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Channel stability in alluvial gravel-bed streams MacKenzie, Lucy 2019

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Channel stability in alluvial gravel-bed streamsbyLucy MacKenzieB.Sc., University of British Columbia, 2012M.Sc., University of British Columbia, 2014A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Geography)The University of British Columbia(Vancouver)July 2019c© Lucy MacKenzie, 2019The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Channel stability in alluvial gravel-bed streamssubmitted by Lucy MacKenzie in partial fulfillment of the requirements for thedegree of Doctor of Philosophy in Geography.Examining Committee:Brett Eaton, GeographySupervisorMarwan Hassan, GeographySupervisory Committee MemberMatthias Jakob, BGC EngineeringSupervisory Committee MemberNicholas Coops, ForestrySupervisory Committee MemberMichele Koppes, GeographyUniversity ExaminerRoland Stull, Earth, Ocean and Atmospheric SciencesUniversity ExamineriiAbstractAlluvial fans, conic depositional landforms that develop where headwater streamsoutlet into a main valley, are desirable locations for development in mountainousregions worldwide. Alluvial fans may become hazardous during high flow events;the relatively high gradient and the abundance of loosely packed sediment allowsalluvial fan channels to undergo rapid morphodynamic change, putting borderinginfrastructure at great risk. Despite these hazards, our understanding of channeldynamics on alluvial fans remains limited. Through physical modelling, this thesisinvestigates the processes contributing to channel stability in such environments.Using three sets of paired experiments, I show that channel stability is mediated bythe mobility of the largest grains in the channel. Pairs of experiments were identicalin all regards (i.e. discharge, sediment supply, gradient, median grain size), theonly difference was a slight increase in the proportion of large grains found in thebed material, while the median sediment size for the experimental pairs remainedessentially the same. Overall, I found that channels with bed material containingfewer large grains experienced two to four times as much erosion and depositionacross a range of discharges and rates of sediment supply.These findings contradict the conventional models of channel stability, that usethe median grain size to represent the bed surface; these models commonly as-sume that streams undergo morphodynamic change once that grain size is mobile.My experiments demonstrate that channel stability is linked to the mobility of thelargest grains, not the median size. Using high resolution models of the bed sur-face, I show that the channels containing the greater proportion of large grainstend to be more stable due to their increased frequency at the bed surface. Basedon these results, I propose a three phase model of channel stability wherein theiiithresholds between stable/dynamically stable and dynamically stable/unstable aregoverned by the thresholds of entrainment and full mobility of the largest grains,respectively. This new model of channel stability could improve our capacity topredict when catastrophic events may occur in steep, alluvial channels.ivLay summaryLarge flood events can have devastating consequences for nearby communities dueto rapid channel widening and overbank flooding. In this thesis I investigate whatprocesses control when steep, gravel-bed channels will undergo significant bankerosion using a series of stream table experiments. By increasing the proportion oflarge grains in the bed material of the channel I show that channel stability is linkedto the mobility of these grains; depending on the discharge and upstream sedimentsupply, two to four times more erosion and deposition occurs when fewer largegrains are present on the bed surface. These results have important implicationsfor predicting under what flow conditions we may expect significant bank erosionto occur in a given channel.vPrefaceThis dissertation presents research conducted by Lucy MacKenzie under the su-pervision of Dr. Brett Eaton. Lucy MacKenzie was the primary researcher andwas responsible for the main study design, data collection, analysis, interpretation,and writing of the content. Sections of this dissertation have been published oraccepted in peer-reviewed journals, as listed below.A version of Chapter 2 has been published: MacKenzie, L., Eaton, B., Church,M. (2018). Breaking from the average: Why large grains matter in gravel-bedstreams. Earth Surface Processes and Landforms 43(15) 3190-3196. Lucy MacKen-zie wrote the manuscript which was edited and reviewed by the co-authors.A version of Chapter 5 has been published: MacKenzie, L., Eaton, B. (2017).Large grains matter: contrasting bed stability and morphodynamics during twonearly identical experiments. Earth Surface Processes and Landforms 42(8) 1287-1295. Lucy MacKenzie conducted the experiments, analyzed the data and wrotethe manuscript, with guidance from B. Eaton.A version of Chapter 6 has been accepted with revisions in the journal EarthSurface Processes and Landforms. Lucy MacKenzie conducted the experiments,analyzed the data and wrote the manuscript, with guidance from B. Eaton.viTable of contentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . . 52 Conceptual basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Flow resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Sediment entrainment and transport . . . . . . . . . . . . . . . . 102.4 Channel stability . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16vii3 Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.1 Adjustable-Boundary Experimental System (A-BES) . . . . . . . 193.2 Experimental procedure and data collection . . . . . . . . . . . . 203.3 Model design and scaling . . . . . . . . . . . . . . . . . . . . . . 223.4 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 Summary of experiments . . . . . . . . . . . . . . . . . . . . . . . . 284.1 Paired experiments (Chapter 5 and 6) . . . . . . . . . . . . . . . . 284.1.1 Overview of paired experiments . . . . . . . . . . . . . . 284.1.2 Channel evolution in the paired experiments . . . . . . . . 314.2 Pseudo-recirculating sediment experiment (Chapter 7) . . . . . . 344.2.1 Overview of the pseudo-recirculating sediment experiment 345 Identifying the large grain effect . . . . . . . . . . . . . . . . . . . . 385.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.2 Summary of experimental design . . . . . . . . . . . . . . . . . . 405.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496 Validating the large grain effect . . . . . . . . . . . . . . . . . . . . 516.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.2 Summary of experimental design . . . . . . . . . . . . . . . . . . 536.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.3.1 Channel evolution . . . . . . . . . . . . . . . . . . . . . 536.3.2 Morphodynamic change . . . . . . . . . . . . . . . . . . 546.3.3 Bedload and surface grain size distributions . . . . . . . . 576.3.4 Shear stress and stream power . . . . . . . . . . . . . . . 616.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626.4.1 Persistence across discharges . . . . . . . . . . . . . . . . 636.4.2 Persistence across rates of sediment supply . . . . . . . . 656.4.3 Factors governing stability . . . . . . . . . . . . . . . . . 666.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71viii7 Characterizing the large grain effect . . . . . . . . . . . . . . . . . . 747.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787.2.1 Characterizing roughness . . . . . . . . . . . . . . . . . . 787.2.2 Summary of experimental design . . . . . . . . . . . . . 807.2.3 Surface texture analysis . . . . . . . . . . . . . . . . . . 807.3 Results: Morphologic change . . . . . . . . . . . . . . . . . . . . 837.4 Results: Surface texture . . . . . . . . . . . . . . . . . . . . . . . 857.4.1 Grain size distribution . . . . . . . . . . . . . . . . . . . 857.4.2 Bed elevations . . . . . . . . . . . . . . . . . . . . . . . 857.4.3 Variograms . . . . . . . . . . . . . . . . . . . . . . . . . 917.5 Surface texture and morphologic activity . . . . . . . . . . . . . . 947.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957.6.1 Surface roughness and flow characteristics . . . . . . . . 1017.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1038 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114A DEMs of difference . . . . . . . . . . . . . . . . . . . . . . . . . . . 127B Sediment properties tables . . . . . . . . . . . . . . . . . . . . . . . 134C Flow modelling results tables . . . . . . . . . . . . . . . . . . . . . . 137D Statistical results tables . . . . . . . . . . . . . . . . . . . . . . . . . 141E Model of stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146E.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146E.2 Predicting the immobile fraction . . . . . . . . . . . . . . . . . . 147E.3 Integrating the immobile fraction . . . . . . . . . . . . . . . . . . 148E.4 Calculating the immobile fraction . . . . . . . . . . . . . . . . . 149ixList of tablesTable 3.1 Grain sizes given in mm for the two bulk mixtures. . . . . . . . 24Table 4.1 Summary of the experimental conditions for the paired experi-ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Table 4.2 Discrepancies in results for experiments GSD1a and GSD2a be-tween Chapter 5 and 6. . . . . . . . . . . . . . . . . . . . . . 30Table 6.1 Summary of total cumulative morphodynamic change for eachexperiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Table 7.1 Standard deviation (in m), skewness and kurtosis for the entirebed over time . . . . . . . . . . . . . . . . . . . . . . . . . . 88Table B.1 Sediment properties of GSD1a and GSD2a . . . . . . . . . . . 134Table B.2 Sediment properties of GSD1b and GSD2b . . . . . . . . . . . 135Table B.3 Sediment properties of GSD1c and GSD2c . . . . . . . . . . . 136Table B.4 Sediment properties of the pseudo-recirculating experiment. . . 136Table C.1 Hydraulic properties of GSD1a and GSD2a . . . . . . . . . . . 138Table C.2 Hydraulic properties of GSD1b and GSD2b . . . . . . . . . . 139Table C.3 Hydraulic properties of GSD1c and GSD2c . . . . . . . . . . . 140Table C.4 Hydraulic properties of the pseudo-recirculating experiment . . 140Table D.1 Linear regression results for temporal trends in bedload and bedsurface grain sizes for GSD1a and GSD2a using the data pro-cessing techniques of Chapter 5 . . . . . . . . . . . . . . . . . 141xTable D.2 T-test results comparing grain sizes of bedload and surface be-tween paired experiments using the data processing techniquesof Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 142Table D.3 Linear regression results for temporal trends in bedload grainsizes for all paired experiments. . . . . . . . . . . . . . . . . 142Table D.4 Linear regression results for temporal trends in surface grainsizes for all paired experiments. . . . . . . . . . . . . . . . . 143Table D.5 T-test results comparing grain sizes of bedload and surface be-tween paired experiments. . . . . . . . . . . . . . . . . . . . . 143Table D.6 Linear regression results for temporal trends in surface texturevariables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144Table D.7 Linear regression models results for reach-averaged morphody-namic change versus surface texture indices . . . . . . . . . . 144Table D.8 Linear regression models results for morphodynamic changeversus surface texture indices at each cross section . . . . . . . 145xiList of figuresFigure 1.1 Cougar Creek before and after the June 2013 flooding . . . . 2Figure 2.1 Stable, dynamically stable and unstable channel definitions . . 14Figure 2.2 Bed surface stability at the boundaries between channel stabil-ity classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 3.1 Adjustable-Boundary Experimental System . . . . . . . . . . 20Figure 3.2 Grain size distributions of the two bulk mixtures . . . . . . . 23Figure 4.1 DEMs of difference for GSD1a and GSD2a . . . . . . . . . . 31Figure 4.2 Specific discharge at hour 8 for GSD1a and GSD2a . . . . . . 32Figure 4.3 DEMs of difference for GSD1b and GSD2b . . . . . . . . . . 33Figure 4.4 Specific discharge at hour 8 for GSD1b and GSD2b . . . . . . 34Figure 4.5 DEMs of difference for GSD1c and GSD2c . . . . . . . . . . 35Figure 4.6 Specific discharge at hour 8 for GSD1c and GSD2c . . . . . . 35Figure 4.7 DEM of difference and specific discharge shown for pseudo-recirculating sediment experiment . . . . . . . . . . . . . . . 37Figure 5.1 Detail of hillshaded DEMs for GSD1a and GSD2a at 8 hrs. . . 41Figure 5.2 Cumulative sediment output and bedload transport rate throughtime for GSD1a and GSD2a . . . . . . . . . . . . . . . . . . 42Figure 5.3 Load and surface grain sizes for GSD1a and GSD2a . . . . . 43Figure 5.4 Mean surfaceD50 andD90 through time for GSD1a and GSD2a44Figure 5.5 Histograms of shear stress values for GSD1a and GSD2a . . . 45xiiFigure 5.6 The ratio of the texture of the transported material to the bedsurface for GSD1a and GSD2a . . . . . . . . . . . . . . . . . 48Figure 6.1 Cumulative morphodynamic activity (M) and cumulative changesin sediment storage (∆S) in m3 over time. . . . . . . . . . . . 55Figure 6.2 Hourly morphodynamic activity (M) and hourly changes insediment storage (∆S) in m3 over time. . . . . . . . . . . . . . 55Figure 6.3 Cumulative sediment output (Qb,out) and cumulative net sedi-ment output (Qb,out Net) over time. . . . . . . . . . . . . . . . 57Figure 6.4 Comparison of bedload GSD between paired experiments. . . 58Figure 6.5 Bedload d50 and d84 over time for all experiments . . . . . . . 58Figure 6.6 Comparison of surface GSD between paired experiments. 95%confidence interval bounds, calculated using the method pre-sented in Eaton et al. (2019), have been added to the distribu-tions as overlying polygons to show the range of uncertaintyassociated with a sample of 200 grains. . . . . . . . . . . . . 59Figure 6.7 Surface D50 and D84 over time for all experiments . . . . . . 60Figure 6.8 Ratio of surface D50 and D84 to bedload d50 and d84. . . . . . 61Figure 6.9 Boxplots showing dimensionless shear stress calculated bothD50 and D84 . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure 6.10 Boxplot comparing measurements of unit stream power . . . . 63Figure 6.11 Morphodynamic change versus shear stress and surface/bed-load grain size using both the D50 and the D84. . . . . . . . . 68Figure 6.12 Morphodynamic change as a function of relative roughness. . 70Figure 7.1 DEM of difference between initial and final channels overlaidwith location of cross sections at which Photoscan models ofthe surface were created. . . . . . . . . . . . . . . . . . . . . 81Figure 7.2 A) Sediment input and output; B) Morphologic activity . . . . 81Figure 7.3 Examples of original DEM (left) and orthomosaic (right) forXS5 after 15 minutes of flow. . . . . . . . . . . . . . . . . . 82Figure 7.4 Total morphologic activity for each cross section through time 84xiiiFigure 7.5 Average surface grain size distributions of all cross sectionsgiven for each 15 minute interval of the experiment . . . . . . 86Figure 7.6 Temporal trends of the D50, D84 and the sorting index (σ ) forall cross sections over time . . . . . . . . . . . . . . . . . . . 86Figure 7.7 Plots showing the probability distribution functions and the av-erage standard deviation of the entire bed . . . . . . . . . . . 87Figure 7.8 Examples of detrended DEMs of XS5 after the first 15 mincreated using a range of averaging filter sizes. . . . . . . . . . 90Figure 7.9 Standard deviation at end of experiment for all cross sectionsacross a range of averaging filter sizes. . . . . . . . . . . . . . 91Figure 7.10 Temporal trends of the standard deviation, skewness and kurto-sis values from bed elevations distributions of all cross sectionsover time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Figure 7.11 Average variograms for all cross sections given for each timewith the regression lines for the fractal dimensions at the grainand bedform scales plotted. . . . . . . . . . . . . . . . . . . 93Figure 7.12 Range of Hurst Exponent values for grain and bedform scalesfor all cross sections through time. . . . . . . . . . . . . . . . 94Figure 7.13 Plots showing the relationship between total morphodynamicchange and reach-averaged surface roughness indices . . . . . 96Figure 7.14 Plots showing the relationship between morphodynamic changeand surface roughness indices for all cross sections . . . . . . 97Figure 7.15 Total morphologic activity versus relative roughness, shown asa function of the reach-averaged D84 and σz. . . . . . . . . . . 102Figure A.1 Hourly DEMs of difference for GSD1a . . . . . . . . . . . . 128Figure A.2 Hourly DEMs of difference for GSD2a . . . . . . . . . . . . 129Figure A.3 Hourly DEMs of difference for GSD1b . . . . . . . . . . . . 130Figure A.4 Hourly DEMs of difference for GSD2b . . . . . . . . . . . . 131Figure A.5 Hourly DEMs of difference for GSD1c . . . . . . . . . . . . 132Figure A.6 Hourly DEMs of difference for GSD2c . . . . . . . . . . . . 133Figure E.1 A plot of the function based on Wilcock (1997a) . . . . . . . 147xivFigure E.2 Example of a bed surface grain size distribution . . . . . . . . 149Figure E.3 Critical shear stress values calculated using the hiding functionproposed by Wilcock and Crowe (2003) . . . . . . . . . . . . 150Figure E.4 Fraction of the bed immobile at the entrainment threshold ofthe D50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151Figure E.5 Fraction of the bed immobile at the threshold of full mobilityof the D50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Figure E.6 Fraction of the bed immobile at the threshold of full mobilityof the D84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153xvAcknowledgmentsI cannot understate the importance of having both strong academic support as wellas unfaltering community support from outside the institution to finish a PhD the-sis. I am very fortunate to have had both in equal parts.Thank you, Brett Eaton – you are a role model, mentor, supervisor and friend.You gave me the opportunity to pursue this project and for that I am incrediblythankful. While you have shaped much of my learning over the last decade, youhave also given me the space to pursue my independence as a researcher. I lookforward with excitement to our future as colleagues.A huge thank you must also go out to the fellow graduate students who havesupported me along the way. To my lab members, Anya Leenman, Will Booker,Caitlin Tatham, David Adams and Sarah Davidson, you have not only helped meto collect and analyze data, refine my arguments and produce the best research Icould, you have also been there as friends whenever I needed you. I also acknowl-edge others outside of my lab group, in particular David Reid, Leonora King, MarcTadaki, Shawn Chartrand and Ashley Dudil. You have all contributed in some wayto this thesis and I never could have finished without your support.I am grateful for the support of my committee members, Matthias Jakob, Mar-wan Hassan and Nicholas Coops. You have dedicated your time and attention tomaking sure I have produced the best work I can – I have learned so much fromeach of you in the process. There are several other faculty members outside ofmy committee I would like to thank: Dan Moore, Michael Church and MicheleKoppes. In authoring papers with each of you during the course of my degree and Ihave been exposed to a wider range of ideas than those contained within my thesisalone.xviOf course, my thesis could not exist without all those who helped in the col-lection of data. Thank you to all of the lab assistants who helped me over theyears, Alex Tran, Rose Beagley, Nicole Mak, Dylan Weyell, Deanna Shrimptonand Emily Ballon, there is no way I could have collected and processed this datawithout you. Additional thanks go to the lab technicians, Rick Ketler, Luke Terhartand David Waine, who helped make sure the stream table always performed at itsbest.This research would not have been possible without the financial and in-kindcontributions of two industry partners: BGC Engineering and Geo Morphix. Incollaboration with NSERC and Mitacs, these partners have made it possible for meto conduct the research I have undertaken towards my degree. In particular, I thankMatthias Jakob and Hamish Weatherly from BGC Engineering and Paul Villardfrom Geo Morphix.Turning to my community outside of school; I acknowledge the immense rolemy family and friends have played in supporting me through this degree. To myfamily, thank you not only for the emotional support but also for putting in the timeto understand and value the work that I do; I know that fluvial geomorphology is afar reach from visual art, but each of you have taken the time to listen, reflect andto give me really interesting feedback on my work. To my friends, while all of youhave been so very supportive of my work, I want to thank you most for giving mean opportunity to NOT think about school. Your friendship is an invaluable part ofmy life and there is no way I could be the scientist I am without you. To my cats,thank you for bringing me joy and comfort, and Henrietta, my constant companion,any typos in this thesis are because of you.Through my degree there has been nobody more attentive, supportive and lov-ing than my partner Geoff McVarish. You been there whenever I needed you,always pushing me to be my best self, even when I thought I couldn’t do it. I knownow that I will be able to accomplish anything as long as I have you by my side.xviiDedicationThis thesis is dedicated to my daughter. I hope that by my defending thesis nearlynine months into my pregnancy with you will show that you can do anything youset your mind to. I can’t wait to meet you!xviiiChapter 1Introduction1.1 MotivationThere are many aspects that make regions next to rivers appealing locations todevelop, from the natural beauty of these water corridors, to their source of fresh-water, fish and other aquatic life, to the fact that they can be used to generatehydro-power. However, like with any part of the natural landscape, they do comewith their share of hazards: while channels may behave in one way for a prolongedperiod of time, when atmospheric and pre-existing ground conditions are just right,they may change dramatically in a matter of hours due to high rates of runoff fromsurrounding slopes. Such an event happened in western Alberta, Canada, in June2013: two weather systems stabilized over the region, dropping over 30 cm of pre-cipitation over three days in some areas onto already saturated and frozen ground(e.g., Pomeroy et al., 2016; Teufel et al., 2017). While flows of such magnitudemay be of little concern to humans when they occur in uninhabited regions, theycan have devastating consequences where channels are bordered or bisected byinfrastructure, as was the case formany locations in the southeastern Rocky Moun-tains in June 2013, and especially in Canmore and the adjacent Municipal Districtof Bighorn (Figure 1.1).Cougar Creek, a channel which is dry for large portions of the year, flowsdirectly through the town of Canmore, Alberta. It is bordered primarily by resi-dential neighbourhoods and runs under both the Trans-Canada Highway, Highway1Jonathan Hayward/The Canadian PressGoogle Streetview: Sept 2012Figure 1.1: Cougar Creek before and after the June 2013 flooding. The topimage shows the view of Cougar Creek looking upstream from the edgeof the Trans-Canada Highway before the flood event. The image belowis an aerial shot of the flooding of Cougar Creek over the Trans-CanadaHighway and the upstream widening.21a and the Canadian National (CN) Railway line. During the storm event of June2013, Cougar Creek experienced substantial flooding which resulted in dramaticwidening and flooding along its length, resulting in the damage of many privateproperties and the shutdown of both the Trans-Canada Highway and the CN Railline (see Figure 1.1). The consequences of this event highlight a central questionwhich forms the basis for our ability to mitigate against such events: is it pos-sible to predict the conditions under which a channel will experience substantialmorphologic change?This applied question motivates my thesis, as it turns out that our understandingof channel stability in steep, alluvial channels, such as those found on alluvial fans,remains limited. Much of the existing work and models of channel response arebased on, and developed for, low gradient rivers with cohesive banks (e.g., Millarand Quick, 1993; Darby et al., 2007, 2010; Eke et al., 2014). In these channels, theprimarily response of the channel to high flow conditions is for the water to floodonto the surrounding low lying floodplain (Magilligan, 1992; Gomez et al., 1995);when bank erosion does occur, the mechanism of erosion is typically slumping orslab failure due to undercutting or oversteepening (Andrews, 1982; Darby et al.,2007). Comparatively, the primary response of higher gradient channels formed inmaterial with little to no cohesion is to erode laterally (Magura and Wood, 1980;Jakob et al., 2015), like what was seen at Cougar Creek and nearby channels inthe region in 2013. While overbank flooding does occur in these steeper systems,it typically remains localized to areas of aggradations within the channel (Maguraand Wood, 1980). The mechanism of bank erosion in steep channels is also dif-ferent from their lower gradient counterparts, as bank erosion occurs due to boththe entrainment of individual grains from the banks, as well as due to the failureof the non-cohesive banks due to evacuation of material near the toe of the bank(Andrews, 1982; Nanson and Hickin, 1986; Millar and Quick, 1993). Given thediscrepancies in both the response of the channel and mechanisms of bank erosionbetween low gradient channels with cohesive banks (due to cohesion between finegrain particles) and higher gradient channels with non-cohesive banks, it seems un-likely that the underlying physics of channel response to flood events are similar.At the most basic level, nearly all models used to predict bank erosion are basedon the Relative Bank Stability (RBS) approach (e.g., Griffiths, 1981; Jowett, 1989;3Millar and Quick, 1993). This approach compares the shear stress (or velocity)in the channel to the critical shear stress (or velocity) required to entrain the bedmaterial. While the premise of this model is conceptually sound, in that we wouldexpect bank erosion to occur where forces acting on the bank are greater than whatthe bank can withstand, it relies heavily on the value chosen to define the criticalthreshold of entrainment. Based on seminal work on sediment transport conductedin the 1980s (e.g., Parker et al., 1982b; Andrews, 1983), this threshold is widelyequated to the critical shear stress required to entrain the median grain size ofthe bed surface (τ∗c50). Consequently, it has become standard practice to focuson solely quantifying the size of the surface median grain size (D50) in channelstability assessments. This is exacerbated by the fact that uncertainty in quantifyingthe size of any grain size percentile other than the median is quite large usingstandard Wolman pebble counts (Eaton et al., 2019); relatively large sample sizesmust be collected in order to precisely determine the size of grains associated withhigher percentiles of the grain size distribution. As such, it is more common to findreported values of the D50 than it is to find data about larger grain size percentilesin existing literature and reports.But does the entrainment threshold of the median grain size correspond to thedramatic changes seen in Cougar Creek or other similar creeks in the southwesternRockies? If not, what characteristics of a channel actually impart stability?What began as a seemingly simple applied question has blossomed into anexploration of the fundamental processes controlling channel morphodynamics insteep alluvial gravel bed streams. This thesis tackles the issue of channel stabilityby first defining what is actually implied by the term “stability” in the context of al-luvial channels, and then investigating the fundamental processes behind this termthrough a series of stream table experiments. The work presented in herein demon-strates that our traditional understanding of channel stability, wherein changes inchannel morphology coincide with the entrainment of the D50, is fundamentallyflawed in the context of steep alluvial channels and instead, channel stability isassociated with the largest grains present in the channel.41.2 Thesis organizationThe basic arguments for why the use of the median grain size as the characteristicgrain size for predicting channel response is questioned and why I propose usingsome measure of the largest grains are laid out in Chapter 2. I look at how the D50has been integrated into three important fields of fluvial geomorphology: flow re-sistance, sediment transport and channel stability. I demonstrate that, in the field offlow resistance, most researchers have moved away from using the D50 to charac-terize surface in favour of some measure of the largest grains. In comparison, in thefields of sediment transport and channel stability research, the use of the mediangrain size to characterize sediment is still widely used. I point to new and exist-ing research that indicates the importance of large grains in these processes andsuggest that further inquiry should be made into understanding these processes.In this thesis, the primary evidence for the importance of large grains in channelstability comes from a series of stream table experiments; Chapter 3 lays out theexperimental design used to produced and collect this data. In this chapter, I firstdescribe A-BES, the Adjustable-Boundary Experimental System, located in thefluvial laboratory at UBC. I next lay out the experimental procedure and the meth-ods of data collection employed. Model design and scaling is briefly discussed,and the chapter ends with a description of the data processing methods used.Chapter 4 summarizes the results from the two categories of experiments pre-sented in this thesis: (1) the paired experiments, and (2) the pseudo-recirculatingsediment experiment. The paired experiments, which comprise three sets of pairs,were run to test the effects of the addition of a small proportion of large grainson channel morphodynamics. The results from these experiments are investigatedin-depth in Chapters 5 and 6. The pseudo-recirculating sediment experiment, runto explore the evolution of the bed surface in relation to morphodynamic change,is explored in Chapter 7.To back up the arguments presented in Chapter 2, Chapter 5 uses data from asingle set of the paired experiments to show that a small change in the proportion oflarge grains present in the bulk mixture of the bed material has a crucial effect onchannel morphodynamics, this despite no significant change in the median grainsize of the mixture. Building on these preliminary results, Chapter 6 aims to5answer two arising questions: does the influence of large grains persist at higherdischarges? Does it persist with increased rates of upstream sediment supply?In Chapter 6, I show that large grains control channel morphodynamics acrossa range of discharge and sediment supply conditions; channels with fewer largegrains experience more morphologic change and degrade more than their pairedcounterparts with slightly more large grains present. These results are used toargue that our understanding of channel stability should be fundamentally shiftedto incorporate the role of large grains.Chapter 7 investigates how large grains at the surface of the bed influencechannel