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The controls of morphodynamics in steep, aggrading channels : a flume investigation Booker, William 2018

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The Controls of Morphodynamics inSteep, Aggrading Channels:A Flume InvestigationbyWilliam BookerB.Sc., Durham University, 2016A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Geography)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2018©William Booker, 2018The following individuals certify that they have read, and recommend to the Faculty ofGraduate and Postdoctoral Studies for acceptance, a thesis/dissertation entitled:The Controls of Morphodynamics in Steep, Aggrading Channels: A Flume Investigationsubmitted by: William H. Booker in partial fulfillment of the requirementsfor the degree of Master of Sciencein GeographyExamining Committee:Brett Eaton, GeographySupervisorDan Moore, GeographySupervisory Committee MemberJennifer Williams, GeographyAdditional ExamineriiAbstractThis thesis presents the results of ten experiments conducted to examine the role grain sizedistributions play in the behaviour and evolution of one dimensional alluvial fans using anovel flume setup. The two grain size distributions share the same median grain size (D50= 1.42 mm), one (GSD1) is composed of log normally distributed material from 0.25 to 5.6mm and the other (GSD2) is only composed of two classes: 1.4 and 2.0 mm. Images of thedeposit profile and surface were used to monitor the evolution of the deposit and allow for thequantitative and qualitative assessment of behaviour, respectively. A detailed comparisonof the aggrading phase of one run condition (Q = 0.1 l s−1, Qb = 1 g s−1) demonstratesa difference in the morphology that must originate from the grain size distribution. Theaddition of coarser grains in GSD1 creates patches of immobility and allows the formationof bars more resistant to flow than in GSD2. This reduction in transport efficiency of thematerial results in a higher slope and more stable bed configuration for GSD1. More widely,this pair of experiments shows that differences in mobility may still manifest in aggradingenvironments. For all five pairs of experiments this difference is present. Overall, GSD1exhibits more stable behaviour: lower transport rates, higher slopes and later transportthan GSD2. However, the difference between the two grain size distributions decreases asdischarge increases. That is, the difference is most pronounced at the lowest dischargewhere grains are less mobile due to the lower maximum stress and lower frequency of itoccurring. This reduced mobility is due to a threshold of entrainment present in GSD1 thatis less commonly exceeded at low discharges, but that is not present to the same extent inGSD2. Therefore, the proportion of immobile grains controls the behaviour and stability ofan aggrading channel.iiiLay SummaryThe mechanics controlling how mountain streams behave when they accumulate materialare poorly understood. As a result the current body of work does not accurately predicthow such rivers evolve and respond to changes. This research used five paired experimentsto show that introducing both smaller and larger material to the stream will significantlychange how able the stream is to move the overall mixture. The presence of these large grainsdecreases how often and how far the average grain moves, making it harder for all grains tobe moved by the stream. However, this impedance decreases the more energy is supplied tothe stream such that the paired experiments begin to demonstrate similar behaviour at thehighest energy.ivPrefaceThis dissertation is result of ten experiments designed in conjunction with Brett Eaton,and run by myself. The flume, and associated apparatus, were constructed by or withsubstantial help from Rick Ketler. Chapter 3 forms the basis of a paper, that will besubmitted for publication, written in collaboration with Brett Eaton. All other data analysisand processing, as well as all other chapters were written by me.vContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Alluvial Fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Sediment Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Natural Variations in Threshold Stress . . . . . . . . . . . . . . . . . . . . . 41.4 Armour Formation and Equal Mobility . . . . . . . . . . . . . . . . . . . . . 61.5 Stochastic Sediment Transport . . . . . . . . . . . . . . . . . . . . . . . . . . 81.6 Flow Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.7 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.8 Research Objectives and Thesis Structure . . . . . . . . . . . . . . . . . . . 112 Experimental Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1 Experimental Design and Data Collection . . . . . . . . . . . . . . . . . . . 132.1.1 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1.2 Experiment Operation . . . . . . . . . . . . . . . . . . . . . . . . . . 162.1.3 Perpendicular Camera . . . . . . . . . . . . . . . . . . . . . . . . . . 18vi2.1.4 Channel Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Contrasting Morphodynamics in Paired Systems . . . . . . . . . . . . . . 223.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.1.1 Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.1.2 Channel State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 Comparing Morphodynamics Across Systems . . . . . . . . . . . . . . . . 344.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47A Model Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57B Channel States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59B.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59B.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65viiList of Tables2.1 Run conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Grain size characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.1 Class percent (G1Q100L & G2Q100L) . . . . . . . . . . . . . . . . . . . . . 253.2 Flume dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.1 Slope statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.2 Raw regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.3 Transport rate statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.4 Sediment storage statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.5 Transport efficiency statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 41B.1 Class type statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59B.2 Class type statistics continued . . . . . . . . . . . . . . . . . . . . . . . . . . 61B.3 Stability index statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61viiiList of Figures2.1 Flume setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 Grain size distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Example Photograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1 Slopes (G1Q100L & G2Q100L) . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Distribution of water depths (G1Q100L & G2Q100L) . . . . . . . . . . . . . 233.3 Transport efficiency (G1Q100L & G2Q100L) . . . . . . . . . . . . . . . . . . 243.4 Class proportions (G1Q100L & G2Q100L) . . . . . . . . . . . . . . . . . . . 253.5 Class changes (G1Q100L & G2Q100L) . . . . . . . . . . . . . . . . . . . . . 263.6 Class change distribution (G1Q100L & G2Q100L) . . . . . . . . . . . . . . . 263.7 Bar head dissection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.8 Thalweg sweep migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.1 All slope values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2 Distribution of slopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.3 Raw slope regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.4 Sediment transport rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.5 Sediment storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.6 Transport efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42B.1 Class types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60B.2 Relative channel stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62B.3 Relative channel stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63B.4 Lagged stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64ixList of SymbolsSymbol Definition Unitsd water depth LD grain diameter LDb grain diameter LDi percentile of grain diameter LDs surface grain diameter Lg acceleration due to gravity L T−2ks surface roughness LKb base grain diameter Lqb specific bed load transport rate m L−1 T−1q∗b dimensionless specific bed load transport rate -Q discharge L3 T−1Qb sediment transport rate m T−1Qc sediment concentration m L−3R hydraulic radius LS slope -t time Tx distance downstream Lz bed elevation LU mean downstream velocity L T−1U∗ shear velocity L T−1γ specific weight of water m L−2 T−2γs specific weight of sediment m L−2 T−20 packing density m L−3η sediment transport efficiency m L−3θ Shields number -θc critical Shields number -xµ dynamic viscosity m L−1 T−1ρ density of water m L−3ρs density of sediment m L−3τ shear stress m L−1 T−2τc critical shear stress m L−1 T−2τd distraining shear stress m L−1 T−2τe entraining shear stress m L−1 T−2τr reference shear stress m L−1 T−2τ ∗ dimensionless shear stress -τ ∗c critical dimensionless shear stress -xiAcknowledgementsI would like to thank my supervisor Brett Eaton, without whose support and guidanceI would not have been able to finish this project. I came to Brett’s lab group with theintention of doing a Masters degree and leaving, but my time spent working with Brett hasfurthered my love for the subject and is the reason why I wish to pursue Geography further.Thanks must also be given to my lab group, Anya and Lucy in particular, for giving meample opportunities to discuss my work with them and provide ever insightful comments.I would also like to give thanks to Rick Ketler and David Waine in the Ponderosa Geoflu-vial Lab for their help and expertise in getting my flume(s) up and running, and teachingme enough to look like I know what I am doing. Also every member of the department Ibothered throughout the last two years with any number of daft questions.Of course I would not be where I am today without the support of my friends and family.My parents, Craig and Emma, despite being almost 5000 miles away have helped me throughevery step of my education with the utmost selflessness and care, for which I will always begrateful.xiiChapter 1IntroductionAs rivers are formed from the material they carry, they physically respond to the suppliedloads of water and sediment. One of the most well known expressions of this was formulatedby Lane (1955), who considered a river at grade as a function of its major components:S ∝ QbDQ(1.1)wherein slope (S) is proportional to the sediment supply (Qb), calibre (D) and water dis-charge (Q). Grade, or equilibrium, is the state at which the channel is able to convey thesupplied water and sediment without substantial change over some period of time (Mackin,1948). This conceptual model assumes changes to one of these factors will result in com-pensation in any of the others. As the achievement of grade is concerned with bed mobility,the implication of the use of Lane’s formula is that we can simplify the behaviour of a bedsurface into a characteristic grain size. This is especially true when we consider the laterreformulation by Church (2006), which explicitly defines the bed calibre as the median grainsize (D50). These ideas correspond to the bed mobility and channel stability being directlyproportional to the D50, which is valid in some environments but invalid in many others, andignores the effects other grains have on the overall mobility of the bed as well as its spatialdistribution.Stability is, here, synonymous with the propensity for movement but varies with thescale of investigation. At the grain scale stability is the lack of motion; a stable grain isone currently not in motion or entrained into the flow. For meso-scale bed forms, such asbars and stone lines, stability is their ability to resist destruction or large scale deformation(e.g. Lisle et al., 1991). In reference to bed and banks, stability is their resistance to erosionthrough either armouring (e.g. Parker and Klingeman, 1982) or through cohesive strength(e.g. Hickin, 1984). Finally, the stability of a channel reach refers to its average dimensional1variance and rate of migration. That is, a reach may either be considered stable if it remainsin the same position (if confined) or is migrating at a low rate (if unconfined) without greatchange in its dimensions and characteristics over the timescale of its migration. Due to thehierarchy of processes acting up from the grain-scale (Schumm, 1985), stability originateswith the likelihood of entrainment of the material of which the channel is composed.The majority of work in this field has been concerned with the adjustment of channelsto grade in a degrading setting. In other words, how channels are capable of self-organisingto provide stability to prevent further deformative work (i.e. sediment transport). The be-haviour of aggrading channels and their stability conferring mechanisms are, in comparison,poorly studied. Presumably, aggrading systems set their slope and form to some combinationthat reflects the relative inputs of mass and energy in a manner comparable to degradingsystems (e.g. Eaton et al., 2004). Alluvial fans are suited to study this phenomenon asthey represent a natural response to supplied water and sediment discharges, capable ofself-organisation to maintain sediment conveyance whilst aggrading. The rest of this chapterassesses the current literature on grain and bed mobility in order to better understand themechanisms by which channels can stabilise their form.1.1 Alluvial FansWhere reductions in confinement or slope occur, there are concurrent changes in transportcapacity and competence which trigger the deposition of sediment into semi-conicular fea-tures known as alluvial fans. They are often found in mountain environments due to the highdegree of coupling between the hillslopes and fluvial system, and the high rates of sedimentproduction. A separation can be made between alluvial fans driven by colluvial or alluvialprocesses (Blair and McPherson, 1994). This separation controls the magnitude and typeof sediment delivery to the fan, constraining the characteristics, behaviour and evolution ofthe fan. The fans discussed herein will be concerned only with those constructed by alluvialprocesses, given their prevalence in the literature and the poor understanding of the physicscontrolling colluvial processes (i.e. debris flows).A channel avulses when its supplied load exceeds transport capacity, requiring a moreefficient path to maintain conveyance. The pattern of avulsion proposed by Field (2001)is based upon changes in channel location observed with aerial imagery, and is describedas follows. A reduction in the