand intermediate scales. Bed elevations η are relative to the floor of the flume. Thedownstream end of the flume was at x = 0 m. Lateral bars and upstream sedimentwedge are delineated and examples of transverse features that intercalate with poolsare indicated.In general, ση was an indicator of bed morphology and it was large at times when thechannel developed large-scale bedforms like lateral bars. The large increase in ση upstreamduring R2 was due to the development of a lateral bar, the same as the overall increase inση observed downstream (at x < 4 m) through R3–R6. The decrease in ση upstream duringR3 could relate to the filling of previously degraded areas as sediment feed was transmitteddownstream and the wedge expanded. More moderate adjustments of ση , as those observedwith small sediment pulses in R4, could be related to the evolution of smaller bedforms liketransverse features and pools. Bed DEMs for 1 h and 10 h after the first pulse in R4 (Figure4.8c-d ) show the same large-scale bedforms (> 2 channel width) in both of them. Instead,smaller-scale bedforms (< 1 channel width) were more developed after 10 h than they wereright after the pulse. We present DEMs for the bed at both times together with bed surfacephotos at some specific locations (Figure 4.9) to relate changes in bed elevations η with the694.4. Resultsdevelopment of bed structures.Ten hours after the small pulse, transverse features that were barely visible after one hourbecame prominent, small pools were scoured, and bed structures became larger. Upstream (atx > 10 m), DEMs show a central channel, which developed transverse elevated features inter-calated with depressions under no feed (Figure 4.9a-b). Adjustments in the particle size of thebed surface over an upstream transverse feature can be appreciated on photos (Figure 4.9c-d).The feature became considerably coarser after 10 h and the connection between the coarsestgrains (> 22 mm, which includes light green, white, and blue) increased. The same photosshow the enlargement of a pebble-cluster, which development we suspect was an importantmechanism to increase bed roughness at small scales. Bed structures developed further down-stream (at x = 3–6 m) over a lateral channel (Figure 4.9e–f). Here, a stone line became evidentafter 10 h because of the deposition or excavation of coarse grains in between other coarsegrains, which were already there one hour after the pulse.To evaluate differences in textural adjustments on the bed surface and grain roughnessalong the flume, we estimated geometric mean grain size Dg on the surface for different bedsections (Figure 4.10). The bed surface became finer in the downstream direction, probablydue to selective transport and preferential storage of coarse sediment upstream. With episodicsediment feed regimes, changes in Dg were consistent with changes in sediment feed, so Dgbecame finer with sediment pulses and coarsened without feed. Adjustments with constantfeed were variable. In R2 some sections became coarser, whereas in R6 they either remainedunchanged or became finer.Although, small changes in ση were noticed at x ≈ 6 m from the downstream end (Figure4.7), large textural differences on the bed surface for this area can be appreciated in a sequenceof photos (Figure 4.11). The bed surface was coarse after 40 h of flow without sediment feed inR1 (Figure 4.11a) and remained coarse after 40 h of constant feed in R2 (Figure 4.11b). By thistime, a new cluster had developed, which indicates that the arrangement of grains was notinhibited by constant feed. The bed surface texture became significantly finer one hour afterthe large pulse in R3 (Figures 4.11c), which shows that fine gravels were rapidly transporteddownstream when fed in a large pulse. Although, many of the bed structures observed at theend of R2 (Figure 4.11b) were still present one hour after the large pulse (Figures 4.11c), thegrains that filled the spaces between them were significantly finer than at the end of R2. After39 h of no sediment feed, the bed surface re-coarsened with the evacuation of fine gravels andre-arrangement of coarse grains (Figure 4.11d).704.5. Discussion4.5 Discussion4.5.1 Hypothesis 1: Preferential deposition of coarse partially-mobile gravelsnear the feed source promote increased storage upstream and downstreamfining on the bed surfaceThis hypothesis is supported by an increase in the percent of mass stored from mass fed withgrain size within gravel fractions (Figure 4.1b) and by increases in cumulative mean changein bed elevation η (Figure 4.8) and Dg of the bed surface (Figure 4.10) with distance fromdownstream. During the experiment, the limit between partial and full mobility was stablearound 8 mm (Elgueta-Astaburuaga et al., 2017). The storage of gravels > 8 mm was larger thanthe storage of finer fully-mobile gravels, although the storage of sand was also significant(Figures 4.1 and 4.2). The increase in storage with grain size for gravel fractions is consistentwith grain-size dependence observed in their bedload rates (Elgueta-Astaburuaga et al., 2017).Whereas the storage of fine gravel was different among runs, the storage of coarser sedimentwas more stable. Sediment coarser than 8 mm, for which transport conditions ranged betweenpartial mobility and incipient motion, had positive mass balances. Very coarse gravel (> 16mm) was near incipient motion and when supplied, it got mostly deposited upstream. Thesegrain sizes moved at very low frequencies and mostly over short distances, so not many ofthem exited the flume. For example, they