morphodynamics using high spatial and temporal scale data collected dur-ing the pseudo-recirculating sediment experiment. In this chapter I take measuresof surface roughness, traditionally used to characterize flow resistance in channels,and relate them to the morphologic change measured in the channel. While the re-sults from this chapter generally support the assertion that large grains play a rolein channel dynamics, they do more to highlight how little is actually understoodregarding the interplay between the surface texture and morphologic change.Lastly, Chapter 8 summarizes the contributions made, assesses the implica-tions of this work on our understanding of gravel-bed systems and proposes futurerelated research directions.6Chapter 2Conceptual basis2.1 IntroductionDeveloping any kind of quantitative geomorphic model requires that complex at-tributes of a system be described using a small number of representative parame-ters. For example: the time distribution of stream flow is most often reduced toa single, so-called formative discharge; the spatial distribution of hydraulic headwithin the channel is often reduced to a reach-average energy gradient; and therange of grain sizes in the bed material is often reduced to a single, character-istic grain size. These assumptions were initially necessitated by practical datacollection and analysis constraints, and consequently, their validity can becomeaxiomatic without ever being rigorously tested. Accordingly, it is important toperiodically re-evaluate the parameters upon which our geomorphic models arebased. Here, I re-evaluate the use of the bed surface D50 as the characteristic grainsize and ask: is the reliance on the D50 justified, or merely convention; is therewidespread evidence to suggest that D50 is a physically meaningful characteristicgrain size in gravel bed channels? Or instead, can we find enough evidence tosuggest that large grain sizes – which is considered to be equal to or greater thanthe size of the 84th percentile of the bed surface distribution (D84) – may actuallycontrol channel dynamics in a more meaningful way?The idea that the largest grains on the bed surface control important aspects ofchannel morphodynamics in gravel bed channels is not new: many researchers have7recognized the influence of large grains (Brayshaw et al., 1983; Hassan and Reid,1990; Lisle et al., 1991; Church et al., 1998; Hassan and Church, 2000; Ferguson,2012) and, surprisingly, the classic work that most steadfastly argues the impor-tance of the D50 has also acknowledged the differing behaviour of large grains. Forexample, following an argument for the ubiquity of equal mobility in gravel bedchannels, Andrews (1983) concludes that “all particle sizes, except the very largest,were entrained at nearly the same discharge” [p.1229, emphasis added]. Similarly,Parker and Klingeman (1982) observed from their experimental work that “appar-ently [the armour layer] cannot adjust to equalize the mobility of very rare, largegrains” [p. 1422]. The fact that entrainment of the largest grains deviates from thegeneral trend of the rest of the bed suggests that they may play an important rolein stabilizing the channel bed where fluvial processes are dominant.In this chapter I highlight how large grains, rather than the median, have be-come widely accepted as the characteristic grain size for flow resistance equations.I then proceed to argue that the continued use of the D50 as the characteristic grainsize in sediment transport and channel stability equations should be re-evaluated.I conclude by proposing that our understanding of both channel stability and sedi-ment entrainment/transport could be improved by explicitly recognizing the influ-ence of large grains.2.2 Flow resistanceFlow resistance equations allow reach-averaged flow velocity to be estimated fora given flow depth, width and gradient (e.g., Ferguson, 2007; Rickenmann andRecking, 2011). These equations include a measure of roughness imparted by thechannel surface determined either empirically (e.g. n in Manning’s equation), orquantified directly from measurements of particles on the bed surface, as it is inthe Keulegan (1938) equation. Experiments by Nikuradse (1933) demonstratedthat the effect boundary roughness (ks) is equal to the size of grains (i.e. ks = D)when the sediment is uniform, but for poorly-sorted sediment in a natural river,setting ks = D50 underestimates the roughness length and overestimates the meanvelocity (Bray, 1979). To account for this discrepancy, researchers have applied a8correction factor to scale ks to the measure of the bed surface texture, as follows:ks =CiDi (2.1)Ci is the correction factor corresponding to grain size Di, wherein i signifies thepercentile of the cumulative GSD. Empirically, the best flow resistance relations areassociated not with the D50, but with grains much larger than average – typically theD84 (Hey, 1979) or the D90 (Bray, 1980) – as these grains most strongly influencethe near-bed channel hydraulics (Recking et al., 2009; Monsalve et al., 2017).That a correction factor is necessary even when using the D84 or D90 is at-tributable to the fact that roughness in natural channels is imparted not only fromthe surface of the bed but also from self-organizing bedforms and structures that de-velop within the channel (Clifford et al., 1992; Millar, 1999; Wilcox et al., 2006).Large grains again play an important role in the development of bedforms thatmake a contribution to overall channel resistance to flow: at the channel-widthscale, large grains make up the keystones around which riffles form (Church andJones, 1982; Grant et al., 1990; Montgomery and Buffington, 1997), while grain-scale structures, such as clusters and stone cells, are created when finer, more mo-bile, grains accumulate around large, relatively immobile grains (Laronne and Car-son, 1976; Brayshaw, 1985; Church et al., 1998; Strom and Papanicolaou, 2008).Similarly, larger grain-scale bedforms, like stone lines and transverse ribs, are cre-ated when large particles interact during high flows, as they rotate and roll into con-tact with each other, forming long lines or reticulate structures (Tribe and Church,1999).Recent research on flow resistance provides an excellent example of the po-tential for re-evaluating our assumptions; instead of continuing to associate flowresistance with a given characteristic grain size, researchers have shown that ks ismost accurately estimated from statistical descriptors of the bed topography, whichreflects both the role that individual large grains exert on resistance, as well the bedstructures that they are facilitate the formation of (e.g., Nikora et al., 1998; Smartet al., 2002; Aberle and Nikora, 2006). Thus, researchers studying flow resistancehave readily accepted that larger than average grains control flow resistance byinfluencing the roughness length, ks, and triggering the formation of bed and bar9forms that further increase the flow resistance.2.3 Sediment entrainment and transportDeveloping an understanding of the entrainment and transport of bed material hasbeen an important research focus for geomorphologists and engineers for over acentury. A detailed review of the topic is beyond the scope of this chapter, andexcellent reviews have been published (e.g., Ferreira et al., 2015). In this chapter, Iidentify some of the key milestones in the evolution of sediment transport studies ofgravel bed streams, that emphasize the assumptions made about the characteristicgrain size.Perhaps the single most influential study was conducted by Shields (1936),who developed a model for particle entrainment using unimodal sediment of sizeD.τc = θc(γs− γ)D (2.2)This equation predicts the minimum shear stress (τc) required to entrain a particleof size D as a function of its submerged unit weight (γs− γ), and an empiricallydetermined constant θc, found to vary between 0.03 and 0.06 for D larger thanabout 3 mm.One of the most influential bedload transport formulas was developed by Meyer-Peter and Muller (1948) using the concept of excess shear stress (τ − τc, where τis the mean boundary shear stress), assuming that θc = 0.047. While most of thedata they used to develop their formula came from experiments with unimodal sed-iment, they did experiment with sediment mixtures and concluded that the mediansize of the bulk material (d50) was approximately equivalent to D for unimodalsediment. While many other transport models have been developed (see reviewin Gomez, 1991), the work by Shields (1936) and Meyer-Peter and Muller (1948)was fundamental to the early development of sediment transport theory for gravelbed streams.Seminal work from the early 1980s ultimately led to the adoption of the bedsurface median grain size (D50) as the most appropriate characteristic grain size,as it is the surface layer, rather than the underlying bulk material, that the flowinteracts with (e.g., Parker, 1990). Although earlier researchers had recognized10that sediment transport in mixed-size beds is influenced by relative-size effects(e.g., Einstein, 1950; Egiazaroff, 1965), the observation by Parker and Klingeman(1982) that the distribution of sediment in transport was similar to that of the bulkmaterial led researchers to focus on quantifying the role of relative particle size inmodifying the entrainment threshold (Parker et al., 1982a; Andrews, 1983; Komar,1987; Ashworth and Ferguson, 1989). Initially, Parker et al. (1982b) developed asediment transport model using the bulk d50 which asserts that bed surface textureadjusts so that all grain sizes are entrained at nearly the same shear stress. Thisidea is referred to as the equal mobility hypothesis (Parker et al., 1982a). A revisedversion of this model more explicitly recognizes the importance of the bed surface,and is based on the surface D50 (Parker, 1990). Since this paper was published,D50 has been almost exclusively used as the characteristic grain size in all types ofsediment transport studies (e.g., Buffington and Montgomery, 1997; Wilcock andCrowe, 2003; Lamb et al., 2008; Prancevic and Lamb, 2015).Currently, most commonly used bedload sediment transport models calculateindividual transport rates for each size fraction in a distribution (e.g., Parker, 1990;Wilcock and Crowe, 2003). These models integrate a hiding function which ac-counts for the effect of relative grain size on particle entrainment:τri = τr50(DiD50)b(2.3)In this equation, the concept of a threshold shear stress is replaced by a referenceshear stress (τri), following Parker (1990). The exponent b describes the degree towhich relative grain size (Di/D50) affects entrainment, with equal mobility associ-ated with b= 0, and purely size-selective transport associated with b= 1. Wilcockand Crowe (2003) concluded that particle entrainment is not well described by asimple power law, and they showed that b approaches an exponent of 0.12 (i.e.,near-equal mobility) for Di << D50, and to an exponent of 0.67 (i.e., more size-selective entrainment) for Di >> D50.Work by Wilcock and McArdell (1993) further emphasized the importance ofthe surface grain size distribution, and refined our understanding of the entrainmentprocess by recognizing that entrainment is best conceptualized by a gradient, notas a binary. They defined two conditions of mobility: that of partial mobility,11during which a given grain size may be present in the bedload but will be under-represented relative to its frequency on the bed surface; and that of full mobility,during which a grain size fraction will be present in the bedload in direct proportionto its frequency on the bed surface. They observed that the transition betweenpartial mobility and full mobility occurs gradually over the range τri < τ < 2τri.Laboratory experiments and field data show that full mobility of many grainsize fractions does occur, but that the largest grains on the channel bed are nearlyalways either immobile or only partially mobile (e.g., Komar, 1987; Ashworthand Ferguson, 1989; Parker, 1990; Leopold, 1992; Wathen et al., 1995; Wilcockand McArdell, 1993, 1997; Church, 2002), even during channel-forming flows(Haschenburger and Wilcock, 2003; Eaton and Church, 2004). As a consequence,the grain size distribution of bedload in gravel bed streams is often slightly but per-sistently finer than the bulk distribution (Lisle, 1995). It is only during exception-ally large flood events that the largest grains are fully mobilized and equal mobilityconditions are approached (e.g., Wathen et al., 1995; Eaton and Church, 2004),however these events are rarer and typically only occur on the order of decades oreven centuries (e.g., Haschenburger and Wilcock, 2003; Tamminga et al., 2015).Some researchers have argued that it is unnecessary to include large grainsin the formulation of sediment transport models as they make up only a smallpart of the total sediment transported (e.g., Wilcock and Kenworthy, 2002). Whilethis may be true, what is not considered is the role that these large grains playin forming the coarse surface layer that moderates the availability of the typicallyfiner bulk material beneath. Several studies have found that the mobility of largegrains controls the availability of bulk material (Warburton, 1992; Lenzi et al.,1999; Masteller and Finnegan, 2016), as they act to trap mobile finer grains, therebydecreasing their proportion in the bedload (Wilcock and McArdell, 1997). Thus,when large grains become entrained, they are not only adding themselves to thebedload but releasing a large amount of finer material below. This has importantimplications for paleoflood analyses as we might expect that more fines should befound in deposits from large flood events relative to those of smaller, more frequentevents.122.4 Channel stabilityChannel stability for gravel bed streams has primarily been approached by wayof analogy with sediment transport whereby the entrainment of the surface D50is said to coincide with the loss of stability of the channel (e.g., Andrews, 1984).While this approach has had some limited success (e.g., Millar and Quick, 1993),the building evidence from previous studies (e.g., Brayshaw et al., 1983; Hassanand Reid, 1990; Lisle et al., 1991; Church et al., 1998; Hassan and Church, 2000;Ferguson, 2012), as well as results from experiments presented into the forthcom-ing chapters (Chapters 5 and 6), has led us to develop an alternative conceptualmodel that is related to the proportion of the bed surface that remains stable at agiven flow, rather than the strength of the flow relative to the shear stress requiredto entrain the D50. While these two propositions are related, they represent twodistinct views of bed stability. The prevailing approach based on the mobility ofthe D50 is inherently based on the premise that equal mobility is an appropriate (ifnot exact) representation of the behaviour of the entire bed. However if – as hasbeen suggested by previous research – bed stability is strongly influenced by thelargest grains in the bed (e.g., Lisle, 1995; Olsen et al., 1997; Church et al., 1998;Ferguson, 2012), then the mobility of the D50 is probably not a good representationof the underlying physics.I propose that the stability of a bed is related to the fraction of the bed area cov-ered by immobile grains, and that these grains create a framework over which bedmaterial sediment transport may occur without significantly altering the channelmorphology, similar to what has been observed in steep step-pool channels (e.g.,Phillips, 2002; Lenzi et al., 2006; Piton and Recking, 2017). Both immobile sizefractions and partially mobile size fractions contribute to stability, a nuance thatis lost when we simply focus our attention on a single grain size. My model iscast in terms of the commonly accepted three-stage sediment transport model forgravel bed streams, drawing largely on previously published ideas (Carling, 1988;Ashworth and Ferguson, 1989; Warburton, 1992; Schneider et al., 2016). In thismodel I assume, based on the work of Wilcock and McArdell (1997), that at τ = τci10% of grains of a given size class on the bed surface are entrained and transportedwhile as τ approaches 2τci the proportion of this size class that is mobile increases,13following a logistic curve, to 90%. Using this function, it is possible to estimate thetotal fraction of a bed surface that will remain immobile for a given shear stress,accounting for the differences in the entrainment threshold of different grain sizesusing the hiding function of Wilcock and Crowe (2003) (see Appendix E for a fulldescription of the model).Shear Stressτ1τ2DischargeSTABLEDYNAMICALLY STABLEUNSTABLEIIIIIICIII. UnstableII. DynamicallyStableI. StableOriginal ChannelBDischargeTimeIIIIIIAFigure 2.1: Stable, dynamically stable and unstable channel definitions. A)hydrographs typical of stable/dynamically stable/unstable channels. B)Characteristic changes to channel cross sections associated with thethree flood hydrographs. C) Shear stress versus discharge for the threeflood hydrographs.During small flood events (Hydrograph I, Figure 2.1A) the channel remains sta-ble, in that both the bed topography and bank alignment are essentially unchangedby the flow, and reach-averaged shear stress (τ) remains below some threshold (τ1).For these events, the bedload is significantly finer than the surface material and ismade up primarily of sand-sized sediment, although material up to and slightlylarger than the D50 may also be entrained (Jackson and Beschta, 1982; Carling,1988; Ashworth and Ferguson, 1989; Warburton, 1992). A typical gravel bed hav-ing D84/D50 = 2.0 would experience entrainment over less than 5% of the bed14surface (by area) for flows at which τ = τc50 (Figure 2.2, see supplementary mate-rial for details). This estimate is produced by accounting for the stability of bothimmobile and partially mobile grain size fractions (as described by Wilcock andMcArdell, 1997). Even when τ = τc84, only 20% of the bed surface will be mo-bilized, with 80% of the surface remaining immobile (Figure 2.2); based on myexperimental observations, I choose τ1 = τc84 to represent a reasonable upper limitfor the stable channel condition, as the key stones that lend stability to the channelbegin to be mobilized at flows higher than this.During moderate flood events, such as bankfull flow (Hydrograph II), τ likelyrises above τc84 and the channel enters the dynamically stable phase. While lo-calized bank erosion and compensating bar building occurs during these flows, thereach-average channel dimensions remain about the same. This phase is associ-ated with the partial mobility of large grains (Andrews, 1984; Carling, 1988; War-burton, 1992; Haschenburger and Wilcock, 2003; MacKenzie and Eaton, 2017).Under moderate flood events, the magnitude of morphologic changes may be me-diated by bank strength; channels with well vegetated banks may undergo onlyminor adjustments to channel alignment while systems lacking riparian vegetationmay experience more considerable bank erosion (e.g., Eaton and Giles, 2009). Thesame is likely true for channels with cohesive (due to the presence of clays) orcemented banks (due to calcium carbonate).Only during large flood events (Hydrograph III), that typically exceed the ca-pacity of the bankfull channel, does the D84 become fully mobile, and the channelbecomes unstable. The size of floods associated with instability depend largely onthe size of material composing the channel banks, gravel-beds streams are likely tobecome unstable at lower flows than channels containing a cobbles and boulders.During these large floods, a period of channel restructuring often occurs, involv-ing widespread bank erosion and relocation of the bars, pools and riffles. Reach-average characteristics also change as the channel widens, leading to a new channelgeometry for which τ is lower at a given discharge (Tamminga et al., 2015). Basedon observations documented in previous studies (Carling, 1987, 1988; Ashworthand Ferguson, 1989; Eaton and Church, 2004; Tamminga et al., 2015), I proposethat the threshold between dynamically stable and unstable channels is character-ized by the onset of full mobility of the D84, which occurs at τ2 = 2τc84. These15flows can mobilize 85% or more of the surface of a typical gravel bed, leaving only15% of the surface grains (by area) in place (Figure 2.2). For comparison, fullmobility of the D50 corresponds to the mobilization of only about half the grainspresent at the bed surface, which is consistent with dynamic stability, but not withunstable channel behaviour.Existing models are at odds with our view of channel stability; almost all in-dices use the mobility threshold of the D50 (τc50) as that which controls the thresh-old of channel stability/instability (e.g., Dietrich et al., 1989; Buffington and Mont-gomery, 1999; Kaufmann et al., 2008; Kappesser, 2002; Jowett, 1989; Frothing-ham, 2008). To my knowledge only one study equates the stability threshold withthat of the entrainment threshold of the D84 (Olsen et al., 1997). The idea thatchannel stability is related to the D50 can be traced to the modified concept of athreshold channel proposed by Parker (1978), which asserts that self-formed chan-nels will adjust such that their banks are at the threshold of motion of the D50 whilebedload is transported along the center of the channel. However, there is buildingevidence to suggest that mobility of the D50 has little to do with the stability of achannel.2.5 ConclusionIn this chapter I argue that substantial evidence suggest that large grains play a morefundamental role in controlling channel dynamics than any measure of the centraltendency of the GSD for processes related to flow resistance, sediment transportand channel stability. While in the case of flow resistance equations it has beenwidely accepted that the D84 is a better representative grain size than the D50, therehas been a comparative lack of interest in alternative definitions for the character-istic grain size in the fields of sediment transport theory and channel stability.In sediment transport equations, the shift from using the bulk d50 as a charac-teristic grain size to using the surface D50 was essentially driven by a preference fora more physically meaningful index (Parker, 1990; Wilcock and McArdell, 1993).Given the mounting evidence to suggest that it is the largest grains at the surface ofthe channel that act to govern processes of entrainment and transport (e.g., Lenziet al., 1999; Masteller and Finnegan, 2016; MacKenzie and Eaton, 2017), I contend16that the proposition to adopt the D84 as a fundamental reference grain size insteadof the D50 is simply another step along the same path towards more physicallymeaningful models of sediment transport.Lastly, I point to the mounting evidence that the entrainment of the D50 does notcoincide with the loss of channel stability (e.g., Brayshaw et al., 1983; Lisle et al.,1991; Church et al., 1998; Ferguson, 2012) as is commonly assumed in modelsof bank erosion. Instead, I propose that stability is imparted by large immobile,or partially mobile, grains on the channel bed. I describe a three phase model ofchannel stability wherein the transitions from a stable, to a dynamically stable, toan unstable channel are defined by the threshold of entrainment and that of fullmobility of the D84, respectively.Continuing to question the fundamental components of equations in light ofnew research is a key part of the scientific method as it allows us to refine the mod-elling of dynamic processes. The representation of a channel’s grain size distribu-tion through the use of a characteristic grain size is integral to many calculationswithin the field of fluvial geomorphology. The characteristic grain size should bechosen on the basis of careful consideration and solid evidence of causal relation-ships rather than by immediately assuming that it is equivalent to some centralvalue of the GSD.17III. UNSTABLEII. DYNAMICALLYSTABLEI. STABLEShear Stress (Pa)Onset of motion of the surface materialτc50τ1 = τc842τc50τ2 = 2τc8401206053%Immobile15%Immobile78%Immobile10 20 50 100 2000.000.020.040.060.080.10Grain size (mm)Proportion in size class96%ImmobileMobileproportionSurfaceproportionD50D84Figure 2.2: Bed surface stability at the boundaries between channel stabilityclasses. The fraction of the bed surface that will be mobilized duringa flood applied to a generic gravel bed grain size distribution is calcu-lated, accounting for the stable grains for all partially mobile size frac-tions (after Wilcock and McArdell, 1997). Assuming that the thresholdscorrespond to τ = τc84 and τ = 2τc84, I find that τ1 and τ2 correspondto stable bed fractions of 78% and 15%, respectively. Although for thisfigure I assume that the two thresholds correspond to some measure ofτc84, further study may show that these thresholds are better describedby the critical shear stress associated with some percentile greater thanthat of the 84th. The stable fractions for τ = τc50 and τ = 2τc50 areshown for comparison.18Chapter 3Experimental design3.1 Adjustable-Boundary Experimental System (A-BES)Experiments were conducted using the Adjustable-Boundary Experimental System(A-BES) at the University of British Columbia (Figure 3.1A). A-BES comprises a1.75 m wide by 12.2 m long tilting stream table, a recirculating water pump, mon-itored by a flow gauge and connected to a series of water storage tanks (maximumflow capacity of 5 L/s), and a computerized instrument cart that uses a laser scan-ning system, described below, to collect bed elevation data (Figure 3.1B). Both thewater pump and the instrument cart are run on LabVIEW software using code de-veloped by Dr. Andre Zimmerman. Additional components of A-BES include: (a)a bucket trap lined with wire mesh (Figure 3.1C) for collecting output sediment;(b) a rotating-pipe sediment feeder (Figure 3.1E); (c) an iPad for capturing time-lapse videos; and (d) a SONY DSC-RX100 camera used to collect images of thebed surface.Water enters the system across a weir connecting an upstream head tank to therest of the sediment-filled stream table. The water is dyed blue using a pond dyeso that the wetted extent of the channel can be clearly seen in timelapse videos col-lected by the iPad. The bulk material in the main portion of the stream table is handmixed and spread evenly to a depth of 10 cm. At the outlet, water and sedimentleaving the system flows over a 10 cm tall concrete barrier into the sediment buckettrap lined with wire mesh. This bucket trap allows water to flow through freely but19ABCDFigure 3.1: Images of the components of the Adjustable-Boundary Experi-mental System (A-BES) at the University of British Columbiacaptures all sediment greater than 250 µm, which represents the smallest size classof material used in the bulk mixture.3.2 Experimental procedure and data collectionPrior to each experiment the bed is fully mixed to destroy any sedimentary unitsformed during previous experiments and a 30 cm wide and 1.5 cm deep straightrectangular channel is cut into the floodplain. Water is then run at a low flow of 0.2L/s for a period of 15 to 20 minutes in order to fully saturate the bed, without initi-ating any sediment transport. Once the bed is saturated, flow is slowly increased tothe desired rate. Once that flow rate is attained, a timer is set, and the stream tableis run at a constant discharge for a pre-defined length of time. For experiments runwith sediment supplied to the channel at the upstream boundary, the rotating feederis turned on only once the chosen flow rate is reached. Once the desired length ofrun-time has elapsed, both the water pump and the sediment feeder are turned off20and the stream table drains.Three primary sources of data are collected from A-BES: bed elevation data,surface texture data and sediment output data. While sediment output data is col-lected while the stream table is running, it is necessary to drain the bed in order tocollect the bed elevation and surface texture data. Consequently, each experiment isdivided into a series of shorter runs between which the experiment timer is stopped,and the bed is drained of water, but the entire channel is not re-templated (i.e. thechannel morphology is preserved). These periods of drainage are not included inthe total length of the experiment.With the bed drained, bed elevation data is collected using the laser scanner cart(Figure 3.1B). This cart uses a stepping motor to collect cross-section profiles ofthe bed surface at 2 mm increments for the entire length of the stream table. Theseprofiles are compiled to create a Digital Elevation Model (DEM) of the entire bedsurface with a resolution of 2 mm in both the x and y directions. The area coveredby the DEM extends 12 m in the downstream direction and 1.6 m in the cross-stream direction. The cross section elevation data is collected by capturing imagesof a laser line pointed down at the bed using two inward facing cameras mountedto the upstream and downstream ends of the scanner cart. In order for the laser lineto be isolated from the images, it is necessary to run the scans in partial darkness.However, even when the scan in run under low light conditions, there are oftenstill small parts of the bed that are not captured at the edges of the stream tabledue to shadowing effects. However, as the majority of missing data resulting fromshadowing along the edges of the stream table, it has little effect on calculations ofbed elevation as it is typically some distance away from where the main channel islocated. A more in-depth description of the technical aspects of the laser scanningsystem can be found in Zimmermann (2009).Images of the bed surface are also collected in between runs when the bedis drained. These images are used to create orthomosaics and DEMs of the bedsurface using AgiSoft PhotoScan Professional (Version 1.4.5). Images of the bedwith >60% stereographic overlap are taken using a downward-facing SONY DSC-RX100 camera at regular intervals (either 1 or 2 meter spacing) along the streamtable. Raw images of the bed are input into Photoscan and processed using theworkflow described below.21Unlike bed elevation and surface texture data, sediment output data is collectedwhile the stream table is running. During each run, sediment output from the sys-tem is collected using the bucket trap (Figure 3.1C). This trap is emptied every 15minutes into drying pans. Each pan is labeled and put into a drying oven until allwater is evaporated. The dried sediment is then weighed in order to determine thesediment output rate for each 15-minute interval. Following that, the entire sampleis split in order to come up with a 100 g sample. This sample is sieved to determinethe grain size distribution of the bedload for the 15-minute interval.3.3 Model design and scalingThe experiments presented here were run as generic Froude-scaled models of steepalluvial gravel-bed streams. The dimensions of these models are based on streamslocated on alluvial fans near Canmore, Alberta. Field measurements of these pro-totype streams were conducted by BGC Engineering in 2013. For all experimentspresented here, the stream table gradient was set to 2% which is consistent withgradients of flood-dominated (rather than debris-flow-dominated) channels on fansin that region. I estimate that these models represent 1:25 scale versions of theprototype channels, which means that the initial templated channel used for allexperiments represents a 7.5 m wide and 0.4 m deep alluvial channel.Two slightly different bulk material grain size distributions were used in the ex-periments presented here (see Figure 3.2). These distributions were derived basedon nine samples of bulk material collected by BGC Engineering on alluvial fansin