transport capacity occurs through the reduction in channelcross-sectional area, and the channel may no longer enlarge but rather be modified by smallerfloods. The channel’s ability to convey water and sediment decreases as the bed elevationrises and approaches bank height, further decreasing the magnitude of flooding that will2trigger overbank flow. As this overbank flow is relatively clear of sediment, it is capable oferoding the fan surface and will seek an alternate path, typically a former channel, triggeringthe relocation of the active channel and the formation of a new, deeper channel. In this caseavulsion frequency is controlled by the rate of supplied sediment; if the rate of transportcapacity reduction is higher avulsion will occur sooner through increased bed superelevationrates (Bryant et al., 1995).A reduction in channel capacity may instead stem from backfilling in the main channel.Material is deposited where the channel meets the lower slope of the floodplain, whichmigrates upfan and reduces the space available for sediment and water conveyance (Reitzand Jerolmack, 2012). The migration reaches a critical point along its length where channelsuperelevation is enough to promote overbank flow, causing sheetflooding until a new channellocation is found and a new channel is formed. In addition to this, Reitz and Jerolmack (2012)proposed a critical volume was necessary to trigger avulsion of the main channel, the timingof which is proportional to the feed rate.The timescales over which other authors may consider equilibrium to be observed onalluvial fans is far greater than those for rivers. This stems from two main sources. Firstly,the higher slope of alluvial fan channels results in more power available for the channel, thusa higher likelihood of sediment transport and a lower likelihood of deposition. Secondly, thesize of alluvial fans means that more sediment must accumulate before channel avulsion canoccur, which means that less sediment will be trapped and the critical volume of Reitz andJerolmack (2012) is larger, extending the time between avulsions. Thus geomorphologistshave turned to experiments to fill the gap left by a lack of adequate field data. Experimentshave been widely used to study fans given their quick runtime and the high degree of controlover boundary conditions (e.g. Hooke, 1968; Hooke and Rohrer, 1979; Bryant et al., 1995;Clarke et al., 2010; Reitz and Jerolmack, 2012).1.2 Sediment TransportSediment transport is integral to channel stability because stability originates at the grainscale. Shields (1936) considered sediment transport as occurring after the resistive force,proportional to the weight (diameter) of the grain, is exceeded by the driving fluid force. Atthe threshold of motion the resisting force is related to the characteristic shape and packingdensity of the grains through the critical Shields number (θc) and the diameter of the grain(D):τc = θc(γs − γ)D (1.2)3where τc is the shear stress necessary for entrainment and γs and γ are the specific weightsof sediment and water, respectively. Shields’ experiments resulted in the derivation of arange of values for the critical Shields number of 0.03-0.06, representative of the uniformsediment. This equation was extended to consider transport of grains from a mixture ata rate proportional to the excess fluid force; the amount by which the fluid force exceedsthe threshold for entrainment. A commonly used version of which was adapted from thegeneralised Meyer-Peter and Mu¨ller (1948) equation:q∗b = 8(θ − θc)32 (1.3)where dimensionless specific bed load transport rate (q∗b ) is related to the 1.5 power ofthe excess Shields number. The excess Shields number integrates the effects of grain sizeinto the total transport calculation. Dimensionless specific bed load transport rate (i.e.dimensionless bed load transport rate per unit width) is derived from the consideration ofsediment transport by Einstein (1950) as a non-dimensionlisation of specific transport:q∗b =qb√((ρs − ρ)/ρ)gDD (1.4)where dimensionless specific bed load transport rate is a function of acceleration due togravity (g), grain diameter, and density of water and sediment (ρ and ρs) .The natural distribution of sediments in their flume experiments led Meyer-Peter andMu¨ller (1948) to using the average size of the particle mixture in calculating a critical Shieldsnumber, resulting in a θc value of 0.047. Many other studies have investigated the role offlow and experimental conditions on the value of the Shields number, mostly reported aslower (e.g. Fenton and Abbott, 1977) but occasionally higher (e.g. Church et al., 1998)than Shields’ values. It should also be noted that the loose definition of sediment transportinitiation has also led to methodologically induced variation in the critical Shields number(Buffington and Montgomery, 1997). Sediment transport literature, and by extension anyliterature concerning river stability, is pervaded by the use of the median grain size (D50) asthe threshold value in formulae derived from field and experimental data (MacKenzie andEaton, 2017).1.3 Natural Variations in Threshold StressWhilst the entraining stress of a single grain may be proportional to its size, it is mediatedacross scales by several compounding factors (Church et al., 1998). Firstly, the fluid forceexperienced by the grain varies with its exposure to the flow. As Fenton and Abbott (1977)4identified, enabling the exposure of grains to a turbulent flow may substantially reducethe critical entraining stress. Conversely, Einstein (1950) observed the tendency for grainssmaller than the characteristic grain size to be hidden from the flow between larger grainsand in the laminar sublayer. This reduction in contact with the fluid force, termed the hidingfactor, thus acts to increase the stress necessary for entrainment of these smaller grains.Second, the arrangement of the grains relative to those below is important in determiningthe degree through which the grain must rotate in order to be entrained. Komar and Li (1986)demonstrated the natural heterogeneity of critical Shields numbers with their analysis ofnon-uniform bed material. As larger grains (given by the ratio of grain size to those below;Db/Kb) must move through a smaller angle, the critical stress is lowered. It also followsthat smaller grains have a greater pivot angle thus increasing their threshold entrainmentstress, which results in a reduction in the range of entraining stresses across the distributionof grain sizes.Third, local grains strongly affect structure. The narrow, essentially uniform, gradationused in Shields’ experiments led to a high upper limit of transport initiation due to thepacking and organisation of the bed (Church, 2010). Dancey et al. (2002) demonstratedthis experimentally; as packing density increases the critical shear stress increases due tothe disruption of flow fields, with the addition of intergrain contact at the highest packingdensities. Grain scale structure is a product of the exposure, protrusion and pivot angles ofthe grains (Hodge et al., 2013) which varies across a heterogeneous bed; a distribution ofcritical shear stresses is generated for a random grain placed onto or into a given bed surfacejust from its location. Therefore there may not be a definite threshold of entrainment for agrain upon a bed surface (Kirchner et al., 1990).Where there is sediment much finer than the median grain size present in the bed surfacethere will be an increased mobility of the coarse grains. In the experiments of Iseya and Ikeda(1987) alternating sections of smooth, congested and transitional beds developed in responseto a mixed feed of sand and gravel, and they observed increases in mobility as the sandfraction increases due to two mechanisms. The presence of sand in a mixture fills intersticesand smooths the bed, increasing large grain exposure. The transfer of kinetic energy fromsaltating or distraining coarse grains will also likely trigger the motion of other grains viacollision. Across a sand portion of a mixed sediment bed there is a lower threshold stress andapplied stress relative to gravel sections, resulting in the higher entrainment likelihood ofgrains dependent upon the relative magnitudes of the two opposing forces (Ferguson et al.,1989). This differential entrainment causes the variation in bed load transport rates observedby Iseya and Ikeda (1987) despite the constant hydraulic parameters used throughout theirexperiments, with the peaks in transport rate corresponding to the passage of smooth beds.5Therefore, the mobility of both the largest grains and the bulk mixture is capable of beingincreased through the presence of sand.Structures may also emerge from the spatial organisation of the bed by flow, conferringstability to the channel. Immobile grains form loci about which structures can be developed(Church, 2010). Three examples are often described: stone networks, lines and clusters, thepresence of which exert a strong control over the sediment transport rate in natural streams(Oldmeadow and Church, 2006). The most complex of these, stone networks, emerge asadditional surficial responses to surface armouring as large immobile keystones move intomore stable positions and protect the finer grains below from entrainment (Church et al.,1998). This is similar to the observations of MacKenzie and Eaton (2017) who attributeddecreases in bed mobility to the addition of stabilising immobile coarse grains (i.e. D95)to an otherwise identical pair of experiments. Transverse to the direction of flow, stonelines form spanning the channel width that act as sources of roughness or energy extrac-tion, emblematic of a single reach at grade carrying widely graded material (McDonald andBanerjee, 1971). The least complex of the bed structures are pebble clusters, formed fromthe grain-grain contact of large clasts during transport extending upstream (e.g. Cin, 1968)or in deposition events lacking lee side turbulence downstream (e.g. Laronne and Carson,1976) of the keystone stabilising the bed (Brayshaw et al., 1983).In small and steep channels there is the additional effect of jamming structures formedfrom both keystones and large wood. For threshold channels where median grain size isroughly equivalent to the flow depth the maximum slope which unconstrained clasts canexist upon, assuming τ ∗c = 0.045, is 0.07 m m−1 (Church, 2006). However, sediment isclearly observed to exist in channels with slopes steeper than this. The additional resistanceis sourced from the creation of channel spanning structures centred about a keystone orwood, such as step-pools, whose grain-grain contact is strong enough to resist all but thehighest flows (Zimmermann et al., 2010). The presence of these structures increases theexpenditure of energy through the large roughness elements, reducing deformation.1.4 Armour Formation and Equal MobilityThe formation of an armour layer has been well documented as a bed surface self-organisedresponse to degrading settings (Yager and Schott, 2013). The presence of a surface layercoarser than its subsurface requires higher shear stresses for transport and decreases trans-port rates. Armour layers can be classified as one of two types: static, in settings with lowto zero sediment supply, or mobile, with sediment supply (Parker and Sutherland, 1990).Gravel-bedded rivers downstream of dams offer the best example of static armour forma-6tion, due to their release of clear water capable of entraining material (Kondolf, 1997). Here,the flow is capable of winnowing fine sediment from the bed leaving the coarser materialbehind, having two main impacts. Firstly, the median grain size increases, increasing thecritical stress. Secondly, the bed surface becomes more uniform as the fine tail is removed,further increasing critical stress. The surface can be expected to coarsen in response to theimposed discharge until the bed ceases to allow further transport as long as the armour layeris not disrupted (Parker and Sutherland, 1990).In contrast, mobile armour represents the case of Parker and Klingeman (1982) whereinthe grains comprising the bed surface are equally mobile and transported at the same stress.The vertical organisation of the bed requires motion of the bed to enable spaces for thesettling of fine grains away from the flow. If intrusion of fines occurs without the movementof coarse grains a sand seal is formed at the surface, preventing further passage into the bed(Beschta and Jackson, 1979). It is the transport of coarse grains that creates space for thefine grains to winnow into the bed subsurface and prevent further transport (Parker et al.,1982b), thus the whole bed must be capable of being mobilised at the same stress.Andrews (1983) argued that the combination of exposure and hiding effects of a non-uniform bed were strong enough to result in an inverse relation between Shields number andgrain size, and the equalisation of critical stress for almost all grain sizes. Thus the mediandiameter of the bed load should be the same as the bed material if transport occurs at thesame function of excess shear stress (Ashworth and Ferguson, 1989). In contrast to stressequalisation, Parker et al. (1982a) suggested a surficial response in armour makeup to forceequal mobility of the fine and coarse halves of the bed material in terms of the transport raterather than the likelihood of entrainment for a graded stream. Given the relative difficultyof transporting larger grains a stream at grade must increase the availability of the coarsefraction to equalise the likelihood of mobility for the two fractions. That is, their transportrates will not be equal relative to their proportion on the bed, as in Wilcock and McArdell(1997), but their transport rates will be absolutely equal at the channel scale.Ashworth and Ferguson (1989) instead argued that size selective transport dominates innatural gravel-bed rivers, having observed increases in maximum mobile particle diameter,transport rates of smaller grains and the frequency of small tracer motion as dischargeincreases, and a bed load unequal to bed material. Instead of only considering equal mobility,they propose a three stage transport model which progresses from the overpassing of fines(1), through individual coarse grain movement (2), to large scale mobilisation of bed and nearfull mobility (3) as shear stress increases. Despite their lower frequency, phase two and threeevents strongly influence gravel-bed morphology. It is during phase three transport, wherethe largest previously immobile clasts are capable of being transported, that the bed will7undergo significant change and result in large volumes of transported material (Warburton,1992).The equal mobility that Andrews (1983, p.229) observed, in which ‘all the particles, ex-cept for the very largest, were entrained at nearly the same discharge’, therefore representedthe second stage of this