exhibited the same output in runs with no feed (R1and R7), even though, the effects of fines on the surface were expected to be stronger in R1due to an initial well-mixed bed. This indicates that very coarse grains were mostly depositedand moved at slow virtual velocities (Einstein, 1937). Gravel 8–16 mm was more mobile thancoarser material, as indicated by larger sediment outputs over runs with no feed and slightdecreases in the cumulative storage curve that were not evident for coarser grains. Whenfed, at least some gravel 8–16 mm was expected to move further downstream. These grainshad faster virtual velocities and reached the end of the flume more frequently than coarsergrains, but less frequently than fully-mobile gravel. Preferential storage caused an increasein the cumulative change in bed elevation η and Dg of the bed surface with distance fromdownstream (Figures 4.6 and 4.10).Sand did not behave in the same way as fully-mobile gravel (Figure 4.1 and 4.2). Theoutput of sand was significantly smaller than the output of fine gravel in runs without feed(R1 and R7) and the percent represented by stored mass from feed mass was considerablylarger for sand than for fine gravel. The transport and storage of sand was also more stableand did not change significantly with feed regime like in the case of fine gravel. More than60% of the sand that entered the flume during each run was deposited on the bed, which canbe related to hiding effects and infiltration. We did not measure infiltration rates for sand, butwe think infiltration was an active process. The significant storage of coarse gravels and thedevelopment of armor on the bed were expected to provide shelter for the finest fractions. Wedid not observe large areas covered by sand on the bed surface at the end of the experiment,714.5. Discussionbut we did notice the presence of sand (and fines) within larger grains. A significant amountof sand could have also got trapped within the coarse sediment wedge that formed upstream(Figure 4.8e-f). We think fine gravel were entrained more easily because of protruding moreand infiltrating less than sand.Dowsntream fining on the bed surface was clear at the end of the experiment (Figure 4.12).Near the upstream end, a large area of the bed surface was covered with grains under incipientmotion (22–45 mm, light green and white particles). Towards the center of the flume, the areaof the bed surface covered by white particles (32–45 mm) was considerably less than upstreamand more areas were covered by finer, but still partially-mobile material (8–22 mm, whichincludes yellow, red, and black grains). Near the downstream end, grains under incipientmotion were also present, but were less abundant. Instead, areas of the bed covered by fully-mobile gravel (4–8 mm, light blue and dark green grains) became more frequent. Downstreamfining have been previously reported over gravel beds under partial transport. Ferrer-Boixand Hassan (2015) found that downstream fining was flow dependent and it likely developedduring bank-full flows, which promoted some degree of selective transport, and could becomeless evident after larger floods.Although found in a considerably larger proportion upstream, coarse grains under incip-ient motion (e.g., > 22 mm, which includes light green, white, and blue) were found on thebed surface all along the flume. Some of these grains could have been already there at thebeginning of the experiment. Others could have been excavated from the bed as finer grainsgot mobilized (e.g., over R1 that had an output > 150 kg under no feed) or mobilized for shortdistances and organized into arrangements of grains and bed structures. An example can beappreciated in the sequence of photos at ∼6 m from downstream in Figure 4.11. Many of thewhite (32–45 mm) and all the blue (45–64 mm) particles remained within the area of the photo(< 1 m2) during R2 (constant feed) and R3 (1 pulse). Apparently, one blue particle that was atthe right edge of the photo at the end of R1 (Figure 4.11a) moved over a distance< 1 m and be-came part of an arrangement of grains identified at the end of R2 (Figure 4.11b). We think thespread of very large grains along the flume during the experiment was defined by their initialspread (they tended to remain close) and by size-selective transport conditions that promotedan increased frequency of coarse material upstream due to feed.Lag sediment deposits that become armored as a result of poorly sorted sediment supplyand size-selective transport have been reported in the field (Brumer and Montgomery, 2006),which is consistent with the sediment wedge that developed upstream during our experiment(Figure 4.8). The topography of the wedge was controlled by the way in which the sedimententered the channel. Initially, sediment feed concentrated in a pile, which could have causedthe development of lateral bars due to flow obstruction. Later, it spread better across thechannel, which might have promoted sequences of transverse features and depressions up-stream. There is field evidence that the sediment injection point influences spatial patterns ofaggradation–degradation and that the effects of sediment pulses are not restricted to aggra-724.5. Discussiondation, which can be localized promoting significant degradation over other areas (Gaeumanet al., 2017) as we observed.The resulting bed from our experiment was inherited for a subsequent experiment de-signed to study the effects of larger floods and bankfull flow duration on channel adjustments(Ferrer-Boix and Hassan, 2015). Sediment