the Canmore area. Using the scale of 1:25, the largest grains used in the mod-els (8 mm) correspond to 200 mm boulders in the prototype channels. The lowerend of the model sediment mixture is truncated at 0.25 mm in order to maintaina hydraulically rough boundary. This corresponds to a field sediment distributiontruncated at 6.25 mm; consequently, these models ignore the dynamics of smallgravel and sand which constitutes about 15% of the bulk material in the prototypechannels.Across all experiments I refer to the two grain size distributions as GSD1 andGSD2. These distributions are nearly identical, however GSD1 contains approxi-mately 4% less coarse material (i.e. greater than 4 mm) than GSD2. The median22Particle Size (mm)Cumulative Proportion Finer1 100.00.20.40.60.81.084th percentile50th percentileGSD1GSD2Figure 3.2: Grain size distributions of the two bulk mixtures used in the ex-periments.grain sizes of the two bulk mixtures (d50) are approximately equivalent: the d50of GSD1 is 1.60 mm and that of GSD2 is 1.63 mm. Comparatively, the size ofgrain associated with the 84th percentile of the bulk distribution (d84) differs morewidely between the two: the d84 is GSD1 is 3.09 mm while that in GSD2 is 3.32mm, with the difference increasing further at larger percentiles (Table 3.1). Bothbulk mixtures span the same range of grain sizes (0.25 to 8 mm).Two sediment supply scenarios were used in my experiments. In the first,which I refer to as the low sediment supply scenario, no sediment was fed in atthe upstream boundary meaning that the only sediment supplied to downstreamreaches originated from bed and bank erosion. In the second, referred to as thehigh sediment supply scenario, sediment was fed directly into the channel at theupstream boundary, thus sediment received by downstream reaches originated both23GSD1 GSD2d50 1.60 1.63d84 3.09 3.32d90 3.67 3.94d95 4.37 5.09Table 3.1: Grain sizes given in mm for the two bulk mixtures.from the feed as well as due to vertical and lateral erosion. In the high sedimentfeed scenario sediment was introduced to the top of the stream table using a ro-tating tube sediment feeder (Figure 3.1D). This set-up comprises a storage bin forsediment and a small motor used to rotate a steel pipe that connects into the storagebin; the rate of sediment supply is set by changing the slope of the apparatus. Theinput rates of material, and their respective GSD, for the high supply scenarios aresummarized with the rest of the experimental conditions in a section below.3.4 Data processingThe DEMs collected using the laser scanner are the primary data used to examinemorphodynamic change in these experiments. Prior to their use in analysis, allof the raw DEM models are processed using code written in the R ProgrammingLanguage (R Core Team, 2018) in order to remove any erroneous peaks in the datacaused by light leaks and to fill in any areas of missing data due to shadows duringthe scanning process. The processing of DEMs comprises three steps: first, allunreasonably high elevations above a given value are filtered out; second, the bedsurface is smoothed using a 7 x 7 pixel (14 x 14 mm) averaging filter to eliminatesmaller specious bumps and dips; and lastly, a second 15 x 15 pixel (30 x 30 mm)averaging filter is run to fill in any missing data.DEMs of Difference (DoD) are created by subtracting subsequent DEMs inorder to examine channel change over time. From these, I calculate two primarymeasures of morphodynamic change: the morphodynamic activity of the channel(M) and the change in storage of sediment in the channel (∆S). M is calculated asthe total volume of erosion and deposition, in m3, measured in the channel for agiven interval of time:24M =Ve+Vd (3.1)where Ve is the volume of erosion (in m3 )and Vd is the volume of deposition(in m3). Volume change is calculated as the elevation change of each cell timesthe resolution of that cell squared (in m3). ∆S is calculated as the net volume ofchannel change:∆S=Ve−Vd (3.2)Compared to sediment output rates, both M and ∆S better represent the mag-nitude of morphologic change occurring along the entire length of the channel, assediment output rates are only indicative of the amount of erosion occurring inproximity to the channel outlet.To create high resolution orthomosaics and DEMs of the bed surface, imagesof the bed taken at cross sections located at regular intervals along the length ofthe stream table are input into Agisoft Photoscan. Images are georeferenced usingknown distances and processed using the Photoscan workflow. The resulting 3-Dmodels of each cross section encompass the entire width of the wetted channel andextend about 30 cm in the streamwise direction. The typical resolution for both theorthomosaics and the DEMs is about 0.1 mm, which is less than the smallest grainsize present on the bed surface.The grain size distribution (GSD) of bed surface is measured from orthomo-saics using a Wolman count method wherein the b-axis of 200 grains are measuredoff each image based on user input. Grain sizes are only measured for particlesfound within the wetted area. The wetted area is determined by comparing theorthomosaic image to the wetted area as calculated by the flow model discussedbelow. Uncertainty for the surface GSD is calculated from a binomial distributionand depends on the size of the sample used. For single cross sections where only200 grains are measured, the uncertainty of the D50 and D84 is on the order of 0.2mm and 0.5-0.9 mm, respectively, which is why surface GSD measurements arenever given for individual cross-sections. Only when the surface GSD is estimatedbased measurements from all cross sections for a given time period that uncertaintybounds are reduced to an average of 0.05 mm for the D50 and 0.2 mm for the D84.25The flow conditions (water depth, velocity, shear stress) area reconstructed foreach DEM by applying a 2D numerical flow model (Nays2DH) to the bed surfaceDEMs. Flow modelling rather than direct measurements were used, as it is difficultto measure flow depth and velocity in stream table experiments due to the shallowdepths (Y ≈ 0.005 m) and a rapidly evolving channel bed (see time lapse videosin the supplementary material). To minimize rounding errors associated with themagnitude of depths being simulated and the size of the grid, the DEM size anddischarge are adjusted to prototype scale (i.e. using the length scale of 25) for in-put into the flow model. After running the model, the water depths, shear stressesand velocities from Nays2DH are then back-transformed to the model scale. I havevalidated the results of the flow model by overlaying maps of specific discharge(e.g. Figure 4.2), which are derived from the flow model results, onto downlook-ing images of the bed taken during the run. The extent of the modelled wettedarea has been found to agree well with the observed wetted area during the runs.However, as I cannot directly quantify the error associated this method, we onlypresent reach-averaged values in my analysis on the grounds that while local vari-ations present in the models may not be wholly accurate, the flow model is able topredict reach-averaged characteristics reasonably well. Further, the reach-averagedhydraulic data is calculated only for “wetted areas” which had a specific discharge(q) of 2.5x10−5m2/s or greater. This threshold was chosen as one which selectedonly for areas within the channel where sediment transport could be expected tooccur (i.e. not areas of overbank flow).Channel roughness is parameterized in the Nays2DH model using Manning’sroughness coefficient (n). To most accurately characterize the channel rougness Iuse a two-step method wherein Nays2DH was run twice on each DEM. In the firstrun, a constant value of n = 0.05 is used for the entirety of the bed and floodplainsurface area. Then, using the modelled local water depths and energy gradientsoutput from the first model run, a spatially varying model of roughness is calcu-lated for each cell using the continuously varying power law equation presented byFerguson (2007); at this stage, the reach-average D84 is used for the flow resistancecalculations. Nays2DH is then run a second time for each DEM using the spatiallyvarying values of n for areas within the channel. For those areas not covered byflowing water during the first run, n is set to 0.2, which corresponds to the high-26est values computed for the smallest water depths using the Ferguson (2007) flowresistance equation.Using the reach-averaged shear stress output from the flow model, I calculatereach-averaged dimensionless shear stress (τ∗i ) as:τ∗i =τg(ρ−ρs)Di (3.3)where τ is the reach-averaged shear stress (calculated in Nays2DH), g is gravi-tational acceleration, ρ is the density of water, ρs is the density of sediment andDi is the size of material associated with the ith percentile. In my analysis I cal-culate reach-averaged dimensionless shear stress using both the Di = D50, whichis the traditional way in which it is calculated, as well Di = D84, which is moreuncommon.27Chapter 4Summary of experimentsThis section provides a brief overview of all seven experiments presented in thisthesis. These experiments are grouped into two categories: (1) the paired exper-iments, and (2) the pseudo-recirculating experiment. DEMs of difference (DoD),showing the total change in the channel morphology over the course of the entireexperiment, as well as maps of specific discharge, representing the flow patternat the culmination of the experiment, are presented for each experiment. Tablessummarizing the hourly changes in sediment and flow characteristics for each ex-periment are given in Appendices B and C, respectively.4.1 Paired experiments (Chapter 5 and 6)4.1.1 Overview of paired experimentsChapter 5 and 6 use data collected from three sets of paired experiments. For eachpair, both experiments were run with the same channel bed gradient, discharge andsediment supply scenarios but had different bulk mixtures (Table 4.1). As describedin Section 3.3, the two bulk mixtures used are referred to as GSD1 and GSD2(Figure 3.2). The first pair of experiments, GSD1a and GSD2a, were run at lowdischarge (0.7 L/s) following the low supply scenario, in which no sediment wassupplied at the upstream boundary. Low discharge approximates bankfull flow ofthe channel as it is the discharge that fills the initial rectangular templated channel28to the top. The second pair, GSD1b and GSD2b, were run at high discharge, doublethe low discharge (1.4 L/s), again with the low sediment supply scenario. The lastpair, GSD1c and GSD2c, were run at high discharge (1.4 L/s) following the highsupply scenario with a sediment feed of 100 g/min at the upstream boundary. Forthe high supply experiments, the material fed into the channel had the same sizedistribution as the material output during the corresponding high discharge lowsupply experiment. The sediment input rate was chosen based on trial experiments;I chose the highest possible feed rate that did not produce aggradation and overbankflooding at the inlet.While sediment output data was collected every 15 minutes at the outlet ofthe stream table, flow was only stopped to collect scans of the bed and images ofthe surface texture every hour. As such, the temporal resolution of the sedimentoutput data is greater than that of the DEM, flow modelling and surface texturedata. Images of the bed surface were taken at 2 m intervals along the length of thestream table to create a total of five high resolution models of the bed surface fromwhich surface grain sizes were digitized.Exp d50 d84 Q Qb ChapterGSD1a 1.60 3.09 0.7 0 4, 5GSD2a 1.63 3.32 0.7 0 4, 5GSD1b 1.60 3.09 1.4 0 5GSD2b 1.63 3.32 1.4 0 5GSD1c 1.60 3.09 1.4 100 5GSD2c 1.63 3.32 1.4 100 5Table 4.1: Summary of the experimental conditions for the paired experi-ments. Where d50 is the median grain size of the bulk mixture, d84 isthe 84th percentile of the bulk mixture, Q is the discharge in L/s, Qbis the sediment feed in g/min. The “Chapter” column indicates whichchapter(s) the experiments were used in.Although the data used in Chapter 5 and some of the data used on Chapter6 are from the same paired experiments (GSD1a and GSD2a), some of the val-ues presented in the results differ slightly due to discrepancies in the data analysismethods employed, although the data trends agree generally (see Tables D.4 andD.1). The results presented in Chapter 5 are from a preliminary analysis of the29data; the methods used in Chapter 5 tend to be simpler, while the results presentedin Chapter 6 are from derived more evolved methods of data processing. Overall,differences exist for the following data: (1) the average values of bedload d50 andd84 over the 8 hours, (2) the surface grain size distributions, and (3) the flow mod-elling results. The differences in the data analysis methods used as well as a shortdescription of the primary differences in the resulting data values are presented inTable 4.2. The values presented in Tables B.1 and C.1 are those derived using thedata analysis methods from Chapter 6.Data Chapter 5 Chapter 6 Main differencesAverage valuesof bedload d50and d84Calculated as meanof all d50 and d84values from thehalf-hour samplesCalculated as aweighted aver-age of half-hoursamples, weightedusing the sedimentoutput for that timeperiodValues in Chapter 6are slightly higherthan those in Chap-ter 5Surface GSD Measuredfrom a singledownlooking-image of thebedMeasured froman orthomosaiccreated of the bedsurfaceValues in Chapter6 are slightly lowerthan those in Chap-ter 5Flow roughnessinto Nays2DHConstant value ofn = 0.05 across theentire channel andfloodplainn varies spatiallyand is calculatedusing Ferguson(2007)Modelled flowshave lower w : d ra-tios and higher val-ues of τ in Chapter6, particularlyfor ExperimentGSD1aTable 4.2: Discrepancies in results for experiments GSD1a and GSD2a be-tween Chapter 5 and 6.304.1.2 Channel evolution in the paired experimentsLow discharge, low supply (GSD1a and GSD2a)For the experiments run at low discharge and low sediment supply, differencesin channel morphodynamics between the two bulk mixtures became immediatelyapparent; during the first hour, the experiment run with the finer bulk material(GDS1a) developed a meandering pattern while that run in the coarser material(GSD2a) remained straight. In GSD1a banks eroded, forming the outside of thebends and submersed point bars formed on the inside of these bends. Compara-tively, in GSD2a bank erosion was minimal and sediment transported was limitedto a small amount of fine sediment winnowed from the bed surface. This mate-rial was not sufficient to form any significant bedforms, instead it was transportedthrough the system as fine bedload sheets. From hour 2 onwards, the channel inGSD2a remained nearly entirely unchanged, although some fine sediment did ex-change between submerged bars. Meanwhile in GSD1a, while bank erosion slowedand the channel stabilized into a meandering pattern by the end of the second hour,bank erosion on the outside of meander bends continued in the lower part of thechannel until the end of hour 6. Morphodynamic change had essentially ceased inboth experiments by the end of the last hour (hour 8).Figure 4.1: DEMs of difference for GSD1a and GSD2a showing the differ-ence in bed elevation (in m) between the initial templated channel andthe bed at the end of the 8th hour. Extent of initial templated channel isindicated by the dashed grey lines. Flow is from right to left.3100.00250.0050.00750.010.0125GSD1aGSD1b0.5 mFigure 4.2: Specific discharge (in m2/s) at hour 8 is overlaid on top of thehillshaded DEM, shown for GSD1a and GSD2a. Flow is from right toleft.High discharge, low supply (GSD1b and GSD2b)Both experiments run at high discharge with low sediment supply saw channelwidening along the entire length of the stream table during the first hour withgreater lateral erosion occurring in the downstream half of the stream table. InGSD1b, the initial rapid widening led to the formation of mid-channel bars andcoincided with extensive overbank flooding that continued until around hour 5.During this period, the location of the channel shifted back and forth across thefloodplain, forming a braided pattern and eroding the banks on either side of thechannel. In contrast, in the experiment conducted with the coarser bulk material(GSD2b), bank erosion was not as rapid or extensive during the first hour andquickly became limited to localized areas on alternating banks, forming a fairlystable meandering pattern by the end of the second hour. Some overbank flow didoccur at the beginning of GSD2a, however it was limited relative to that seen inGSD1b.Channel morphology and thalweg location never fully stabilized during theduration of GSD1b as it did in the coarse bulk material. Instead, over the courseof the eight hours, the channel reworked almost the entirety of the floodplain inthe lower two thirds of the stream table, eroding to the stream table walls in twolocations, first near the outlet of the channel during hour 6 and again halfway upthe channel during hour 8. In contrast, in GSD2b the channel only encountered the32wall just above the outlet on right side of the stream table during hour 5. Bank andbed erosion continued to occur up in both experiments until the end of the 8 hoursunlike in the low discharge experiments.Figure 4.3: DEMs of difference for GSD1b and GSD2b showing the differ-ence in bed elevation (in m) between the initial templated channel andthe bed at the end of the 8th hour. Extent of initial templated channel isindicated by the dashed grey lines. Flow is from right to left.High discharge, high supply (GSD1c and GSD2c)The paired experiments run at high discharge with high sediment supply started outsimilarly to the low supply runs; both saw rapid bank erosion and significant over-bank flow during the first hour, with the lateral erosion rate in the finer bulk material(GSD1c) elevated relative to that in the coarser bulk material (GSD2c). Followingthe first hour, the rate of lateral erosion slowed in the coarser bulk material, how-ever it did not develop the same meandering channel pattern as it did during thelow supply runs. Instead a series of irregularly spaced and shaped mid-channelbars formed and persisted until the end of hour 7 at which point the channel finallydeveloped a meandering pattern, although this transformation was accompanied bysignificant overbank flooding (as shown in Figure 4.6). By the end of the experi-ment, the channel in GSD2c had developed a morphology similar to that seen inGSD2b, except with the meandering pattern beginning closer to the inlet than in theexperiment with low sediment supply. In GSD1c, the channel remained active andmulti-threaded throughout the entire experiment, much like in the GSD1b, how-ever during the high sediment supply runs, lateral erosion occurred along the entire3300.00250.0050.00750.010.0125GSD1cGSD2a0.5 mFigure 4.4: Specific discharge (in m2/s) at hour 8 is overlaid on top of thehillshaded DEM, shown for GSD1b and GSD2b. Flow is from right toleft.length of the stream table, causing mid-channel bars to form all the way up to theinlet. Bank erosion caused the channel to encounter the left side of the stream tableduring the first hour, during hour 5 and again during hour 8. Further, beginning atthe end of hour 6 and progressing into hour 7, the channel began to rapidly incisealong the entire length of the stream table, resulting in the formation of an almostentirely single thread meandering channel with very little overbank flow. This pat-tern persisted for the majority of hour 7, until bank erosion in the bottom half ofthe channel widened it again enough that a mid-channel bar formed, and a multi-thread channel developed again, although overbank flow remained limited for therest of the experiment. Overall, during the high sediment supply runs, the channelswere more dynamic and laterally active along the entire length of the streamtable,however the morphologies that developed remained distinct between the two bulkmaterials.4.2 Pseudo-recirculating sediment experiment (Chapter7)4.2.1 Overview of the pseudo-recirculating sediment experimentChapter 7 presents data collected from a pseudo-recirculating sediment experi-ment, separate from the series of paired experiments. Pseudo-recirculating sedi-34Figure 4.5: DEMs of difference for GSD1c and GSD2c showing the differ-ence in bed elevation (in m) between the initial templated channel andthe bed at the end of the 8th hour. Extent of initial templated channel isindicated by the dashed grey lines. Flow from right to left.00.00250.0050.00750.010.0125GSD2bGSD2c0.5 mFigure 4.6: Specific discharge (in m2/s) at hour 8 is overlaid on top of thehillshaded DEM, shown for GSD1c and GSD2c. Flow from right toleft.ment conditions were set up to best model the conditions of sediment supply wemight expect in a natural channel. In natural channels, the supply into a givenreach comes from bank and bed erosion upstream, in a pseudo-recirculating sys-tem I aim to mimic the amount and the grain size distribution of material comingfrom upstream by feeding in the output from the stream table during the previous15-minute period. This method is preferable to constant feed systems as recircula-tion replicates the natural temporal variability in supply that could be expected innature.35The pseudo-recirculating sediment experiment was conducted at the same gra-dient as the paired experiments, however it was only run for a total of two hours andsediment was pseudo-recirculated through the system. Unlike true recirculatingsediment experiments, this one is referred to as “pseudo-recirculating” due to thetime lag in sediment feed: in pseudo-recirculating sediment conditions, sedimentoutput from the streamtable during each 15-minute interval was dried, weighed,sieved and fed back in the system during the subsequent 15-minute run. The re-circulated sediment was introduced at the top of the streamtable using a rotatingfeeder set to input sediment at the average output rate from the previous 15 min-utes. As the experiment was begun from a templated channel, zero sediment wasfed into the system during the first 15 minutes.In order to establish the pseudo-recirculating sediment condition, it was neces-sary to stop the flow every 15 minutes to dry the sediment output during that period.As such, both laser scans of bed elevation and surface texture data was collected ata 15-minute temporal resolution, which is four times higher than that of the pairedexperiments. Images of the bed surface were taken at 1 m intervals along the lengthof the stream table to create a total of ten high resolution models of the bed surfacefrom which surface grain sizes were digitized, or twice the number collected in thepaired experiments. Consequently, this experiment provides a formidable datasetfor examining both morphodynamic and surface texture adjustments.The description of channel evolution over the course of the pseudo-recirculatingsediment experiment is presented in Section 7.3, however Figure 4.7 shows thechange in bed elevation seen over the course of the two hour experiment as well asthe flow pattern that established.36−0.0300.0300.00250.0050.00750.010.0125Figure 4.7: DEM of difference showing the difference in bed elevation (inm) and specific discharge (in m2/s) at the end of hour 2 overlaid ontop of the hillshaded DEM, shown the pseudo-recirculating sedimentexperiment. Flow is from right to left.37Chapter 5Identifying the large grain effect5.1 IntroductionWhile the stabilizing function of large grains in step-pool streams has long beenrecognized, the role they play in gravel-bed streams is less clear. Most researchershave ignored the role of large grains in gravel bed streams, and have assumed thatthe median bed surface size controls the erodibility of alluvial boundaries. In thischapter, I present the results from two stream table experiments that exhibit signifi-cant differences in sediment transport characteristics and channel morphology thatcan only have been caused by the addition of a small amount of coarse sedimentto bed material. It is also demonstrated that the observed differences in channelbehaviour are inconsistent with the notion that the relative mobility of the mediangrain size is a suitable index for channel stability.Shields’ classic work on grain entrainment using a bed of uniform grain sizesis a seminal contribution that strongly influenced the direction of future research influvial geomorphology. Shields (1936) concluded that the onset of mobility of par-ticles in a channel occurs when the dimensionless shear stress in a channel exceedsa critical threshold (θc). While Shields (1936) found θc to be a function of theparticle Reynolds number, subsequent researchers found that relative particle ex-posure (e.g., Fenton and Abbott, 1977) and grain hiding (e.g., Parker et al., 1982b)also exert first-order control on the threshold of grain entrainment. Entrainment ofbed material can be further modified by the proportion of fine sediment on the bed38surface (Ikeda et al., 1988; Wilcock et al., 2001; Venditti et al., 2010), as well asby both channel gradient and relative roughness (Mueller et al., 2005; Bunte et al.,2013; Scheingross et al., 2013; Prancevic and Lamb, 2015).Investigations of entrainment from a bed composed of a mixture of grain sizeshave demonstrated that a wide range of particle sizes are entrained over a narrowerrange of flows than predicted by Shields’ original work (Andrews, 1983; Brayshaw,1985; Ashworth and Ferguson, 1989). Similarly, full mobility of most sedimentsizes in the bed corresponds to the onset of full mobility of the D50 (Wilcock andMcArdell, 1993, 1997). Such observations have led researchers to conclude thatthe bed surface D50 exerts a first-order control on the entrainment of the entiremixture (Komar, 1987; Parker, 1990; Buffington and Montgomery, 1997), even iftrue equal mobility of all sediment sizes is seldom if ever observed (Church et al.,1991; Wathen et al., 1995; Lisle, 1995; Parker and Toro-Escobar, 2002).Researchers have made the logical association between D50 mobility and chan-nel form stability. Stable channel geometry has been predicted assuming that theaverage boundary shear stress is equal to the entrainment threshold for D50 (Liet al., 1976; Parker, 1978; Diplas and Vigilar, 1992), or by estimating the shearstress acting on channel banks and setting that equal to the threshold for D50 (Mil-lar and Quick, 1993; Millar, 2005). The surface D50 is also incorporated intoequations predicting the meandering/braiding threshold (Henderson, 1961; Mil-lar, 2000, 2005; Eaton and Giles, 2009; Eaton et al., 2010), as well as variousgeneral frameworks for understanding fluvial mechanics (Andrews, 1984; Parkeret al., 1982b, 2007). Church (2006) advocates using the Shields parameter as thekey variable to distinguish between various channel morphologies, transport char-acteristics and stabilizing processes. Clearly, there is a great deal of evidence thatthe D50 is a very useful index that captures many essential features of stream mor-phodynamics.Some phenomena cannot be explained with reference to the D50. For example,Eaton and Church (2004) identified a threshold channel gradient above which theirexperimental stream table channels failed to establish and maintain a steady statecondition. The only apparent difference between experiments above and belowthis threshold was a change in the mobility for the largest sizes of sediment in thebed material. Similarly, the initial setup phase of stream table experiments is often39plagued by experiments that appear to defy expectations based on Froude scaling ofsome known prototype; initial trials sometimes exhibit unexpected stability duringwhich bars and pools fail to form, despite their presence in the field prototypes, orthey develop an unstable, braided pattern where a stable, single thread pattern isexpected.5.2 Summary of experimental designThis chapter presents the results from the paired experiments run at low discharge(0.7 L/s) and low sediment supply: GSD1a and GSD2a. Overall, the only dif-ference between this pair of experiments was the bulk material used; in all otherrespects, the experiments were identical. The first experiment (GSD1a) was con-ducted using a bulk grain size distribution for which d50 = 1.60 mm, d90 = 3.67mm, and d95 = 4.37 mm. For the second experiment (GSD2b) additional coarsematerial ranging in size from 4 to 8 mm was added to GSD1, producing a distri-bution for which d50 = 1.63 mm, d90 = 3.94 mm, and d95 = 5.09 mm. Chapter 3provides an in-depth explanation of the model design and set up, the experimentalprocedure, as well as the data collection and processing used to produce the resultspresented here, while Section 4.1 details the specific experimental procedures asso-ciated with paired experiments and provides an overview of the channel evolutionover the course of the experiments.The primary data used in this chapter include: DEMs of bed elevations de-rived from the A-BES laser scanner, sediment output data (both flux and grainsize distribution) collected from the bucket trap at the outlet of the stream table,flow modelling results derived from Nays2DH, and surface grain size distributionsmeasured from downlooking images of the bed. Although the experiments ana-lyzed in this chapter are the same as the first pair analyzed in Chapter 6, there aresome small discrepancies in some of the data due to differences in the methods ofanalysis. These differences are summarized in Table 4.2.5.3 ResultsExperiments GSD1a and GSD2a exhibited very different morphodynamics: GSD1adeveloped a sinuous channel with distinct bars, riffles and pools while GSD2a40GSD1GSD2Figure 5.1: Detail of hillshaded DEMs for GSD1a and GSD2a at 8 hrs.remained straight, and only developed low-amplitude bars (Figures 4.2 and 5.1).The reach-average channel geometry at the end of the experiments also variedmarkedly: at the end of GSD1a, the average channel width (W ) and depth (Y )were 0.65 m and 0.005 m, respectively, while for GSD2a, the values were 0.36 mand 0.008 m, respectively. An overview of the channel evolution over the courseof the 8 hours in both experiments can be found in Section 4.1.2.Both GSD1a and GSD2b experienced net degradation over the course of the 8hours, since there was no sediment feed at the upstream end of the stream table.The total volume of degradation during GSD1a (19.9 kg) was nearly four timesthe total during GSD2a (5.2 kg) (Figure 5.2A). The sediment output rate duringGSD1a fluctuated over several orders of magnitude, reaching peak output rates of178 and 206 g/min at 1 hr and 5 hrs, respectively (Figure 5.2B). In contrast, theoutput rate during GSD2a reached a maximum of 54 g/min at 2 hrs and was lessvariable over the course of the experiment.During GSD1a, degradation resulted primarily from lateral erosion and evac-410 2 4 6 8−20000−10000−50000Time (hr)Cumulative Sediment (g)AGSD1GSD20 2 4 6 8050100150200250Time (hr)Q b (gmin)BFigure 5.2: A) Cumulative sediment output; B) Bedload transport ratethrough time.uation of bank material (Figure 4.1). In fact, most areas within the original tem-plated channel experienced net aggradation, raising the local bed elevation. DuringGSD2a, almost no bank erosion occurred and the relatively small loss of sedimentthat did occur resulted from vertical scour. During the last 2 hrs of both experi-ments, the channels became nearly static, and the average sediment output rate wasless than 10 g/min.While bedload sediment texture did vary over the course of GSD1a and GSD2a,the temporal trends were not significant (Table D.1). Despite slightly different bedmaterial distributions, the distribution of the transported load was nearly identicalfor the two