model, given the presence of immobile grains. Bed load in a gravel-bed river can be separated into a fine fully mobile fraction and a coarse partially mobilefraction (Wilcock and McArdell, 1993). The fully mobile portion is composed of the frac-tions of the bed surface that, according to their proportion on the bed, are transported atthe same rate for a given shear stress; the maximum size of which increases as flow strengthincreases (Wilcock and McArdell, 1993). Where a fraction is partially mobile there is someproportion of the grains on the bed surface that do not move over the duration of a transportevent, and this may apply to a single size fraction or to the bed surface as a whole (Wilcockand McArdell, 1997). This immobile fraction is capable of limiting the overall mobility ofthe bed by preventing entrainment of material below.The assumption of bulk transport as being predictable from a single grain size is, however,flawed. There is no physical evidence as to why the median, or any single, grain size would bepredictive of overall transport; models attempting to predict transport result in unexpectedvariability in their outputs (Wilcock and Crowe, 2003). More accurate estimation of sedimenttransport rates has been achieved through the calculation and summing of fractional sedimenttransport rates. Models that operate in this manner require more information than thesimple excess power models mentioned above, obviating error in lieu of greater functionalrequirements. Given the importance of other grains to the behaviour of a single grain, anymodel that does not include the effects of the distribution will compound these errors. Oneof the more in-depth models is the surface-based model of Wilcock and Crowe (2003). Theinclusion of a wider range of grain sizes includes the effects of the sand fraction and allowsfor the variance of transport rates of each fraction according to their presence on the bedsurface (e.g. Wilcock and McArdell, 1993), rather than the assumption of threshold equallydistributed about the median grain size.1.5 Stochastic Sediment TransportThe use of bed load transport formulae in predicting real transport rates have been evaluatedbefore (e.g. Gomez and Church, 1989). The key to the (limited) success of such formulaeis discriminating use in appropriate environments, especially in steep channels where thereis a great deal of variation in transport rate alongside discharge variations (Ashworth andFerguson, 1989; Warburton, 1992). In such channels formulae developed with data from8flumes and less steep rivers consistently overpredict the transport rates (Barry et al., 2008),due to the considerable roughness elements present (Rickenmann, 2001, 2012).The observation of transport in a gravel-bed river reveals the intermittent and pulsingnature of sediment movement, cycling through entrainment, displacement, distrainment andrepose (Drake et al., 1988). Indeed, fluctuations in the number of transported particles areof the same order as the mean value (Ancey et al., 2008; Ancey and Heyman, 2014). Furthercalling into question why such formulae are used in estimations of transport. This takes usback to Einstein’s original framing of the problem as stochastic and integrable over bed areas,wherein a grain’s likelihood of motion is controlled by its size, shape and the flow near thegrain (Einstein, 1950). However, recent attempts at reclassifying transport as a stochasticfunction are still in their infancy and are associated with several problems. Principally theyoften lead to closure problems that need substantial work to be made more widely applicable(Heyman et al., 2016).1.6 Flow ResistanceThe action of turbulence and sediment transport reduce the energy available for the flowto do work and thus deform the channel, acting as an indirect stabilisation of the channel.A third factor, resistance, emerges across scales as the extraction of energy from the riversystem through its conversion to heat due to the interaction with grains, bedforms, banksand obstructions (Roberson and Crowe, 1997). As flow height and relative submergencevaries the type of resistance (e.g. skin friction or form resistance) changes as elementsbecome protrusive or submerged (Ferguson, 2007). Therefore the greater the degree of flowresistance the more stable a channel will be. It is common to find the total resistanceof a gravel-bed river partitioned into two components: grain and form resistance. Grainresistance is sourced from the interaction of flow with sediment that comprises the bed, andthe associated loss of energy as flow is diverted, and acts at a very fine scale. On the otherhand, form resistance stems from the larger scale variation of channel parameters due to thepresence of meso- and macro-scale bedforms that control the routing of water.In contrast to the highly submerged sand-bedded channels in low gradients, gravel-bedrivers have a high degree of grain protrusion into the flow especially at low discharges. Evenduring bankfull flow, their lateral extent is liable to deform and trigger a concurrent increasein width and decrease in depth. Therefore, grains are important flow resistance elements ingravel-bed rivers throughout the hydrograph. The degree of protrusion is often taken as afunction of the grain size distribution and, like sediment transport, related to some multipleof a characteristic grain diameter (Ferguson, 2013). Larger characteristic grain sizes perform9better than the median (Ferguson, 2007), typically due to their greater protrusion into theflow. However, many authors have noted the difficulty in predicting resistance from a singlesmall scale parameter such as grain size (Millar, 1999; Wohl, 2000; Ferguson, 2007).Whilst grains are an important component of flow resistance, form scale is the moredominant of the two components of resistance; Millar (1999) attributed up to 90% of thetotal resistance to form. For example, the addition of bars to a system induces a larger scalevariation in flow that necessitates expanding the scale of investigation in order to maintainthe relevance of uniform flow equations (Hey, 1988). Furthermore, riffle-pool sequencesexhibit a strong variation in flow depth and roughness brought about by their hydraulicconditions. Therefore, not only is the overall roughness altered, it is altered in a spatiallyvariable manner.In addition to the above partitioning of total resistance, it has been proposed that thereis a third component of total system resistance. Early work by Cowan (1956) and Chow(1959) had identified the importance of roughness elements (e.g. grain and form resistance)as well as the degree of meandering. Eaton et al. (2004) conceptualised this sinuosity inducedreach-scale resistance as f ′′′, in addition to grain (f ′) and form (f ′′) resistance, where thetotal resistance fsys of an equilibrium channel is the sum of these factors:fsys = f′ + f ′′ + f ′′′ (1.5)Using maximum resistance to optimise the solution for a regime channel, this providesan additional source by which the channel can adjust to prevent deformation. As channelsincrease in sinuosity the length of the channel relative to the valley increases, increasing thelength over which energy may be extracted and decreasing stream power through channelslope. Any increase in the extraction of energy across the spatial gradient of investigationwill decrease the ability of the flow to do deformative work to the channel, increasing thelikelihood that the channel will remain stable over the timescale of importance.1.7 EquilibriumThe free deposition of material and the subsequent adjustment to ‘equilibrium’ occurs ontimescales defined by the water and discharge regimes, and the variations thereof, suppliedto the system and varies according to the ideas proposed by Lane (1955). The benefit ofsuch a framework is that it allows for an a priori estimation or an a posteriori explanationof channel behaviour, given demonstrable changes in few system characteristics. However,outside of this simplistic view, equilibrium is not pragmatic as it pertains to geomorphology.10The inherent complexity and complicatedness of natural systems means that equilibria maybe achieved for components of a system, but may never manifest themselves at the systemscale. As a result, the imposition of equilibrium to such a system may cause improperassignment of behaviour as normal or desired even though such behaviour is only a facetof the total behavioural regime exhibited by a system; “any study that does not frame thescale of reference appropriately is likely also to be flawed” (Bracken and Wainwright, 2006,p. 175). Indeed, Eaton et al. (2017) identify that a crucial failure of regime models is theinability to predict specific channel behaviour in highly complex systems. To that end, thereplication of systems by models, which are inherently an abstraction of reality, should aimfor the lowest complexity so that the explanations of the model behaviour can be given withconfidence (Mulligan and Wainwright, 2013).1.8 Research Objectives and Thesis StructureWhat is clear, from the existing literature, is the strong degree of interaction between thethree main variables controlling channel stability. In an environment where there is suchstrong covariance between variables experimental methods serve to bridge the gap betweenobservations and theory, and isolate the influence of variables over wider behaviour. In par-ticular the advent of modelling and improved data collection has provided a set of toolssuited to the observation of natural systems and the description of the displayed phenom-ena, whilst retaining truthfulness in their necessary simplification. For example, MacKenzieand Eaton (2017) recently demonstrated the ability of grains coarser than 84% of the bulkmixture to stabilise the bed surface of a Froude scaled stream table model in a degradingsetting. There is not supporting evidence, however, to explain how this would expand to anaggradational setting, or even how stability can be conceived of in such settings.The formation and behaviour of steep, self-formed deposits are somewhat well studied.However, the resultant evolution from differing grain size distributions has been neglected.Typically as such studies are concerned with the behaviour of alluvial fans, the scaling issuesmean that there is a limited range of grain sizes suitable for their study (Section 2.1). Theinfluence of grain mobility, a factor of the distribution of grain sizes, in paired alluvial fanexperiments also remains unconstrained, with the role of surface structure unstudied due toscale issues. Further, the body of work concerning sediment transport frequently uses theD50 as its benchmark for considerations of bulk mobility (e.g. Buffington and Montgomery,1997; Church, 2010). To address the validity of this approach a single hypothesis was used toguide the work of this thesis: two deposits that share the same D50 should exhibit the samebehaviour due to the identical mobilities of their grain mixtures. The rejection of which11would lead us to ask the following research questions:1. How does the shape of a grain size distribution affect the behaviour of a steep, depo-sitional channel?2. Are the changes observed in 1) affected by changes in discharge and sediment feed?The following chapters are designed around these two questions. Chapter 2 presents anoutline of the experiment setup and its rationale. The methods of data collection and analysisare also presented, including the derivation of profile slopes through supervised classification,and the qualitative classification of the bed surface.Chapter 3 addresses the difference in behaviour for two aggrading grain mixtures thatshare the same median grain size, but differ in their distribution. This is assessed for thelowest discharge and sediment feed during the period before which sediment is output, whichdemonstrate the largest difference in behaviour of the experiment pairs. A joint quantitativeand qualitative approach is used to offer explanations of the differences.Chapter 4 analyses the effect of a range of run conditions on the behaviour of two grainmixtures. Slope values, transport rates, mass projections and transport efficiencies were usedto classify the resultant behaviour into a spectrum of results, with which regimes may beassigned. The main aim of this chapter was to assess the degree of convergence in behaviouras conditions changed, or whether the two mixtures maintained a consistent difference.Chapter 5 summarises the findings of the preceding two chapters, as well as locating thework within a real context and suggests further possible research avenues.Appendix A describes, in more detail, the scaling relationships and key flow and sedimentparameters used to identify distortions between model and prototype streams.Appendix B reports the qualitative bed surface classification of Chapter 5, excluded fromthe body of the thesis for brevity and clarity.12Chapter 2Experimental Outline2.1 Experimental Design and Data CollectionThe primary concern with the physical modelling of river systems is ensuring a similarityof process. A model must be comparable in behaviour and outcome to either a specificprototype river or, more generally, rivers of certain characteristics. In order to maintainthis similarity, scaling relationships describable through dimensionless variables must bemaintained between the prototype and model river (Appendix A).For two rivers, model and prototype, to be considered equal there must be consistentscaling kept between all aspects of the model. However, it is rarely possible to maintaincoherency of all these conditions as this otherwise requires a 1:1 scale model; it is impossibleto maintain the properties of dynamic similarity whilst simultaneously using water as themodel fluid (Yalin, 1971). Therefore one of the flow parameters must be relaxed to compen-sate for the distortion caused by reducing the scale of the model whilst retaining the samefluid viscosity. Typically, as long as flow remains within the turbulent regime, the modelflow Reynolds number may be relaxed allowing the rest of the dimensionless variables toremain close to their true values (Yalin, 1971). In other words, the behaviour of the modelriver is similar enough to the prototype to be considered comparable, as long as the flow isturbulent, and is termed ‘Froude scaling’.If a relatively smaller scale is desired, that is a smaller model or larger prototype, addi-tional length scale alterations are employed to ensure a similarity of process. Such modelsalso typically have similar Froude numbers, but distort the vertical scale of the model (hencedistorted Froude scale models) so as to have larger water depths than expected to maintainsediment transport dynamics (Peakall et al., 1996). This can be taken to the extreme byincreasing the difference between the prototype and model to such great lengths that thereis no specific similarity