Arts, Faculty of
Geography, Department of
DSpace
UBCV
Vincent, Lauren
Master of Science - MSc
University of British Columbia
Alluvial fans form through primary and secondary processes. Primary processes act to transport sediment from the drainage basin to the fan and secondary processes re-mobilize and rework sediment previously deposited on the fan. There is still a poor understanding of how primary and secondary processes interact on alluvial fans. The primary objective of this research is to isolate the role of secondary processes in determining alluvial fan behaviour and morphology. Four experiments were conducted, in which alluvial fans were created under different durations of secondary processes. In these experiments secondary processes were run between each primary process, or flood period. The duration of secondary process periods ranged from 5 to 40 minutes across the four experiments. Here primary processes reflect inputs of Q = 100 ml/s and Qb = 10 g/s, and secondary processes reflect inputs of Q = 50 ml/s and Qb = 0 g/s, wherein Q refers to water discharge and Qb refers to sediment feed rate. For each experiment, alternating primary and secondary processes were run until a total of 72 kg of sediment had been added to the fan. Following this, a sequence of nine flood events was run over the fan surface to evaluate fan response to flooding. Experiments with longer durations of secondary processes generated fans with larger areas and gentler gradients. In addition, longer secondary process durations led to increased flow channelization and channel incision between flood periods. The dominant channel pattern throughout the experiments was the formation of a single, centralized channel during secondary process periods, and the bifurcation of flow following the onset of primary processes. The increased incision and flow confinement during prolonged periods of secondary processes resulted in a decreased avulsion frequency during subsequent flood periods. In addition, the onset of avulsion was delayed for experiments with longer secondary process duration. These results indicate that the duration of secondary processes has important effects on both fan morphology and flow behaviour.
The Importance of SecondaryProcesses on Alluvial Fan Morphology,Channel Behaviour, and FloodHazardsbyLauren VincentB.Sc.E., Queen’s University, 2010A 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)December 2020c© Lauren Vincent 2020The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, a thesisentitled:The Importance of Secondary Processes on Alluvial Fan Morphology, ChannelBehaviour, and Flood Hazardssubmitted by: Lauren Vincent in partial fulfillment of the requirementsfor the degree of Master of Sciencein GeographyExamining Committee:Brett Eaton, Professor, Geography, UBCCo-supervisorMatthias Jakob, BGC Engineering Inc.Co-supervisorSarah Davidson, BGC Engineering Inc.Supervisory Committee MemberDan Moore, Professor, Geography, UBCAdditional ExamineriiAbstractAlluvial fans form through primary and secondary processes. Primary pro-cesses act to transport sediment from the drainage basin to the fan andsecondary processes re-mobilize and rework sediment previously depositedon the fan. There is still a poor understanding of how primary and sec-ondary processes interact on alluvial fans. The primary objective of thisresearch is to isolate the role of secondary processes in determining alluvialfan behaviour and morphology. Four experiments were conducted, in whichalluvial fans were created under different durations of secondary processes.In these experiments secondary processes were run between each primaryprocess, or flood period. The duration of secondary process periods rangedfrom 5 to 40 minutes across the four experiments. Here primary processesreflect inputs of Q = 100 ml/s and Qb = 10 g/s, and secondary processesreflect inputs of Q = 50 ml/s and Qb = 0 g/s, wherein Q refers to waterdischarge and Qb refers to sediment feed rate. For each experiment, alter-nating primary and secondary processes were run until a total of 72 kg ofsediment had been added to the fan. Following this, a sequence of nineflood events was run over the fan surface to evaluate fan response to flood-ing. Experiments with longer durations of secondary processes generatedfans with larger areas and gentler gradients. In addition, longer secondaryprocess durations led to increased flow channelization and channel incisionbetween flood periods. The dominant channel pattern throughout the exper-iments was the formation of a single, centralized channel during secondaryprocess periods, and the bifurcation of flow following the onset of primaryprocesses. The increased incision and flow confinement during prolongedperiods of secondary