experiments. The range of values for the bedload median size (d50) andthe 90th percentile (d90) are shown in Figure 5.3A; the mean values of d50 and d90are not statistically different for GSD1a and GSD2a at the 95% confidence level(Table D.2).The bed surface texture coarsened over time during both experiments (Figure5.4), though the trends for D50 and D90 are not statistically significant for GSD1a(Table D.1). The bed surface developed during GSD2a was slightly coarser thanthat which developed during GSD1a (Figure 3.2) as both D50 and the D90 forGSD2a were statistically larger than the values for GSD1a (Figure 5.3B; TableD.2). Excluding data from the first hour of the experiment, the armour ratio calcu-42GSD1 GSD23.03.54.04.5A GSD1 bulk d90GSD2 bulk d90GSD1 GSD23.03.54.04.5BLoad D90 (mm)Surface D90 (mm)Figure 5.3: Load and surface grain sizes for GSD1a and GSD2a.lated from the surface D50 and the subsurface bulk d50 varied from about 1.00 to1.18 for GSD1a, and from about 1.10 to 1.25 for GSD2a (Table B.1). These armourratios are lower than they would be in the field prototype, since the model grain sizedistribution is truncated at 0.25 mm (equivalent to 6.25 mm in the prototype).The flow modelling results indicate differences in the reach average flow con-ditions resulting from the different bed morphologies developed during GSD1a andGSD2a. The distribution of τ is not a simple, normal distribution, because exten-sive areas of the channel bed during GSD1a were covered by slow moving, shallowwater, which dramatically reduces the reach-average shear stress (Figure 5.5). Dur-ing the first hour, both GSD1a and GSD2a saw a decrease in reach-averaged shearstress (τ) from that associated with the initial channel (for which τ = 2.2 Pa). Themagnitude of change was greater in the GSD1a experiment and τ continued to de-crease until 3 hrs, at which point it stabilized at approximately 0.95 Pa. In theGSD2a experiment, τ dropped to 1.68 Pa during the first hour and remained atabout this value for the rest of the experiment.In order to make a more meaningful comparison of the shear stresses in themain channel around the thalweg, the median shear stress (τ50) was estimated fora flow field that excludes data from grid cells for which q< 0.0005 m2/s (where q431 2 3 4 5 6 7 81.01.52.02.53.03.5Time (hr)D 50 (mm)GSD1 D50GSD2 D50GSD1 d50GSD2 d501 2 3 4 5 6 7 83.03.54.04.55.05.5Time (hr)D 90 ( mm)GSD1 D90GSD2 D90GSD1 d90GSD2 d90Figure 5.4: Mean surface D50 and D90 through time for the two experiments.The solid lines represent the results of linear regressions conducted onthese mean values (Equations and R-squared values presented in TableD.1). Whiskers show the standard error of the mean (n = 5).is the specific discharge, calculated as Q/W ). An estimate of the 95th percentileof the shear stress distribution in the main channels (τ95) was also used as an indexof the upper range of the shear stress distributions. For GSD1a, the values of τ50oscillated about a mean value of approximately 1.6 ± 0.013 Pa, while they variedabout a mean of 1.9 ± 0.024 Pa for GSD2a. This comparison implies that thetypical bed shear stresses during GSD2a were systematically greater than thoseacting on the bed during GSD1a, though the differences (in the main channel, atleast) are not as large as estimates of the mean reach-average τ would suggest. Thedifference in the maximum bed shear stresses for the two experiments is not aslarge; the values of τ95 for GSD1a and GSD2a varied about mean values of 2.6± 0.011 Pa and 2.7 ± 0.041 Pa, respectively, suggesting that the peak bed shearstresses were approximately the same in both experiments.Using Equation 2.2, it was determined that for GSD1a, τ∗50 varies from 0.052 to0.065 with a mean value of 0.056, while for GSD2a, τ∗50 varies from 0.059 to 0.066with a mean of 0.063. So, not only are the reach-averaged shear stresses higher44Frequency0 1 2 3 4050010001500200025003000GSD1GSD2Shear Stress (Pa)Figure 5.5: Histograms of shear stress values for GSD1a and GSD2a basedon Nays2DH modelling using the bed topography after 8 hrs. The his-togram presents the number of grid cells having shear stress values in aparticular range, and the sum of all columns is proportional to the totalarea covered by flowing water.for GSD2a, but τ∗50 is slightly higher, too. However, despite the higher τ∗50 valuesduring GSD2a, the channel was much less active and the sediment transport rateswere much lower, relative to GSD1a.5.4 DiscussionThese experiments demonstrate that the median surface grain size does not controlchannel stability. Traditional approaches for predicting the threshold for channelchange compare the reach-averaged dimensionless shear stress (τ∗50) to the entrain-ment threshold for the D50 (e.g., Li et al., 1976; Parker, 1978; Diplas and Vigilar,1992; Millar and Quick, 1993). The current consensus on stream channel dynamicspredicts that channel change should occur when τ∗50 exceeds some critical value,with the magnitude of the changes proportional to the degree to which the threshold45is exceeded. This premise appears to be incorrect, since the experiment with thehigher τ∗50 remained stable while the one with the lower value widened, developeda sinuous, riffle pool morphology and transported four times as much bed mate-rial. The results from this study suggest that the largest grains in the bed materialcontrol channel stability, a phenomenon which I will refer to as the “large graineffect”.While some researchers have noted the importance of coarse material in barstabilization (Leopold and Wolman, 1957; Lewin, 1976; Lisle et al., 1991), othershave ignored the issue, conducting experiments that use very narrowly graded sed-iments to explore bar dynamics (Jaeggi, 1984; Ikeda, 1984; Termini, 2009), whicheliminates the potential effects described herein. Furthermore, the traditional useof fixed-wall flumes (e.g., Lewin, 1976; Ikeda, 1984; Lisle et al., 1991; Lanzoni,2000; Termini, 2009) to study sediment transport and bedform dynamics make itimpossible to study channel stability, since channel width and slope are fixed quan-tities, rather than adjustable properties of the system, as they are in the field. It isonly in stream table experiments (or in the field) that the full suite of processes con-trolling channel stability can be studied, which perhaps explains why the scientificcommunity has failed to make a distinction between sediment mobility (compris-ing the entrainment and transport of grains) and sediment stability (involving theinteractions between large bed particles, the near-bed flow structure, and other bedparticles).For the two experiments studied herein, most of the channel adjustments tookplace during the first hour. By the second hour, bed shear stress, wetted width,and depth reached reasonably stable values. While τ∗50 is different for the twoexperiments, the reach-averaged dimensionless shear stress, when calculated inEquation 2.2, using Di = D95, is approximately the same for both GSD1a andGSD2a, having an average of 0.022 (excluding data from the first hour), whichis consistent with the entrainment threshold of 0.02 for large grains, reported byAndrews (1983). This suggests that, after the initial period of bank erosion, beddeformation, bar deposition and/or surface coarsening during the first hour, bothexperiments reached a stable state defined by the threshold of motion for the largestgrains on the bed, despite consistently different τ∗50 values.Although the stable channels developed by the end the experiments are both46consistent with a threshold channel associated with the largest grains, the pro-cesses producing the threshold state were quite different. Despite the lower θ50values during GSD1a, erosion of channel banks during that experiment triggereda feedback mechanism between channel form and local transport capacity that ledto the development of a sinuous channel with a riffle-pool morphology, ultimatelyresulting in a wider, shallower channel. This lateral instability also supplied thesystem with sediment via extensive bank erosion, such that much of the initialchannel was subject to local net aggradation (GSD1a in Figure 4.1). In contrast,during GSD2a, the initial channel degraded and coarsened, and did not receive anysignificant sediment inputs due to lateral channel migration. In this circumstance,only low amplitude, poorly developed bars formed (GSD2a in Figure 4.1). In lightof this, the explanation for such different response trajectories must relate to theinitial mobility of the largest grains, and through that, the capacity of the channelto erode its banks.At the beginning of both experiments, τ50 was approximately 2.2 Pa (see Ta-ble C.1). Assuming that the bed surface initially had the same median size as thebulk sediment distribution, the values of τ50 were 0.082 and 0.085 for GSD1a andGSD2a, respectively. According to these calculations and considering the rela-tively unstructured and unarmored state of the channel bed at the beginning of theexperiments, the bed surface D50 should have been fully mobile and both channelsshould have been laterally active. Previous work summarized by Lisle et al. (1991)suggests that alternate bars should form for these conditions, as well. Nevertheless,the experiment with the slightly higher τ50 value (GSD2a) remained laterally stableand did not develop a well-defined set of alternate bars, whereas that with the lowervalue deformed its boundaries and developed a sinuous planform with prominentbars, pools and riffles. The processes governing channel stability can clearly not beassociated with mobility of the D50, even if mobility of the D50 is a useful index.If the D50 is not controlling channel stability, then what is controlling it? Ananalysis of relative mobility using the ratio of the bedload sediment size, outputfrom the stream table, (di) to the bed surface sediment size (Di) indicates that thelargest grains in the bed material were systematically underrepresented in the bed-load for GSD2a (but not GSD1a), suggesting that they were only partially mobile(Figure 5.6). Assuming that full mobility corresponds to di/Di ratios of between47lllll ll l1 2 3 4 5 6 7 80.60.81.01.21.4Time [hr]d iDiGSD1lllllllFull MobilityllD50D90D95lll lllll1 2 3 4 5 6 7 80.60.81.01.21.4Time [hr]d iDiGSD2lll ll l llFigure 5.6: The ratio of the texture of the transported material to the bed sur-face is shown for the median (solid circles), the 90th percentile (opencircles) and the 95th percentile (plus signs) of each distribution forGSD1a (red) and GSD2a (blue).0.85 and 1.15, the bed surface D50, D90 and D95 were all fully mobile for the du-ration of GSD1a. However, for GSD2a, the bed surface D50 was fully mobile, butthe larger size classes (i.e. D90 and D95) were not.Perhaps the difference between the morphodynamics of GSD1a and GSD2acan be associated with the areal concentration of stable grains on the bed surface.According to Wilcock and McArdell (1997), grains in a given size class becomepartially mobile once shear stress of the bed exceeds the critical shear stress of en-trainment and become fully mobile at twice the critical shear stress of entrainment.However, not all partially mobile grains contribute to channel stability (i.e., someof those grains will have moved during the experiment). Work by Wilcock andMcArdell (1997) suggests that, for a size class at the threshold between stabilityand partial mobility (i.e., τ = τci, where τci is the critical shear stress to entrainthat size class), 90% of the grains on the bed within that class will remain immo-bile; in contrast, for a size class at the threshold between partial mobility and fullmobility (i.e., τ = 2τci), only 10% of the grains on the bed will remain immobile.Assuming that the proportion of immobile grains on the bed decreases linearly asτ increases from τ = τc to τ = 2τc, it is estimated that 3.5± 1% of the initial bed48surface was immobile during GSD1a and 6.1±1% of the initial bed was immobileduring GSD2a (the estimated error is based on uncertainty for the bed surface tex-ture values). By the end of the experiments (when both channels had achieved astable configuration), it is estimated that the proportion of the bed that was stablehad increased for both experiments, reaching statistically similar values (12±1%for GSD1a and 13±1% for GSD2a).These results suggest that: (1) for channel planform to be stable (in the pres-ence of bed material transport), approximately 5% of the bed must be immobile;and (2) for a channel to reach a static state (i.e. having both a stable channel patternand experiencing transport rates close to zero) approximately 10% of the bed mustbe immobile. While it may seem that an immobility threshold of 5% is small, thisvalue is comparable to the results reported by Gao et al. (2016), who found thataeolian dunes do not form when the initial proportion of coarse (i.e. immobile)grains within the bed is greater than 4-5%. While more work remains to be doneto explore the mechanisms by which these coarse grains stabilize a surface, thereis strong evidence to suggest that small changes to the coarse tail of a deposit canplay a significant role in altering the morphodynamics of a sedimentary surface.5.5 ConclusionsThe results of two experiments conducted with nearly identical bed material distri-butions demonstrate an incomplete understanding of the factors controlling channelstability. The experiments suggest that channel stability is most likely controlledby the large grain effect: stability does not seem to be controlled by the median sur-face grain size, which is fully mobile during floods, instead it is the largest grainsthat remain immobile and impart stability to the channel. It was found that addinga relatively small volume of coarse sediment to the bed material (which producedonly a 15% increase of the d95 of the bulk material) resulted in a 48% decrease inchannel width and a 75% decrease in average sediment transport rate. The additionof coarse material also produced a transition from a lateral style of channel adjust-ment, in which bank erosion allows for the development of a sinuous channel andpool-riffle morphology, to a primarily vertical style of adjustment involving essen-tially no bank erosion. Given the design of the models used in these experiments,49results from this study are strictly applicable to relatively small, sediment supplylimited threshold channels. However, observations from related experiments, pre-sented in the next chapter, using the same grain size distributions seem to confirmthat large grain sizes control channel stability over a wide range of discharge valuesand sediment supply rates.50Chapter 6Validating the large grain effect6.1 IntroductionIn Chapter 5, I describe “the large grain effect”, an phenomenon named for thesmall proportion of large grains that appear to exert a surprising influence on mor-phodynamics in an alluvial channel. With the only difference between a pairedexperiments being a slightly greater (< 5%) proportion of large grains in the bulkmaterial, I find that the channel with the coarser bulk material output four timesless sediment and experienced only half as much bank erosion of that run in thefiner material. Given that the median grain size of the surface was approximatelythe same in both experiments, I infer that the processes driving the difference inmorphodynamics between the two systems are controlled not by behaviour of thethe median grain size, as it has commonly been accepted (e.g., Parker et al., 1982a;Andrews, 1983), but instead by the coarse tail of the distribution. Further, thesedifferences cannot be accounted for by the average dimensionless shear stress (τ∗50)as τ∗50 was actually higher in the more stable channel. These results lead us tore-examine our understanding of channel stability in alluvial systems and to lookdeeper into the influence of the large grain effect on channel morphodynamicsacross a wide range of conditions.Some literature supports the observation that large grains play a role in channelmorphodynamics, particularily in regards to their influence on flow resistance (e.g.,Hey, 1979; Recking et al., 2009; Monsalve et al., 2017); however most researchers51have done little to study their role in sediment transport and channel stability (seeChapter 4). Large grains influence flow resistance by disrupting the velocity pro-file near the bed, dissipating the energy available for work (Monsalve et al., 2017).These grains do not always do so individually, instead it is well documented thatlarge grains interact to form structures, such as stone cells, clusters and ribs, that tofurther increase bed roughness and increase flow resistance (Clifford et al., 1992).However, these structures also influence sediment transport and channel stability(Hassan and Church, 2000); groupings of large grains act to shelter smaller sur-rounding grains, thus limiting sediment entrainment and increasing the surface sta-bility. Consequently, these large grains can be thought of as forming a frameworkover which finer material is transported and by which a stable channel geometry isable to persist (MacKenzie et al., 2018), much in the way that it has been observedin steeper channels (Phillips, 2002; Piton and Recking, 2017).Channel stability has traditionally been assessed by comparing the thresholdshear stress of the median grain size to the shear stress in the channel (e.g., Jowett,1989; Kaufmann et al., 2008). The experiments presented in Chapter 5 disrupt thisnotion, as the dimensionless shear stress was higher in the more stable channel (i.e.with more large grains present). Further, studies have observed multiple “stages” ofchannel stability, which suggests that there may not be a single threshold of channelstability that can be defined. These studies tend to distinguish between annual peakflows in which the transport of material around the median size occurs, but thechannel geometry remains fairly constant, and infrequent flood flows for whichall grains are entrained and significant channel restructuring occurs (Jackson andBeschta, 1982; Carling, 1988; Ashworth and Ferguson, 1989; Warburton, 1992).These observations, in concert with my own experiments, point to the role of largegrains in providing channel stability and has lead to development to a multi-phasedmodel of channel stability based on the entrainment threshold of some measure ofthe largest grains in a channel (see Chapter 2).The results of Chapter 5, in conjunction with the in-depth review of literaturepresented in Chapter 4, provide evidence for the large grain effect, however, thereremains a lack of evidence that large grains remain influential across different con-ditions, particularly at higher discharges and sediment supply rates. In this studyI present three pairs of experiments which aim to answer two important questions:52(1) Does the difference between the two grain size distributions persist at higherdischarges where a greater fraction of the bed is mobile? (2) Does the differencepersist at high sediment supply where the development of armouring is suppressed?6.2 Summary of experimental designThis chapter presents the results from all three sets of paired experiments: thoserun at low discharge (0.7 L/s) without feed (GSD1a and GSD2a), those run at highdischarge (1.4 L/s) without feed (GSD1b and GSD2b), and those run at high dis-charge with feed (100 g/min) (GSD1c and GSD2c). Overall, the only differencebetween each pair of experiments was the bulk material used; in all other respects,the experiments were identical. Chapter 3 provides an in-depth explanation of themodel design and set up, the experimental procedure, as well as the data collectionand processing used to produce the results presented here, while Section 4.1 detailsthe specific experimental procedures associated with paired experiments and pro-vides an overview of the channel evolution over the course of the experiments. Theprimary data used in this chapter include: DEMs of bed elevations derived fromthe A-BES laser scanner, sediment output data (both flux and grain size distribu-tion) collected from the bucket trap at the outlet of the stream table, flow modellingresults derived from Nays2DH, and surface grain size distributions measured fromorthomosaics of the bed surface created using Photoscan.6.3 Results6.3.1 Channel evolutionIn nearly all experiments the stream channel widened relative to the initial rectan-gular channel and developed bars, pools and riffles 1. In general, widening wasgreatest in the downstream half of the channel for experiments following the lowsediment supply scenario, and fairly equal along the length of the channel for ex-periments following the high sediment supply scenario. These trends are exempli-fied in Figures 4.1, 4.3, and 4.5 which show the difference in elevation, and thus1The only experiment to not change notably from initial templated channel was GSD2a, run inthe coarser bulk material at low discharge with low sediment supply.53morphology, between the initial channel and that at the end of the 8 hours for eachof the paired experiments.Distinct differences in flow patterns developed between paired experiments.At low discharge, the channel developed a meandering pattern in the finer bulkmaterial (GSD1a) while flow remained straight in the coarse material (GSD2a).This is demonstrated in Figure 4.2 which shows the modelled flow in the channel(represented by the specific discharge) at the end of hour 8 for the pair run at lowdischarge and low sediment supply. In experimental pairs run at high discharge(with both high and low sediment supply), experiments using GSD1 developeda braided pattern, whereas the experiments using GSD2 developed a meanderingpattern (Figures 4.4 and 4.6).In-depth summaries of channel evolution in each paired experiment can befound in Section 4.1.2. Further, additional DoDs showing the change in morphol-ogy between subsequent hours for each experiment can be found in the Appendix(Figures A.1, A.2, A.3, A.4, A.5, A.6).6.3.2 Morphodynamic changeThe differences in channel evolution described in Chapter 4 (Section 4.1.1) arequantified using indices of morphodynamic change derived from the DEMs of dif-ference. In all experiments, the magnitude of change seen over the course of the8 hours was strongly controlled by the bulk mixture in which it was run. Betweenpaired experiments, morphodynamic activity was always much greater in the ex-periments run with the finer bulk material (Figure 6.1).Morphodynamic activity (M) was greatest during the first hour for all exper-iments. M subsequently tended towards zero in the low discharge experiments(GSD1a and GSD2a) but remained relatively high for the other experiments (GSD1b,GSD1c, GSD2b and GSD2c; see Figure 6.2). Comparing the experimental pairswith the same discharge and sediment supply, it is clear that those run with GSD1had relatively greater values of M relative to their GSD2 counterparts (Figure6.1B). The greatest cumulative difference between pairs was for those run at lowdischarge (Table 6.1). GSD1a experienced 3.6 times more cumulative morphody-namic change than did GSD2a, while GSD1b and GSD1c experienced approxi-541 2 3 4 5 6 7 8−0.10.00.10.20.30.4Low Discharge, Zero FeedGSD1 MGSD2 MGSD1 ∆SGSD2 ∆S1 2 3 4 5 6 7 8−0.10.00.10.20.30.4High Discharge, Zero Feed1 2 3 4 5 6 7 8−0.10.00.10.20.30.4High Discharge, FeedCumulative M and ∆S (m3 )Time (hr) Time (hr) Time (hr)Figure 6.1: Cumulative morphodynamic activity (M) and cumulative changesin sediment storage (∆S) in m3 over time.1 2 3 4 5 6 7 80.000.040.08M (m3 )1 2 3 4 5 6 7 8−0.04−0.020.00Time (hr) ∆ S (m3 )GSD1aGSD1bGSD1cGSD2aGSD2bGSD2cFigure 6.2: Hourly morphodynamic activity (M) and hourly changes in sedi-ment storage (∆S) in m3 over time.55mately twice the morphodynamic activity of GSD2b and GSD2c.Doubling the discharge for the low sediment supply scenario increased M inboth bulk mixtures. However, M differed by a factor of 10 for the high and lowdischarge experiments in GSD2, while M differed by only a factor of 4 for thecorresponding experiments using GSD1. Increased rates of sediment supply (i.e.the high sediment supply scenario) did not exert a large influence on M for exper-iments conducted in either bulk mixture, although total cumulative M was slightlyhigher under the high supply scenario with the difference between low and highsupply experiments being slightly greater in the finer bulk mixture.Changes in sediment storage (∆S) are used to determine whether a channel isdegradational (∆S < 0), aggradational (∆S > 0) or at equilibrium (∆S ≈ 0). Myresults show that all experiments were degradational as they experienced a net lossof sediment over the course of the 8 hours (Figure 6.1) with the greatest loss occur-ring during the first hour (Figure 6.2). Between paired experiments, those run withthe finer bulk material (GSD1) lost more sediment than those run with the coarsermaterial (GSD2). Like with M, the greatest difference in total cumulative ∆S be-tween pairs was seen at low discharge, as GSD1a was 4 times more degradationalthan GSD2a (Table 6.1). A notable difference exists between the experiments runat high discharge and high sediment supply (GSD1c and GSD2c): although GSD1cremained degradational throughout the entire 8 hours, in GSD2c, ∆S approachedzero following the first hour, suggesting that the channel evolved towards sedimenttransport equilibrium. In general, the high supply scenario was associated with lessnegative values of ∆S, however the high sediment supply scenario seems to havehad a greater influence on the morphodynamics for the experiment run with thecoarser bulk material.The sediment output rates are consistent with those of M and ∆S as experimentsrun in GSD1 output more than those run in GSD2 and the high discharge exper-iments output more sediment than those run at low discharge (Figure 6.3, Table6.1). The cumulative difference between the sediment input and the sediment out-put for the two experiments run with high sediment supply are consistent with theobserved changes in sediment storage (∆S); experiment GSD1c remained degra-dational while that of GSD2c evolved towards a more equilibrium system a totalcumulative net value of near 0.561 2 3 4 5 6 7 8−150000−50000050000150000Time (hr)Cumulative Q b, out and Qb, out NetLow Discharge, Zero FeedGSD1 Qb OutGSD2 Qb OutGSD1 Qb Out NetGSD2 Qb Out Net1 2 3 4 5 6 7 8−150000−50000050000150000Time (hr)High Discharge, Zero Feed1 2 3 4 5 6 7 8−150000−50000050000150000Time (hr)High Discharge, FeedFigure 6.3: Cumulative sediment output (Qb,out) and cumulative net sedimentoutput (Qb,out Net) over time.ΣM ΣS ΣQb,out ΣQb,out NetGSD1a 0.091 -0.03 19916.0 19916.0GSD2a 0.025 -0.01 5182.8 5182.8GSD1b 0.385 -0.14 132269.0 132269.0GSD2b 0.197 -0.07 73692.0 73692.0GSD1c 0.451 -0.11 126750.0 78750.0GSD2c 0.220 -0.03 54497.0 6497.0Table 6.1: Summary of total cumulative morphodynamic change for each ex-periment. Where ΣM is the total cumulative morphodynamic activity inm3, ΣS is the total cumulative storage in m3, ΣQb,out is the total cumu-lative sediment output in g and ΣQb,out Net is the total cumulative netsediment output in g.6.3.3 Bedload and surface grain size distributionsWe present the bedload grain size data as time-averaged distributions (weighted bythe sediment output rate for that given time period) for each experiment (Figure6.4). This is because while many experiments exhibited a slight fining trend overthe course of the 8 hours (Figure 6.5), the trend was only statistically significantfor the bedload d50 the d84 in GSD1c and the bedload d84 in GSD1b (Table D.3).Comparing then the average bedload GSD between pairs, the material transportedwas surprisingly similar for the two bulk mixtures, there was no statistical differ-ence in average bedload transported between any of the pairs (Figure 6.4 and TableD.5).570.5 1.0 2.0 5.0 10.00.00.20.40.60.81.0Particle Size (mm)Cumulative Proportion FinerLow Q, Zero FeedGSD1GSD20.5 1.0 2.0 5.0 10.00.00.20.40.60.81.0Particle Size (mm)High Q, Zero Feed0.5 1.0 2.0 5.0 10.00.00.20.40.60.81.0Particle Size (mm)High Q, FeedFigure 6.4: Comparison of bedload GSD between paired experiments.2 4 6 81.01.21.41.61.82.0GSD1aGSD1bGSD1cGSD2aGSD2bGSD2c Bulk GSD1 Bulk GSD22 4 6 82.02.53.03.54.0Time (hr)Bedload D50 (mm)Bedload D84 (mm)Figure 6.5: Bedload d50 and d84 over time for all experiments. Experimentswith significant temporal trends in bedload grain size are shown in bold.580.5 1.0 2.0 5.0 10.00.00.20.40.60.81.0Particle Size (mm)Cumulative Proportion FinerLow Q, Zero FeedGSD1GSD20.5 1.0 2.0 5.0 10.00.00.20.40.60.81.0Particle Size (mm)High Q, Zero Feed0.5 1.0 2.0 5.0 10.00.00.20.40.60.81.0Particle Size (mm)High Q, FeedFigure 6.6: Comparison of surface GSD between paired experiments. 