between the two. These microscale models seek only to replicate13the process occurring in the field from a basic similarity in scaled conditions (Peakall et al.,1996), and not scale up the observations made in the model for direct application to the field(Hooke, 1968). The inapplicability of sediment transport to scaled prototypes is a function ofthe influence of distortions upon the timescales of grain movement and active bed formation,relative to the motion of the fluid (Yalin, 1971).Once a model has been made, there exists a scaling ratio between it and the prototype.This may be defined by the relative magnitudes of discharge, for example between maximumdischarge of the model and prototype (Yalin, 1971):QpQm= λQ (2.1)λQ = (λL)2.5 (2.2)furthermore, the time scale of the model is set at:λT = (λL)0.5 (2.3)thus models contract over both time and space.In addition to which, sediment finer than 0.25 mm cannot be used in physical modelsdue to its effect on bed smoothness and sublayer flow. As a result, sediment transport doesnot behave in the same manner for grains smaller and larger than 0.25 mm and thereforematerial coarser than 0.25 mm can only represent any other grain larger than 0.25 mm.This results in a truncation of grain size distributions, at the lower of end, at 0.25 mm whenusing natural sediments in order to ensure similarity of behaviour throughout the grain sizedistribution. Although if desired, non-natural analogues may also be used, such as crushedcoal, glass beads or silica flour to varying degrees of success (e.g. Peakall et al., 1996).2.1.1 Model SetupThe model used to conduct these experiments was designed as a generic analogue for steepstreams, based on the grain size distribution taken from other experiments of similar envi-ronments conducted by Lucy MacKenzie in the UBC Geofluvial Lab (e.g. MacKenzie andEaton, 2017). The design was influenced by previous experiments undertaken by Gueritet al. (2014), wherein a deposit was allowed to self form under fixed sediment feed and wa-ter discharge inputs, in order to study alluvial fan evolution. Their idea was expanded toinclude a slope break within the flume itself, to study the dynamics of self-formed depositbehaviour where substantial changes in flow conditions occur; during a large decrease instream power. This change was implemented to mimic the input from a steep (> 0.02 m14Figure 2.1: Simplified diagram of the experimental setup for the steep channel flume.m−1) stream onto a flat valley floor, such as those in mountain ranges forming alluvial fans,without confinement, or shallower morphological units (Montgomery and Buffington, 1997),where confinement remains.The model design, a straight, acrylic walled flume measuring 2 m long, 0.128 m wideand 0.5 m high (Figure 2.1), was chosen for two reasons. Firstly, its small size relative toother experimental models means that runtime is relatively rapid. Secondly, the width wassuch that the ratio of width to D84 exceeded 6, the jamming ratio proposed by Zimmermannet al. (2010), so as to avoid structures forming that relied upon strong intergranular jammingforces. A foam insert was placed within the flume consisting of a steep (0.1 m m−1) uppersection and flat (0 m m−1) floodplain. This insert was populated by roughness elements inorder to force a subcritical regime to the discharge and encourage deposition of the suppliedload. Whilst deposition can occur in supercritical flow on alluvial fans (Blair, 1987), theextreme smoothness of the material that comprised the bed of these experiments would notenable such deposition. Additionally, this freedom allowed the channel bed to organise tothe appropriate roughness owing to the supplied sediment after deposition occurred.Water discharge was provided by a head tank and varied through a gate valve, whilstsediment supply was provided through a rotary sediment feeder whose rate was adjusted byits angle. Both were input using the same funnel to ensure mixing at the top end of thefoam insert and allowed to freely deposit into the roughness elements and then to form thechannel bed surface. Through the experiments both water and sediment discharges were keptconstant, allowing the changes in the paired experiments to be attributed to the differences ingrain size distribution. The experiments were run until one of two conditions were achieved:sediment supply was exhausted or the input funnel became filled with sediment.15The suite of experiments used for each grain size distribution are given in Table 2.1, andare referred to by their assigned string. This string encodes the grain size distribution (i.e.G1 or G2), the discharge (e.g. Q100) and the relative sediment feed (i.e. L = 1 g s−1). Thesevalues were chosen in order to create a framework that had conditions of a constant sedimentconcentration with increasing power, as well as double and half sediment concentration.This allows comparison of increasing or decreasing relative sediment concentration throughchanges to either water discharge and sediment supply. That is, 100H serves as both adoubling of relative sediment concentration for experiments 100L by increasing sedimentsupply, and 200H through decreasing water discharge.Table 2.1: Run conditions for experiments 100L-200L.Discharge (l s−1)0.10 0.15 0.20Sediment Feed(g s−1)1.0 100L - 200L1.5 - 150M -2.0 100H - 200HThe purpose of these experiments is two-fold. Primarily these experiments were designedto assess the impact of a grain size distribution upon the behaviour of self formed andadjusting deposits. That is, to identify the differences in the bed characteristics and sedimentmobility, and the subsequent effects upon the deposit as a whole. Additionally they serveas a tool applicable to other experimental geomorphology studies on the effects of differentways representing a grain size distribution.2.1.2 Experiment OperationTwo sets of five experiments were conducted, paired in their run conditions and median grainsize (D50 = 1.42 mm) but separated by the grain size distribution used. The first grain sizedistribution (GSD1) comprised a log-normal distribution from 0.25 mm to 5.6 mm (Figure2.2). In contrast, the second (GSD2) is only made up of two size classes; 1.4 mm and 2 mm(Figure 2.2). The difference between the two experiments is exemplified by their D84 andstandard deviation values; GSD1 has a substantially higher standard deviation generatedfrom its coarser and finer tails (Table 2.2).Table 2.2: Grain size metrics of the two distributions.D50 D84 σGSD1 1.42 2.57 0.98GSD2 1.42 1.79 0.301601020304050Proportion of Total Mass (%) GSD1GSD2a)0.1 0.2 0.5 1.0 2.0 5.0020406080100Grain Size (mm)Cumulative Finer Than (%) b)Grain Size (mm)Figure 2.2: Grain size distributions for half-phi classes (a) individually and (b) cumulatively.17The output of sediment from the self formed deposit was captured using a trap at theoutlet of the flume at 15 minute intervals. This flux was calculated by drying and weigh-ing the volume of sediment captured in the trap, enabling sediment transport rates to becalculated.The evolution of the long profile of the channel was also captured through photographstaking from a side-looking camera, rather than the conventional method of constrainingvertical changes through field surveys or bed surface elevation scans. An Allied Vision Makocamera was positioned perpendicular to the long (2 m) axis of the flume, and captured imagesevery 60 seconds. The camera was outfitted with an ultra wide angle lens and contains aroutine capable of flattening the strongly radially distorted images into nearly perfectlyorthometric images.A third scale of data was collected from a GoPro Hero 3 positioned above the flume outlet,oriented upstream, in order to capture the evolution of the bed surface (i.e. organisation ofthe channel and morphology). Images of the bed surface were taken at 30 second intervalsand, like the long profile images, were captured using a wide-angle lens. In contrast tothose captured by the Mako camera, these images were left unrectified, instead serving toqualitatively record the behaviour of the surface.2.1.3 Perpendicular CameraSlope DerivationA supervised image classification process was used to classify the images captured by theside-looking camera in order to retrieve slope values of the deposit. A training image wasused to develop a random forests model in order to classify the test dataset. This model wasderived from the pixel RGB values, smoothed by a 3 x 3 mean filter, of each of the seven sub-classes designated, by hand, in the training image and the proximity of one pixel to another(e.g. Foody and Mathur, 2004). The seven sub-classes are: deposited sediment, clear water,water in front of sediment (e.g. a pool), water surface, white background, background withshadow and the roughness elements. Sub-classes were chosen to assign more specific andwell constrained RGB value ranges and positions for the classification stage reducing pixelmisidentification. These sub-classes are then regrouped into the umbrella classes of sedimentdeposit, water, background and roughness elements and smoothed using a 7 x 7 mode filterto reduce image noise. The clump function in R’s raster package was then used to removesmall clumps of pixels (n < 15), likely to be erroneously identified, to further reduce imagenoise and incorrect boundary identification.In order to use these images to derive slope values, a calibration dataset had to be18developed to convert pixel values into real space coordinates. A dot matrix overlay was usedto create a series of points of which the real position were known, as well as the pixel locationsin the images. A third-order polynomial was fit between points in the horizontal axis and asecond-order polynomial through the vertical axis, and were used to create rasters whereinthe cell location corresponded to the real location of that point in the image, enabling theextraction of real data from the images.Once the image has been classified and a calibration dataset created, the boundariesbetween classes can be identified, and thus their slopes may derived. In each side-lookingimage the water surface was identified as the boundary between the background pixels andthe highest of either the water or sediment pixels, until the downstream-most extent of thesediment class pixels. During the growth of the self-formed deposit, however, sediment maynot be deposited as the advance of a wave, but rather depositing in a pocket separate from themain deposit. Such pockets could lead to the misidentification of boundary locations furtherdownstream than the actual bed surface. To avoid this a mask was applied to the imagesup to the height of the roughness elements in order to exclude them from the calculationof the water surface profile in the image, and not report erroneous values. The slope valueswere then calculated from a linear regression applied to the real-space height and lengthcoordinates of the boundary pixels.Water Depth DerivationThe bed surface was also identified in the images; between the sediment pixels and either thewater or background. A LOESS curve (span = 0.25) was fit through the points of both thewater and bed surfaces in order to best represent the true surface without sharp variations.Knowing the water and bed surfaces provides the water depths of each image and the distri-butions thereof for each frame. In order to calculate depth, a mid-line was constructed as themean of the two surfaces, which lines were drawn perpendicularly from until they intersectedwith the water and bed surfaces. The intersection points were converted into real coordinatesin order to calculate their Euclidean distance and depth. The intersections were made at afrequency of every pixel, resulting in a large amount of depth data from which populationstatistics can be drawn: mean, maximum and minimum values and the standard deviationof depths. Therefore each frame captured the distribution of water depths it contained.The data available – water depths, slope, discharge and sediment feed – allow the cal-culation of the sediment transport efficiency (η) and relative roughness (Di/d) exhibitedby both experiments. The sediment transport efficiency parameter is taken from Bagnold(1966), which relates the work rate of the flow to the stream power available. Here it isreformulated neglecting the mass flux term from its original form, instead replicating the19volumetric consideration used by Eaton and Church (2011):η =QbQS(2.4)This parameter describes the efficiency of the system exhibits in converting stream power towork (i.e. sediment transport of the median grain size). The relative roughness statistic wascalculated from the D84, given its usage within both flow resistance and sediment transportliterature (Wiberg and Smith, 1991; Ferguson, 2007; Recking, 2010).2.1.4 Channel ObservationThese experiments were originally conducted in order to study the evolution of a one di-mensional fan surface in response to boundary condition changes. However the width of theflume, designed to exceed the jamming ratio (Zimmermann et al., 2010), was great enoughto allow lateral organisation of the bed surface and subsequent formation of bed features.Instead of the original one dimensional design, these deposits are acting in 1.5 dimensionswhere their lateral extent is limited but there is some second order organisation of the sur-face occurring (Figure 2.3). The GoPro capturing bed surface dynamics was treated as anadditional source of qualitative data from which categorisation of the bed surface and itstemporal evolution could occur. Two forms of categorisation were used. The first was adetailed examination of bed morphodynamics only in experiments G1Q100L and G2Q100L,conducted for the period when the systems were solely aggradational, storing 100% of thesupplied sediment. During this time, each frame was identified as one of three categories:ˆ Featureless; bars absent from bed surface, no channelisationˆ Complex Bar State; bars present, multiple channels activeˆ Lateral Bar State; bars present, single channel activeIn addition the presence and behaviour of thalweg meandering was recorded during thelateral bar state as one of two states:ˆ Narrow; thalweg was well confined by adjacent high amplitude barsˆ Wide; thalweg was poorly confined by lower amplitude bars, allowing overtopping ofbar tails and heads to occurThe second classification method was applied to all 10 experiments, segmented into the15 minute intervals coinciding with the sediment transport periods, and employed a simpler20Figure 2.3: Example photograph of the flume taken during initial testing, demonstrating the1.5 dimensional nature of the channel.system relating to the behaviour seen during the experiments. In this method, the channelwas assigned a mean representative value of the relative stability of system channel accordingto the spectrum of behaviour observed during all of the experiments. That is, the