feed was constant at the same rate as in our exper-iment and they used the same bankfull flow discharge. The flow was ocasionally increasedto 1.4 times bankfull and the duration of bankfull flows was varied. In general, large floodscaused initial increase in bedload rate, decrease in bed slope, and increases in the amplitudeand wavelength of bedforms and in ση . Even though grain size statistics for bed surface didnot adjust significantly to flow regime (e.g., Dg = 15–17 mm), the degree of downstream grainsorting varied with flow and bed history. They explained a decrease in the degree of down-stream sorting by partial removal of the upstream wedge.4.5.2 Hypothesis 2: Constant feed, which makes sediment available moregradually, promotes larger sediment storage than sediment pulses becauseof a greater probability for sediment being sequestered in the bedThis hypothesis is supported by the large difference in sediment storage noticed between R3that received one large sediment pulse and runs with constant feed (R2 and R6), although vari-ability in the storage for runs with same feed regime indicates that initial bed characteristicsinfluenced the results. The largest contrast in storage was between R2 and R3 (Figure 4.1).R2 stored almost twice the mass stored in R3 because of larger storage of fine gravel, whichinstead exhibited significant negative mass balance in R3. Regardless of the presence of largescale bedforms at the beginning of R3, which were absent in R2, differences in bed slope andbed surface texture were small. Instead, these runs received contrasting feed regimes (constantvs. one large pulse), so we think the feed was largely responsible for differences in sedimentstorage. With constant feed (R2), sediment entered gradually. A significant amount of coarsematerial was deposited, which created a sediment wedge upstream that probably allowed forthe storage of fine sediment within the coarse material. Fully-mobile grains that moved down-stream could be deposited before reaching the end of the flume, to be entrained at later stages(i.e., bedload step migration). The time that it took for bedload to respond to constant sed-iment feed downstream (∼7 h, from Elgueta-Astaburuaga and Hassan (2017)) and the gradualadjustments of particle size on the surface (Figure 4.10) support this idea. Under constant feed,sediment transport processes were relatively slow and grains might have remained at rest forlonger periods of time (i.e., less interaction between moving grains) or moved for shorter dis-tances in their way downstream. As reported in vonFlotow (2013), dynamics of bed structuresand clusters were also active during constant feed (i.e., Figure 4.11b) and not exclusively dur-ing degradation without feed. Bed structures and clusters could have slowed the movementof fine gravel by forcing grains to deposit more often in their way downstream. These effectsmight have been reduced by bed surface fining after sediment pulses.734.5. DiscussionThe large pulse made a significant amount of fine gravel available in a short time, whichcaused significant surface fining (Figures 4.10). The response of bedload rate was also fasterthan with constant feed (∼0.5 h, from Elgueta-Astaburuaga and Hassan (2017)), indicating sed-iment transport processes occurred faster with the pulse. Fine sediment from the large pulsewas transmitted fast downstream and at 6 m from the downstream end (∼7 m from feed loca-tion), the bed surface got considerably finer one hour after the pulse (Figure 4.11c). The largepulse caused the development of well-delineated patches of fine sediment upstream, whereasfining was more extensive downstream. We think the large availability of fine gravel decreasedthe probability of grains getting trapped and could have also decreased the resting periods ofgrains due to the interaction with other grains. Collective dynamics (i.e., displacement or en-trainment due to grain collisions) have been observed to affect bedload transport significantly(Ancey et al., 2006; Heyman et al., 2013). The large pulse in R3 caused intensive sediment trans-port during an early stage, over which multiple interactions between grains were expected.We think this influenced the large negative mass balance for fine gravel observed for this run.Net storage decreased with pulse size and in R4 (four small pulses), fine gravel exhibitedpositive mass balance as in runs with constant feed. In Elgueta-Astaburuaga and Hassan (2017)we proposed that feed regimes for which the time required for the channel to reach dynamicequilibrium after a pulse Tr exceeds the recurrence interval of the pulse Tp, could show similarresponses to constant feed regimes. These results support this idea because for R4 Tp < Tr,whereas for R5 and R3 Tp > Tr (Elgueta-Astaburuaga and Hassan, 2017). Even though, in R5(two pulses) fine gravel exhibited negative mass balance as in R3, it was not as significantand total mass stored in R5 was similar to the mass stored in R6 that received constant feed.This result contradicts the hypothesis (H2) and indicates that bed slope and bed configurationinfluenced the mass of sediment stored during each run. Large differences in storage over runswith the same feed regimes are evidence of the influence of bed history and initial conditionson the results.Bed characteristics and configuration could have affected sediment transport and storagein many ways and at a range of scales. Differences in the availability of fully-mobile sedimentbetween R1 that started from a well-mixed bed and R7 that started from an armored