95%confidence interval bounds, calculated using the method presented inEaton et al. (2019), have been added to the distributions as overlyingpolygons to show the range of uncertainty associated with a sample of200 grains.The bed surface tended to coarsen slightly during nearly all experiments; theonly experiments with significant temporal trends were GSD2a (for the D50 and theD84) and GSD2b (for the D50 only)(Figure 6.7 and Table D.4). Thus, the surfaceGSDs for each experiment are calculated using all measurements of surface grainsfrom all eight hours (Figure 6.6). Overall, experiments run in the coarser bulk ma-terial (GSD2) consistently have a greater proportion of large grains present on thesurface. Further, the differences in surface texture were greater at high discharge,under both high and low sediment supply scenarios, as GSD2b and GSD2c hadsignificantly larger values of D50 and D84 than GSD1b and GSD1c, respectively.At low discharge, there was only a significant difference for the D84.In all experiments, large grains were overrepresented at the surface of the bedrelative to their proportion in the bedload, whereas the median size of material onsurface was more comparable to that transported as bedload (Figure 6.8). Betweenpaired experiments, the ratio of D84/d84 was significantly greater in the GSD2experiments than it was in those conducted with GSD1. In comparison, there wasno significant difference between the ratios of D50/d50 between any of the pairedexperiments.591 2 3 4 5 6 7 81.21.62.02.4Surface D50 (mm)GSD1aGSD1bGSD1cGSD2aGSD2bGSD2cBulk GSD1 Bulk GSD21 2 3 4 5 6 7 82.03.04.05.0Time (hr)Surface D84 (mm)Figure 6.7: Surface D50 and D84 over time for all experiments. Experimentswith significant temporal trends in bedload grain size are shown in bold.95% confidence interval bounds have been added to GSD1a and GSD2ato demonstrate the range of uncertainty for a sample of approximately3500 grains.60GSD1aGSD2aGSD1bGSD2bGSD1cGSD2c0.91.01.11.21.31.41.51.6D84d 84AGSD1aGSD2aGSD1bGSD2bGSD1cGSD2c0.91.01.11.21.31.41.51.6D50d 50Figure 6.8: Ratio of surface D50 and D84 to bedload d50 and d84.6.3.4 Shear stress and stream powerWe found that reach-averaged dimensionless shear stress normalized using the D50(τ∗50) was on average higher for experiments conducted in the coarser bulk material(GSD2), although the difference was only significant for the pair run at high dis-charge and low sediment supply. The relationship between the two bulk mixturesreversed when the reach-averaged dimensionless shear stress was calculated usingthe D84 (τ∗84); those run with the finer bulk material tended to have higher values ofτ∗84 than their pair run with the coarser bulk material, however the differences werenot statistically significant. Like with τ∗50, the change in τ∗84 between high and low61GSD1aGSD2aGSD1bGSD2bGSD1cGSD2c0.0600.0650.0700.0750.0800.085 τ50*GSD1aGSD2aGSD1bGSD2bGSD1cGSD2c0.0300.0320.0340.0360.0380.0400.042τ84*Dimensionless Shear StressFigure 6.9: A) Boxplot comprising all measurements of dimensionless shearstress calculated with D50 for each experiment, except the initial value(i.e. that associated with the templated bed); B) Boxplot comprisingall measurements of dimensionless shear stress calculated with D84 foreach experiment.discharge was greater with GSD2, however, with τ∗84 there was less of a differencebetween GSD2b and GSD2c than what was seen for τ∗50.Between paired experiments, unit stream power (ω) was higher in experimentsconducted with the coarse bulk material (GSD2). For the low sediment supplyscenarios (both high and low discharges) the temporally-averaged value of ω wassigificantly higher in GSD2 than in GSD1. For the high sediment supply scenario,while ω was higher in GSD2c than in GSD1c, it was not significantly different.These results are similar to those of τ∗50, although the differences between the twobulk mixtures are slightly greater for ω .6.4 DiscussionDifferences in channel morphodynamics persist between two nearly identical ex-periments even with the doubling of discharge and under high and low sedimentsupply scenarios; all experiments run in the finer bulk material (GSD1) were con-sistently more morphodynamically active than their counterparts run with the slightly62GSD1aGSD2aGSD1bGSD2bGSD1cGSD2c0.0200.0250.030Unit Stream Power (W/m)Figure 6.10: Boxplot comprising all measurements of unit stream power, ex-cept the initial value (i.e. that associated with the templated bed).coarser bulk material (GSD2; Figure 6.1 and Table 6.1). These results indicate thatchannel response may be largely governed by the behaviour of a small volume ofcoarse grains and thus suggest that the large grain effect persists across a range ofconditions.6.4.1 Persistence across dischargesIn my experiments, increasing the discharge caused greater morphodynamic activ-ity (M) and more degradation (-∆S) in both bulk mixtures, however the differencein response was larger in the coarser bulk material. I measured eight times themorphodynamic activity at high discharge relative to low discharge in experimentsrun with GSD2, whereas doubling the discharge resulted in just under four timesthe morphodynamic activity in the finer bulk material (Table 6.1). Likewise, thechange in ∆S with discharge was greater for GSD2 than it was for GSD1; GSD2bexperienced nearly ten times times as much degradation as GSD2a, while GSD1bexperienced five times much degradation as GSD1a.Doubling the discharge reduced differences between the two bulk mixtures; atlow discharge, cumulative morphodynamic activity was over 3.5 times greater in63GSD1a than in GSD2a, whereas at high discharge, it was only two times greater inGSD1b than in GSD2b. The value of ∆S for GSD2b was four times that for GSD2a,while ∆S for GSD1b was about twice that for GSD1a. Overall, these results suggestthat while discharge exerts a significant influence on channel morphodynamics, themagnitude of response is mediated by the bulk mixture.Differences in morphodynamic activity between the two bulk mixtures acrossdischarges (Figure 6.1) be considered from the perspective of the channel stabilitymodel presented in Chapter 2. This conceptual model groups channel responseinto three stability phases: 1) stable, wherein the channel undergoes little to nomorphodynamic change; 2) dynamically stable, wherein localized bank erosionand compensating bar deposition occur; and 3) unstable, wherein significant bankerosion causes the channel to widen. Based on these definitions, I broadly classifyGSD2a as stable, GSD1a and GSD2b as dynamically stable and GSD1b as unsta-ble, although in all cases the channels transition across these phases over the courseof the 8 hours (see DoD Figures in Appendix A). Considering GSD2, the large shiftin morphodynamic activity between high and low discharge can be attributed to thetransition from a stable channel, where bed and bank erosion is almost negligible,to a morphodynamically active one where erosion and deposition occurs for theentire 8 hours. Comparatively, because GSD1 is already morphodynamically ac-tive at low discharge, the increase in discharge simply increases the rate at whichbanks are eroded and the length of time for which this high rate of morphodynamicchange is sustained.Many studies have observed that the size of material transported as bedload in-creases with discharge (Lisle, 1995; Lanzoni, 2000; Haschenburger and Wilcock,2003), however in my experiments, the grain size distribution of bedload trans-ported at high discharge is not remarkably different from that transported at lowdischarge in either bulk mixture (Figure 6.5). The same is true for the surface tex-ture (Figure 6.7). Comparing the ratios of the size of material left on the surface tothat transported as bedload for the low sediment supply scenarios (Figure 6.8), itcan be seen that differences between D84/d84 across the bulk mixtures are signifi-cant (i.e. between GSD1 and GSD2) while those between high and low dischargefor a given bulk mixture are not (e.g. GSD1a and GSD1b); D50/d50 is not statisti-cally different between any of these experiments. These results suggest that, while64increasing the discharge causes more of the channel to experience erosion and de-position, the ultimate magnitude of that change is governed by the relative stabilityof large grains. When a greater proportion of large grains are left on the surface(i.e. are immobile or partially mobile), as is the case in the GSD2 experiments, theyact to stabilize both the bed and banks. Conversely, where large grains are close tofull mobility, as in the in the GSD1, they are not present in sufficient amounts at thesurface to stabilize the channel. Consequently, it can be concluded that the largegrain effect is mediated by the relative stability of such grains in the channel; theeffect will be strong where large grains are immobile or partially mobile, and willbe weak where they are close to full mobility. Thus, channels with a wider rangeof grain sizes will likely be more stable across discharges, while those composedof a narrow range may experience instability at a lower discharge.6.4.2 Persistence across rates of sediment supplySediment supply acts to suppress the formation of the armour layer (Dietrich et al.,1989) and thus limit the presence of large grains at the channel surface. Changes insediment supply have been linked to changes in reach-scale attributes, such as bedsurface texture and channel geometry (e.g., Montgomery et al., 1999; Eaton andChurch, 2004), as well as to larger scale processes such as the transition betweenchannel patterns (e.g., Eaton and Church, 2009; Mueller et al., 2014). In this study,I find that while increasing the rate of sediment supply does increase the morpho-dynamic activity of the channel, overall differences between the two bulk distribu-tions persist even in the high sediment supply scenario. The change in M betweenthe low and high sediment supply scenarios was roughly similar between the twobulk mixtures, as with those at high sediment supply were roughly twice as mor-phodynamically active as those run at low (Table 6.1). In comparison, the changein sediment storage between low and high sediment supply deviated between thetwo bulk mixtures; while GSD1c remained a degradational system for the entireexperiment, GSD1c started as degradational but then evolved towards a sedimenttransport equilibrium. This is shown by the temporal evolution of ∆S (Figure 6.2),as while ∆S remained negative for GSD1c, in GSD2c ∆S tended towards zero andeven became positive for a period of time. Consequently, the difference in total65cumulative ∆S due to the increase in sediment supply was twice as great in GSD2as it was in GSD1. These results suggest that the presence of a greater numberof large grains may influence how sediment is transmitted through a reach, moresediment input from upstream can be stored where more large grains are present,possibily due to the stabilizing effect that these harder-to-move grains exert. Con-sequently, it may be important to integrate the role of these large grains into modelsof sediment flux.The role of sediment supply on morphodynamics can be seen in the DoD show-ing the hourly evolution of the bed under low sediment supply conditions (FigureA.1, A.4, A.3); in three of the experiments run under the low sediment supplyscenario (i.e. all except GSD2a), the channel stabilized from the inlet downward.This is particularly notable for GSD1a where downstream meanders become pro-gressively stable as the supply from upstream becomes limited. Comparatively,the areas near the inlet remained active throughout the entire experiment with feedpresent (Figure A.5, A.6), however the activity in the lower half of the stream ta-ble does not deviate notably from the experiments run at high discharge with feed.This suggests that, where banks are erodible, the input of sediment from upstream(or from a feeder) has a relatively localized effect on channel morphology, as theinput sediment drops out of transport to forms bars, however because bank erosionrates are increased due to the diverted flow around these bar, an elevated amountof sediment is available for transport to the downstream areas. Consequently, therates of morphodynamic change are sustained for the entire channel over the courseof the experiments run with feed (Figure 6.2).6.4.3 Factors governing stabilityA Relative Bank Stability (RBS) calculation is the most commonly used approachto estimate channel stability. It is calculated as either the ratio of critical velocity ofentrainment to velocity in the channel (Vcritical/V ) or as the ratio of the critical shearstress of entrainment to the shear stress in the channel (τcritical/τ) (e.g., Biedenharnet al., 1997; Olsen et al., 1997). Of the two, the critical shear stress, also calledtractive force, is more conventionally used. According to the RBS analysis (e.g.,Millar and Quick, 1993; Kaufmann et al., 2008), channels are unstable when the66shear stress of the channel exceeds the critical shear stress of the median grainsize of the bed surface (τ > τc50). Based on this, I would expect there to be aconnection between channel stability and shear stress in the channel. My results donot show this; within the paired experiments I do not find a predictable relationshipbetween shear stress and channel stability. Instead, the reach-averaged shear stress,τ , is consistently higher for the more stable experiments, those run with GSD2(Table 4.1). The RBS analysis can also be conducted using the dimensionlessform of shear stress (Millar and Quick, 1993). I find that τ∗50 is greater in theGSD2 experiments (Figure 6.9), which is again inconsistent with our observationsof channel stability. When shear stress is normalized using the D84, however, I findthat average τ∗84 is slightly greater in experiments conducted with GSD1, which iswhat I would expect. This suggests that my estimates of shear stress are highlyvariable, and that those local estimates are not well paired with the local grainsize, however these results indicate that large grains are much more important thanpreviously recognized, even if the differences are not statistically significant.These trends hold true across experiments conducted with varying governingconditions by comparing measurements of morphodynamic change (M) from allhours of all experiments to τ∗50 and τ∗84 calculated for those same periods (Figure6.11). I use M to represent channel stability, as channels that are more stablewill have little to no morphodynamic change while those that are less stable willhave more. Based on this data, I find no significant relationship between M andτ∗50. This finding contradicts much of the existing literature which tends to showa significant positive relationship between rates of sediment transport and shearstress (e.g., Wilcock, 1997b; Mueller et al., 2005). I do, however, find a significantpositive relationship between M and τ∗84. This suggests that the D84 is a betterrepresentative grain size than the median when non-dimentionalizing shear stressfor use in a stability analysis.That sediment transport is only tangentially related to the processes drivingchannel stability is supported by my finding that the bedload material transportedis roughly similar between paired experiments (Figure 6.4). Thus, it is not neces-sarily the capacity for the channel to carry a given grain size that dictates stability.So, if neither the reach-averaged shear stress nor the bedload GSD can be aloneused as an index to differentiate between varying degrees of channel stability, it is670.055 0.065 0.075 0.0850.000.020.040.060.08τ50*M (m3 )AR2 = 0.0179p = 0.18 GSD1aGSD1bGSD1cGSD2aGSD2bGSD2c0.8 1.0 1.2 1.4 1.60.000.020.040.060.08D50 d50M (m3 )CR2 = −0.0122p = 0.510.030 0.034 0.038 0.0420.000.020.040.060.08τ84*M (m3 )BR2 = 0.36p = 3.9e−060.8 1.0 1.2 1.4 1.60.000.020.040.060.08D84 d84M (m3 )DR2 = 0.157p = 0.0031Figure 6.11: Plot of morphodynamic change (M) versus: A) shear stress nor-malized using the D50; A) shear stress normalized using the D84; C) theratio of the surface D50 to the bedload d50; D) the ratio of the surfaceD84 to the bedload d84.68necessary to look to other variables that differ between pairs. In my experiments,one characteristic that is consistently different between bulk mixtures is the surfaceGSD; I find that the surface is significantly coarser in experiments run with GSD2,particularly for the coarse end of the GSD (Figure 6.6). Building on this, if I com-pare the size of material in transport to the size of material that is left on the bedsurface between pairs, we find the ratio between the size of bedload and surfacematerial is greater for those run with GSD2, with the difference being significantfor the D84. The relationship between the bedload and the surface has been used tosome success in other studies to characterize channel stability, however these stud-ies have employed the ratio of D50/d50 (Dietrich et al., 1989; Montgomery et al.,1999; Bunte et al., 2013). In this study, I find that D50/d50 does not vary signif-icantly between pairs (Figure 6.8). In contrast, there are clear differences in theratio of D84/d84; for all pairs D84/d84 is significantly higher for experiments run inGSD2, regardless of the discharge or sediment supply conditions.Stepping back to consider the results of all experiments together, I find thatthere is no significant relationship between D50/d50 and M; instead, while M varieswidely, D50/d50 only varies between about 0.8 and 1.2, with most observationsfalling near 1. This suggests that the median grain size of the bedload is approx-imately equal to that of the surface, regardless of the amount of morphodynamicchange occurring. In comparison, I find a significant negative relationship betweenD84/d84 and M, meaning that channels are less morphodynamically active whenthe size of grains on the surface are large relative to those transported as bedload.These results suggest that the process of partial mobility plays an importantrole in channel stability for alluvial gravel-bed channels. Channels are more sta-ble when large grains are disproportionally left (i.e. partially mobile) on the bedsurface and less stable when nearly all grain sizes are entrained (i.e. fully mobile).Consequently, channels are more stable when there are more large grains presentwithin the bulk mixture or when the range of grain sizes is greater. When there aregreater numbers of large grains, which remain stable or partially mobile across awider range of conditions, they can interact the form stabilizing structures, for ex-ample stone cells, which reduce sediment transport and promote stability (Churchet al., 1998). Thus not only do large grains themselves limit the number of grainsentrained by the flow, they also act to stabilize other surrounding grains that may690.25 0.30 0.35 0.40 0.450.000.020.040.060.08D84 dM (m3 )R2 = 0.433p = 2.3e−07GSD1aGSD1bGSD1cGSD2aGSD2bGSD2cFigure 6.12: Morphodynamic change as a function of relative roughness.otherwise be entrained (Mueller et al., 2005). Conversely, in channels where thereis only a narrow range of grain sizes, the largest grains are less effective at impart-ing stability to the channel as they are entrained at approximately the same flow asthe median grain size. As a result, the transitions from stable to dynamically stableto unstable occur across a narrower range of flows.One more variable is considered in relation to the morphodynamic activity inthe channel: relative roughness. It is widely accepted that large grains, rather thanthe median, exert a significant control on flow resistance in gravel-bed channels(e.g., Hey, 1979; Recking et al., 2009; Monsalve et al., 2017). Flow resistance iscontrolled in part by the relative roughness of the bed (Ferguson, 2012), which isgiven as the ratio between the height of the largest grains on the bed surface andthe average depth of flow in the channel, or the relative roughness (D84/d). Higherbed roughness creates greater resistance which slows the flow and thus limits theenergy available for entrainment and transport of sediment from the bed (Nitscheet al., 2011). Consequently, I propose that channel stabilization may also be relatedto the flow resistance in the channel as the more stable channels tend to have more70large grains present at the surface. In Figure 6.12, there is a significant negativerelationship between M and D84/d; in fact, with a R2 value of 0.433, D84/d has thestrongest relationship with M out of all the variables considered. This is interest-ing considering that relative roughness is essentially the same as τ∗84, without thecomponent of slope (S). The data presented here shows that the greatest morpho-dynamic activity occurs where the size of grains on the surface are smaller relativeto the depth of flow, thus where roughness is lower. Consequently, understandingwhat characteristics of the bed surface contribute to flow resistance may also helpto understand the dynamics that underlie channel stability. For example, studieshave found that the way large roughness elements (i.e. grains) are distributed onthe bed influence resistance; resistance is elevated when large grains organize intoclusters, stone cells and other structures (Clifford et al., 1992; Wilcox et al., 2006).Based on the relationship between M and D84/d, I propose that these resistancestructures may also be key in channel stability.6.5 ConclusionThree sets of paired experiments were run following up on the results of Chapter5 to further explore the role that large grains play in channel morphodynamics inalluvial gravel-bed channels. The results presented in Chapter 5 demonstrate thatadding a small amount large grains to a channel can significantly increase channelstability. However, the data presented in that chapter comes from a single set ofpaired experiments with flows near the threshold of entrainment, conducted un-der low sediment supply conditions. In this chapter I expand on these results totest show that large grains exert a significant stabilizing influence across a rangeof conditions, more similar to those found in natural channels. Overall, these ex-periments show that a small proportion of large grains influence channel dynamicseven under a doubling of discharge and with the addition of sediment feed.Two different grain size distributions (GSD) of bulk materials were used inthe paired experiments: GSD1 and GSD2. Of the two, GSD2 contained a slightlygreater proportion of large grains, however the two had nearly identical mediangrain sizes. In all paired experiments, those run with the finer bulk material, GSD1,were significantly more morphodynamically active, as measured by hourly volu-71metric changes within the channel calculated using DEMs of the bed. The greatestdifference in morphodynamic activity between pairs was seen at low discharge(0.7 L/s), as the experiment run with GSD1 was cumulatively 4 times as activeas that run with GSD2. Differences were still significant even at high discharge(for both high and low sediment supply scenarios) as the GSD1 experiments sawapproximately twice as much morphodynamic change. Surprisingly, despite beingthe more active of the two, experiments conducted with GSD1 had lower reach-average dimensionless shear stress values (τ∗50) than those run with GSD2. Thisresult is inconsistent with our current paradigm of channel stability, where chan-nels experiencing greater values of τ∗50 are less stable. Consequently, we mustre-evaluate our understanding of how channels achieve and maximize stability.Another surprising finding was that the size of material transported as bedloadwas approximately similar between paired experiments regardless of discharge andsediment supply conditions. Instead, there was only a difference in the size of ma-terial composing the bed surface; the size of material left on the bed surface wassignificantly coarser in the experiments run with GSD2. Consequently, a notabledifference between the paired experiments was the ratio of the size of surface ma-terial to the the surface material. Between experiments this difference was onlysignificant for the largest grains, as represented by the D84, the ratio of D50/d50was not statistically different between pairs.These results lead us to believe that differences in the morphodynamics of thepaired experiments must be related to thresholds of partial/full mobility of mate-rial, particularly for grains near the top end of the distribution; channels are lessstable when the majority of the largest grains can be transported as bedload andmore stable when a greater fraction of the large grains remain on the bed surface.Traditionally in studies exploring the role of selective transport the behaviour ofthe largest material is not given much consideration; throwaway lines such as ”allgrains but the largest were entrained” are common. I argue that it is the relativestability of these largest grains, even when all other size classes are mobile, thatallow channels to maintain their form.While the majority of existing models use the mobility of the median grainsize to predict channel instability, I propose that using the partial and full mobilitythresholds of the largest grains (i.e. ≥ D84) may better represent under what flows72channels will remain stable. Using the mobility threshold of the largest grains stillpresents an issue however, as I show in this study that is not actually the entrain-ment of the largest grains that imbues stability to a channel, it is the amount oflarge, immobile grains left on the bed surface that act to stabilize the channel. Theissue with using a shear stress threshold is highlighted by the results that showhigher values of shear stress in more stable channels, and even if it is normalizedusing the D84, no significant difference exists between the two. This suggests thatlarge grains act to stabilize the channel to an extent where the entrainment thresh-old of the bed is actually elevated over what it would be if the larger grains wereless populous. These complicated dynamics between the bed surface texture andthe hydraulics within the channel show that significantly more work must be com-pleted in order to improve our understanding of channel stability. However, mostimportantly, what these experiments show is that it is large grains, rather than themedian, that control channel stability, even across a range of conditions.73Chapter 7Characterizing the large graineffect7.1 IntroductionThe ability to predict channel stability has many applications. For one, it is im-portant that engineers have the capacity to anticipate when significant bank ero-sion may occur in order to prevent the damage or destruction of infrastructure. Italso useful in protecting and rehabilitating aquatic and riparian habitat, as largechanges in channel morphology greatly alter the availability of certain types of en-vironments (Tamminga et al., 2015). Despite the need for accurate predictions ofchannel response, we still do not have a strong understanding of what processesgovern stability in alluvial, gravel bed channels. The term stability itself is poorlydefined and has been applied at different times to a wide range of channel be-haviours; for example, the term “unstable” has been used both to describe channelswhere there is significant bedload moving but where adjustments to channel formis minimal (e.g., Carling, 1988), as well as channels that have undergone tens ofmeters of bank erosion (e.g., Surian et al., 2016). Part of the issue with our def-inition of channel stability is that the processes driving channel stability largelydepend on type of material composing the channel bed and banks; channels withcohesive banks formed from silt and clay will fail under different conditions and bydifferent processes than those with sand or gravel banks (Millar and Quick, 1993).74That channel stability differs depending on the bulk material of the channel givessome insight into the processes driving it: specifically, that stability must be re-lated in some way to erodibility of the bed and banks. In cohesive channels, bankerodibility depends on the material strength of the bed and bank material (van Dijket al., 2013) which is imparted by the chemical and physical bonds between thegrains. In gravel-bed streams there must be a completely different set of processesthat impart stability to the channel, as true cohesion is typically negligible in thesesystems. In this chapter, I consider exclusively the processes driving stability inalluvial gravel-bed channels; approaches to understanding channel stability in co-hesive or fine-grained channels have been addressed in other studies (e.g., Darbyet al., 2010; van Dijk et al., 2013).The most widely used method of estimating channel stability is the RelativeBank Stability (RBS) model which compares the shear stress (or velocity) avail-able in the channel to that required to transport the bed material, which is typicallycharacterized by the median grain size of the bed surface (Griffiths, 1981; Jowett,1989). This model is limited in three notable ways: first, using the entrainmentthreshold of the median grain size poorly represents the point at which significantchange occurs in a channel as majority of the bed surface may be stable even underconditions where the median grain size is fully mobile, as seen in Chapters 5 and 6;secondly, there is evidence to suggest that channel stability in gravel-bed channelscannot be defined by a single threshold (e.g., Carling, 1988; Ashworth and Fer-guson, 1989); and lastly, the reach-averaged shear stress often does not accuratelyrepresent that which is available for sediment transport, as the energy available fortransport is often significantly reduced by form drag (Church et al., 1998). Therole of form drag in limiting sediment transport has been integrated into the chan-nel stability model of Darby et al. (2010), however, this model is formulated forfine-grained, cohesive channels where block failures of the bank are the primaryform of bank erosion, and consequently cannot be directly applied to gravel-bedchannels.In Chapter 2 I propose that stability is defined by two thresholds: that betweenstable and dynamically stable channels, and that between dynamically stable andunstable channels. These phases of channel stability are related to the modes of75sediment transport described by Wilcock and McArdell (1997) 1. The first phaseof channel stability (i.e. the stable channel phase) is associated with a channel inwhich there is very little sediment transport occurring and geometry and location ofthe channel remains the same throughout the flood event. The second phase (i.e. thedynamically stable phase) is when the channel is dynamically stable, meaning thatthe geometry of the channel remains roughly the same due to compensating erosionand deposition, however the location of the banks can shift over a flood event. Themedian grain size may be fully mobile in this phase; however the largest grainsremain only partially mobile. The last phase (i.e. the unstable channel phase) iswhen the channel experiences a rapid channel widening due to bank erosion onboth sides of the channel. Based on observations from studies such as Eaton andChurch (2004) and from experimental work presented in Chapters 5 and 6, themodel of channel instability presented in Chapter 2, the threshold of instability islinked to full mobility of the largest grains. Based on this, I suggest that simplemodels of channel stability, such as the RBS, should at least employ a measure ofthe mobility of the largest grains rather than the median, similar to what is done inOlsen et al. (1997).Although experimental work presented in Chapters 5 and 6 indicate that a smallfraction of large grains can significantly influence channel morphodynamics, weare still far from being able to properly define the processes that act to stabilizegravel-bed stream. If energy available for transport is mediated by form drag, it islogical to propose that that stability is related to bed surface roughness. Surfaceroughness, like channel stability, is a widely defined term, that has been used torepresent a property of the surface (i.e. the relief and/or structure of the surface), aproperty of the flow (i.e. the flow resistance or roughness height), and the propertyof a model (i.e. as a calibration variable) (Smith, 2014). For the purposes of thischapter I employ the first definition which is that roughness is a physical, quantifi-able property of the bed surface. Studies have generally agreed that roughness isnot well represented by a single grain size index for many reasons (e.g., Aberle and1The modes of sediment transport described by Wilcock and McArdell (1997) are: (1) immobile,where all grains of a given size class remain stable on the bed (τ < τci); (2) partially mobile, wheresome grains of a given size class are transported by the flow (τci ≤ τ < 2τci); and (3) fully mobile,where all grains of a given size class are transported by the flow (τ ≥ 2τci).76Nikora, 2006; Smith, 2014): first, grain size does not necessarily determine its pro-trusion from the bed; second, grain size does not account for differences in grainshape and angularity and how they may influence roughness, and lastly, clustersof smaller grains may interact to form roughness elements which influence chan-nel roughness similarly to individual protruding large grains. Consequently, recentstudies have started to investigate other measures that can be used to approximatesurface roughness in gravel-bed streams.In this chapter I explore the relationship between surface roughness and chan-nel stability by comparing a variety of surface roughness indices to rates of mor-phodynamic change measured over the course of a two hour stream table experi-ment. The goal of this work is to develop a better understanding of how surfaceroughness may influence morphodynamic response by investigating the conditionsof surface texture that coincide with higher and lower rates of morphologic change.By doing this we can evaluate the use of characteristic surface grain sizes to predictchannel stability thresholds and potentially propose other indices that may be bettersuited to more accurately describe the processes that contribute to channel stabil-ity. To date, no other studies have directly related measures of surface roughness tomorphodynamic change. Most studies of surface roughness are interested primar-ily in evaluating the use of different indices of roughness and comparing betweensurfaces that have evolved under different flow conditions (e.g., Aberle and Nikora,2006; Qin and Ng, 2012). Fewer studies have attempted to link surface roughnessto actual in channel processes, for example there are a couple studies that have ex-plored the relationship between shear stress and surface roughness (Vericat et al.,2008; Aberle et al., 2010). Through this chapter I hope to