processes resulted in a decreased avulsion frequencyduring subsequent flood periods. In addition, the onset of avulsion was de-layed for experiments with longer secondary process duration. These resultsindicate that the duration of secondary processes has important effects onboth fan morphology and flow behaviour.iiiLay SummaryAlluvial fans are triangular shaped deposits of sediment transported by wa-ter, they form in mountainous regions where high gradient streams entervalleys and deposit sediment. Previous work on alluvial fans has focused onthe processes which add material to the fan. These processes may be referredto as primary processes and encompass everything from flood events to massmovements. While primary processes reflect important fan-building events,they occur infrequently compared to secondary processes. In this thesis, Iexamine how the duration of secondary processes impacts the shape andsize of the fan, the position of channels on the fan surface, and the be-haviour of the fan under flood conditions. I found that fans with longerdurations of secondary processes were larger and less steep than those withshorter secondary process durations. In addition, I found that the channelsformed under secondary processes were better able to contain flow duringflood events. Flow was diverted from the primary channel less frequentlyduring flood events on these fans. My results indicate that the duration ofsecondary processes has important effects on both the fan dimensions andtheir response to flood events.ivPrefaceThis thesis is the result of four experiments designed and run by LaurenVincent with input from Brett Eaton. The stream table on which the ex-periments were run was designed and created by Anya Leenman. The dataprocessing steps used to convert the photographic data to digital elevationmodels, orthomosiacs and binary channel maps were all the work of AnyaLeenman. Much of the code used to characterize fan morphology (i.e. fangradient, area, and wet fraction) was also provided by Anya Leenman andmodified for these experiments by Lauren Vincent. Additional data analysisand all of the writing presented in this thesis were done by Lauren Vincent.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 The Alluvial Fan Environment . . . . . . . . . . . . . . . . . 11.2 Alluvial Fan Dynamics . . . . . . . . . . . . . . . . . . . . . 31.3 Alluvial Fan Processes . . . . . . . . . . . . . . . . . . . . . . 41.3.1 Primary Processes . . . . . . . . . . . . . . . . . . . . 51.3.2 Secondary Processes . . . . . . . . . . . . . . . . . . . 91.4 Research Questions and Thesis Structure . . . . . . . . . . . 122 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . 142.1 Model Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.1 Experiments . . . . . . . . . . . . . . . . . . . . . . . 222.3 Data Collection and Analysis . . . . . . . . . . . . . . . . . . 262.3.1 Channel Entrenchment . . . . . . . . . . . . . . . . . 292.3.2 Avulsion Analysis . . . . . . . . . . . . . . . . . . . . 313 Fan Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . 333.1 Fan Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.1.1 Fan Gradient by Azimuth . . . . . . . . . . . . . . . . 36vi3.2 Fan Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 Channel Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . 424.1 Fan Wet Fraction . . . . . . . . . . . . . . . . . . . . . . . . 424.1.1 Phase 2 Wet Fraction . . . . . . . . . . . . . . . . . . 444.2 Channel Pattern . . . . . . . . . . . . . . . . . . . . . . . . . 474.3 Channel Entrenchment . . . . . . . . . . . . . . . . . . . . . 504.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.4.1 Fan Wet Fraction . . . . . . . . . . . . . . . . . . . . 534.4.2 Channel Pattern . . . . . . . . . . . . . . . . . . . . . 534.4.3 Channel Entrenchment . . . . . . . . . . . . . . . . . 545 Avulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.1 Manual Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 575.1.1 Avulsion Type . . . . . . . . . . . . . . . . . . . . . . 595.2 Automated Analysis . . . . . . . . . . . . . . . . . . . . . . . 645.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.3.1 Predicted Avulsion Frequency . . . . . . . . . . . . . 685.3.2 Links to Fan Gradient . . . . . . . . . . . . . . . . . . 705.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 706 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.1 Impacts to Fan Morphology . . . . . . . . . . . . . . . . . . 716.2 Channel Behaviour . . . . . . . . . . . . . . . . . . . . . . . 726.3 Avulsions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.4.1 Links to Climate Change . . . . . . . . . . . . . . . . 766.5 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78AppendicesA Results of Experiment 1B . . . . . . . . . . . . . . . . . . . . 