followingsystem orders the observed behaviour of the channel according to its stability relative to othertypes of behaviour seen in other experiments, to allow for the definition and comparison ofchannel activity across experiments and flow conditions. The primary classification followedthe featureless (1), complex (2) and lateral (3) bar states of the first system, where thenumber represents the modal representative state observed over the 15 minute period. Forcomplex and lateral bar states the degree of thalweg activity was recorded and assignedvalues 1-4 of decreasing lateral activity, where 1 represents a highly active thalweg whichmoved significantly in both the longitudinal and lateral directions, and 4 represents a fixed(i.e. immobile) thalweg over the observation period. Further, the complex bar state wasassigned values from a - d, representing the proportion of the length of the visible channeloccupied by multi-threaded flow (in the vein of ecological presence surveys), where a is 100%and d is 25% of the channel length. Accordingly, the lateral bar state represents 0% presenceof multi-threaded flow.The ten experiments can be separated into two distinct groups. The first comprisesexperiments G1Q100L and G2Q100L in order to assess the morphodynamics, and controlsthereof, of the two systems. The second comprises all ten experiments, and seeks to explainthe overall differences in behaviour between the flow conditions (100L-200L) and the grainsize distributions, using the prior proposed mechanisms.21Chapter 3Contrasting Morphodynamics inPaired SystemsThis chapter is concerned with the comparison of behaviour for the lowest sediment feedand discharge experiments (Q100L). A quantitative analysis is combined with a qualitativedataset to explain the differences in observed behaviour.3.1 Results3.1.1 SlopeThe slope data show similar time dependent patterns for both experiments G1Q100L andG2Q100L, an initially high slope as sediment is deposited, followed by a substantial decreaseand stabilisation at a lower slope (Figure 3.1). This pattern is a product of the depositionalenvironment: the deposit is formed on the 0.1 m m−1 foam insert leading to an artificialinflation of the slope deposit that then decreases as it grows onto the 0 m m−1 section,somewhat replicating the pattern of alluvial fan growth observed by Guerit et al. (2014).The overall system developed by GSD1 builds to a higher deposit slope; the mean slope isabout 35% higher for GSD1 (0.092 m m−1) than GSD2 (0.068 m m−1). This similarity ofthe mean water depths in the two experiments is shown by Figure 3.2. The distribution oftransport efficiencies and relative roughnesses are shown in Figure 3.3. GSD2 plots in a moreefficient position in both the x and y planes; with the means plotting considerably far apart.220 50 100 150 200 250 3000.000.050.100.150.20Time (min)Slope (m m−1 )GSD1GSD2Mean GSD1Mean GSD2Figure 3.1: Slope values for experiments G1Q100L and G2Q100L.0.0 0.2 0.4 0.6 0.8 1.00.00.51.01.52.02.53.0Mean Water Depth (cm)DensityGSD1GSD2Figure 3.2: Distribution of mean water depth for the aggrading phase of experimentsG1Q100L and G2Q100L.230.2 0.5 1.0 2.00.020.040.060.08D84 dηGSD1GSD2Figure 3.3: Transport efficiency of the aggrading phase of experiments G1Q100L andG2Q100L.3.1.2 Channel StateThe two experiments exhibited similar progressions from initial feed, with the depositionof material into the flume bed forming an equivalent natural bed for the correspondingfeed. However the speeds at which progression occurred in both experiments were markedlydifferent; GSD1 took 327 minutes for the sediment deposit to reach the end of the flume,in comparison to 150 minutes for GSD2. This time difference is a function of the volumesrequired for progradation; a steeper deposit is accumulating more sediment thus requiresmore time at the same feed rate to advance. In addition, the depositional front during GSD1progressed via a sequence of discrete lobate advances; in contrast, the front of the sedimentdeposit during experiment GSD2 advanced more-or-less continuously.Once bars began to form the two experiments behaved differently, reaching differentlevels of self-organisation. GSD1 was initially dominated by a complex bar state with multi-threaded channels moving around diffuse mid-channel bars and dissecting lateral bars, butthen developed into the more organised lateral bar state about 50 minutes after the start ofthe experiment. Thereafter, the system gradually alternated between relatively persistentlateral bar states and complex bar states. While GSD1 exhibited a wide thalweg version ofthe lateral bar state more often than the narrow thalweg, lateral bar state, it was relatively24None Complex Single Lat − Wide Lat − NarrowProportion of Time (%)01020304050608.5513.1241.5453.852.56 2.7129.2326.718.123.62GSD1GSD2Figure 3.4: Relative time spent as each class for the aggrading phase of experiments G1Q100Land G2Q100L, values are shown at the top of the bars.common for high amplitude bars to create a narrow thalweg throughout the experiment(Table 3.1 and Figure 3.4). GSD2, on the other hand, displayed a higher frequency ofalternation between complex bar and lateral bar states. In addition, the bars almost neverdeveloped sufficiently to create a narrow thalweg lateral bar state during experiment GSD2(Table 3.1 and Figure 3.4). It also look much longer for a lateral bar state of any kindto develop during GSD2 (despite the more rapid downstream progression of the sedimentdeposit during this experiment), with a much greater proportion of time spent in the lessorganised, featureless bed and complex bar states. GSD1 developed self-organised structuresmuch more readily than did GSD2, establishing a complex bar state quicker than duringGSD2, and reaching the lateral bar state 32.5 minutes before it was reached during GSD2.Table 3.1: Count and percentage (of all non-NA frames) for the five channel classifications.None Complex Single Lateral Wide Lateral NarrowCount % Count % Count % Count % Count %GSD1 50.00 8.55 243.00 41.54 15.00 2.56 171.00 29.23 106.00 18.12GSD2 29.00 13.12 119.00 53.85 6.00 2.71 59.00 26.70 8.00 3.62The frequency of changes from one state to another during each experiment also appearto be different in important ways, implying that their evolution and morphodynamics were25a)NoYes0 50 100 150 200 250 300Time (min)b)NoYesChannel ChangeTime (min)Figure 3.5: Occurrence of class changes through the aggrading phases of experimentsG1Q100L and G2Q100L.0.0 0.5 1.00.00.51.01.52.02.53.0Normalised TimeDensityGSD1GSD2Figure 3.6: Distribution of class changes (Figure 3.5). Time is normalised relative to thelength of experiment.26fundamentally different. While the two have a similar time averaged frequency of channelstate change (0.18 and 0.15 changes per minute), the distributions of time between statechanges greatly differ. Against time, GSD1 shows a relatively evenly distributed occurrenceof channel state change events (Figure 3.5). In comparison, most of the state changes duringGSD2 occur near the end of the observation period; all of the 23 state changes occur after84 minutes (56% through the experiment) (Figure 3.5). This pattern is further supportedwhen the data is normalised by time; GSD2 demonstrates a strong preference for changestowards the end of the experiment (Figure 3.6.3.2 DiscussionThe results of these experiments clearly demonstrate that the range of grain sizes in the bedmaterial of a stream exerts first-order control on the channel morphodynamics, and that itis inappropriate to simply use the median surface grain size to characterise the system.The primary response variable, slope, exemplifies the difference between these experi-ments. One system (i.e. GSD1, which is poorly sorted) evolves to a slope that is 38% higherthan for the system with narrowly graded sediment, having the same supplied sediment andwater discharge. Because both systems were aggradational, surface armouring could notoccur due to selective transport, and the bed surface grain size distribution is the same asthe sediment feed distribution, by definition. Therefore, the observed differences in slopecannot be attributed to different degrees of surface armouring.The differing depositional slopes are at odds with what we know about sediment entrain-ment. Previous studies suggests that most of the bed material becomes entrained at aboutthe same shear stress as a result of the relative hiding and exposure of grains smaller andlarger than the median surface size, respectively (Parker et al., 1982b; Parker and Klinge-man, 1982), and that the entrainment threshold for a unimodal mixture is similar to theentrainment threshold for a bed surface having the same median size (Komar, 1987). Ifwe extend this concept of equal mobility to the estimation of sediment deposition angles,then the existing body of work seems to suggest that the deposition angles for these twoexperiments ought to be effectively the same.One potentially critical explanation for this discrepancy is that equal mobility does notapply to all of the bed sediment: for example, Andrews (1983) found equal mobility appliedonly to sediment finer than about the bed surface D84 in his field study, and nearly all of thedata on bed mobility published by Haschenburger and Wilcock (2003) showed similar relativestability of the largest grains at even the highest shear stresses. I believe that this suggeststhat the size of the largest sediment in the bed may determine the deposition threshold for27a mixture, at least for those situations in which competence controls sediment deposition,not sediment transport capacity. The implication of this position is that the gradient offans, floodplains and other alluvial deposits is likely to be related to the size of the largestsediment in transport, not the median bed surface size, as has been previously assumed.The idea that the stable slope angle for these experiments is determined by the mobilityof the largest grains in the bed is consistent with existing equations predicting entrainmentthresholds based on relative grain size. The reference stress (τr) required to mobilise a grainsize fraction (i) is calculable using the approach published by Wilcock and Crowe (2003):τriτrs50=(DiDs50)b(3.1)where τrs50 is the reference stress for the median surface grain size and b is an exponent ofvalue 0.67 when i is larger than the mean surface grain size. Equation 3.1 produces a shearstress necessary for entrainment of the D84 48.8% greater than the median for GSD1 and16.7% greater for GSD2; a difference of 32%. While not conclusive, the similarity betweenthis result and the difference in observed depositional slopes is quite striking.Further, given the ability of the channel to adjust laterally within the constraints of theflume, the slope of the deposit does not equal the actual slope of the channel. Given thedifferences in thalweg length between the two, sinuosity values of 1.10 and 1.05, for GSD1 andGSD2 respectively, were derived from centrelines drawn on the final DEM of the aggradingphase for each experiment. A correction can be made to the slopes so that mean adjusted(channel) slopes are 0.084 m m−1 and 0.064 m m−1, resulting in a difference of 32% comparedto 38% previously, almost the same as the difference in D84 entrainment thresholds.Interestingly, there is also a marked difference in the efficiency of the two systems withrespect to sediment transport (Figure 3.3). For GSD1, the characteristic efficiency wassubstantially lower than it was for GSD2, which is at odds with the concept of channelgrade, at least in its commonly used form. Lane (1955) posited that grade represents abalance that can be written as:QbQS∝ 1D(3.2)wherein the left hand side of the proportionality represents the sediment transport efficiencyand the right hand side represents the calibre of the sediment flux, and is typically assumed tobe the median size of the bed material. Church (2006) recast this relation in a dimensionallybalanced version, which can be written as follows.QbQS∝ dD(3.3)28In Church’s version, D is specifically defined to be the median bed surface size, based onthe understanding of the hiding/exposure processes controlling the entrainment of sedimentfrom a mixture. Therefore functions that are derived from Church’s formulation, for examplethe transport efficiency consideration from Eaton and Church (2011), implicitly include thisassumption and suffer the same limitation.According to the conventions established by Lane (1955) and Church (2006), both ofthese experiments had the same sediment calibre, so why did they not equilibrate at thesame slope, and achieve the same transport efficiency? As Figure 3.2 clearly shows, the val-ues of d are similar for both experiments. Furthermore, the average size of the sediment feedcalibre is identical for both GSD1 and GSD2. While the failure of Eq. 3.2 can be explainedby the fact that it was intended as a qualitative guide for thinking about channel grade,Eq. 3.3 is based on the existing semi-empirical representations of bed sediment entrainment,so the discrepancy between Eq. 3.3 and the results in Figure 3.3 point to a more fundamentalproblem. Simply put, these results clearly indicate that D50 is a poor choice for the charac-teristic grain size, at least when considering the processes forming alluvial deposits, ratherthan those eroding them. This preliminary analysis suggests that some representation of thecoarse tail is probably more appropriate (such as the D84, which is commonly used in flowresistance equations).The morphodynamics observed during GSD1 are not unprecedented, and have been pre-viously reported by Lisle et al. (1991), albeit here using a higher slope (Table 3.2). Lisleet al. (1991) also observed the formation of stationary (non-migrating) lateral bars with thebed surface separated into congested and smooth zones for an experiment having a similargrain size distribution.Table 3.2: Flume dimensions and run conditions for Lisle et al. (1991) and the two experi-ments included here.Lisle et al. (1991) GSD1 GSD2Length (m) 7.5 2 2Width (m) 0.3 0.128 0.128Slope (m m−1) 0.03 0.068 0.092Grain Size Range (mm) 0.35-8 0.25-5.6 1.4-2.0D50 (mm) 1.4 1.42 1.42Specific Flow Rate (l s−1 m−1) 1.94 0.78 0.78Specific Feed Rate (g s−1 m−1) 28 7.81 7.81Run Time (min) 560 327 150Bed forms can influence sediment transport efficiency through the dissipation of energyand increased channel stability (Cherkauer, 1973; Hey, 1988; Prancevic and Lamb, 2015),29and the bar characteristics are strongly linked to the maximum size of sediment in the bedmaterial. In GSD1, bars were more persistent in time and space than those in GSD2 dueto the importance of large grains as stabilising features for bars. In the case of GSD1 thelargest grains clearly deposited first, creating a locus of deposition around which the bar headformed, allowing additional sediment to accumulate in its wake. The