broaden our understand-ing of the conditions that impart stability to a channel in order to build a bettermodel of channel response in alluvial gravel-bed streams by using high resolutiondigital elevation models of the bed surface taken at 15-minute intervals.777.2 Methods7.2.1 Characterizing roughnessIn this chapter I explore three commonly used methods of characterizing surfaceroughness: (1) the surface grain size distribution (GSD); (2) the distribution ofsurface elevations; and (3) variograms of bed surface elevations.The surface GSD represents the size of material present at the interface be-tween the bed and the water and comparing between distributions shows whetherthe surface has fewer or more large grains present. The surface GSD is typicallycharacterized using grain size percentiles; the most commonly reported percentilesare the 50th (i.e. the median grain size) and the 84th, denoted as D50 and D84,respectively. The distribution of the surface material can also be characterized bythe sorting of grains; here I use a sorting index (σ ) defined in Hodge et al. (2009):σ = 3.32log(D84/D0)− log(D16/D0)4+3.32log(D95/D0)− log(D5/D0)6.6(7.1)where D0 is a reference diameter, equal to 1 mm (to make the equation di-mensionally consistent) and Di represents the grain size associated with the ithpercentile of the distribution. Greater values of the sorting index are associatedwith bed surfaces that have a wider range of grain sizes present, and are thus morepoorly sorted, while smaller values of σ are associated with well sorted beds.Although surface grain size is the most widely used measure to characterizethe bed surface, recently this approach has come under scrutiny as it has beenpointed out that the grain size distribution of the surface does a poor job actuallycharacterizing the texture of the surface as it gives no indication of grain packing orthe shape and orientation of grains (e.g., Gomez, 1993; Nikora et al., 1998; Smartet al., 2004; Hodge et al., 2009). Consequently, many studies have turned to othermeasures of surface roughness.One of the newer and more widely used measures of bed roughness is the dis-tribution of bed elevations. Unlike the GSD, the distribution of bed elevations givesa better indication of the bed state, as it factors in the effects of grain packing aswell as grain orientation and shape. Additionally, it incorporates the effects of78clusters of grains on surface roughness, as these groupings, like large grains, canprotrude into the flow thereby increasing the roughness of the bed. The distribu-tion of bed elevations is typically presented as a probability distribution function(PDF) and typical indices used to compare between PDFs include standard de-vation (σz), skewness and kurtosis. The standard deviation is a representation ofthe range of bed elevations at the surface and has been taken to be indicative ofthe surface roughness and armour layer development (Aberle and Smart, 2003;Aberle and Nikora, 2006). Several studies have found that the standard deviationcan be correlated with the size of grains found at the surface (Aberle and Nikora,2006), meaning that grain packing is roughly similar between patches, howevernot all studies have found such a relationship (Aberle and Smart, 2003; Hodgeet al., 2009). The skewness of the distribution of bed elevations (Sk) indicates thedegree of distortion of the distribution from a symmetrical bell curve (which hasa skewness of 0). Positive values of Sk are associated with bed surfaces wheremost hollows between larger grains are filled with smaller grains, which reducesthe magnitude of surface elevations below the mean elevation, while negative val-ues of Sk are associated with a surface displaying more protrusions and hollowsand less infilling of finer grains between large grains (Aberle and Nikora, 2006).The kurtosis of a distribution (Ku) gives an indication of the number of outlierspresent; a normal distribution has Ks value of 3, values above that indicate that thedistribution has a large number of outliers, while low kurtosis indicates that thereare few. In distributions of elevations from gravel-bed rivers, high values of Ku aretaken to represent the presence of rare large particles on the bed surface (Aberleand Nikora, 2006).Variograms are another method that has been used to characterize bed rough-ness as they show the correlation between bed elevations on a surface at differentlag lengths (e.g., Robert, 1991; Nikora et al., 1998; Butler et al., 2001; Qin andNg, 2012). Variograms ultimately represent the fractal behaviour of the surface, orhow “self-similar” that surface is. Here I utilize the Hurst Exponent (H = 4−b/2,where b is the slope of the variogram on a log-log plot), which has been found towell describe differences bed roughness (e.g., Robert, 1991; Butler et al., 2001).Previous studies have observed that there are two distinct slopes in the variogramsof waterworked gravel beds; these two slopes have been interpreted to represent79the grain and bedform scales (e.g., Robert, 1988). By comparing the Hurst Expo-nent of these two slopes, it has been found that the fractal behaviour of these twoscales differ; the surface is smoother at the grain scale and rougher at the form scale(Hg > H f , where Hg is the Hurst exponent associated with the grain scale and H fis that associated with the bedform scale), which suggests that bedforms contributeto a greater proportion of roughness in gravel-bed channels (Robert, 1988).7.2.2 Summary of experimental designIn this chapter I use data collected during the two-hour pseudo-recirculating sed-iment experiment described in Chapter 4 (Section 4.2). Chapter 3 provides anin-depth explanation of the model design and set up, the experimental procedure,as well as the data collection and processing used to produce the results presentedhere. The primary data used in this chapter are the DEMs of bed elevations derivedfrom the A-BES laser scanner as well as the high-resolution DEMS and ortho-mosaics of the bed surface created using Photoscan. The locations of where theimages were taken of the bed surface to create the models of surface texture areshown in Figure 7.1.The bulk mixture used in this experiment was GSD2, which had a D50 of 1.63mm and a D84 of 3.32 mm. The experiment was run under pseudo-recirculatingsediment conditions, as described in Section 3.5.2, and the sediment output andinput rates over the course of the experiment are shown in Figure 7.2A.7.2.3 Surface texture analysisImages taken of the bed at each of the cross sections were input into Agisoft Photo-scan in order to create high resolution DEMs and orthomosaics with typical resolu-tions for both of approximately 0.1 mm (Figure 7.3). As this resolution is slightlysmaller than the size of the smallest sediment in the streamtable (i.e. 0.25 mm), itwas possible to isolate all grains present on the bed surface. The scale of the Pho-toscan models were determined using known distances in the cross section photos,however the models themselves are not georeferenced in space; as a result it is notpossible to quantify morphologic changes through time from these models. Con-sequently, it was necessary to estimate the morphologic change from the lower80−0.0300.031 2 3 4 5 6 7 8 9 10Figure 7.1: DEM of difference between initial and final channels overlaidwith location of cross sections at which Photoscan models of the surfacewere created.20 40 60 80 100 1200100200300400500Time (min)Q b (gmin)Input + OutputOutputInput20 40 60 80 100 1200.0050.0100.0150.020Time (min)M (m3 )MErosionDepositionFigure 7.2: A) Sediment input and output; B) Morphologic activity81resolution DEMs of the entire bed; this was done by delineating the approximaterange of the Photoscan models (see Figure 7.1) and estimating the magnitude ofmorphologic change for that given area.5 cm−1−0.500.51Elevation above mean (cm)Figure 7.3: Examples of original DEM (left) and orthomosaic (right) for XS5after 15 minutes of flow.Grain size distributions were determined from orthomosaics of the bed surfaceat each cross-section. Each distribution was determined from data collected usinga Wolman-style sampling technique, wherein the b-axis of 200 randomly chosengrains were measured at the given cross section.The two types of DEMs were used to calculate bed elevation distributions:the DEMs of the entire bed collected using the laser scanner, and DEMs of theindividual cross sections created using Agisoft Photoscan. Most studies do nottake elevations directly from the original DEM of the bed surface, instead theyuse a detrended DEM to determine the distribution; some have detrended using alinear surface in order to normalize for the slope of the bed (e.g., Aberle and Smart,2003; Hodge et al., 2009; Aberle et al., 2010), while others have used an averagesmoothed surface to eliminate the influence of larger bedforms on the distribution(e.g., Smart et al., 2002, 2004). For the DEMs of the entire bed, it is not necessaryto detrend the data as slope of the stream table is already removed by the method inwhich it is collected (i.e. the laser scanner collected detrended DEMs of the bed),however I do subtract the mean elevation from all elevation values to facilitate82comparison between cross sections. For the DEMs of the individual cross sections,I experiment with detrending the bed using a range of smoothing filter sizes. Thefirst step of detrending the surface is to run a filter over the original bed surfaceto create a smoothed bed surface, to do this I use the focal filter which is partof the raster package in R (Hijmans, 2017). This smoothed bed surface is thensubtracted from the original DEM to create the detrended surface from which thedistribution of elevations is determined.Variograms were created of the bed surface for each of the cross sections usingthe variogram function in the gstat package in R (Pebesma, 2004). Sincevariance is greatest in the streamwise direction versus in the cross-flow direction(Butler et al., 2001), in this study, I derive variograms from profiles oriented in thepredominant flow direction. Variogram analysis is most successfully conducted ondatasets with no spatial trends, thus prior to creating a variogram it is common todetrend the surface of interest (Butler et al., 2001); here I use an averaging filterequivalent to 10 times the average D84.7.3 Results: Morphologic changeOver two hours the templated straight rectangle channel evolved into a meander-ing channel (Figure 7.1). The width of bank erosion was approximately constantalong the length of the stream table with slightly more widening near the inletand near the outlet. During the first 15 minutes the channel did not erode later-ally but did incise vertically. During this period erosion rates were highest whiledeposition rates were lowest. Lateral bank erosion was first observed between 15and 30 minutes of run time as the thalweg developed a meandering pattern. Thisperiod corresponds to the highest rate of morphologic activity, with high rates ofboth erosion and deposition. This period also represents the first in which sedimentwas fed in at the inlet. For the second half of the first hour, bank erosion contin-ued gradually at regular intervals at the outside of bends, while mid-channel barsand point bars formed within the channel. Following the peak in morphodynamicactivity between 15 and 30 min, M began to drop gradually, with rates of botherosion and deposition decreasing. Overbank flooding, caused by the formationof a large mid-channel bar that developed right near the inlet, started at the begin-8320 40 60 80 100 1200.00020.00060.00100.0014Time (min)M (m3 )20 40 60 80 100 1200.0010.0020.0030.0040.0050.006Time (min) Cumulative M (m3 )1m2m3m4m5m6m7m8m9m10mFigure 7.4: Total morphologic activity for each cross section through timening of the second hour and continued until the end of the experiment, meanwhilebank erosion near the outside of meander bends continued along the length of thechannel. As seen from the DoD showing the change in morphology across the twohours (Figure 7.1), erosion was concentrated along the edges of the channel, wherebank erosion occurred and near the outlet, while deposition was limited to the areaswithin the initial templated channel and near the inlet.Most cross sections echoed the same trend in morphologic change with timeseen for the stream table as a whole, with a slight increase in M during the first30 minutes followed by a slowly decreasing trend (Figure 7.4). Some exceptionsto this were seen for cross sections closer to the middle of the stream table; atthese locations there was no initial increase in M and the rate of change remainedmore constant throughout the entire experiment, rather than decreasing slowly overtime. Another exception was the first cross section (XS1) which, although it fol-lowed the trend of M seen more generally across the entire bed, experienced muchgreater values of M than all other cross sections for the first hour, resulting in a cu-mulative M value about twice what other cross sections experienced. This is likelyassociated with the fact that sediment was fed directly into this cross section.847.4 Results: Surface texture7.4.1 Grain size distributionThe bed surface tended to coarsened over time, although besides the surface GSDof the first 15 minutes, none of the GSD are significantly different from one another(Figure 7.5). The temporal coarsening trend was more apparent for the larger grainsizes than for the median grain size, as was there was a significant coarsening trendfor the average D84 but not for the average D50 (Figure 7.6). In general, the mediangrain size did not deviate largely through time at any given cross section (i.e. lessthan 0.5 mm change), whereas the size of the D84 varied widely at each crosssection, fluctuating upwards of 1 mm over the two hour experiment. Consequently,the D50 was more similar between cross sections than the D84.Compared to the sorting index of the bulk mixture (σ = 2.6) the surface re-mained relatively more sorted than the underlying bulk material throughout theentire experiment. The average value of σ for all cross sections increased signifi-cantly over time (Figure 7.6), although the magnitude of this change was not large.This increase can be attributed to the median grain size remaining approximatelyconstant through time while the size of the D84 increased (Figure 7.6).7.4.2 Bed elevationsThe distribution of elevations for the entire bed evolved over the course of theexperiment (Figure 7.7A). The initial templated bed is associated with a narrowdistribution with most bed elevations found around the mean, and the peak of thedistribution just slightly less than the mean. During the first half of the experiment(15 to 60 minutes), the bed rapidly evolved such that elevations were more widelydistributed, while the peak of the distribution shifted more to the mean. Duringthe second half of the experiment (75 to 120 minutes), the range of elevationscontinued to widen, although more slowly than during the first hour, while thepeak of the distribution shifted towards a higher elevation.I quantify these changes in the distribution of elevations from the entire bed us-ing the measures of standard deviation, skewness and kurtosis (Table 7.1). Thesevariables show three distinct trends with time: σz increases, Sk becomes more neg-850.5 1.0 2.0 5.0 10.00.00.20.40.60.81.0Particle Size (mm)Cumulative Proportion FinerTime (min)153045607590105120Figure 7.5: Average grain size distributions of all cross sections given foreach 15 minute interval of the experiment. 95% confidence intervals ofeach distribution are plotted on as transparent polygons.20 40 60 80 100 1200.51.01.52.02.53.03.5Time (min)D 50 (mm)R2 = 0.458p = 0.071m2m3m4m5m6m7m8m9m10mAverage20 40 60 80 100 1202.02.53.03.54.04.55.0Time (min)R2 = 0.497p = 0.0520 40 60 80 100 1201.01.52.02.53.0Time (min)R2 = 0.598p = 0.02D 84 (mm)σ Figure 7.6: Temporal trends of the D50, D84 and the sorting index (σ ) for allcross sections over time. The average trend for for all cross sections foreach grain size index are given as a solid black lines and the results ofthe linear regression model created for the average values are given inthe lower left hand corner of each plot.86−0.025 −0.015 −0.005 0.0050.00000.00100.00200.0030Elevation (m)ProbabilityTime (min)15304560759010512020 40 60 80 100 1200.0000.0020.0040.0060.0080.010Time (min)Standard Deviation (m)Entire DEMXS DEMsFigure 7.7: (A) Probability distribution functions of the entire bed (from theDEM scans) for each time step, normalized by the mean bed elevation ofthe templated channel; (B) Average standard deviation calculated fromthe DEM of the entire bed compared to the average standard deviationas calculated from the individual cross sections (with 95 % confidenceintervals shown as a grey polygon).ative and Ku decreases over time. The increase in σz indicates that the range of ele-vations present at the bed surface becomes wider, which is consistent with a rough-ening of the bed surface. The transition toward more negative Sk values meansa larger proportion of the bed is found at higher elevations, presumably due to ahigher proportion of large grains at the surface. Lastly, the values of Ku transitionacross the threshold of 3, which represents a normal distribution, between 30 and45 minutes of run time, meaning that while the distribution began with a greaternumber of outliers, by the end the more extreme values became more common.This suggests a transition from only isolated large grains present at the surface tolarge grains and clusters becoming more common.Although σz, when calculated from DEMs of the entire bed, increases overtime, the results from the individual cross sections show that the changes in σzare quite variable along the length of the stream table, although their average iscomparable to that of the entire bed (Figure 7.7B). In Figure 7.7B, the values of σz87Table 7.1: Standard deviation (in m), skewness and kurtosis for the entire bedover timeTime Std.Dev. Skewness Kurtosis15 0.0036 -0.29 3.7530 0.0048 -0.54 3.0945 0.0051 -0.41 2.8460 0.0054 -0.52 2.8975 0.0055 -0.49 2.8190 0.0059 -0.79 3.42105 0.0059 -0.80 3.29120 0.0060 -0.66 2.78presented for the cross sections are calculated from cross sectional DEMs that havebe normalized by the mean elevation but have not been detrended. While normal-izing the cross sectional DEMs by their mean elevation allows direct comparisonbetween them, the fact that they range so widely suggests that their values of σz stillencompass the range of elevations associated with larger bedforms, such as bars,pools and riffles. Consequently, I could hypothesize that the wide range in valuesof σz between cross-sections could in part be due to the differences in bedformspresent at the locations at which the cross sections are taken. This is consistentwith what is seen when examining the range of bedforms that fall at each of thecross-sectional locations when they are mapped onto the DEM of the whole bed(Figure 7.1). To minimize the effects of differences in larger scale bedforms on σzbetween cross sections and thus allow for direct comparison of bed surface rough-ness, I compare between distributions of elevations that have been derived fromdetrended DEMs, using averaging filters, from the cross sections.The size of averaging filter used to detrend the bed surface plays an importantrole in the representation of the surface elevation distribution. When a small filtersize is used, for example one equal to the size of the D84 (Figure 7.8), all bedformslarger than the size of individual grains are removed, resulting in a very narrow dis-tribution of elevations. Further, with such a filter there is very little difference in thedistributions at a given cross section over time as the range of elevations possibleare essentially limited to the grain sizes present on the bed. In comparison, using afilter approximately equal to 5 times the size of D84, both large grains and smaller88grains deposited around them are discernable (Figure 7.8) and the distribution ofelevations is wider. With this size of averaging filter, the most apparent bedformsare linear clusters of grains, about 5 cm long that form around one or two largegrain nuclei and run parallel to the direction of flow. With this size filter, the mainchange in the elevations over time is again the peak of the distribution, althoughthere is slightly more variability in elevation near the upper and lower ranges. TheDEMs created using averaging filters of 10 and 15 times the D84 create surfacesthat are roughly similar (Figure 7.8): individual grains are no longer discrete andclusters of grains create bedforms that are not quite as large or as organized as barsand are still typically formed around one or more larger grains. The distributionsof elevations for these two larger filters are quite wide and it is possible to visi-bly distinguish differences in the shape of the distributions over time, unlike withthe finer filters. With a larger filter the distributions begin narrower and widen outover time, becoming slightly more skewed to the right, although the distributionassociated with the last 15 minutes is more normally distributed.The influence of the size of the averaging filter on the portrayal of the bedroughness is illustrated by the change in the standard deviation of bed elevations(σz) across a range of averaging filter sizes: Figure 7.9 shows the change in σz withaveraging filter size for all cross sections at the end of the experiment. Overall,standard deviation is lowest for filter lengths less than or equal to the size of theD84 but increases rapidly until the averaging filter is approximately twice the D84,after which point the rate of increase of σz lowers until a filter size of about 10times the D84 where it again starts to increase rapidly. The standard deviation ofthe bed elevation distribution is highest (approximately 0.5) when no averagingfilter is used and the DEM is only normalized by the mean elevation (Figure 7.7B).For the rest of this study I utilize filtered DEMs created using an averaging filter of10 times the size of the average D84 (i.e. 3.6 cm). I believe that this filter size doesa good job representing the structure of the surface as both individual grains as wellas clusters less than the size of channel-spanning bedforms are still included.Examining the values of σz, Sk and Ku for all cross sections over time (Figure7.10), it can be seen that trends in these values are less distinct than trends in thesesame variables when calculated for the bed as a whole (i.e. Table 7.1). It shouldbe noted again that while the DEMs of the entire bed are only normalized by the89−0.004 0.000 0.004050010001500Elevation (m)Density−0.004 0.000 0.004050010001500Elevation (m)Density−0.004 0.000 0.004050010001500Elevation (m)DensityTime (min)153045607590105120−0.004 0.000 0.004050010001500Elevation (m)DensityD84 5xD8410xD84 15xD845 cm- 44- 220Elevation abovemean (mm)Figure 7.8: Examples of detrended DEMs of XS5 after the first 15 min cre-ated using a range of averaging filter sizes (size of filter indicated inthe upper left hand corner). Probability distribution functions (PDFs) ofbed elevations for that cross section at each time step created using thegiven filter size are shown in the lower right corner.mean elevation, the DEMs from the cross sections analyzed here are detrendedusing an averaging filter of 10D84. The σz measured at all cross sections remainsnearly constant over time, other than a slight, but not significant, increase duringthe first 30 minutes of the experiment. This is basically consistent with the resultsfor the entire bed, although the actual values of σz are lower for the individual crosssections. The Sk values from the cross sections vary widely and irregularly withtime and there is no discernible temporal trend in either the average values or therange of values seen between cross sections. One important thing to note is that,unlike negative values of Sk calculated from the DEMs of the entire bed, the values900.5 1.0 2.0 5.0 10.0 20.01e−042e−045e−041e−032e−03Focal Window/D84σCross Section1m2m3m4m5m6m7m8m9m10mFigure 7.9: Standard deviation at end of experiment for all cross sectionsacross a range of averaging filter sizes.of Sk for the individual cross sections are positive. This discrepancy may be dueto the detrending of the cross sections, which tends to remove the effects of largebedforms on bed elevations. Lastly, the values of Ku from the cross sections areoverall higher than those calculated for the bed as a whole, however, like for theentire bed, the average values of kurtosis decline over time, although this change isnot significant. Overall, these results are broadly in line with those from the bed asa whole as they suggest that large grains become more common at the bed surface,as indicated by increasing values of σz and decreasing values of Ku.7.4.3 VariogramsThe results from the variogram analysis show that surface roughness variability in-creased across all scales during the first 30 minutes after which point it remainedrelatively constant (Figure 7.11). The increase in variability is illustrated by the9120 40 60 80 100 1200.00060.00080.00100.00120.0014Time (min)R2 = 0.335p = 0.11m2m3m4m5m6m7m8m9m10mAverage20 40 60 80 100 1200.00.20.40.60.8Time (min)S kR2 = 0.295p = 0.220 40 60 80 100 1203.03.54.04.55.0Time (min)K uR2 = 0.908p = 2e−04σ z (m)Figure 7.10: Temporal trends of the standard deviation (σz), skewness (Sk)and kurtosis (Ku) values from bed elevations distributions (using a fo-cal window of approximately 10D84) of all cross sections over time.The average trend for for all cross sections for each grain size indexare given as a solid black lines and the results of the linear regressionmodel created for the average values are given in the lower left handcorner of each plot.upward shift of the points during this period. The variograms of bed surface el-evations also show two distinct linear trends, similar to what has been observedin previous studies (e.g., Butler et al., 2001; Qin and Ng, 2012). These two lin-ear segments represent two distinct fractal bands which I equate to the grain andbedform scales. The transition from grain to bedform scale occurs at a lag lengthsomewhere between 0.5D84 and D84 , while the transition from bedform scale tothe saturation zone (where variance does not change with increasing lag length)occurs just below 5 times the D84. It is possible to fit linear trends through thepoints at the grain and bedform scales and use the slopes of these lines to calculatethe Hurst Exponents for these two scales (Figure 7.12).Within the grain scale, the slope of the linear trendlines do not vary much overtime, instead the main difference is that lines from later on in the experiment plothigher than those from earlier on (Figure 7.11), meaning that variability increasesslightly at the grain scale over the experiment. Another thing to note is that the lo-cation of the lowest point of the variogram (i.e. the nugget height) also increases;this suggests that variability is also increasing at lag sizes smaller than what isshown on the variogram. As there is very little difference in slope between lines,920.1 0.2 0.5 1.0 2.0 5.0 10.0 20.01e−085e−082e−075e−07Lag/D84γ (m2 )Grain Scale Bedform ScaleSaturation Zone153045607590105120Figure 7.11: Average variograms for all cross sections given for each timewith the regression lines for the fractal dimensions at the grain andbedform scales plotted.the Hurst Exponent for the grain scale (Hg) is nearly constant over time (Figure7.12); further the range of Hg for all cross sections at any given time is quite small.On average, the Hurst Exponent for the grain scale is 0.75 which represents a ten-dency of the surface towards positive autocorrelation.Like at the grain scale, there is little visible difference in the slope of linesat the bedform scale, however a slight trend downward of Hurst Exponent valuesfor the bedform scale (H f ) indicates that there is some change in slope over time(Figure 7.12), although the actual magnitude of change is not great. Again, fromthe variograms, the main discernible change at the bedform scale is an increasein variance, particularly for the first 30 minutes. The range of H f values betweencross sections at any given time is slightly greater for the bedform scale than forthe grain scale, which suggests that bed surfaces are structured slightly differentlybetween cross sections at this scale. The average value of H f is just over 0.3 whichmeans that the bed surface structure is negatively correlated at the bedform scale.9315 30 45 60 75 90 105 1200.20.30.40.50.60.70.80.9Time (min)Hurst Exponent0.20.30.40.50.60.70.80.9Bedform ScaleGrain ScaleFigure 7.12: Range of Hurst Exponent values for grain and bedform scalesfor all cross sections through time.7.5 Surface texture and morphologic activityIn comparing all measures of surface roughness explored in this chapter to themagnitudes of morphodynamic change measured from the DoDs, it can be seenthat there is very little correlation between the two. First, considering the relation-ships between average surface roughness values across all cross sections and M forthe entire bed we see that there are no significant correlations at a significance levelof α = 0.05 between M and any of the reach-averaged surface roughness indices(Figure 7.13 and Table D.7). However, a slightly higher significance level (i.e.α = 0.1) is chosen, three roughness indices become significant: grain sorting (σ ),standard deviation of the bed elevations (σz) and the Hurst Exponent of the bed-form scale (H f ). My data shows that M decreases rapidly with increasing surfacesorting of surface grain sizes, meaning that well-sorted beds are more stable thanpoorly sorted ones. The data also suggests that stable beds are rougher, as indicatedby both the relationship of σz and H f with M, as there is a negative relationshipbetween M and σz and a positive relationship between M and H f . Rougher beds are94associated with higher values of σz and lower values of H f ; at higher σz, a widerrange of elevations are present, while lower values of H f indicate more irregularsurface where the bed alternated rapidly between high and low points. The restof the roughness indices examined in this chapter show no significant correlationswith M.Next, considering the relationships between values of M and roughness indicesmeasured at each of the cross sections over time, it can be seen that again, thereis very little correlation between the two (Figure 7.14 and Table D.8). The onlythree roughness indices to show a significant correlation (α = 0.05) with M areKu, Hg and H f . However, again it must be noted that these linear models, whilesignificant, do not actually explain very much of the variation in the data, as theR2 value are all less than 0.1. Consequently, I am hesitant to put much trust intothese results. The “significant” relationships that seen between these roughnessindices and M at individual cross sections suggest that large grains are influentialin channel stability. There is positive correlation between M and Ku, meaning thatthe channel is more stable at individual cross sections when there are more outlierspresent at the surface. For the two Hurst Exponents, there is a negative relationshipbetween M and Hg and a positive relationship between M and H f , meaning thatchannels are more stable when the grain scale is smoother and the bedform scaleis rougher. The only other roughness index to come close to having a significantrelationship with M is skewness. Again, although the p-value is close to 0.05, Ihave very little confidence in this positive relationship as the linear model has anextremely low R2 value (i.e. less than 0.05).7.6 DiscussionThere is not one particular index of surface roughness that stands out as univer-sally effective at predicting channel morphodynamic change (M) in my experiment.There is only a significant relationships between indices of surface roughness andM at the cross sectional scale (Figure 7.14), none of the indices show significantcorrelation with M at the reach scale (Figure 7.13). However, all three variablesthat show a significant correlations with M at the cross sectional scale (Ku, Hg andH f ) can be understood to show that large grains are a primary contributing factor to951.0 1.5 2.0 2.50.0000.0100.020D50 (mm)M (m3 )R2 = 0.259p = 0.22.5 3.0 3.5 4.0 4.5 5.00.0000.0100.020D84 (mm)R2 = 0.205p = 0.261.5 2.0 2.5 3.00.0000.0100.020σR2 = 0.447p = 0.070.003 0.004 0.005 0.006 0.0070.0000.0100.020σzR2 = 0.456p = 0.066−0.9 −0.7 −0.5 −0.30.0000.0100.020SkR2 = 0.316p = 0.152.5 3.0 3.5 4.0 4.5 5.00.0000.0100.020KuR2 = 0.0298p = 0.680.70 0.72 0.74 0.76 0.78 0.800.0000.0100.020HgR2 = 0.031p = 0.680.20 0.25 0.30 0.35 0.400.0000.0100.020HfR2 = 0.436p = 0.075M (m3 )M (m3 )(m)Figure 7.13: Plots showing the relationship between total morphodynamicchange (for the entire bed) and reach-averaged surface roughness in-dices. Linear regression lines are plotted onto each as a dashed line,and the R2 and p-values of that analysis are given in one of the uppercorners. None of the roughness variables have significant relationshipwith M at a significance level of α = 0.05, but three variables, plottedwith semi-filled points, show significance at α = 0.1.961.0 1.5 2.0 2.50.00000.00100.0020D50 (mm)M (m3 )R2 = 0.0164p = 0.262.5 3.0 3.5 4.0 4.5 5.00.00000.00100.0020D84 (mm)R2 = 0.0214p = 0.21.5 2.0 2.5 3.00.00000.00100.0020σR2 = 0.00424p = 0.570.0008 0.0010 0.0012 0.00140.00000.00100.0020σzR2 = 0.00848p = 0.20.