bedprobably caused larger degradation during the first few hours of R1 (Figure 4.2). Besidesthe larger availability of fully-mobile sediment at the beginning of R1, the bed surface wassignificantly finer and did not exhibit bedforms, for which it was expected to be smoother thanit was at later stages of the experiment. This could have increased the intensity of movementfor coarse gravel (8–16 mm), which output in R1 was twice the output in R7, although in bothruns it was very small in comparison to that of fine gravel. Sediment > 16 mm moved veryoccasionally in both runs.Differences in storage among runs with constant feed (R2 and R6) were probably related tothe increase in bed slope due to preferential storage of coarse sediment. Between R2 and R6,bed slope increased from 0.017 to 0.022 m/m (Table 4.1), which could have increased transport744.5. Discussioncapacity under constant flow discharge. Cumulative storage (Figure 4.2 and 4.6) indicatesthat R6 started from a higher level of total mass stored than R2, although it started with alarger deficit in fine gravel, which was the most mobile fraction. The Dg of the bed surfacewas almost the same for both runs and the D90 was only slightly finer at the beginning of R6(Table 4.1), so we think textural differences do not explain patterns of storage observed forthese runs. The evolution of Dg (Figure 4.10) shows that at most bed locations, there were nobig textural changes between R2 and R6. Bed roughness estimated as ση exhibited differencesamong R2 and R6 for bed sections located at more than 10 m or less than 5 m from downstream.These differences were caused by the development of bars and bed features at a larger scalethan those found at the beginning of R2, which had a relatively flat channel with an armoredand structured bed. Any increase in roughness due to the development of a more complextopography apparently did not counteract the effects caused by the steeper bed slope in R6, sothe channel transported sediment more efficiently during R6. Other studies have also reportedthe importance of bed history on sediment transport patterns (e.g., Waters and Curran, 2012;Ferrer-Boix and Hassan, 2015).4.5.3 Hypothesis 3: Hysteresis in sediment transport-storage relations largelydepends on differences in bed surface texture and sediment availabilityThis hypothesis was supported by differences in the direction and magnitude of hysteresisobserved between R1-R2 and between R6-R7. The flat well-mixed bed at the beginning ofR1 was responsible for larger bedload rates during degradation for cycle R1-R2. Bedload rateswere larger during aggradation for cycle R6-R7 because of the increase in sediment availabilitycaused by the feed and maybe also because of bed surface smoothing. Differences in bedloadrate between aggradation and degradation stages were significantly smaller for cycle R6-R7because the bed texture was similar in both runs. Over a short range of storage, bedloadrates were the same during aggradation and degradation as in the first scenario proposed byLisle (2012). These occurred over a period of time when the bed surface texture and sedimentavailability did not change significantly (between a few hours before the end of R6 and a fewhours after the start of R7) and could be related to the time delay τ in downstream bedloadresponse to changes in feed. We think that cycle R6-R7 was more representative of naturalstreams because it started from a more complex and armored bed than cycle R1-R2, for whichthe initial well-mixed bed conditioned results. We think that bedload rates should be largerduring aggradation than during degradation, unless large differences on the bed texture andsediment availability change this situation. Our results support the idea that the state of thebed influences transport-storage relations (Madej et al., 2009; Pryor et al., 2011).The large pulse in R3 also caused larger bedload rates during aggradation as the bed sur-face became finer and more fine gravel was available for transport. The short duration ofsediment feed d f in smaller pulses relative to time delay τ, caused variability in the observedpatterns of hysteresis. Despite the large increase in sediment availability caused by pulses,754.6. Conclusionsbedload rates were larger during degradation after some of the small pulses in R4 becaused f ≤ τ. A similar situation was observed for the two pulses in R5. In our experiment, τmostly depended on feed regime (smallest with large pulses, largest with constant feed), butchanges in the bed state, slope, and morphology could have also influenced τ. Flow condi-tions, distance from feed location to flume output, and sediment texture could also affect τ,but were held constant during the experiment. Small cycles of hysteresis during constant feedwere observed within R6, which is consistent with Luzi (2014) that reported similar cycles forruns at dynamic equilibrium. In our case, large occasional bedload rates that exceeded thefeed rate caused degradation over a relatively short period of time.The two-phase transport–storage relation proposed for degrading channels by Lisle andChurch (2002) was not always observed under no feed. The relation proposed by Lisle andChurch (2002) consists of an initial phase were bedload rate remains high as the bed degradesfollowed by a phase in which armor development prevents degradation causing bedload rateto decrease. In our experiment, sediment transport–storage under no feed could either exhibita two-phase relation like that following the pulses in R5, transition directly into the