87B Principal Component Analysis . . . . . . . . . . . . . . . . . 90viiList of Tables1.1 Debris-flood characteristics by type, adapted from Churchand Jakob (2020) . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 Watershed parameters used for fan process classification . . . 92.1 Experimental inputs for fan formation (Phase 1) . . . . . . . 242.2 Experimental inputs for fan flooding (Phase 2) . . . . . . . . 245.1 Results of manual avulsion assessment completed over Phase 2 585.2 Observed vs. predicted avulsions during Phase 2 . . . . . . . 69B.1 Eigenvalues for each of the first four PCA modes by experiment. 90viiiList of Figures1.1 Anatomy of an alluvial fan . . . . . . . . . . . . . . . . . . . 21.2 Summary of hydrogeomorphic processes . . . . . . . . . . . . 51.3 Primary processes as a function of Melton ratio and watershedstream length . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.4 Secondary process fan entrenchment schematic . . . . . . . . 102.1 Relationship between model scale and specificity . . . . . . . 162.2 Idealized experimental setup . . . . . . . . . . . . . . . . . . . 192.3 Photos of experimental setup . . . . . . . . . . . . . . . . . . 202.4 Field and experimental grain size distributions . . . . . . . . 212.5 Example flood sequence for two complete experiments . . . . 252.6 Data type examples . . . . . . . . . . . . . . . . . . . . . . . 292.7 Cross-section of an experimental fan showing channel incision 303.1 Mean fan gradient vs. flood timing . . . . . . . . . . . . . . . 343.2 Mean fan gradient by experiment . . . . . . . . . . . . . . . . 363.3 Mean gradient by azimuth . . . . . . . . . . . . . . . . . . . . 373.4 Mean fan area by experiment . . . . . . . . . . . . . . . . . . 384.1 Wet fraction of the fan over the complete experimental duration 434.2 Wet fraction of the fan over Phase 2 . . . . . . . . . . . . . . 454.3 Box plot of fan wet fraction for Phase 2 . . . . . . . . . . . . 474.4 Binary fan channel maps . . . . . . . . . . . . . . . . . . . . . 484.5 All PCA results for Experiment 3 . . . . . . . . . . . . . . . . 494.6 Mode 2 PCA results for Experiment 3 . . . . . . . . . . . . . 504.7 Maximum values of channel incision over time . . . . . . . . . 514.8 Characteristic channel incision following secondary processes 525.1 Channel cross-sections showing avulsion types . . . . . . . . . 605.2 Depositional avulsion example . . . . . . . . . . . . . . . . . . 615.3 Erosional avulsion example . . . . . . . . . . . . . . . . . . . 625.4 Reoccupation avulsion example . . . . . . . . . . . . . . . . . 63ix5.5 Unclassified avulsion example . . . . . . . . . . . . . . . . . . 635.6 Channel pattern change identified using threshold (automated)method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.7 New flow area between each flow map pair, normalized by fanarea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.8 New and abandoned flow area between each Phase 2 flow mappair, normalized by fan area . . . . . . . . . . . . . . . . . . . 676.1 Summary of secondary process effects on fan morphology. . . 75A.1 Mean fan gradient by experiment, with Experiment 1B . . . . 87A.2 Mean fan gradient vs. flood timing, with Experiment 1B . . . 88A.3 Mean fan area by experiment, with Experiment 1B . . . . . . 89B.1 PCA results for Experiment 1 . . . . . . . . . . . . . . . . . . 91B.2 PCA results for Experiment 2 . . . . . . . . . . . . . . . . . . 92B.3 PCA results for Experiment 4 . . . . . . . . . . . . . . . . . . 93xAcknowledgementsI would first like to thank Brett Eaton for his often unwarranted beliefand trust in my ideas and my work; his lack of doubt is what ultimatelyconvinced me I could pull this off. Thank you to Matthias Jakob for keepingme grounded in the real world, and giving me the background knowledge Ineeded to pursue this project in a meaningful way. This research would nothave been possible without the endless support, help, and advice of AnyaLeenman. She has become a true friend over the course of my time at UBCand I am not exaggerating when I say I would have been at a loss withouther and all of her hard work. This thesis also benefited from the valuableadvice of Sarah Davidson, Will Booker, David Adams, Lucy Mackenzie, andMarwan Hassan.Writing a thesis mostly from home has been an interesting and challeng-ing project. Being away from my lab mates has made the other supportsystems in my life all the more important. I would like to thank all my fam-ily and friends who have encouraged me, fed me, listened to me rant, anddistracted me just when I needed it most. Thank you to my parents whotaught me that, with a healthy dose of stubbornness, I could do anythingI set my mind to. A special thank you to