bars formed duringGSD2 were composed of virtually the same size sediment, which can be entrained over anarrow range of shear stresses. As a result, the whole bar may be entrained at a similarshear stress, making these features more transient, and reducing their overall effect on bedstability. It is important to note that the stabilisation of the large grains in experimentGSD1 was not the result of jamming, as described by Church (2006).The formation of lateral bars allows the transport of bed load through the contractionof the channel width increasing unit stream power as flow is concentrated (Lisle, 1987).This maximisation of channel efficiency by bed surface organisation into zones of transportand deposition (i.e. the smooth and congested zones described by Iseya and Ikeda, 1987;Lisle et al., 1991), thus enables the previously prohibited transmittance of sediment and thegrowth of the depositional lobe. In these experiments GSD2 is observed to occupy the widelateral bar state more frequently than narrow in GSD1 and with a lower radius of thalwegmeandering, all the while progressing downstream at a more-or-less constant rate. Wherethe channel is more liable to deform under stress (i.e. for GSD2), a wider active channelis maintained through the lower power needed to exceed threshold stress and transportsediment. Therefore the higher frequency of less organised bed states indicates the highertransport efficiency of GSD2 as it does not require channelisation to maintain sedimenttransport.Overall, the deposit resulting from GSD1 was characterised by a greater number of bars,(i.e. shorter wavelength), and bar locations were more persistent. The lateral bars formedin GSD1 were also shorter and had a tighter radius of curvature, appearing less elongate.The complex bar states for GSD1 were primarily produced as a result of bar head dissection(Figure 3.7) or flow separation due to central bars (see Ashmore, 1991) at the sediment feedinput or at pool tails; even during the complex bar state, the GSD1 bed closely resembledthe lateral bar appearance more strongly than did the complex bar state observed duringGSD2. The dissection of a bar head during GSD1 generally occurred as follows. The flowwould first diverge and ultimately separate at the bar head, and then travel over the baritself. This would cause erosion of the bar top, and deposition in the original thalweg dueto the conservation of flow mass, narrowing that channel. The larger-than-average grainswould then deposit and re-stabilise the bar head due to a decrease in competence of the flow.These larger grains would then trigger the deposition of finer sediment and allow the original30Figure 3.7: Conceptual diagram of bar head dissection. T1 shows a typical pool, bar, rifflesequence, with the large grains at the bar head identified. In T2 high curvature of bendcauses flow to separate at the bar head and erode into the bar (stippled). At T3 flow hasseparated enough to cause deposition in previous tail (grey) and at bar head (additionallarge grains), reforming previous flow.bar head to reform, thereby re-establishing a lateral bed state with a meandering thalweg.GSD2 also exhibited dissection and flow separation during the complex bar state for thatexperiment, but the associated morphodynamics were dominated by lateral thalweg migra-tion, not by the bar head erosion and re-stabilisation processes evident during GSD1. Thefundamental difference in channel behaviour that is qualitatively evident from a comparisonof the two time lapse videos is presumably responsible for the longer wavelength and lessercurvature of the bars for GSD2 (Figure 3.8). Lateral thalweg migration occurred when thethalweg alignment upstream of the bar rotated progressively, resulting in a lateral sweep ofthe thalweg through the bar, eroding it, and re-forming a new bar in the former thalweglocation. This process of thalweg migration and bar erosion would occasionally produce acompletely inverted morphology, in which the bar effectively was shifted from one side of thechannel to the other. Throughout the experiment bars were less permanent in position anda greater degree of lateral thalweg activity was observed.The wavelengths of the barforms observed in GSD2 are longer than those of GSD1, indi-cating a difference in the mobility of their mixtures; Pyrce and Ashmore (2005) demonstrated31Figure 3.8: Conceptual diagram of thalweg sweep migration. The downstream angle ofthalweg from the meander bend progressively decreases, over topping the downstream barand eroding material (progression from least to most dense stippling).that the wavelength of bar spacing is a function of the transport lengths of bed load particlesat channel forming flows. Transport length is the distance between entrainment (τce) anddistrainment (τcd), therefore it is dependent on when the grain is deposited. Ancey et al.(2002) observed a type of hysteretic difference between these two thresholds, where the spe-cific flow rate (and thus stress) necessary to induce deposition is lower than the entrainingflow. Given the differences in entraining stresses between the mixtures, assuming that it iscontrolled by the coarse tail, it follows that the distraining threshold for GSD1 will be higherthan for GSD2, such that a smaller decrease is needed to trigger deposition. Therefore thesystems can be characterised by the difference in behaviour of the coarse grains comprisingthe bar head loci (Pyrce and Ashmore, 2005). For the more equally mobile GSD2 this is man-ifested in a decreased likelihood of deposition of these grains, triggering longer path lengthsand greater bar wavelengths in the system. In other words, the likelihood of entrainment(P [τ > τce]) is greater in GSD2, setting a lower overall deposit slope, whereas the likelihoodof distrainment (P [τ < τcd]) is higher in GSD1, decreasing transport length.3.3 ConclusionsThe two experiments presented here demonstrate a difference in the self-adjusted slope andmorphodynamics of two aggrading systems derived from the difference of their grain sizedistributions. According to the prevailing theory that the median grain size is predictiveof channel behaviour, the two systems described within this chapter should have exhibitedsimilar slopes and patterns of morphodynamics. Instead, the deposit formed from the more32widely distributed GSD1 developed to a higher slope, with lower transport efficiency, anddemonstrated a greater degree of surface organisation. I argue that this is the result of thelarge grains in GSD1 that exceed the competence of the flow, and require channel narrowingin order to mobilise. Where these grains are absent (i.e. GSD2) the channel fails to achievethe highest state of organisation (i.e. lateral bars with narrow thalweg) as regularly becauseof the equally mobile sediment and bars. Thus channel stability is linked not to the mobilityof the median grain size, but to the mobility of the largest grains (e.g. coarser than the D84).I therefore conclude that the difference in behaviour between these systems is driven by acompetence limitation of the larger grains. These findings indicate that models that includesediment transport and conceptualise stability, such as regime models, need to consider thecharacteristic grain size as a coarser fraction than the median in order to better representaggrading systems.33Chapter 4Comparing Morphodynamics AcrossSystems4.1 ResultsThe slope values of all data derived from the experiments are shown in Figure 4.1, separatedby experiment code. As in Chapter 3, a common pattern emerges with the observed slopechanges: an initially high value that decreases to a relatively stable lower value, consistentwith the growth from the 0.1 m m−1 foam insert onto the flat 0 m m−1 section. At thelargest scale, the slopes formed by GSD1 tend to organise to a higher mean slope than theirGSD2 counterparts, although the difference between the two decreases as discharge increases.For example, the greatest difference in mean slope is between experiments G1Q100L andG2Q100L, where the mean slope of GSD1 is 44% higher than GSD2. In contrast there is only6.6% difference in mean slopes for experiments G1Q200H and G2Q200H and 8.8% differencein experiments G1Q200L and G2Q200L; in other words, the two systems are increasinglysimilar as discharge increases. The difference in mean slopes stems from the relative changeswithin each grain size distribution for constant relative sediment concentration; G1Q200Hshows a 43% decrease in mean slope relative to G1Q100L, whilst the equivalent differenceis 23% for GSD2. That is, the observed changes in mean slope are absolutely and relativelysmaller for GSD2. In addition, the distribution of slope values for both grain sizes showdiffering relationships (Figure 4.2). Those found in GSD1 show a bimodal distributionsroughly located at 0.051 and 0.086 m m−1, whereas GSD2 shows a more tightly distributedpopulation with three modal peaks at 0.046, 0.058 and 0.074 m m−1.The experimental conditions enable the a posteriori assignment of slope changes to thevariation in flow strength or feed rate. For example, the relative sediment concentration340.000.050.100.15 G1Q100L G2Q100L0.000.050.100.15 G1Q150M G2Q150M0.000.050.100.15 G1Q200H G2Q200H0.000.050.100.15 G1Q100H G2Q100H0 100 200 300 400 5000.000.050.100.15 G1Q200L0 100 200 300 400 500G2Q200LTime (min)Slope (m m−1 )Figure 4.1: Slope values for all recorded data points. Thick grey dashed horizontal lineindicates mean slope value for that experiment, blue dashed vertical line indicates onset oftransport.35Table 4.1: Mean slope values for experiments 100L-200L and difference relative to GSD2between grain size distributions.GSD1 (m m−1) GSD2 (m m−1) Difference (%)100L 0.0882 0.0611 44.4150M 0.0653 0.0506 29.1200H 0.0502 0.0471 6.6100H 0.0879 0.0784 12.1200L 0.0506 0.0465 8.8may be doubled by either doubling sediment feed rate, or halving the discharge. Whensediment concentration is doubled by increasing sediment feed (100H) for the same flowstrength (100L), mean slope for GSD1 changes by <1%, whereas GSD2 increases by 28%.When concentration is instead doubled by halving flow rate (100H) relative to the same feedrate (200H), mean slope for GSD1 and GSD2 increase by 75% and 66% respectively. Instead,when concentration is halved by increasing flow rate (200L) for the same feed rate (100L),mean slope for GSD1 decreases by 43% in contrast to 24% in GSD2. When concentrationis instead halved by decreasing feed rate (200L) for the same flow rate (200H), mean slopefor GSD1 and GSD2 change by <1% and 1.2% respectively. Therefore, when both systemsare altered by increasing or decreasing flow rate they exhibit more substantial changes intheir mean slopes than the overall influence due to feed rate. Although GSD2 does showsubstantial change when sediment feed rate is doubled at the lowest discharge.When the raw data are considered, all slopes are predicted (R2adj = 0.65) by a modelthat includes discharge, grain size distribution and the interaction term between them. Thebest performing significant model only returned an R2adj value of 0.66, but included twomore parameters; sediment feed rate and the interaction term between it and grain sizedistribution. The raw data from GSD1 is predicted well by all combinations of variablesincluding discharge (R2adj = 0.80) although no improvement is made with more parameters.The model chosen was the simplest; only discharge, which described 80% of the variation inslope values. In contrast, models using GSD2 only slopes show a weaker fit; the best modelof discharge and sediment concentration only has an R2adj value of 0.38. Overall, consistentpatterns emerge between slope and the coefficients of the constituent variables both for themean and raw data. That is, discharge and grain size distribution type show an inverserelationship with slope, whereas sediment feed and slope have a positive relationship.As sediment throughput begins when the toe of the deposit reaches the outlet, the timingof the onset of transport is a function of the slope of the deposit (i.e. volume necessary toreach the flume outlet). Time series of sediment transport rates are given in Figure 4.4, thetime of transport initiation and mean values are given in Table 4.3. Transport rates as a whole360.00 0.05 0.10 0.15010305070Slope (m m−1)DensityGSD1GSD2Figure 4.2: Distribution of all slopes recorded in experiments 100L-200L separated by grainsize distribution.0.10 0.12 0.14 0.16 0.18 0.200.000.050.100.15Discharge (l/s)Mean Slope (m m−1 )GSD1 Radj2 0.80.10 0.12 0.14 0.16 0.18 0.20Discharge (l s−1)Mean Slope (m m−1 )GSD2 Radj2 0.330Discharge (l s−1)Slope (m m−1 )Figure 4.3: All slope values against discharge with linear regression, separated by grain sizedistribution. Both regressions are significant.37Table 4.2: Coefficients for regression models based on all raw slope values. Models shownare the best simple (bold) and highest performing (italics) models, with all parameterssignificant.