secondphase as in R1 , or remain in the first phase for a long time like after the third pulse in R4(i.e., bedload rate was nearly constant for all levels of storage). Deviation from the two-phaserelation proposed for transport–storage in degrading channels have been noticed (Madej et al.,2009; Pryor et al., 2011) and explained by differences in the bed state.Size-selective sediment transport promoted the deposition of coarse material upstream,which caused a general increase in cumulative storage over the experiment. In previousstudies (Madej et al., 2009; Pryor et al., 2011), sediment storage after cycles of aggradation–degradation did not return to the same level it had before the cycle, but remained at higherlevels. The effects of aggradation at a large scale (e.g., development of bedforms, the upstreamwedge, overall increase in bed slope, cumulative mass balance, and mean change in bed el-evation) were persistent. This is probably related to bed armoring and structuring in poorlysorted beds under partial mobility, which counteracts bed degradation by stabilizing the bedsurface.4.6 ConclusionsWe found that patterns of sediment storage were significantly affected by partial mobility,sediment feed regime, and bed characteristics. Partial mobility caused size-selective storageof coarse material and sand within it. Evidence of this was an increased bed elevation by theend of the experiment that was larger upstream and downstream fining on the bed surface.Sediment supply regime affected the mass of sediment stored in each run, which was largerduring constant feed. Bed characteristics significantly influenced the temporal response ofsediment storage, especially for fine gravel that was the more responsive size fraction. Sedi-ment transport–storage relations were also influenced by sediment supply regime. Whereasconstant feed produced a very mild relationship that could (or could not) exhibit small cycles764.6. Conclusionsof hysteresis, sediment pulses caused large cycles. Differences in the direction of hysteresis inbedload rates respond to differences in bed surface texture and sediment availability. Spatialpatterns of sediment storage and the evolution of large-scale bedforms were not explainedby feed regime. We think they responded to the topography of a sediment wedge createdupstream due to size-selective transport and storage.774.6. ConclusionsFigure 4.9: Evolution of small-intermediate scale bedforms after the first small pulse inR4. (a) DEM of the bed one hour after the first small pulse in R4. (b) DEM tenhours after the pulse. Examples of bed features are presented with roman numbers:(i) transverse feature, (ii) stone cluster, (iii) stone line, and (iv) small arrangementof grains. The downstream end of the flume was at x = 0 m. (c–f) Bed surfacephotographs showing the evolution of bed features i–iv between 1–10 h after thepulse.784.6. Conclusions01020mmR1-no feed R2-constant R3-1 pulse R4-4 pulses R5-2 pulses R6-constant R7-no feedx = 1.5 m01020mmx = 3 m01020mmx = 4.5 m01020mmx = 6 m01020mmx = 7 m01020mmx = 8.5 m0 40 80 120 160 200 240 280Time (h)01020mmx = 10 mFigure 4.10: Evolution of geometric mean particle size Dg on the bed surface for sevenbed sections along the flume. The downstream end of the flume was at x = 0 m.794.6. ConclusionsFigure 4.11: Evolution of bed surface texture at ∼6 m from downstream between the endof R1 and the end of R3. (a) The bed surface was coarse by the end of R1 that hadno feed. (b) After 40 h of constant feed in R2, there was no significant fining on thesurface. (c) In contrast, one hour after the large pulse of R3, significant fining wasobserved. (d) Forty hours after the large pulse, the bed surface was coarse again.804.6. ConclusionsFigure 4.12: Downstream fining at the end of the experiment. Photos of the bed surface atthree locations. The downstream end of the flume was at x = 0 m.81Chapter 5Concluding remarksThe goal to study the effects of episodic sediment supply on channel adjustment was accom-plished by analyzing an extensive data set on bedload transport and bed properties, collectedsystematically by the author during a 280-h long flume experiment with constant flow, butchanging sediment feed. The long duration of each run allowed assessing the effects of feedregime on bedload transport statistics at a wide range of time scales. The use of a wide rangeof grain sizes allowed the effects of the feed on size-selective bedload transport and storageto be studied. To collect fractional sediment transport data the video-based method presentedin (Zimmermann et al., 2008) was improved by increasing the resolution considerably to accu-rately detect grains as small as 1 mm. Obtaining representative grain-size distributions of thebed surface was possible by systematically taking photographs of the bed surface along theflume, which alllowed an accurate identification of gravel grain sizes. Research was directedby the following questions, for which summarized answers are provided in the next subsec-tions: (1) which episodic sediment feed regimes could be represented by constant feed and atwhich time scales?, (2) how do bed history and bed state affect channel reponse to changes insediment feed regime?, and (3) what are the consequences of size-selective bedload transporton this response?The results support the idea that sediment supply is a first order control in mountainstreams, for which evidence had been provided in previous experiments and field studies(e.g., Hassan et al., 2006, 2008). The variables that responded more consistently to sedimentfeed