Dylan for following me back toVancouver to pursue this degree, and for supporting my research and myextra-curriculars in equal measure.xiChapter 1IntroductionAs development in mountainous areas increases, infrastructure built on allu-vial fans continues to be at risk from flooding and hydrogeomorphic hazards.The type of flooding occurring on alluvial fans is uniquely characterized bysignificant flow path uncertainty, abrupt deposition of sediment and a highhazard environment (Federal Emergency Management Agency, 2000). Phys-ical modelling of alluvial fans has long been used to isolate variables and pro-cesses of interest from the complex system of fan behaviour (Hooke, 1967;Clarke, 2015). The mitigative effects of secondary fan processes, or inter-flood periods, on fan flood hazards are explored within this thesis using anexperimental approach. The experiments described herein are loosely mod-elled off the debris-flood driven catchment of Three Sisters Creek located inCanmore, AB.Sections 1.1 to 1.3, below, review the characteristics and processes con-trolling the formation and evolution of alluvial fans to provide a context forthe objectives of the current research, which are provided in section 1.4.1.1 The Alluvial Fan EnvironmentAlluvial fans are sedimentary deposits formed by the net accumulation ofalluvium from clear-water and sediment laden flows (House et al., 2010).Viewed from above, they appear as extended fans or a segment of a cone(Bull, 1977; Blair and McPherson, 2009). Fans are formed of a mosaic ofalluvial deposits deposited over time; in unglaciated terrain these depositsmay date up to 100,000s of years in the past (House et al., 2010; de Haaset al., 2018a).Alluvial fans occur in a wide range of geomorphic settings and over arange of climates (Ventra and Clarke, 2018). Despite this, the conditionsnecessary for fan formation are common across continents and even extendto water-bearing planets (Kleinhans, 2010; de Haas et al., 2014). Theseconditions are: (i) the intersection of an upland catchment and a valley,(ii) sufficient sediment production within the catchment and (iii) a triggermechanism – usually high stream discharge (Blair and McPherson, 2009).1These criteria may be met in most mountainous environments (de Haaset al., 2014), where high topographic relief leads to increased precipitationthat is then funneled through steep and narrow drainage basins. Together,these factors provide the triggers necessary to move coarse sediment throughthe upland catchment to the alluvial fan environment (Blair and McPherson,2009).In their role as a sediment sink, alluvial fans bridge erosive upland catch-ments and valley floors (Bowman, 2019). It is at this transition from a highlyconfined channel to an open valley where flow can expand freely into multi-ple distributary channels (Figure 1.1). This allows sediment to be depositedover a wide area below the point of expansion – or the fan apex (Houseet al., 2010). For fans that experience net deposition, the accumulation ofmaterial forming alluvial fans represents an interruption to sediment trans-port (Harvey, 2010). The relative importance of sediment delivery to thesystem and the capability of the system to transport material dictate theprecise position, shape and size of an alluvial fan (Bull, 1979). The extent ofa fan is most commonly measured by referencing its radius, or the averagedistance from the fan apex to the edge of the fan.Figure 1.1: Anatomy of an alluvial fan. The watershed area is shown in green,the upstream channel in blue, the fan complex in orange and the location ofthe fan apex is circled in grey. Adapted from Merriam-Webster (n.d.).21.2 Alluvial Fan DynamicsFan behaviour may be broken into autogenic and allogenic dynamics. Auto-genic dynamics drive morphologic change resulting from the system’s inter-nal processes, while allogenic dynamics drive morphologic change throughexternal forcings (Paola et al., 2009). Autogenic and allogenic forces com-pete for control of fan dynamics, and the resulting process-form feedbacksdictate the course of fan evolution.Autogenic dynamics may be described as self-organized complexity (Paolaet al., 2009), or internal thresholds, which when crossed result in morpho-logic change (Bowman, 2019). This morphologic change may be evidencedby alternating sequences of sheet flow and channelized flow, or avulsion andbifurcation events. It is these processes that allow alluvial fan systems toevenly distribute their sediment load and maximize channel stability andpotential energy (Postma, 2014). An example of autogenic dynamics is theprocess of fan over-steepening, resulting in increased sediment transport fol-lowing exceedance of an intrinsic threshold gradient (Bowman, 2019).Allogenic forcings relate