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.00000.00100.0020SkR2 = 0.0338p = 0.0562.5 3.0 3.5 4.0 4.5 5.00.00000.00100.0020KuR2 = 0.0949p = 0.00320.70 0.72 0.74 0.76 0.78 0.800.00000.00100.0020HgR2 = 0.0591p = 0.0170.20 0.25 0.30 0.35 0.400.00000.00100.0020HfR2 = 0.0578p = 0.018M (m3 )M (m3 )(m)Figure 7.14: Plots showing the relationship between morphodynamic changeand surface roughness indices for all cross sections. Linear regressionlines are plotted onto each as a dashed line, and the R2 and p-values ofthat analysis are given in one of the upper corners. Variables that havea significant relationship with M at a significance level of α = 0.05 areplotted with filled points.stability (Figure 7.14). This finding is consistent with the model of channel stabil-ity presented in Chapter 2 and the results from stream table experiments presentedin Chapters 5 and 6.To understand how the data in this chapter supports the assertion that largegrains play a role in channel morphodynamics, it is necessary to explore the in-dices of surface roughness that are found to significant correlate with M at thecross sections, namely the kurtosis of the PDF of surface elevations and the Hurst97Exponents of the grain and bedform scales. Kurtosis is an indication of the numberof outliers in a distribution; higher values of Ku indicate the presence of a greaternumber of outliers. Given that the distributions are of surface elevations, high val-ues of Ku suggest that large grains protruding above the level of the surroundinggrains are more rare, while lower values indicate that a greater proportion of thebed surface lies above the mean elevation, which is consistent with what is shownin Figure 7.7. In my data I find that higher values of M are associated with highervalues of Ku, which I take to mean that more morphodynamic change occurs whenthere are fewer large grains at the surface, and thus roughness is minimized.The Hurst Exponents of the grain and bedform scale are derived from vari-ograms of surface elevations and are indicative of the spatial variability and orga-nization of the surface; higher values of the Hurst Exponent are associated withsmoother, more organized surfaces, while lower values indicate surfaces that arerougher and more variable in elevation. When considering the actual spatial scalesassociated with the grain and bedform scales, it is possible to see that they are mis-nomers from the perspective of my data: the grain scale doesn’t even extend tothe average size of the D84, meaning that large grains are considered to be part ofthe bedform scale. Although individual grains are not, by definition, bedforms itis interesting that they are grouped with larger cluster bedforms as part of the var-iogram analysis. This suggests that the fractal characteristics of these large grainsare actually more similar to multigrain clusters than they are to smaller individ-ual grains on the bed surface. This observation may be integral to understandinghow and why large grains play such an important role in flow resistance (Reckinget al., 2009) and channel stability (MacKenzie and Eaton, 2017) and is deservingof deeper investigation.At the grain scale, higher values of M are associated with lower values of Hg,meaning that the channel was more stable when the surface of the grain scale wassmoother. I interpret a smoother grain scale to mean that a greater number of largergrains are present at the surface as larger grains have longer axes and thus appear”smoother” from the perspective of a variogram. However, it should be noted thatin the case of the grain scale, these ”larger” grains are not what would typicallyconsider to be ”large” grains, as the grain scale for my data does not extend up tothe D84. Consequently, from the perspective of Hg I can only link an decrease in98M to an increase in the number of grains in the size range of D50 and D84 at thesurface. Considering the bedform scale, H f shows a positive relationship with M,meaning that increased channel stability is associated with rougher surfaces. Theroughening of the bedform scale is interpreted to indicate the presence of morelarge grains and clusters of grains at the surface, which is consistent with my inter-pretation of the relationship of Ku with M.It may be possible to attribute the fact that there are only significant correla-tions between surface roughness and morphodynamic change at the cross-sectionalscale, and not at the reach-averaged scale, to the fact that the channel dynamicsseen in this experiment fall within the dynamically stable phase of channel stabil-ity. As this phase of channel stability is associated with compensating erosion anddeposition, we expect only localized morphodynamic change under conditions ofdynamic stability; consequently individual cross sectional scale will tend to onlyencompass areas that are experiencing a consistent type of localized change; forexample on Figure 7.1, XS2 falls on the area of maximum curvature of a meanderbend, whereas XS3 lands on a riffle. Each feature is likely to experience slightlydifferent values of M and surface roughness over time, but ultimately, we wouldexpect the two to be related at each point. On the other hand, if we consider thereach scale, the values of M and surface roughness are averaged across all typesof bedforms and are less descriptive of the processes occurring at any given time,but instead represent more the general state of the channel. We might expect to seea greater relationship between M and surface roughness at the reach scale for un-stable channels, as morphologic change, in the form of channel widening, is moreevenly distributed along the length of the entire reach. Thus, while reach-scaleanalysis of surface roughness may be suitable for unstable channels, my resultssuggest that further inquiry into the relationship between channel stability and sur-face roughness may be best explored at a bedform scale.Another factor that influences my analysis of surface roughness is method cho-sen to detrend the DEM. The most basic and widely used method of detrending aDEM is to remove the linear trend, which in the case of fluvial data corresponds tothe slope of the stream (e.g., Aberle and Smart, 2003; Hodge et al., 2009; Aberleet al., 2010). Removing the linear trend of the data assures that all differences inelevation are due to variability associated with in-stream features, but preserves99elevational differences associated with larger scale features such as bars and pools.Consequently, the values of standard deviation derived from linearly detrendedDEMs best describe the variability of bed elevations associated with these largerbedforms; planar beds will tend to have lower values of σz, while beds with highamplitude bars and deep pools will have much higher values of σz. This increase inσz associated with bedforms is illustrated by noting the increase in σz over time asthe entire bed transitions from a flat surface associated with the templated channelto one where there are well developed bedforms (Figure 7.7 and Table 7.1).To quantify differences in surface roughness at a finer scale it is necessary toemploy another type of spatial filtering to remove changes in elevation associatedwith larger bedforms. As shown in Figure 7.9, the size of the spatial averagingfilter has a large effect on the resulting values of standard deviation: larger filtersizes preserve a greater amount of the surface variability, while smaller filters willremoves all variability in elevation except those associated with individual grains(Smith, 2014). The use of smaller filters have been shown to be effective for deter-mining surface roughness values for use in flow resistance equations, for exampleSmart et al. (2002) used an averaging filter with a diameter of 2.5D90 to remove alldifferences in elevation except those associated with individual grains and smallclusters. An example of what a DEM surface looks like following the use of asmall spatial averaging filter is shown in the top left panel of Figure 7.8. The re-sulting PDF of elevations for such a surface is quite narrow and there are very littlechanges in values of σz, Sk and Ku over time for the same bed, as the PDF is lim-ited in extent to the range of grain sizes present in the bulk mixture. In this chapterI choose to employ a spatial averaging filter equal to approximately 10D84 (seebottom left panel in Figure 7.8) as I find that this size filter strikes the right bal-ance between preserving the roughness associated with both individual grains andsmall clusters while removing the differences in elevation associated with largerbedforms. In the case of my analysis, I deem it necessary to remove the influenceof larger bedforms on the PDFs of elevation in order to compare directly betweencross sections that are taken at different locations along the channel. Consideringthe change in σz with averaging filter shown in Figure 7.9, for this data there is no“right” filter size to use as there is no distinct range of filter size for which there isno change in σz. In light of this, I suggest that future studies of surface roughness100choose a filter size that is justified given the type of data to be analyzed and the goalof the research; the use of small filters is reasonable for studying grain roughnessalone, while larger filters are more appropriate for characterizing roughness at awider range of scales.7.6.1 Surface roughness and flow characteristicsOne future promising avenue of investigation is the relationship between surfaceroughness, flow dynamics and morphologic change. One notable relevant findingpresented in the discussion of Chapter 6 is the significant relationship between rel-ative roughness, given as D84/d, where d is the reach-averaged flow depth, andmorphodynamic change; results from those experiments showed that morphody-namic change was greatest where depths were large relative to the size of grainsat the surface (see Figure 6.12). To test whether this relationship holds for theexperiment presented in this chapter, I created flow models in Nays2DH for thebed at each 15-minute interval. The methods by which this were done are givenin-depth in Chapter 3, Section 3.4. The reach-averaged channel geometry derivedfrom these flow models (Table C.4) show that reach-averaged flow widths (w) in-creased by 20 cm over time, while reach-averaged flow depths (d) decreased by 3.5mm.I compare morphodynamic change to two slightly different methods of calcu-lating relative roughness: that calculated using the reach-averaged D84 (i.e. D84/d)and that calculated using σz derived from the PDF of bed elevations for the entirechannel (i.e. σz/d). I find that there are significant negative correlations betweenboth indices of relative roughness and M (Figure 7.15), which is consistent with thetrend seen in Chapter 6 (Figure 6.12). Compared to all other variables consideredin this chapter, relative roughness has the strongest correlation with M, particu-larly when relative roughness is calculated as σz/d. These results demonstrate thatsurface roughness alone, to the extent that it can be described using relatively sim-ple indices, is not what imparts stability to the channel. Instead, to understandand predict morphodynamic change it appears necessary to consider the role ofwidth adjustments on channel stability; channels stabilize as the depth of flow de-creases relative to the size of grains at the surface, which occurs as the channel1010.20 0.25 0.30 0.35 0.40 0.45 0.500.0000.0100.020D84 dM (m3 )R2 = 0.594p = 0.030.2 0.3 0.4 0.5 0.6 0.7 0.80.0000.0100.020σz dM (m3 )R2 = 0.648p = 0.02Figure 7.15: Total morphologic activity versus relative roughness, shown asa function of the reach-averaged D84 and σz.widens. Thus, in channels where bank erosion can occur (i.e. unstable or dynam-ically stable channels), the primary stabilizing mechanism may actually be widthadjustment; it is only in channels where bank erosion is limited or not possible(i.e. dynamically stable or stable channels) that textural changes to the bed surfacedominate the channel response and act to further stabilize the bed.Although not possible here due to the uncertainty of the flow model results atspatial scales less than that of the reach scale, I recommend that the fundamentalprocesses underlying channel stability be investigated at the bedform-scale usinghigh resolution photogrametry of the bed in conjunction with measurements offlow. While it is difficult to gather such measurements from stream table exper-iments using in-channel means of measuring (i.e. rulers) as flow depths are onthe order of millimeters, new research into using colour shifts in remotely sensedimages to determine flow depths in channels may prove applicable and useful inlaboratory studies using stream tables.1027.7 ConclusionThe results of paired stream table experiments presented in Chapters 5 and 6 un-equivocally show that the addition of a small proportion of large grains dramati-cally decreases the amount of morphodynamic change that occurs within the chan-nel. One of the most consistent differences between experiments run with finer(GSD1) and coarser (GSD2) bulk material is the surface GSD that evolves; in allpairs, there is a greater proportion of large grains present at the surface in thecoarser bulk material. These results suggest that the presence of large grains at thesurface acts to stabilize the channel and limit rates of both erosion and deposition.In this chapter I investigate the relationship between characteristics of the surfacetexture and rates of morphodynamic change using high spatial and temporal reso-lution data of the bed collected during a pseudo-recirculating sediment experiment.Here I apply three commonly used methods of characterizing surface rough-ness – the surface grain size distribution, the distribution of surface elevations andvariograms of bed surface elevations – to cross sectional DEMs of the bed and com-pare it to the magnitude of morphodynamic change measured in the same regionin order to determine whether any of these indices can be used to predict channelresponse. I find that although my data confirms the results of previous chapters byshowing that the presence of a greater number of large grains on the surface actto stabilize the channel, none of the indices of bed surface roughness alone can beused to predict M, particularly at the reach-scale.In this chapter I find that while the GSD, as determined using Wolman-stylepebble counts of surface grains off of orthomosaics of the bed, does coarsen toa certain extent over the course of the experiment, the indices of D50, D84 andsize sorting (σ ) do not statistically predict M at either the reach- or cross-sectionalscale. The use of grain size percentiles to characterize the bed surface texture hasbeen critiqued by several researchers, particularly in the field of flow resistance, asit is noted that an index of grain size alone does not take into account differences inthe bed structure, such as grain shape, orientation and packing, between channelsthat may exert significant influence on the actual surface texture that interacts withthe flow (e.g., Gomez, 1993; Nikora et al., 1998; Smart et al., 2004; Hodge et al.,2009). Consequently, it is not unexpected that measures of grain size alone are103poorly correlated with M.With increasing capacity to quickly develop high resolution models of a chan-nel surface using photogrammetry, surface elevation distributions are quickly be-coming one of the most widely used methods of interpreting surface texture be-sides grain sizes measurements (e.g., Aberle and Nikora, 2006; Hodge et al., 2009).While several studies have found strong relationships between the standard devi-ation of surface elevations and flow roughness (e.g., Smart et al., 2002; Aberleand Nikora, 2006), results from this experiment suggest that the relationship be-tween the distribution of surface elevations and morphodynamic change may beless straight-forward. In my analysis, after removing variations in elevation asso-ciated with larger bedforms, I find no relationship between the standard deviation,the skewness or the kurtosis of the distribution of surface elevations with M atthe reach-scale. At the cross-section scale, while there is a significant correlationbetween kurtosis, which is indicative of the number of outliers present in the dis-tribution, and morphodynamic change, the model only accounts for about 10% ofthe variability in the observations. I interpret the relationship between M and kur-tosis to suggest that channels are more stable with a greater number of large grainspresent on the surface, however the weakness of the correlation means that thisrelationship should not be used to predict morphodynamic change.The last indices used in this chapter are the grain and bedform Hurst Exponents,derived from variograms of the bed surface elevations. Variograms are used toexamine how surface texture changes spatially, with two Hurst Exponents usedas indices of this variation at the grain and bedform scales. Although there is nostatistical relationship between the Hurst Exponents and M at the reach-scale, bothare significantly correlated with M at the cross-sectional scale, although the R2values of both linear regression models are very low. My interpretation of theseresults further supports the assertion that the presence of a greater number of largegrains at the surface lower rates of morphodynamic change, however, like withkurtosis, neither of these relationships are strong enough to form the basis of amodel for predicting channel response.The most promising path forward in regards to predicting morphodynamicchange in alluvial channels seems to be in considering the relationship between sur-face texture and flow, as the two measures of relative roughness (D84/d and σz/d)104have the strongest relationships with M out of all variables considered (Figure 7.15.This is consistent with the experimental results from the paired experiments pre-sented in Chapter 6 (Figure 6.12). These results suggest that width adjustments,which cause changes to the relative roughness, are the primary stabilizing mecha-nism in laterally active channels. Unfortunately, the means of estimating flow depthused in this analysis are not accurate enough to sample at any spatial scale belowthe reach-scale so these results are preliminary and limited in scope. I propose thatfurther investigation into the relationship between flow dynamics, surface textureand morphodynamic change may prove to be integral to developing a strong modelof channel response.105Chapter 8ConclusionsDestructive events, such as the flooding seen in Alberta in 2013 (Figure 1.1),highlight weaknesses in our understanding of earth systems; they happen so in-frequently it makes them hard to study in nature, but yet they are something thatcommunities must constantly be prepared for, particularly in face of climate changewhere such events are likely to increase in frequency. The rapid bank erosion ex-perienced at Cougar Creek is an example where the majority of existing models ofbank stability are not sufficient to explain the dramatic change in morphology expe-rienced in these channels. This thesis takes the question of ”what controls channelstability in alluvial gravel-bed streams?” and considers it both from a theoreticalstandpoint, as well as through the use of experimental data from a series of streamtable experiments. Together these investigations are used to show that channel sta-bility it governed by a small proportion of large grains. While the extent to whichthis small population of large grains exerts an effect on channel morphodynamicsis remarkable, this result is not unforeseen: a thorough investigating of existing lit-erature reveals that many studies have previously observed that the behaviour andpresence of large grains plays an influential role in a range of channel processes.This thesis opens up a new path of investigation into the role of large grains inchannel response.To date, the most widely used grain size to characterize the sediment in gravel-bed channels is the median grain size of the surface (D50); it has been used in alltypes of equations, from flow resistance, to sediment transport, to channel stability106(e.g., Millar and Quick, 1993). However, despite its ubiquity, its use is often un-founded; in fact, there is building evidence to suggest that grain sizes larger than themedian play a more central role in many of the processes operating in gravel-bedchannels. This is particularly true in the field of flow resistance: while early re-searchers used the median grain size to approximate surface roughness (e.g., Bray,1979), its use within that field is now nearly obsolete with most studies using somemeasure of the largest grains to define roughness height (e.g., Hey, 1979; Bray,1980). Comparatively, the most widely used models of sediment transport (e.g.,Meyer-Peter and Muller, 1948) and channel stability (e.g., Millar and Quick, 1993)still use the median grain size as the characteristic grain size. While the mobiliza-tion of the median grain size does seem to correlate with the mobility of muchof the bed surface (e.g., Parker et al., 1982a), it is widely observed (but typicallyoverlooked) that the largest grains present in the channel do not comply; insteadthey remain stable at a much wider range of flows (Parker and Klingeman, 1982;Andrews, 1983). While in the case of sediment transport, this fact can be ignoredas large grains only constitute a small proportion of the material present in thechannel and thus do not add significantly to the measurements of bedload flux.Comparatively, in the case of channel stability, these large grains must undoubt-edly play an important role, as in this case we are interested not by the materialtransported, but instead by the material that stays in place. Despite this, the mostwidely used basic model of channel stability, the Relative Bank Stability Model(Griffiths, 1981; Jowett, 1989) does not consider the effect that these relativelyimmobile large grains have on the stability of the channel as a whole.In light of this, a new conceptual model of channel stability is presented inChapter 2. This model defines three phases of channel stability: stable, dynam-ically stable and unstable (Figure 2.1). These phases are based roughly on thephased model of sediment transport described in previous studies (Carling, 1988;Ashworth and Ferguson, 1989; Warburton, 1992; Schneider et al., 2016), but in-stead links these stability thresholds to the phases of mobility of the largest grains.That these thresholds are linked to mobility of the largest grains, rather than themedian, is supported by estimates of the fraction of the bed surface that remainsstable at a given shear stress. These estimates are based on the experimental resultsof Wilcock and McArdell (1993) who documented the amount of grains in a given107size class left on the bed surface at the threshold of entrainment and that of full mo-bility. Employing a grain size distribution characteristic of an alluvial gravel-bedchannel, we show that only 5% of the bed is mobile at the entrainment threshold ofthe median grain size (Figure 2.2), which is deemed to be insufficient to drive anysignificant morphologic change. Instead, the stability thresholds between stable/-dynamically stable and dynamically stable/unstable are linked to the entrainmentand full mobility thresholds of the D84, respectively (Figure 2.2). It is necessary tonote that in this model I use the D84 as the characteristic percentile, however futurework may show that these thresholds are more closely related to some percentilegreater than this (e.g. D90 or D95).Unlike in a straight-walled flume, it possible to test the influence of large grainson channel stability in a stream table as channel boundaries can adjust both verti-cally and laterally to the flow. Chapter 5 presents a pair of nearly identical experi-ments, run at the same discharge, gradient, sediment supply and with the same me-dian grain size; the only difference between the two is the proportion of large grainspresent in the bulk material (Figure 3.2). Given the existing paradigm of channelresponse wherein processes are driven by the behaviour of the median grain size,we would expect that the two channels should respond in a similar manner to thesame governing conditions; instead we found that the channel containing about 4%more large grains (GSD2a) was significantly more stable than its counterpart run inwith the finer bulk material (GSD1a). With fewer large grains present, the channeloutput nearly four times as much sediment (Figure 5.2) and transformed into a sin-uous channel with well-developed pools, bars and riffles (Figure 5.1). Although thedifferences in channel response in themselves were remarkable given the relativelysmall proportion of large grains added, one of the most striking findings from thispair of experiments was that the values of shear stress modelled in the two chan-nels conflicts with our current understanding of sediment transport: reach-averagedshear stress was found to be higher in the experiment run with coarser bulk material(GSD2a), despite the fact that it was the more stable of the two. Instead of shearstress, it is the proportion of large grains left on the bed surface appears to drive thedifferences in channel response observed between the pair of experiments – whileeven the largest grains (i.e. up to the D95) were fully mobile throughout the experi-ment in the finer bulk material, large grains remained consistently overrepresented108on the bed surface relative to the bedload in the coarser bulk material (Figure 5.6).The results of the preliminary set of paired experiments were striking andbrought up more questions than they answered. Given they were run under a sin-gle discharge and under low sediment supply conditions, the next logical step wasto address whether differences in discharge and sediment supply would modify oreven suppress the stabilizing effects of the small proportion of large grains. Two ad-ditional sets of paired experiments addressing these issues are presented in Chapter6: one pair run under high discharge (i.e. twice the discharge of those presented inChapter 5) low sediment supply conditions, and another run at this high dischargewith sediment supplied at the upstream end. First, considering the role that dis-charge plays in relation to channel stability and large grains, it is predicted that theeffects of large grains in mediating channel stability are minimized at higher dis-charges as the size of material that can be transported increases (e.g., Lisle, 1995).If a greater proportion of the larger grains are mobilized, fewer of these stabilizinggrains are left at the channel surface to impart stability. Results from the pair ofexperiments run at high discharge demonstrate that while the differences betweenthe two bulk mixtures is reduced at higher discharge, in that the finer bulk mixtureonly saw a doubling, rather than a quadrupling, of morphodynamic change (i.e.total volume of erosion and deposition) relative to the coarser bulk mixture (Fig-ure 6.1), differences between the pair remained considerable. Considering next theinfluence of sediment supply on channel stability, it is predicted that the influenceof large grains may be reduced where more sediment is available for transport asthe development of an armoured surface is suppressed and the surface texture fines(e.g., Dietrich et al., 1989), thus potentially limiting the influence of larger grainson channel morphodynamics. Instead, the difference in channel morphodynamicsbetween the paired experiments persists even under high sediment supply; the ex-periment run in the finer bulk material (GSD1c) still experienced about twice asmuch morphodynamic change as that run in the coarser material (GSD2c; Figure6.1).Overall, the results from these three sets of paired experiments demonstrate thatthe greater representation of large grains at the surface of the bed influences channelmorphodynamics across a range of discharges and sediment supply rates. Differ-ences between the two bulk mixtures can not be explained using traditional models109of channel stability that rely on shear stress, as dimensionless reach-averaged shearstress, when normalizing by the D50, are on average higher in the more stable chan-nels (Figure 6.9). Instead, the primary difference between all pairs of experimentswas the relative size of D84 on the surface compared to the d84 of the bedload:the ratio of D84/d84 was significantly higher in all experiments conducted with thecoarse material (Figure 6.8). These findings suggest that the presence of a slightlygreater proportion of large grains at the surface of a channel act to diminish theability of the channel to erode and transport sediment. One mechanism by whichthis may be achieved is through the modification of relative roughness within thechannel as data collected from all three pairs of experiments show that there is asignificant relationship between relative roughness (D84/d) and morphodynamicchange (Figure 6.12) – channels tend to be more stable where values of relativeroughness are low and more dynamic where they are high.Building on the premise that surface roughness exerts a significant control onchannel morphodynamics, in Chapter 7 I quantify characteristics of surface textureand documenting how it evolves relative to morphodynamic change measured inthe channel. Three common measures of surface texture are examined: (1) thesurface grain size distribution; (2) the distribution of surface elevations; and (3)variograms of the bed surface elevations. Unfortunately, none of these indicesof channel roughness stood out as particularly effective for predicting morphody-namic change, particularly at the reach scale (Figure 7.13). At a more local scale,both the grain and bedform the Hurst Exponents, derived from variograms of thebed surface, and the kurtosis of the distribution of bed elevations show a signifi-cant relationship