regime were bedload transport rate and bed surface texture. Sediment feed promoted bedsurface fining and increased bedload rates as described in previous studies (Lisle and Madej,1992; Madej et al., 2009), whereas no feed caused bed surface coarsening and decreased bedloadrates (e.g., Dietrich et al., 1989).Cumulative storage of sediment, which had been observed under partial transport (e.g.,Brumer and Montgomery, 2006), caused an overall increase in bed slope over the experiment.Bed slope response did not necessarily coincide with changes in feed and thalweg slope be-came nearly stable by the fifth run in a sequence of seven runs, despite changes in feed rate.The poorly sorted sediment and near bank-full flow discharge promoted partial sediment825.1. Which episodic sediment feed regimes could be represented by constant feed and at which timescales?transport, which resulted in bed surface armoring and preferential storage of coarse mate-rial. The effects of cumulative storage and bed slope increase on channel response to changesin feed were tested by comparing the results for runs with the same feed regimes but startedfrom different initial conditions.5.1 Which episodic sediment feed regimes could be represented byconstant feed and at which time scales?The assumption of constant feed might not be suitable to model streams that are subjected tolarge, infrequent sediment episodes as in R3 and R5, but could be appropriate to study chan-nels that receive more frequent pulses as in R4. As verified, channel adjustment to changes insediment supply regime was affected by the magnitude and frequency of sediment feed. Sed-iment pulses caused significant fining on the bed surface, which resulted in larger and fasterincreases in bedload transport rate dowsntream than with constant feed. As fully-mobile sed-iment evacuated, the bed surface re-coarsened, which limited bedload transport decreasingbedload rate as in runs without sediment feed. Larger sediment pulses produced stronger re-sponses in bedload rate, but the time it took for bedload rate to stabilize around a low constantmean after the pulse (relaxation time Tr) did not depend on pulse size. If Tr exceeded the timebetween pulses Tp as for R4, the response exhibited similarities to the response for constantfeed, especially at large time scales (2Tp to run scale). This was supported by similar spansin the variability of cumulative departures from mean bedload rate and the lack of statisticaldifferences in bedload rate signals for runs with constant feed and R4, which was indicatedby results from L-ratio tests for temporal resolution ≥ 30 min. At short timescales (< Tp), theeffects of each sediment pulse were evident and very different from those of constant feed (i.e.,faster response, trend inflection caused by no feed).The memory structure for total bedload rate was also affected by sediment feed regime.Pronounced trends in bedload rate caused by episodic feed increased long-term memory. Thethree stages of fluctuation proposed by Ma et al. (2014) were only observed for runs with con-stant feed. Episodic feed caused an increase in the range of scales with long-term memory(invariant stage of fluctuation) and the absence of a memoryless stage. Another difference be-tween constant and episodic feed regimes was that constant feed promoted larger sedimentstorage, although changes in the initial bed conditions significantly influenced the results.5.2 How do bed history and bed state affect channel reponse tochanges in sediment feed regime?Bed state and bed slope conditioned channel adjustments to changes in sediment feed sig-nificantly. This was supported by differences in temporal patterns of bedload rate betweenruns with the same feed regimes or after pulses with same size. R1 and R7 had the samefeed regimes and initial bed slope, but started from very different bed states that dictated835.3. What are the consequences of size-selective bedload transport on this response?sediment availability (well-mixed and armored bed respectively). This caused significant dif-ferences in the patterns of bedload transport and storage among them. R2 and R6 had samefeed regimes and initial armored beds, but started from very different bed slope and levels ofcumulative sediment storage. Even though, no statistically significant differences were foundwith L-ratios between them at 5 min resolution, the range of bedload rates was higher duringR6, bedload scaling statistics (i.e., H) indicated stronger memory, and patterns of sedimentstorage indicated that the channel transfered fully-mobile gravel more efficiently during thisrun. Transport–storage relations indicated R6 was closer to mass equilibrium as bedload rateoccasionally exceeded feed rate causing small cycles of hysteresis as those described in Luzi(2014).The evolution of bed morphology was dictated by the way in which sediment entered thechannel. This was more localized at the beginning, but became better spread in the cross-section later during the experiment. This caused the development of lateral bars early in theexperiment, followed by the appearance of smaller transverse features intercalated with de-pressions. Mean changes in bed elevation responded to sediment feed, although in all runs alarge amount of sediment was stored near the feed source because of size-selectivity in flowcompetence. The cumulative storage of sediment upstream increased bed slope, which in-creased the intensity of bedload transport towards the end of the experiment. These effectswere likely to inluence relaxation times Tr.5.3 