to any external dynamics influencing the fan,such as climate, tectonism, anthropogenic activity and changes in river levelfor fans terminating in fluvial environments (Bowman, 2019). These forcingsrepresent a break in the equilibrium conditions of the system (Muto et al.,2007). The timescale of these changes is important in determining their ef-fect on the fan. Paola et al. (1992) describe the time-scale of variation for agiven basin as ‘equilibrium time’. This reflects the time required for a basinto achieve steady-state following an allogenic change, and is determined bythe nature of the change, the basin length, and the diffusivity of the basin(Paola et al., 1992). Here, diffusivity refers to the rate at which allogenicchanges are able to move through the catchment. Allogenic changes oc-curring over large timescales relative to a river’s equilibrium time will havelittle impact on the system whereas more rapid allogenic change will resultin greater change to the system (Postma, 2014).In natural systems, autogenic and allogenic dynamics occur simultane-ously, and their effects may be difficult to differentiate. On the timescale offan evolution, autogenic processes cannot operate uninterrupted by allogenicforcings (Muto et al., 2007). Postma (2014) describes the interplay of auto-genic and allogenic processes best, referring to allogenic forcings as controlson generic autogenic behaviour. This implies that the character and fre-quency of autogenic behaviour are dependent upon the allogenic conditionsunder which they occur. In particular, Bryant et al. (1995) cite the impor-tance of channel aggradation as a control on autogenic behaviour frequency.3Channel aggradation is often related to sedimentation rate - an allogenicforcing - which thereby affects autogenic behaviour.This interplay of autogenic and allogenic processes makes their relativeimportance difficult to isolate on natural fans. For this reason, autogenicbehaviour has been studied in the absence of allogenic forcing with the useof numerical (Mackey and Bridge, 1995; Kleinhans et al., 2008) and ex-perimental (Hooke, 1968; Schumm et al., 1987; Paola et al., 1992; Mutoet al., 2007) models. For the experiments described in Chapter 2 the mor-phodynamic changes observed under constant conditions reflect autogenicdynamics, while changes to sediment feed and discharge may be consideredallogenic forcings. The impact of these forcings on autogenic fan behaviourare discussed throughout later chapters.1.3 Alluvial Fan ProcessesAlluvial fan formation is instigated by sediment movement down the water-shed channel. Deposition of sediment below the fan apex is then initiatedby a rapid change in sediment transport capacity. This change occurs asstreams leave their narrow valley source and spread out at the fan apex.Here, stream discharge Q may be related to stream mean width w, depth d,and velocity of flow v as follows (Bull, 1977):Q = wdv (1.1)An increase in channel width causes a decrease in flow depth and/orvelocity, thereby reducing sediment transport capacity. This change in hy-draulic geometry at the fan apex is a principal mechanism by which alluvialfans are formed. Others have argued that a decrease in gradient at the fansite may also contribute to the loss of sediment transport capacity associ-ated with fan formation (Blair and McPherson, 2009). However, Bull (1977)countered that the upper portions of many alluvial fans have gradients ap-proximately equal to those of the upstream channel, indicating that changein gradient is not the primary driver of fan formation.The sedimentary processes active on alluvial fans may be divided into twodistinct types. Blair and McPherson (1994) referred to processes that act totransport sediment from the drainage basin to the fan as ‘primary’ processesand those that re-mobilize and rework sediment previously deposited on thefan as ‘secondary’ processes.41.3.1 Primary ProcessesPrimary processes encompass a variety of mass and water movement types,including: debris floods, debris flows, hyper-concentrated flows, and mudflows, all of which act to transport material from the watershed to the fan.These processes may be grouped by sediment concentration, velocity, watercontent, and typical slope gradient (Figure 1.2) and may collectively be re-ferred to as hydrogeomorphic events. Primary processes transport sedimentto the fan that is generally angular, poorly sorted and coarse-grained (Blairand McPherson, 1994). These processes act to construct the fan throughaggradation and enlarge the drainage basin through sediment removal, andtheir recurrence interval is often strongly influenced by climate, sedimentavailability, vegetation cover, and weathering rates etc. (Jakob, 1996; Webbet al., 2008). Each watershed and