with morphologic change, although in all cases the linear modelused to describe the relationship explains only a very small amount of variance inthe data (Figure 7.14). In the case of all three significant relationships, the resultsare interpreted to show that the presence of large grains at the surface plays animportant role in channel morphodynamics. In the case of the Hurst Exponents,results associated with the grain scale index indicate that channels are less stablewhere fewer large grains are present at the surface, while results from the bedformscale suggest that the channel is more stable when a greater number of large grainsand clusters are present at the surface. Likewise, the relationship between morpho-dynamic change and kurtosis is understood to mean that channels are less stable110when fewer elevation outliers, or large grains, are present at the surface. These re-lationships between indices of surface texture and morphodynamic response, whileconsistent with the experimental results, are tenuous and require further study.To fully understand what processes contribute to the large grain effect docu-mented in this thesis it is necessary to dive deeper into the relationships betweenbed surface texture, flow hydraulics and channel morphodynamics. While Chap-ter 7 provides a preliminary examination of the link between surface texture andchannel stability, somewhat surprisingly, the results suggest that surface textureadjustments may actually trail behind overall channel width adjustments in medi-ating channel response. Where flows are sufficient to erode banks, a change inchannel geometry, and thus relative roughness, is the first step in re-establishinga stable channel morphology; changes in surface texture may become more im-portant as bank erosion slows and channels become dynamically stable or stable.Future work on this issue will involve the collection of high resolution spatial datafrom experiments that can be used to examine both surface texture and morphody-namic change and to produce flow modelling data used to understand hydraulics ata smaller spatial scale (i.e. one to two channel widths).In order to widely convince researchers in the field of fluvial geomorphologyto rethink using the median grain size as the default characteristic grain size, it isimperative to collect enough data from a wide range of environments, conditionsand sources that there can be no question that large grains control channel morpho-dynamics in alluvial, gravel-bed rivers. While physical modelling is unparalleledin its capability to allow researchers to manipulate governing conditions and to seehow such changes influence channel response, there are certain limitations that re-searchers must be aware of. First of all, scaling down any system will change oreliminate certain processes that exist in the prototype systems. For example, in themodels presented here, the grain size distribution of the bulk mixture is truncated at250 µm; while this is done in order to avoid issues of entrainment associated withhydraulically smooth surfaces, it means that the sand fraction of the bed materialof the prototype channel is omitted from the experiments. Similarly, in modellingmuch of the complexity of real-world systems is ignored; for example, in the caseof these experiments, the influence of vegetation, both along the banks and withinthe channel (i.e. large wood pieces), is neglected despite the fact that such vegeta-111tion has been found to have significant effects on channel morphodynamics (e.g.,Abbe and Montgomery, 1996; Eaton and Giles, 2009). These limitations, and oth-ers like them, make it imperative to collect data from real-world systems in orderto support and validate the results derived from physical modelling. One relativelynew method of field data collection that may prove to be invaluable for amassingthe necessary datasets to validate the experimental results presented here is dronephotography; using drones and photogrammetry software it is easy to collect highresolution, repeat data on channel morphology that can be used to investigate chan-nel response to a range of flow conditions through time.The large grain effect documented here has potentially important implicationsfor both hazard mitigation and stream restoration. The results of this work sug-gest that channel stability can be significantly modified by adding or removinga small fraction of the bed material from the coarse tail of the distribution. Inthe case of stream restoration, it is often desirable to increase the level of chan-nel stability without imposing hard engineering solutions (e.g. rip rap) in orderto maintain some habitat diversity. This is often the case in urban streams wherepeak flows have been increased and the channel has been de-stabilized. In such cir-cumstances, the addition of a relatively small number of large grains may help torestabilize the channel without having to completely immobilize it in place. Con-versely, stream managers may also attempt to restore natural channel dynamics inregulated streams where upstream dams have significantly reduced the availablepeak flows, resulting in channels that are no longer capable of eroding their banks,building bars or scouring pools, thereby reducing the complexity of in-stream andriparian habitat. In this case, removing some of the coarse sediment from the bed, itmay help the stream to re-establish its pre-disturbance morphology and function. Inboth circumstances it is necessary to acknowledge that the results presented in thisthesis represent only one line of evidence demonstrating the importance of largegrains in channel stability, it is recommended that more work be done to evaluatethe effectiveness of large grain addition/removal as a mitigation/restoration toolprior to its implementation in real-world streams. Further experimental work onthe subject should examine how the addition or removal of large grains to a “nat-ural” (i.e. non-templated) channel affects not only the treated area, but as well thereaches upstream and downstream. Stream managers looking to eventually employ112this technique should be wary in their selection of sites; early applications shouldbe done in locations where there is only minimal risk to surrounding infrastructure,for example in parklands or forested areas. Further, it would be beneficial for thesesites to be monitored in the years and even decades following the implementationof this technique in order to evaluate how effective the addition/removal of largegrains is in real channels.The research presented here opens up several new paths of investigation. Forexample, the observation that large grains play a governing role in channel stabilityhas important implications for paleoflood analysis and reconstruction; understand-ing that the onset of full mobility of the largest grains, rather than the median,coincides with dramatic channel widening will help in the interpretation of pastevents that exist in the sediment record. Another intriguing avenue of future inves-tigation is the role of that channel gradient plays in modifying how, as well as theextent to which, large grains control channel stability. At the steepest gradients,such as those of headwater channels, it has been well established that large grainsare the keystones that interact to form highly stable steps (e.g., Zimmermann andChurch, 2001). Comparatively, in low-gradient valley channels, large grains playmuch less of an important role, as it is bank cohesion, associated with presence ofa greater proportion of fine particles, that is instead the primary control on bankerosion (e.g., Darby et al., 2007). Understanding how channel stability changesbetween these two extremes will overall improve our ability to make predictions ofchannel response and will ultimately help us to mitigate against undesired shifts inchannel dynamics.113BibliographyAbbe, T. B. and Montgomery, D. R. 1996. Large Woody Debris Jams, ChannelHydraulics and Habitat Formation in Large Rivers. → page 112Aberle, J. and Nikora, V. 2006. Statistical properties of armored gravel bedsurfaces. 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J., and Gibbins, C. N. 2008. Sediment entrainment anddepletion from patches of fine material in a gravel-bed river. Water ResourcesResearch, 44(11):1–15. → page 77Warburton, J. 1992. Observation of bed load transport and channel bed changes ina proglacial mountain stream. Arctic and Alpine Research, 24(3):195–203. →pages 12, 13, 14, 15, 52, 107Wathen, S. J., Ferguson, R. I., Hoey, T. B., and Werritty, A. 1995. Unequalmobility of gravel and sand in weakly bimodal river sediments. WaterResources Research, 31(8):2087–2096. → pages 12, 39Wilcock, P., Kenworthy, S., and Crowe, J. 2001. Experimental study of thetransport of mixed sand and gravel. Water Resources Research,37(12):3349–3358. → page 39Wilcock, P. R. 1997a. Entrainment, displacement and transport of tracer gravels.Earth Surface Processes and Landforms, 22:1125–1138. → pages xiv, 147, 148125Wilcock, P. R. 1997b. The components of fractional transport rate. WaterResources Research, 33(1):247–258. → pages 67, 147Wilcock, P. R. and Crowe, J. C. 2003. Surface-based transport model formixed-size sediment. Journal of Hydraulic Engineering, 129(2):120–128. →pages xv, 11, 14, 148, 150Wilcock, P. R. and Kenworthy, S. T. 2002. A two-fraction model for the transportof sand/gravel mixtures. Water Resources Research, 38(10):1–12. → page 12Wilcock, P. R. and McArdell, B. W. 1993. Surface-based fractional transportrates: mobilization thresholds and partial transport of a sand-gravel sediment.Water Resources Research, 29(4):1297–1312. → pages 11, 12, 16, 39, 107, 147Wilcock, P. R. and McArdell, B. W. 1997. Partial transport of a sand/gravelsediment. Water Resources Research, 33(1):235–245. → pages12, 13, 15, 18, 39, 48, 76Wilcox, A. C., Nelson, J. M., and Wohl, E. E. 2006. Flow resistance dynamics instep-pool channels: 2. Partitioning between grain, spill, and woody debrisresistance. Water Resources Research, 42(W05419). → pages 9, 71Zimmermann, A. and Church, M. 2001. Channel morphology, gradient profilesand bed stresses during flood in a step-pool channel. Geomorphology,40(3-4):311–327. → page 113Zimmermann, A. E. 2009. Experimental investigations of step-pool channelformation and stability. PhD thesis, University of British Columbia. → page 21126Appendix ADEMs of differenceDEMs of difference (DoDs) are created by subtracting two DEMs from one an-other. The DoDs presented in this appendix show the difference in elevation be-tween subsequent hourly runs in each experiment.127−0.05−0.02500.0250.05Hour 0 to 1Hour 1 to 2Hour 2 to 3Hour 3 to 4Hour 4 to 5Hour 5 to 6Hour 6 to 7Hour 7 to 80.5 mFigure A.1: Hourly DEMs of difference for GSD1a showing the differencein bed elevation (in m) between the initial templated channel and thebed at the end of the 8th hour. Flow from right to left.128−0.05−0.02500.0250.05Hour 0 to 1Hour 1 to 2Hour 2 to 3Hour 3 to 4Hour 4 to 5Hour 5 to 6Hour 6 to 7Hour 7 to 80.5 mFigure A.2: Hourly DEMs of difference for GSD2a showing the differencein bed elevation (in m) between the initial templated channel and thebed at the end of the 8th hour. Flow from right to left.129−0.05−0.02500.0250.05Hour 0 to 1Hour 1 to 2Hour 2 to 3Hour 3 to 4Hour 4 to 5Hour 5 to 6Hour 6 to 7Hour 7 to 80.5 mFigure A.3: Hourly DEMs of difference for GSD1b showing the differencein bed elevation (in m) between the initial templated channel and thebed at the end of the 8th hour. Flow from right to left.130−0.05−0.02500.0250.05Hour 0 to 1Hour 1 to 2Hour 2 to 3Hour 3 to 4Hour 4 to 5Hour 5 to 6Hour 6 to 7Hour 7 to 80.5 mFigure A.4: Hourly DEMs of difference for GSD2b showing the differencein bed elevation (in m) between the initial templated channel and thebed at the end of the 8th hour. Flow from right to left.131−0.05−0.02500.0250.05Hour 0 to 1Hour 1 to 2Hour 2 to 3Hour 3 to 4Hour 4 to 5Hour 5 to 6Hour 6 to 7Hour 7 to 80.5 mFigure A.5: Hourly DEMs of difference for GSD1c showing the differencein bed elevation (in m) between the initial templated channel and thebed at the end of the 8th hour. Flow from right to left.132−0.05−0.02500.0250.05Hour 0 to 1Hour 1 to 2Hour 2 to 3Hour 3 to 4Hour 4 to 5Hour 5 to 6Hour 6 to 7Hour 7 to 80.5 mFigure A.6: Hourly DEMs of difference for GSD2c showing the differencein bed elevation (in m) between the initial templated channel and thebed at the end of the 8th hour. Flow from right to left.133Appendix BSediment properties tablesTable B.1: Sediment properties of GSD1a and GSD2aOutput Rate Load (mm) Surface (mm)Hour (g/min) d50 d84 D50 D84GSD1a1 26.3 1.82 3.30 1.54 3.062 75.4 1.89 3.46 1.73 3.243 1.8 1.50 2.24 1.62 3.194 43.0 1.80 3.22 1.77 3.445 138.2 1.78 3.32 1.63 3.196 32.5 1.77 3.19 1.74 3.097 8.5 1.70 3.09 1.73 3.148 6.2 1.69 2.87 1.73 3.57GSD2a1 7.2 1.80 2.98 1.47 2.892 27.2 1.82 3.09 1.67 3.313 19.7 1.67 2.65 1.62 3.294 5.0 1.64 2.73 1.72 3.675 10.1 1.75 3.03 1.73 3.606 11.2 1.73 3.06 1.84 3.757 4.2 1.72 3.13 1.79 3.798 1.9 1.79 3.18 2.02 3.86These values arederived from the data analysis methods used in Chapter 6 and thus may vary slightly from thevalues presented in Chapter 5.134Table B.2: Sediment properties of GSD1b and GSD2bOutput Rate Load (mm) Surface (mm)Hour (g/min) d50 d84 D50 D84GSD1a1 522.6 1.76 3.30 1.59 3.022 274.7 1.71 3.19 1.71 3.253 125.4 1.60 2.85 1.70 2.934 358.3 1.76 3.26 1.84 3.505 237.5 1.77 3.24 1.68 3.426 267.3 1.72 2.96 1.71 3.137 266.9 1.65 2.83 1.71 3.288 151.8 1.52 2.61 1.63 3.18GSD2a1 368.5 1.86 3.60 1.81 3.842 260.9 1.73 3.07 1.70 3.693 196.7 1.76 3.22 1.76 3.834 134.4 1.70 3.07 1.67 3.665 36.2 1.54 2.66 1.77 3.556 171.1 1.77 3.38 1.83 4.057 30.1 1.59 2.69 1.87 4.238 30.2 1.75 3.07 1.99 4.68135Table B.3: Sediment properties of GSD1c and GSD2cOutput Rate Load (mm) Surface (mm)Hour (g/min) d50 d84 D50 D84GSD1a1 563.8 1.79 3.27 1.55 2.792 306.3 1.71 3.12 1.60 2.703 277.4 1.58 2.95 1.76 3.254 207.2 1.67 2.92 1.81 3.405 218.0 1.60 2.85 1.50 3.106 282.3 1.45 2.63 1.61 2.977 173.4 1.52 2.59 1.79 3.208 84.1 1.53 2.70 1.74 3.00GSD2a1 305.3 1.81 3.32 1.73 3.682 95.6 1.59 2.81 1.95 3.583 51.5 1.75 3.12 1.99 3.684 150.5 1.68 3.11 1.81 3.675 19.4 1.59 2.99 1.73 3.866 54.0 1.59 2.87 1.82 3.797 68.8 1.57 2.83 1.90 3.688 163.2 1.75 3.30 1.61 3.27Table B.4: Sediment properties of the pseudo-recirculating experiment.Output Rate Load (mm) Surface (mm)Minutes (g/min) d50 d84 D50 D8415 254.8 1.76 3.32 1.72 3.5930 259.7 1.64 2.97 1.82 3.8345 181.7 1.74 3.28 1.83 3.7360 150.5 1.62 2.84 1.83 3.8975 165.5 1.74 3.40 1.90 4.2090 136.9 1.81 3.41 1.97 4.35105 79.4 1.54 2.72 1.87 4.47120 38.1 1.76 3.12 1.75 4.38136Appendix CFlow modelling results tables137Table C.1: Hydraulic properties of GSD1a and GSD2aHour W d U τ τ∗50 τ∗84 Ω(m) (m) (m/s) (Pa) (W/m)GSD1a0 0.30 8.93E-03 8.51E-03 1.60 0.062 0.032 1.42E-021 0.29 9.35E-03 9.48E-03 1.69 0.068 0.034 1.74E-022 0.30 9.69E-03 8.91E-03 1.71 0.061 0.033 1.65E-023 0.30 9.95E-03 8.85E-03 1.67 0.064 0.032 1.60E-024 0.30 9.83E-03 8.77E-03 1.72 0.060 0.031 1.61E-025 0.27 1.01E-02 9.43E-03 1.77 0.067 0.034 1.80E-026 0.28 1.01E-02 9.25E-03 1.73 0.061 0.035 1.73E-027 0.28 1.01E-02 9.13E-03 1.73 0.062 0.034 1.70E-028 0.28 1.03E-02 8.87E-03 1.76 0.063 0.030 1.68E-02AVG 0.29 9.82E-03 9.02E-03 1.71 0.063 0.033 1.66E-02GSD2a0 0.30 9.81E-03 9.02E-03 1.87 0.071 0.035 1.77E-021 0.31 8.96E-03 9.73E-03 1.74 0.073 0.037 1.78E-022 0.29 9.47E-03 9.52E-03 1.82 0.068 0.034 1.85E-023 0.30 9.28E-03 9.66E-03 1.80 0.069 0.034 1.85E-024 0.29 9.61E-03 9.52E-03 1.86 0.067 0.031 1.88E-025 0.29 9.49E-03 9.55E-03 1.83 0.065 0.031 1.87E-026 0.29 9.51E-03 9.47E-03 1.84 0.062 0.030 1.86E-027 0.29 9.39E-03 9.66E-03 1.81 0.062 0.029 1.88E-028 0.29 9.90E-03 9.22E-03 1.91 0.059 0.031 1.89E-02AVG 0.29 9.49E-03 9.48E-03 1.83 0.066 0.032 1.85E-02These values are derived from the data analysis methods used in Chapter 6 and thus may varyslightly from the values presented in Chapter 5.138Table C.2: Hydraulic properties of GSD1b and GSD2bHour W d U τ τ∗50 τ∗84 Ω(m) (m) (m/s) (Pa) (W/m)GSD1a0 0.33 1.39E-02 1.22E-02 2.59 0.093 0.048 3.35E-021 0.52 9.78E-03 9.99E-03 1.80 0.073 0.038 1.98E-022 0.54 1.01E-02 9.24E-03 1.79 0.067 0.035 1.84E-023 0.53 1.02E-02 9.36E-03 1.72 0.063 0.037 1.76E-024 0.47 1.10E-02 9.89E-03 1.86 0.065 0.034 2.00E-025 0.42 1.16E-02 1.05E-02 1.91 0.073 0.036 2.28E-026 0.49 1.08E-02 9.62E-03 1.83 0.067 0.037 1.95E-027 0.45 1.14E-02 1.00E-02 1.85 0.069 0.036 2.08E-028 0.49 1.12E-02 9.15E-03 1.87 0.070 0.036 1.94E-02AVG 0.47 1.11E-02 1.00E-02 1.91 0.071 0.037 2.13E-02GSD2a0 0.32 1.40E-02 1.25E-02 2.66 0.101 0.050 3.43E-021 0.42 1.08E-02 1.11E-02 1.95 0.076 0.036 2.42E-022 0.39 1.15E-02 1.12E-02 2.08 0.073 0.035 2.60E-023 0.36 1.18E-02 1.20E-02 2.13 0.075 0.034 2.84E-024 0.36 1.22E-02 1.17E-02 2.21 0.086 0.039 2.85E-025 0.38 1.19E-02 1.15E-02 2.11 0.077 0.038 2.66E-026 0.35 1.25E-02 1.16E-02 2.19 0.081 0.037 2.81E-027 0.39 1.19E-02 1.10E-02 2.05 0.076 0.034 2.48E-028 0.38 1.23E-02 1.09E-02 2.13 0.082 0.035 2.59E-02AVG 0.37 1.21E-02 1.15E-02 2.17 0.081 0.037 2.74E-02139Table C.3: Hydraulic properties of GSD1c and GSD2cHour W d U τ τ∗50 τ∗84 Ω(m) (m) (m/s) (Pa) (W/m)GSD1a0 0.35 1.29E-02 1.23E-02 2.40 0.093 0.048 3.13E-021 0.49 1.04E-02 1.01E-02 1.88 0.075 0.042 2.11E-022 0.55 9.77E-03 9.23E-03 1.69 0.065 0.039 1.76E-023 0.60 9.99E-03 8.29E-03 1.73 0.061 0.033 1.62E-024 0.59 1.02E-02 8.36E-03 1.79 0.061 0.033 1.67E-025 0.53 1.04E-02 8.87E-03 1.72 0.071 0.034 1.73E-026 0.42 1.14E-02 1.07E-02 1.98 0.076 0.041 2.39E-027 0.52 1.06E-02 9.14E-03 1.83 0.063 0.035 1.86E-028 0.59 1.07E-02 8.42E-03 1.89 0.067 0.039 1.72E-02AVG 0.52 1.07E-02 9.49E-03 1.88 0.070 0.038 2.00E-02GSD2a0 0.33 1.36E-02 1.24E-02 2.60 0.098 0.048 3.36E-021 0.43 1.19E-02 1.00E-02 2.22 0.079 0.037 2.43E-022 0.45 1.16E-02 9.80E-03 2.19 0.069 0.038 2.36E-023 0.44 1.16E-02 9.89E-03 2.17 0.067 0.036 2.38E-024 0.51 1.09E-02 9.01E-03 2.00 0.068 0.034 2.04E-025 0.57 1.06E-02 8.23E-03 1.92 0.069 0.031 1.78E-026 0.60 1.03E-02 8.01E-03 1.87 0.063 0.030 1.68E-027 0.56 1.05E-02 8.50E-03 1.93 0.063 0.032 1.86E-028 0.50 1.05E-02 9.23E-03 1.93 0.074 0.036 2.06E-02AVG 0.49 1.13E-02 9.46E-03 2.09 0.072 0.036 2.22E-02Table C.4: Hydraulic properties of the pseudo-recirculating experimentMinutes W d U τ τ∗50 τ∗84 Ω(m) (m) (m/s) (Pa) (W/m)0 0.30 1.26E-02 1.01E-02 2.33 0.088 0.043 2.42E-0215 0.31 1.24E-02 1.01E-02 2.36 0.088 0.048 2.49E-0230 0.34 1.17E-02 9.72E-03 2.26 0.080 0.040 2.36E-0245 0.37 1.09E-02 9.32E-03 2.14 0.072 0.036 2.15E-0260 0.39 1.05E-02 9.02E-03 2.04 0.069 0.036 2.01E-0275 0.44 9.85E-03 8.65E-03 1.92 0.062 0.031 1.83E-0290 0.48 9.34E-03 8.28E-03 1.80 0.056 0.029 1.66E-02105 0.52 8.88E-03 7.97E-03 1.70 0.056 0.028 1.52E-02120 0.50 9.06E-03 8.04E-03 1.72 0.059 0.029 1.55E-02AVG 0.41 1.06E-02 9.02E-03 2.03 0.070 0.036 2.00E-02140Appendix DStatistical results tablesTable D.1: Linear regression results for temporal trends in bedload and bedsurface grain sizes for GSD1a and GSD2a using the data processingtechniques of Chapter 5 (the difference in data processing techniquesused between Chapter 5 and 6 are given in Table 4.2). Although the val-ues of the equations are slightly different than those in Tables D.3 andD.4, the same variables show significant trends (i.e. D50 and D84/D90 ofGSD2a).Linear Regression Equation R2 P aTime ∼ GSD1a d50 y=−0.0119x+1.797 0.0831 0.2976Time ∼ GSD1a d90 y=−0.0211x+3.688 0.0294 0.5415Time ∼ GSD2a d50 y=−0.0054x+1.759 0.0289 0.5294Time ∼ GSD2a d90 y= 0.0344x+3.347 0.1210 0.1868Time ∼ GSD1a D50 y= 0.0389x+1.593 0.4794 0.0570Time ∼ GSD1a D90 y= 0.0361x+3.531 0.2314 0.2276Time ∼ GSD2a D50 y= 0.0492x+1.708 0.8807 5.56e-04Time ∼ GSD2a D90 y= 0.0808x+3.998 0.6548 5.11e-08a P< 0.05 indicates a statistically significant trend, shown in bold.141Table D.2: T-test results comparing grain sizes of bedload and surface be-tween paired experiments using the data processing techniques of Chap-ter 5 (the difference in data processing techniques used between Chapter5 and 6 are given in Table 4.2).T-Test X¯1 X¯2 t aGSD1a d50 ∼ GSD2a d50 1.75 1.74 0.284GSD1a d90 ∼ GSD2a d90 3.60 3.49 1.067GSD1a D50 ∼ GSD2a D50 1.77 1.93 -2.427GSD1a D90 ∼ GSD2a D90 3.69 4.36 -6.171a negative t values indicates X¯1 < X¯2. Statisticallysignificant differences are shown in bold.Table D.3: Linear regression results for temporal trends in bedload grain sizesfor all paired experiments.Linear Regression Equation R2 P aTime ∼ GSD1a d50 y=−0.0064x+1.757 0.02 0.62Time ∼ GSD1a d84 y=−0.0169x+3.156 0.01 0.66Time ∼ GSD2a d50 y=−0.0054x+1.774 0.03 0.53Time ∼ GSD2a d84 y= 0.0266x+2.862 0.08 0.30Time ∼ GSD1b d50 y=−0.0210x+1.774 0.21 0.07Time ∼ GSD1b d84 y=−0.0787x+3.357 0.39 9.18e-03Time ∼ GSD2b d50 y=−0.0230x+1.798 0.13 0.16Time ∼ GSD2b d84 y=−0.0716x+3.374 0.18 0.11Time ∼ GSD1c d50 y=−0.0402x+1.764 0.42 6.60e-03Time ∼ GSD1c d84 y=−0.0883x+3.242 0.46 3.73e-03Time ∼ GSD2c d50 y=−0.0102x+1.719 0.05 0.38Time ∼ GSD2c d84 y=−0.0053x+3.084 0.00 0.85a P< 0.05 indicates a statistically significant trend, shown in bold.142Table D.4: Linear regression results for temporal trends in surface grain sizesfor all paired experiments.Linear Regression Equation R2 P aTime ∼ GSD1a D50 y= 0.0190x+1.602 0.33 0.14Time ∼ GSD1a D84 y= 0.0293x+3.108 0.17 0.31Time ∼ GSD2a D50 y= 0.0607x+1.459 0.86 9.90e-04Time ∼ GSD2a D84 y= 0.1248x+2.961 0.86 9.962e-04Time ∼ GSD1b D50 y= 0.0014x+1.459 0.00 0.91Time ∼ GSD1b D84 y= 0.0213x+3.121 0.07 0.51Time ∼ GSD2b D50 y= 0.0266x+1.688 0.47 0.06Time ∼ GSD2b D84 y= 0.1083x+3.455 0.51 4.56e-02Time ∼ GSD1c D50 y= 0.0180x+1.592 0.14 0.36Time ∼ GSD1c D84 y= 0.0333x+2.901 0.12 0.40Time ∼ GSD2c d50 y=−0.0196x+1.906 0.14 0.36Time ∼ GSD2c d84 y=−0.0277x+3.755 0.10 0.45a P< 0.05 indicates a statistically significant trend, shown in bold.Table D.5: T-test results comparing grain sizes of bedload and surface be-tween paired experiments.T-Test X¯1 X¯2 t aGSD1a d50 ∼ GSD2a d50 1.73 1.74 -0.177GSD1a d84 ∼ GSD2a d84 3.08 2.98 1.065GSD1b d50 ∼ GSD2b d50 1.68 1.70 -0.336GSD1b d84 ∼ GSD2b d84 3.02 3.07 0.711GSD1c d50 ∼ GSD2c d50 1.59 1.68 -1.828GSD1c d84 ∼ GSD2c d84 2.87 3.06 -1.979GSD1a D50 ∼ GSD2a D50 1.69 1.73 -0.700GSD1a D84 ∼ GSD2a D84 3.24 3.52 -2.134GSD1b D50 ∼ GSD2b D50 1.69 1.81 -2.686GSD1b D84 ∼ GSD2b D84 3.22 3.94 -4.912GSD1c D50 ∼ GSD2c D50 1.67 1.82 -2.352GSD1c D84 ∼ GSD2c D84 3.05 3.65 -5.816a negative t values indicates X¯1 < X¯2. Statisticallysignificant differences are shown in bold.143Table D.6: Linear regression results for temporal trends in surface texturevariables. Trends are plotted in Figures 7.6 and 7.7Linear Regression Equation R2 P aTime ∼ D50 y= 0.0018x+1.709 0.46 0.07Time ∼ D84 y= 0.0049x+3.270 0.50 0.05Time ∼ σ y= 0.0016x+1.873 0.60 0.02Time ∼ σz y= 6.9e−07x+9.75e−04 0.34 0.13Time ∼ Sk y=−6.80e−04x+0.395 0.29 0.16Time ∼ Ku y=−3.40e−03x+4.127 0.91 2.49e-4a P< 0.05 indicates a statistically significant trend, shown in bold.Table D.7: Linear regression models results for reach-averaged morphody-namic change versus surface texture indices. Plots with linear regressionmodels shown in Figure 7.13.Linear Regression Equation R2 P aM ∼ D50 y=−0.0215x+0.051 0.26 0.20M ∼ D84 y=−0.0074x+0.038 0.21 0.26M ∼ σ y=−0.0358x+0.083 0.45 0.07M ∼ σz y=−3.6393x+0.031 0.46 0.07M ∼ Sk y= 0.0131x+0.019 0.32 0.15M ∼ Ku y= 0.0020x+0.005 0.03 0.68M ∼ Hg y=−0.1154x+0.098 0.03 0.68M ∼ H f y= 0.2556x−0.069 0.44 0.07M ∼ D84/d y=−0.0516x+0.030 0.59 0.03M ∼ σz/d y=−0.0257x+0.025 0.65 0.02a P< 0.05 indicates a statistically significant trend, shown in bold.144Table D.8: Linear regression models results for morphodynamic change ver-sus surface texture indices at each cross section. Plots with linear regres-sion models shown in Figure 7.14.Linear Regression Equation R2 P aM ∼ D50 y=−1.73e−04x+7.61e−04 0.02 0.26M ∼ D84 y=−8.33e−05x+7.43e−04 0.02 0.20M ∼ σ y=−9.93e−05x+6.38e−04 4.24e-03 0.57M ∼ σz y= 0.3294x+1.08e−04 0.02 0.20M ∼ Sk y= 4.42e−04x+2.97e−04 0.04 0.06M ∼ Ku y= 2.35e−04x−4.71e−04 0.10 3.44e-03M ∼ Hg y=−0.0055x+4.55e−03 0.07 0.02M ∼ H f y= 0.0029x−4.78e−04 0.07 0.02a P< 0.05 indicates a statistically significant trend, shown in bold.145Appendix EModel of stabilityE.1 OverviewWhen considering bed entrainment and sediment transport, it makes sense to as-sociate the threshold(s) with grain size. But bed entrainment and the stability of astream’s channel morphology are not the same thing. In fact, we often use the anal-ogy of a ”dynamic equilibrium” to describe channels that maintain their generalshape while transporting sediment and migrating laterally. However, the analogywas made in the past primarily out of necessity, and does not represent the behaviorof most natural streams (even those built in laboratories). In particular, gravel bedstreams are characterized by highly non-linear processes, and exhibit both complexand chaotic dynamics which, while deterministic, are not amenable to prediction.One important aspect of this non-linearity is that field and laboratory evidencedemonstrates that there exists a threshold for gravel bed rivers above which thechannel form changes dramatically and quickly. This kind of threshold behavioras long been acknowledged by geomorphologists (e.g., Schumm, 1969), and hasbeen describe conceptually, but attempts to numerically model this threshold havesimply relied upon analogy with the entrainment threshold; the nature of geomor-phic thresholds in gravel bed streams does not seem to have been seriously studiedin its own right.Rather than being linked to entrainment of a given particle size (Andrews,1982; Henderson, 1961; Kaufmann et al., 2008; Olsen et al., 1997)], we believe146Figure E.1: A plot of the function which predicts the fraction of a sediment ina give size class that will remain on the bed as a function of the relativeshear stress, based on Wilcock (1997a).that the threshold for morphologic stability could just as easily be linked to thefraction of the bed surface that remains stable during a given flow. That is, stabilitymay be attributable to the fraction of the bed covered by imobile particles, whichis slighlty different than saying it is related to a particular grain size.E.2 Predicting the immobile fractionOne issue that seems to be often overlooked when thinking about bed stability isthat, even once a grain size begins to move, most of the particles of that size on thebed will not be moved. It is only when the shear stresses approach two times thethreshold for entrainment that nearly all particles of a given size can be mobilizedand transported. We can use the experimental work done by Wilcock in the 1990’sto constrain the problem, and to estimate the the fraction of the bed surface that isimmobile for a given bed surface grain size distribution and shear stress (Wilcockand McArdell, 1993; Wilcock, 1997a,b).147Based on Wilcock’s work (Wilcock, 1997a), we can generally say that, forτ ≈ τc, only about 10% of the grains on the bed surface are likely to be entrainedand transported. We can also posit that, for τ ≈ 2τc, about 90% of the grainsare likely to be transported. We can approximate the underlying physics using alogistic equation, which predicts the fraction of a sediment in a give size class thatwill remain on the bed as a function of the relative shear stress (which we take tobe the shear stress divided by the entrainment shear stress). The value the functionat the threshold for entrainment is 0.9, while the value at twice the threshold is 0.1.These values are indicated on Figure E.1 using dotted red lines. While the detailsof this approximation curve could obviously be refined, the function captures thetransition from immobility to partial mobility to full mobility in a general way. Italso makes clear that equating channel instability to the shear stress required toentrain the D50 is probably not a good assumption, since:1. 90% of the size class containing the D50 will not be entrained by that flow2. all the sediment coarser than the D50 will be at least that stable, and3. a large fraction of the grain sizes smaller than D50 will also remain immobileE.3 Integrating the immobile fractionWe can use the function shown in Figure E.1 to estimate the total fraction of abed surface that will remain immobile for a given grain size distribution at anygiven shear stress. For example, consider a bed surface with a log-distribution ofsediment sizes, and a D84/D50 ratio of 2 (Figure E.2). We can estimate the criticalshear stress for entrainment using the hiding function proposed by Wilcock andCrowe (2003) to account for relative grain size:τciτc50=(DiD50)b(E.1)Where Di is the grain size of fraction i, and b = 0.12 for Di/D50 < 1 andb = 0.67 for Di/D50 > 1. For our grain size distribution, the critical shear stressvalues are shown in Figure E.3. Using these data, we can estimate the proportionof the bed surface that would be stable for a given shear stress.148Figure E.2: Example of a bed surface grain size distribution with a log-distribution of sediment sizes, and a D84/D50 ratio of 2.E.4 Calculating the immobile fractionFor example, assume that τ = 25 Pa then we can calculate the fraction of the bedthat would remain immobile (Figure E.4). The total fraction of the bed surface thatwould be immobile under these conditions (and given the above assumptions) is asthe area under the red curve, which is about 0.92. The stress required to entrainthe bed surface D50 is about 26 Pa, so the above curve represents the bed stabilityat flows close to that required to entrain the bed surface, which some would haveuse believe represents the formative flow! We know from experiments that shearstresses of this magnitude do little to affect stream channel morphology in gravelbed rivers.But what about for conditions that should fully mobilize the D50 (i.e. 2τc50)?Figure E.5 shows that at the shear stress required to fully mobilize the D50 (i.e. 52Pa), flows mobilize quite a bit more of the bed, but leave 0.29 of the bed immo-bile. Note that the stable fraction for the entrainment of the D50 is also shown forcomparison on this figure, in red.149Figure E.3: Critical shear stress values calculated using the hiding functionproposed by Wilcock and Crowe (2003) for the grain size distributionshown in Figure E.2.In the paired experiments presented in Chapter 4, it is observed that morpho-logic instability occurs when the fraction of the bed that is immobile falls belowabout 0.1. This value corresponds to roughly to the full mobility of something likethe D84. When the D84 is fully mobile, only 0.07 of the bed is likely to remain im-mobile. This is a much higher threshold than is usually discussed when consideringthe thresholds for geomorphic change in gravel bed rivers.150Figure E.4: Fraction of the bed immobile at the entrainment threshold of theD50. The grain size distribution of the surface is shown as the dashedblue line, while the red line shows the distribution the stable fraction atthe bed surface at the entrainment threshold of the D50.151Figure E.5: Fraction of the bed immobile at the threshold of full mobilityof the D50. The grain size distribution of the surface is shown as thedashed blue line, the green line shows the distribution the stable fractionat the bed surface at the threshold of full mobility of the D50 and the redline shows the distribution the stable fraction at the bed surface at theentrainment threshold of the D50.152Figure E.6: Fraction of the bed immobile at the threshold of full mobility ofthe D84. The grain size distribution of the surface is shown as the dashedblue line, the orange line shows the distribution the stable fraction at thebed surface at the threshold of full mobility of the D84, the green lineshows the distribution the stable fraction at the bed surface at the thresh-old of full mobility of the D50 and the red line shows the distributionthe stable fraction at the bed surface at the entrainment threshold of theD50.153

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