What are the consequences of size-selective bedload transporton this response?Grain-size dependence in patterns of bedload transport and storage was almost the same re-gardless of sediment feed regime. Gravel fractions were affected by size-selective transportand the limit between relative partial and full mobility (Wilcock and McArdell, 1993) remainednearly unchanged around 8 mm. The memory structure for total bedload reflected that forfully-mobile gravel (2–8 mm), which dominated bedload transport. Memory strength de-creased with grain size, except for sand that behaved more stochastically than fine gravels.The decrease in memory for partially-mobile gravel was related to their occasional movement,which resulted in preferential storage of coarse grains near the feed source upstream as incoarse lag formations reported in the field (Brumer and Montgomery, 2006). These conditionspromoted increased storage upstream and downstream fining on the bed surface throughoutthe experiment.Although sand was fully-mobile, it behaved differently from fine gravel, which was proba-bly related to the higher potential for sand to be affected by hiding effects and infiltration. Themovement of sand was more stochastic, but this cannot be explained by a lack of movementbecause transport rate time series at 1 s exhibited little intermittency for sand. Mass balancesrevealed more than 60% of the sand fed got stored, which could have got trapped in the up-stream wedge or within larger grains and structures along the bed. Stored sand could become845.4. Limitations of the studyavailable later, if the movement of coarse grains exposed it to the flow. The movement of sandmight have been more influenced by these highly stochastic dynamics and less affected bylonger scale processes such as bedform or pulse evolution.5.4 Limitations of the studyThe experimental design was complex in comparison to many flume experiments (we used apoorly sorted gravel bed with relatively long and varied history of sediment feed), but in com-parison to natural rivers, flumes are always a simplified case. Here, I provide some examplesof factors that increase complexity in natural streams, but were neglected in the experiment.Streams are subjected to variations in flow discharge, which affect channel response to sedi-ment inputs (Sutherland et al., 2002), but in the experiment flow was held constant to isolatethe effects of feed. The flume had a fixed width, whereas many stream have erodable banks.The work of (Eaton and Church, 2004) shows that in unconstrained channels variations in widthcan be important (even more important that the adjustments of particle size). The glass wallsof the flume were also very different from stream banks, which can be irregular and providedifferent types of roughness elements (e.g., vegetation). The presence of large wood (see Mont-gomery and Pie´gay (2003) for examples) and channel constrictions (Chartrand, 2017), which cansignificantly influence channel morphology and spatial variability of flow and sediment trans-port, was also disregarded. Natural rivers are very complex environments, where even livingorganisms can be responsible for changes in sediment supply and channel morphology. Ex-amples of this are salmons that mobilize a significant amount of gravel for spawning (Hassanet al., 2008) and beavers that build dams (Naiman et al., 1986).The main limitations of the experimental design were the lack of replicates and the differ-ences in the initial bed among runs that challenged comparisons. We only repeated constantfeed and no feed regimes. If we had repeated all sediment feed regimes, we could have gotan idea of the variability within them increasing the certainty of comparisons among them.For statistical tests among bedload rate signals, the lack of replicates made it impossible toapply paired t-tests, so a general least-squares model and likelhood L-ratio tests were used.The sequence of runs caused differences in the initial bed that challenged comparisons, but asit allowed for a more realistic bed to develop and to compare among same feed regimes thatstarted from different initial conditions, this limitation was also a strength. We were careful toconsider the influence that these differences had in the results and used them to explain them.Regarding data collection, limitations included the relatively low temporal resolution ofbed data relative to transport data, misdetection of grains < 1 mm with video-based transportmethod, and inability to distinguish among grain sizes < 2.8 mm on bed photographs. As theintensity of bed adjustments decreased with time from changes in sediment feed, bed data wascollected more often when adjustments to changes were more active to optimize results. Mis-detection of small grains might have affected results for sand, although errors were expectedto be small because grains < 1 mm comprised only 2–3% of the sediment mixture. Grain-size855.5. Future research directionsdistributions for the bed surface were truncated at 2.8 mm, which was expected to cause onlya small systematic error that would not affect the temporal patterns of textural adjustment.5.5 Future research directionsThis study increases the understanding of the role of sediment feed regime on channel adjust-ment, but there are still topics that remain unexplored. As mentioned, not all feed regimeswere replicated and those that were, started from different initial beds. Repeating the exactsequence of runs followed in the experiment would give a good idea of how much variabilityshould be attributed to feed