β0 X1 X2 X3 X1:X3 X1:X2 R2adjAll0.162 -5.41 x 10−4 - -3.71 x 10−2 1.64 x 10−4 - 0.650.142 -4.35 x 10−4 1.68 x 10−2 -3.87 x 10−2 1.73 x 10−4 -8.72 x 10−5 0.66GSD10.125 -3.77 x 10−4 - - - - 0.800.126 -3.76 x 10−4 -9.01 x 10−4 - - - 0.80GSD28.80 x 10−2 -2.12 x 10−4 - - - - 0.337.61 x 10−2 -2.08 x 10−4 7.93 x 10−3 - - - 0.38are highly variable, however they seem to exhibit greater step changes and greater variabilityabout a mean in GSD1 through their greater standard deviation. In addition the experimentsusing GSD1 had lower mean transport rates and greater mean absolute difference from supplyrate. The only substantial divergence from this behaviour is experiment G1Q100H, whichhas substantially lower transport rates than all other experiments.The accumulation plots (Figure 4.5) show the pattern of sediment accumulation over thecourse of each experiment. This accumulation is calculated from the volume of sedimentoutput during each sediment transport phase, thus it does not commence until sedimentoutput has begun. The dashed line represents, from this point, an output efficiency of 100%(i.e. no further storage) and the black line a storage efficiency of 100% (i.e. no furtheroutput). Consistent patterns emerge; GSD2 experiments plot closer to the 100% transportefficiency line than the corresponding GSD1 experiments. The cumulative masses also plotcloser to 100% transport efficiency as discharge increases for both sets of experiments. Inboth sets of experiments it is configuration 100H that results in the closest to 100% storageefficiency either set experiences.When considering the masses of transport as a proportion of supplied sediment overtwo timescales, the difference in behaviour between the two grain size distributions is madeevident. Of the total mass, GSD1 outputs a consistently lower mass than GSD2 that follows astrong trend with discharge. In contrast, GSD2 has a higher baseline and high transport ratesfor all experiments stronger than 0.1 l s−1. However, if we instead only consider the materialinput after sediment output begins a far clearer distinction exists. The same patterns arepresent, but their difference is far stronger. The differentiation according to discharge isgreater for GSD1, and the overall higher output proportion for GSD2 approaches equilibriumfor 3 of the 5 experiments.Transport efficiency (η) and relative roughnesses show a similar pattern to transportrates; at lower discharges there is a large difference between two paired experiments, which380123 G1Q100L G2Q100L0123 G1Q150M G2Q150M0123 G1Q200H G2Q200H0123 G1Q100H G2Q100H0 100 200 300 400 5000123 G1Q200L0 100 200 300 400 500G2Q200LTime (min)Sediment Transport (g s−1 )Figure 4.4: Sediment transport rates for all experiments, averaged over approximately 15minute windows. Dashed line indicates sediment feed for each experiment.39010203040G1Q100L G2Q100L010203040G1Q150M G2Q150M010203040G1Q200H G2Q200H010203040G1Q100H G2Q100H0 100 200 300 400 500010203040G1Q200L0 100 200 300 400 500G2Q200LTime (min)Cumulative Mass (kg)Figure 4.5: Net accumulation of sediment in the deposit for each experiment, given by lightred line. Black line indicates 100% storage efficiency, dark red dashed line indicates 100%transport efficiency after the onset of transport.40Table 4.3: Mean transport rates and timing of onset of transport for each experiment.Transport Rate (g s−1) Transport Start (min)Feed (g s−1) GSD1 GSD2 GSD1 GSD2100L 1.00 0.41 0.73 326 149150M 1.50 1.01 1.39 72 74200H 2.00 1.64 1.84 42 44100H 2.00 0.19 1.34 149 116200L 1.00 0.84 0.91 103 87Table 4.4: Proportion of sediment output for each experiment. Separated into the proportionof total sediment input and the proportion of sediment input after sediment output hadoccurred.Proportion of Total (%) Proportion During Output (%)GSD1 GSD2 GSD1 GSD2100L 16.7 47.8 40.7 72.9150M 52.7 74.3 66.7 92.5200H 70.5 77.7 81.7 91.4100H 3.8 40.2 8.5 66.4200L 67.9 76.0 83.7 90.6decreases as discharge increases. GSD2 plots at a higher mean η and lower mean relativeroughness value for all experiments, although there is substantial overlap between the trans-port efficiencies in 200H. This is additionally demonstrated by the decreasing Euclideandistance between the means of transport efficiency and relative roughness (Table 4.5). Thedecreasing differences indicate a convergence of behaviour, as the overall domains of eachvariable overlap.Table 4.5: Mean transport efficiency values for each experiment, including the Euclideandistance between means.Mean Relative Roughness Mean Transport Efficiency Euclidean DistanceGSD1 GSD2 GSD1 GSD1100L 0.712 0.348 0.0431 0.0632 0.650150M 0.424 0.300 0.0592 0.0765 0.348200H 0.406 0.222 0.0761 0.0931 0.314100H 0.665 0.329 0.0864 0.0986 0.567200L 0.387 0.353 0.0376 0.0427 0.344410.010.020.050.10Q100L0.1 0.2 0.5 1.0 2.0Q100H0.010.020.050.10Q150M0GSD1GSD20.1 0.2 0.5 1.0 2.00.010.020.050.10Q200L0.1 0.2 0.5 1.0 2.0Q200H0D84 dηFigure 4.6: Transport efficiency, given by the relationship between relative roughness and η.Grey dashed lines indicate mean values for GSD1, black dashed lines indicate mean valuesfor GSD2.424.2 DiscussionThe two boundary conditions Q and Qb, and the implicit third (sediment concentration,Qc), each offer different explanations for the above observed trends in bed mobility accord-ing to an equilibrium bed state (i.e. Lane, 1955). Increasing the discharge will control theamount of energy supplied to the system, affecting grain (and therefore bed) mobility inthree ways: increasing maximum entrainable grain size (Ashworth and Ferguson, 1989),increasing the frequency of entraining flows and increasing overall work done. These mech-anisms will increase the mobility of individual size fractions (Wilcock, 1993), as well as theoverall mobility of the mixture. The immobility of the largest grains limits the extent ofbed deformation by preventing transport of underlying material and their organisation intostable positions (Wilcock and McArdell, 1997; Church et al., 1998). Only slightly increasingthe fraction of the these grains significantly reduces sediment transport and improves bedstability (MacKenzie and Eaton, 2017). Providing these grains are below the threshold ofmobility, that is, the overall mixture is partially mobile, these grains will exert a reducingeffect on transport. Therefore, it follows that increasing the discharge will increase sedimenttransport and reduce the channel’s stability.An increase in the sediment feed rate will increase the rate and volume of materialinput into the channel. The increased availability of material, for a constant discharge atequilibrium, will result in two different outcomes dependent on the magnitude of discharge.Assuming the discharge is capable, it is possible that the increased sediment feed rate willnot affect the behaviour of the deposit if the material entering is fully mobile and there isadequate excess energy available to mobilise this material. However, if there is not (i.e. ifmaterial is partially mobile or exceeds capacity) then the slope will accordingly increase asmaterial is deposited.As relative sediment concentration reflects the interaction between discharge and sedi-ment feed, the magnitude and direction of change can be derived from either facet. If relativesediment concentration increases to exceed either a competence or capacity threshold, sed-iment will accumulate and steepen the deposit slope. Exner (1925) developed an equationdemonstrating the relationship between bed surface elevation change (δz) and sediment flux(qb):δzδt= − 10δqbδx(4.1)where t is time, 0 is the packing density of grains and x is distance downstream. Sedimentflux is necessarily a function of sediment deposited on and eroded from the bed surface,either through fluid or granular action. Thus the increase in sediment concentration enables43deposition to outpace erosion, provided it now exceeds either a capacity or competencethreshold.The above all consider systems in equilibrium, such as a recirculating flume or a sys-tem given long enough to self-organise to some degree of stability. Whilst equilibrium isapproached for periods of the experiments, when considered as input and output rates ofsediment, the overall behaviour is that of an aggrading mass. Thus predictions based on theformulation of grade by Lane (1955) are likely to be mediated by compensating processes.However, the mechanisms above can be condensed into a fundamental argument. Changesin discharge, sediment feed and thus concentration affect both the competence and capacitythresholds of these systems, dependent upon the mixture used. For GSD1, given the presenceof a range of grain sizes, changes in discharge and sediment feed will manifest as changes incompetence, for fractions partially mobile, and capacity for those fully mobile. On the otherhand, the same changes for GSD2 manifest themselves as only changes in capacity becauseof the full mobility of the mixture, as shown below.The changes in mean slope triggered by the relative changes in run conditions indicatethe likely nature of controls over the systems. The greatest changes in mean slope arebrought about by changes in flow conditions, indicating a strong dependence of systembehaviour upon the energy supplied to it. In contrast, changes in sediment flux do not resultin the same magnitude of effects barring one comparison (G2Q100H:G2Q100L). Therefore,changes in discharge appear to offer, at the most basic level, a stronger point of differentiationbetween the two grain size mixtures. In conjunction with the inter-distribution differences,it can be stated with confidence that there are systematic differences that are manifested inhow the systems respond to changing system energy. It appears, then, that a more generalmechanistic difference is in operation here than proposed in Chapter 3.This view is supported by regressions for all slope values. That the model includes a grainsize distribution term suggests the need to separate the two systems. The models of GSD1outperform GSD2, and show a much stronger explanation of variance with their predictors(discharge). The strong decrease in slope as discharge increases for GSD1 is demonstrative ofincreasing mobility. In contrast, the weaker relationship observed for GSD2 shows an overallmore similar behaviour across run conditions. The difference between the two grain sizesbeing driven by energetic differences between experiments implies that there is a thresholdbeing passed, either in competence or capacity, that triggers the separation in behaviourrather than a response to volumetric supply.In order to explain this the observations made by Wilcock and McArdell (1997), Churchet al. (1998) and MacKenzie and Eaton (2017) are once again revisited. The above rela-tionships clearly demonstrate a mobility difference between the two mixtures, one of which44is strongly controlled by discharge and another that is not. The coarse grains present inGSD1 affect the overall mobility of the mixture dependent upon their mobility. That is, theimmobile fraction on the bed surface decreases as discharge increases because the likelihoodof transport increases for the larger grains. GSD2, on the other hand, is not affected in thesame manner because large grains are absent and the material has a smaller range of criticalshear stresses.The difference between the mean and timing of transport rates for each paired experimentdecreases as discharge increases, indicating a convergence in the behaviour of each pairedchannel. The relative strengths of the discharge and slope relationships for GSD1 and GSD2provide the basis of the explanation for why these two systems show convergence in theirslopes as discharge increases. In other words, because the coarse fraction does not change inproportion, as in MacKenzie and Eaton (2017), its stabilising effect decreases as dischargeincreases and thus begins to behave more like GSD2.The strongest evidence for the difference in the behaviour of the systems is given by theirrelative storage efficiencies. GSD2 consistently has a higher sediment output, although thetwo mixtures are close for the highest discharges when considered as a proportion of thetotal mass supplied. However, as a proportion of supplied mass from when sediment outputbegins the ability for GSD2 to retain sediment is greatly diminished in comparison. Thestrong dependence shown by GSD1 on discharge implies a threshold is passed between 0.1and 0.2 l s−1, where above which feed rate does not play a role in determining output butbelow which it does. In contrast, the differentiation is much weaker for GSD2, there is notas dramatic an increase in proportion of sediment output alongside increases in discharge.Interestingly there is a difference of about 32% in the proportion output between G1Q100Land G2Q100L, mirroring the difference in the reference shear stress of the D84 calculated inChapter 3. The less substantial transport threshold, and operation at close to equilibriumstate for G2Q150M, G2Q200H and G2Q200L, further supports the view that GSD2 is moremobile.Similarly, the transport efficiency plots demonstrate the greatest differences betweenthe two grain mixtures at the lowest discharges. At the lowest discharges, the systemsproduced by GSD2 are significantly more efficient at transporting the supplied sediment asthey organise to lower slopes than their counterparts. However as discharge increases, thedifference of the two means decreases, whilst remaining distributed differently, and convergein the efficiency plane (Figure 4.6). The strongest overlap is observed when the systems areat their highest competency and lowest capacity (Q200L), where the two systems appear tobehave very closely.The slopes of GSD2 do not appear to be as strongly coupled to the experimental bound-45ary conditions as GSD1. In addition to which the material forms to a more contracted rangeof values (Figure 4.2). The distribution of the two slope populations suggest a systematicseparation in their behaviour. Those for GSD1 show a bimodality supporting the idea ofa discharge threshold, and those for GSD2 showing a more continuous distribution accord-ing to both discharge and sediment feed (or a factor combining the two). This threshold(i.e. entrainment) must be significantly exceeded by some parameter (i.e. discharge) in theexperiments involving GSD1 that is not exceeded in the same manner in GSD2.4.3 ConclusionsThe experiments presented in Chapter 4 show a spectrum of responses controlled by the grainsize distribution, discharge and sediment feed rate used. As in Chapter 3, if the mobility ofthe mixtures are controlled by the median grain size a lack of dependence of behaviour ongrain size distribution should be observed. Instead, the resultant deposit should be solelycontrolled by the flow and feed conditions. The difference between two paired experiments isthusly a result of the presence of additional (or, conversely, absence) grains. Those formed ofGSD1 consistently show a steeper deposit, although the degree to which they differ decreasesas discharge increases. This pattern replicates itself in the efficiency of sediment transport;GSD1 results in a less efficient system because of its higher slopes. As discharge increasesthe occurrence of entrainment threshold exceeding flows also increases and the occurrenceof flows lower than the distrainment threshold decreases. Thus the proportion, of both timeand space, for which the largest grains can be considered stable decreases and the overallmobility of the mixture increases. This difference is more prominent for GSD1 because ofits distribution of grains, the stabilising effect of large grains is more pronounced, and thusthe increase in mobility as discharge is exaggerated with respect to GSD2, for which themobility of all grains is higher. The equal mobility of GSD2 This difference in mobilityis best described by the proportion of material output during each experiment; the higherthe proportion the lesser ability the material has to self-organise and retain sediment. Thelowest of which occurs at the lowest discharges for GSD1, during which some threshold (largegrain mobility) is not readily exceeded and thus sediment is preferably stored in the flumerather than transported. Therefore, it can be observed that traditional expectations forgrain mixture behaviour are not met when there is a strong threshold present. As dischargeincreases the influence of the threshold decreases, and the two mixtures approach similarbehaviour as would be otherwise predicted.46Chapter 5Concluding RemarksThe studies conducted during this thesis were designed to improve the understanding ofaggrading deposits, their mechanisms and behaviour, and the role of grain size distributions.This section summarises the two scales of consideration, between a paired experiment andacross the range of experiments conducted.Chapter 3 presents the