regime and how much of it is intrinsic to the stochastic nature ofsediment transport processes. It would also allow the use of more formal statistical tests fordifferences in bedload and bed characteristics among feed regimes. Another possibility wouldbe to use the same feed regimes, but organized in a different sequence, which would give abetter idea of the role of bed history and how important are initial bed conditions. One couldtest, for example, whether a large pulse mobilizes more sediment when introduced towardsthe end of the experiment when cumulative effects of feed on bed slope and storage were thelargest.Although the effects of sediment feed texture relative to bed texture have been analyzed(Curran and Wilcock, 2005; Venditti et al., 2010), it would be interesting to run the same experi-ment, but with a finer sediment feed texture than bed texture to see how this affects channelresponse to changes in feed, grain-size dependence, and downstream fining on the bed sur-face. One could expect the permanent introduction of finer sediment to result in more intensesediment transport and less sediment storage, as the bed surface becomes smoother and theproportion of partially mobile sediment is reduced. Or, it could be expected for the bed surfaceto coarsen even more after finer sediment pulses as observed by Johnson et al. (2015).As described in Gaeuman et al. (2017) and observed in this experiment, the sediment injec-tion point influences the spatial patterns of bed aggradation and degradation, which conditionchanges in bed morphology. It would be interesting to study these effects in an experimentwere sediment feed location is varied. Feed location could vary in the transverse direction(e.g., localized vs. well-spread, at one side vs. the other). Two contrasting feed regimes couldbe used to compare between the effects of feed location and feed regime. One could expectthat differences in feed location would influence the development of large-scale bedforms,whereas feed regime would dictate the overall intensity of changes and their temporal signal.The location of sediment feed could also be varied along the flume (i.e., upstream vs. center)to also discuss the effects of changes in feed upstream of feed location.Although results supported that constant feed promoted larger sediment storage, theywere likely influenced by the cumulative increase in bed slope. It would be interesting totest this hypothesis starting each run from the same initial bed conditions. For simplicity, theexperiment could first use uniform sediment and only two contrasting feed regimes (i.e., con-stant vs. one large pulse), which could be replicated. The same experiment could be done865.5. Future research directionsusing a poorly sorted mixture, like the one used here, to test the effects of sediment sorting inthe results.To isolate the effects of feed regime, the experiment was conducted under steady flow con-ditions, which are not likely found in nature. Flow discharge varies within a flood, seasonally,and from year to year. Previous studies have shown that hydrologic regime influences the de-gree of armor (e.g., Hassan et al., 2006) and that flood recurrence interval influences the degreeof downstream sediment sorting (Ferrer-Boix and Hassan, 2015). Hysteresis in bedload rate iscommonly observed with hydrographs (e.g., Hassan et al., 2006; Mao, 2012) because of differ-ences in bed state and sediment availability between the falling and rising limbs. It wouldbe interesting to study the effects of sediment feed under unsteady flow, but a simple designmight be more suitable to start and separate the effects of feed from those of flow. One pos-sibility would be to use a simple unsteady hydrograph and repeat it, but using feed regimesthat contrast in their magnitude and frequency as the ones used in this study (i.e., constantvs. one large pulse). Another possibility would be to study the effects of the timing of sedi-ment feed on channel adjustments under unsteady flow. In this case one could use the samehydrograph and besides constant feeding and introducing one large pulse in the rising limb,the large pulse could be introduced instead during the falling limb in some runs for compar-isons. Ferrer-Boix and Hassan (2015) studied channel response to water pulses under constantfeed and how flood recurrence interval affected these results. They inherited the bed from thisexperiment and subjected it to constant feed, but increased the flow occasionally changing therecurrence interval. It would be interesting to further explore the influence of flood recurrenceinterval, but using also episodic feed regimes. One could explore, for example, which combi-nations of flood magnitude-duration and recurrence interval are more effective in removingthe signal of a large sediment pulse in bed storage.Changes in land cover due to human activities influence sediment sources and sedimentsupply to streams from local to basin scales. The construction and removal of dams affect sed-iment supply to downstream reaches (e.g., Smith and Mohrig, 2017). Forest activities, whichinclude construction of roads and deforestation near stream banks, can provide additionalsources of sediment to channels (e.g., Croke et al., 1999; Reid and Hassan, 2016). Physical model-ing is a good alternative to explore the effects of human activities on river systems, especiallyconsidering that economic development is usually accompanied by changes on land uses andcreates new challenges for river management. 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