differences in behaviour of a low discharge and sediment feedexperiment for two different grain size distributions. It has been recently shown that grainscoarser than the median are capable of exerting a strong control over the mobility of the totalgrain mixture in a degrading environment. For the case of the suppression of armour for-mation (i.e. aggradation) I show that there are similar mechanisms that alter the behaviourof the overall deposit, strongly enough that the two systems can be considered as behavingdifferently. The mechanisms controlling deposit behaviour focus upon the relatively shortertransport lengths and lower mobility of the largest grains, which act as key stones for theformation of lateral bars in GSD1. Systems formed from the more labile material (GSD2)organise to lower stability states and exhibit less resilient bars, due to the lack of variationin grain entrainment and distrainment thresholds, resulting in a more transport efficientsystem; more work can be done based on the input flow and sediment feed conditions. GSD2forms at a lower slope because the grains are more likely to be mobile (in accordance withLane (1955)). Given the matching median grain sizes, I therefore suggest that it is the largestgrains (present in GSD1) controlling the mobility and behaviour of aggrading deposits.This argument is supported by the results of Chapter 4, where I demonstrate a conver-gence in the behaviour of paired experiments as discharge increases. There are substantialdifferences between experiments using GSD1 that seem to originate from an increased thresh-old stream power, suggesting that these systems are strongly competence limited. That is,the factors representing stability (high slope, low transport efficiency and low sediment out-put) invert and show characteristics of unstable bed surfaces as discharge increases. In47contrast, GSD2 deposits show a greater dependence upon a capacity driven determinant ofdeposit slope, generated from the overall higher mobility of the mixture and its fractions. AsGSD2 has a smaller distribution of threshold stress values, it is less affected by the increasingdischarge than GSD1 therefore the overall behaviour is more closely grouped. The conver-gence in behaviour thus stems from the increased mobility of GSD1 as discharge increasesand the frequency of critical exceeding flows increases, mimicking GSD2.Although these experiments serve as an abstraction of reality there are several key in-ferences that may be made about other steep depositional environments. A self-formingand adjusting deposit will choose its slope given long enough adjustment at constant inputconditions, the angle of which is set by the (im)mobility of the largest material. If the coars-est bed material becomes easier to mobilise through discharge, organisation or composition,then we should expect a commensurate decrease in sediment storage. In terms of avulsionfrequency, for either fan or river channels, a more tenuous connection can be made. Assum-ing that avulsion frequency is set by a critical volume (Reitz and Jerolmack, 2012) sedimentthroughput will therefore define a timeframe for avulsion. This throughput can therefore bestrongly conditioned by material that current flows cannot entrain, supplied either fluvially(Reitz and Jerolmack, 2012) or colluvially (e.g. debris flows).Given the constant nature of these experiments, a large gap still exists between thisidealised setup and any real analogue. The widely varying conditions experienced in naturalstreams introduces unpredictable behaviour that is absent in these experiments and that willsignificantly affect the influence of immobile grains and the role of bed structures. Therefore,these experiments form the basis from which further work utilising these principles may bedesigned. This framework may address three sets of questions. The first; are the same effectsobserved when paired by other characteristic grain sizes (e.g. D84)? 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Journal of Geophysical Research: Earth Surface,115(F2):F02008.56Appendix AModel ScalingThese dimensionless variables are constructed from characteristics of the flow and sediment:ˆ fluid properties; density (ρ), dynamic viscosity (µ) and mean downstream velocity (U)ˆ channel properties; hydraulic radius (R), surface roughness (ks) and slope (S)ˆ gravitational constant (g)ˆ grain size (D) and density (ρs)ˆ combined variables; shear velocity (U∗), immersed specific weight (γs)Yalin (1971) defines three levels by which a model (subscript m) and prototype (subscriptp) demonstrate similarity:1. geometric similarity; physical properties (i.e. channel geometry) are scaled accordingto their relative lengths:λL =λpλm(A.1)2. kinematic similarity; physical properties are scaled, and the consideration of time isincluded. As such, the motion of a fluid packet occurs in the same manner, when scaledto time:λT =TpTm(A.2)3. dynamic similarity; physical properties and time are scaled, also includes the additionof mass, thus the movement of sediment must be scaled according to:λM =MpMm(A.3)57In the case of models with fixed beds four parameters are used to describe the system:Reynolds flow number, Froude number, relative bed roughness and slope, denoted by Πterms 1-4 (Peakall et al., 1996).Π1 =ρRUµ(A.4)Π2 =U√gR(A.5)Π3 =ksR(A.6)Π4 = S (A.7)For moveable beds an additional four concerning sediment emerge: relative roughness ofsediment, relative sediment density, sediment Reynolds number and Shields number.Π1 =RD(A.8)Π2 =ρsρ(A.9)Π3 =ρU∗Dµ(A.10)Π4 =ρU2∗γsD(A.11)Such constraints limit the range of conditions that the model may experience, bringing themin line with the natural conditions of the prototype.58Appendix BChannel StatesB.1 ResultsThe distribution of channel classification type shows a consistently earlier and more fre-quently higher occurrence of single threaded flow for experiments 100L-200H, experiment200L shows the reverse of this and experiment 100H does not achieve single threaded flowfor any more that one analysis section throughout both grain size distributions. The popu-lations of these type distributions are only significantly different for experiments 100L and200H, with 150M, 100H and 200L being otherwise indistinguishable. G1Q100L-200H showgreater similarity (within the same grain size distribution) than the corresponding experi-ments using GSD2, and vice versa. The occurrence of changes between the channel states,that is movement from multi- to single-threaded flow, is higher for GSD1 in all experimentsexcept for 100H and is typically higher at lower discharges.Table B.1: Count and percentage (of non-NA frames) for each major class type in GSD1.Count Occurrence (%)None Multi Single State Change None Multi Single State Change100L 3 26 7 11 8.33 72.22 19.44 32.35150M 2 12 8 10 9.09 54.55 36.36 50.00200H 2 6 12 3 10.00 30.00 60.00 15.79100H 1 16 0 1 5.88 94.12 0.00 6.25200L 2 24 6 11 6.25 75.00 18.75 36.67The mean stability index of experiments G1Q100L-200H were higher than G2Q100L-200H, with G2Q100H having a higher stability index than G1Q100H and G2Q200L beingroughly equal to G1Q200L (Table B.3). The mean stability index does not exhibit anysignificant relationship with any combination of values, even in the presence of interaction59NoneMultiSingleG1Q100L G2Q100LNoneMultiSingleG1Q150M G2Q150MNoneMultiSingleG1Q200H G2Q200HNoneMultiSingleG1Q100H G2Q100H0.0 0.2 0.4 0.6 0.8 1.0NoneMultiSingleG1Q200L0.0 0.2 0.4 0.6 0.8 1.0G2Q200L00Relative TimeChannel StateFigure B.1: Distribution of major class types for each experiment.60Table B.2: Count and percentage (of non-NA frames) for each major class type in GSD2.Count Occurrence (%)None Multi Single State Change None Multi Single State Change100L 1 25 0 0 3.85 96.15 0.00 0.00150M 1 16 7 4 4.17 66.67 29.17 18.18200H 2 16 0 1 11.11 88.89 0.00 6.25100H 1 18 1 3 5.00 90.00 5.00 15.79200L 2 25 9 7 5.56 69.44 25.00 20.00terms, for either grain size distribution or for all ten together. As the data is organised intoan index ranked by relative stability the magnitude of changes can be calculated betweentimesteps (i.e. a lagged difference of one step). Therefore the population metrics of thesevalues provide an indication of the variability and difference between the behaviour of sys-tems. Depending on the test used to assess difference in populations, 100L, 150M and 200Lvariably come out as different, but 200H and 100H are always the same. Briefly, experi-ment G2Q100L has a greater number of small lag changes than G1Q100L. G2Q150M showsa more right-tailed distribution than G1Q150M which shows something closer to a normaldistribution. G2Q200H lacks the tail of G1Q200H, but mimics the body of lag distribution.G2Q100H and G1Q100H share the same distribution. G2Q200L has a greater provenance ofsmall lag changes. The magnitude of these changes can be separated into three categories: 0,no change, <1, intra-class or subtle inter-class change, and >1 substantial inter-class changebetween timesteps. Experiments G2Q100L, G2Q150M and G2Q200L have a substantiallyhigher proportion of small stability changes than their counterparts. G2Q100H also hasmarginally more small steps, whereas G2Q200H has a lower proportion than G1Q200H.Table B.3: Descriptive values for the stability index, lagged stability index and percent timespent per class, for each experiment. Changes are given relative to GSD2.Stability Index Lagged Stability Index Small Stability Occurrence (%)GSD1 GSD2 % Change GSD1 GSD2 % Change GSD1 GSD2 % Change100L 5.12 3.69 27.95 1.63 0.47 71.15 41.18 75.00 82.14150M 5.75 5.09 11.41 1.84 0.93 49.29 20.00 50.00 150.00200H 6.58 4.19 36.21 0.84 0.81 3.52 52.63 43.75 -16.88100H 4.24 4.70 -10.97 0.86 0.87 -1.05 50.00 52.63 5.26200L 5.12 5.15 -0.70 1.67 1.08 35.29 23.33 60.00 157.14610.00.20.40.60.81.0ExperimentRelative Time100L 150M 200H 100H 200L1 2 1 2 1 2 1 2 1 2Figure B.2: Relative stability of the channel compared to all experiments, for each experi-ment. Lighter blue indicates lower stability, darker blue indicates higher stability62024681:length(rankedList[[i]])/length(rankedList[[i]])rankedList[[i]]G1Q100L1:length(rankedList[[i + 5]])/length(rankedList[[i + 5]])rankedList[[i + 5]]G2Q100L024681:length(rankedList[[i]])/length(rankedList[[i]])rankedList[[i]]G1Q150M1:length(rankedList[[i + 5]])/length(rankedList[[i + 5]])rankedList[[i + 5]]G2Q150M024681:length(rankedList[[i]])/length(rankedList[[i]])rankedList[[i]]G1Q200H1:length(rankedList[[i + 5]])/length(rankedList[[i + 5]])rankedList[[i + 5]]G2Q200H024681:length(rankedList[[i]])/length(rankedList[[i]])rankedList[[i]]G1Q100H1:length(rankedList[[i + 5]])/length(rankedList[[i + 5]])rankedList[[i + 5]]G2Q100H0.0 0.2 0.4 0.6 0.8 1.0024681:length(rankedList[[i]])/length(rankedList[[i]])rankedList[[i]]G1Q200L0.0 0.2 0.4 0.6 0.8 1.01:length(rankedList[[i + 5]])/length(rankedList[[i + 5]])rankedList[[i + 5]]G2Q200L00Relative TimeChannel Stability IndexFigure B.3: Same as above but plotted as time series data.63−4−2024G1Q100L G2Q100L−4−2024G1Q150M G2Q150M−4−2024G1Q200H G2Q200H−4−2024G1Q100H G2Q100H0.0 0.2 0.4 0.6 0.8 1.0−4−2024G1Q200L0.0 0.2 0.4 0.6 0.8 1.0G2Q200L00Relative TimeChannel ChangeFigure B.4: Magnitude of lagged stability values for each experiment. Data points high-lighted in red indicate values < 1, that is small inter- or intra-class variations in stability.64B.2 DiscussionThe morphodynamics of the system also show similar patterns to the above observed dif-ferences in the profile-derived data. The considerably higher proportion of time spent byexperiments G1Q100L-200H at the more stable single threaded flow regime demonstrate theinherently higher stability of GSD1. Single threaded flow is strongly indicative of a morestable channel, both in terms of behaviour and in terms of location, in steep gravel streams.Considering the slope (>4% / >2°) and removal of jamming possibility the formation ofsingle threaded flow must have been brought about by a preference in the location of waterconveyance, that is the relative difficulty of bar erosion. The bars formed of GSD1, due tothe presence of larger grains and an overall lower mobility, decrease the likelihood of trans-port at their location and are likely to be eroded through dissection. In contrast the easilytransportable material of GSD2 does not create substantially different zones of entrainmentlikelihood and therefore the bars are not any more difficult for the active channel to passthrough. This is reflected in the patterns of flow type (Figure B.1) and stability (FigureB.2).Within the range of experiment conditions of a grain mixture there is not a consistent pat-tern of behaviour of the morphodynamics according to the variation in discharge, sedimentfeed or relative concentration. This is unexpected, as the transition between meandering andbraiding is a function of the bed slope and width/depth ratio; aggradation will force a tran-sition to braiding with the displacement of the channel (Parker, 1976). However, it must benoted that the presence of lateral constraints will influence the behaviour of the channel byincreasing the overall energy of the system as the energy expended during lateral migrationor avulsion is contained within. Given the chaotic nature of river systems, the sensitivityof channel form to morphology thus provides ample opportunities for divergence within thesame grain size distribution. The overall differences between the two mixtures are strongenough to separate the behaviour, however. As the width/depth ratios become redundantat different slopes (boundary shear stresses necessarily differ) the consistent bias towardshigher transport efficiency, which includes the effect of slope and depth and hence energy,instead confirms this separation in behaviour. Therefore it may not serve to solely discussthe channel pattern but rather the observed characteristics and manner of its stability.Within experiments 100L-200H, the channel formed of GSD2 is more likely to be occupy-ing a lower stability state. These less stable channels are the result of the relatively highermobility of GSD2; both the propensity for movement of the active channel location and thedegree of multi-threaded flow when it occurs are increased relative to GSD1. Even thoughGSD1 does spend a large proportion of time as multi-threaded, it often occupies the more65stable and less braided end of the spectrum in contrast to GSD2. The creation of equallymobile bedforms in the channel serves as nothing more than temporary rerouting of theflow. Where the threshold of entrainment is so slight (i.e. GSD2) the bed acts as a highlymalleable surface and thus enables bar head dissection and the migration of the thalwegthrough the bars. The relatively lower attainment of single threaded flow for GSD2 showsthat sediment conveyance was maintained, and even led to greater sediment transport ratesthan those for GSD1.66

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