fan are subject to a unique set of primaryprocesses of varying frequency, type, intensity, and magnitude.Riverine, or clearwater, flooding occurs on the gentlest gradients and hasFigure 1.2: Hydrogeomorphic processes as a function of slope gradient, sed-iment concentration, water content and relative velocity. Axes refer to thecross-sections, not the plan view sketches. Artwork by Matthias Jakob, usedwith permission from BGC Engineering Inc.5the lowest sediment concentration (< 1%). By contrast, debris avalanchesare almost entirely composed of sediment and their steep gradients resultin rapid movement. These more sediment laden types of events are oftenconsidered mass wasting phenomena and have historically been grouped withlandslides and other hillslope movements (Davies et al., 2013; Hungr et al.,2014). However, the channelization of primary processes may make themhigher magnitude and more destructive than their hillslope counterparts(Davies et al., 2013). In addition, the spatial control imposed by the channelresults in different deposits. In some cases, debris/rock avalanches havetransitioned into debris flows (Iverson, 1997; Guthrie et al., 2012) and evendebris floods (Friele et al., 2020). These transitions between primary processtypes indicate that classification even on the event scale is complex and, asindicated in Figure 1.2, this classification reflects a spectrum of transitionalprocess types.My experiments, described in Chapter 2, are modelled off the ThreeSisters Creek fan in Canmore, AB which is situated at the base of a debris-flood dominated watershed. The characteristics particular to debris-floodevents and the fans they form are described below.Debris FloodsDebris floods are defined in Hungr’s (2014) updated Varnes classificationsystem as very rapid flows of water, heavily charged with debris, in steepchannels. Debris floods have sediment concentrations ranging from approx-imately 10 - 25% and occur on gradients of 10% or less (Figure 1.2). Morerecent work by Church and Jakob (2020) clarifies that debris floods beginwhen the critical shear stress exceeds that required to mobilize at least theD84 of bed material. Debris floods are then defined as movement of theD84 over a minimum of a few minutes and a length of at least ten timesthe channel width. Debris floods are not to be confused with debris flows,which have higher sediment concentrations and may be described as veryrapid to extremely rapid surging of saturated debris (Hungr et al., 2014).Importantly, debris floods are considered Newtonian flows while debris flowsare considered landslide processes (Church and Jakob, 2020).The conditions required for debris-flood generation result in a degreeof bed mobility referred to as Stage 3 transport, in which the entire bedbecomes mobile up to a depth equal to several particles (Carling, 1988;Ashworth and Ferguson, 1989). This type of transport is rare and results inchannel modification by erosion and sedimentation, especially in channelswith non-cohesive bed and bank material (BGC Engineering Inc., 2020).6Often, the channel will experience widening until such a point as the reach-average shear stress is no longer sufficient to entrain the D95 (Eaton et al.,2017, 2020). Although generally considered rare, in some channels this typeof Stage 3 bed mobilization event may occur as frequently as every few years(Theule et al., 2015).Church and Jakob (2020) further classify debris floods into three typesusing a ratio of actual shear stress to critical shear stress. These categoriesare (1) meteorologically generated debris floods, (2) debris flow dilution gen-erated debris floods, and (3) outbreak debris floods. Type 1 debris floodsmay cause both aggradation and degradation and typically experience highervelocities and sediment concentrations in channel reaches upstream of thefan. By contrast, Type 2 debris floods typically result in aggradation, withhigh velocities and sediment concentrations occurring on the fan complex.Type 3 debris floods typically result in extreme erosion, degradation in chan-nels, and aggradation on fans and have high velocities and sediment con-centrations on both the upstream channels and fan complex (Church andJakob, 2020).A brief summary of the characteristics of these three debris flow typesare shown in Table 1.1. All three debris-flood types occur on steep fans (1 to10%) (Church and Jakob, 2020). This is in agreement with data from Blairand McPherson (1994) suggesting that debris-flood and debris-flow fans areconcentrated between gradients of 1-8%. More recent work suggests thatcertain catchment geologies may result in debris-flow fans with gradientscloser to 25% (Lau, 2017).Typical sediment Typical return Typical bulk densityconc. by vol. (%) period (yrs) (kg ·m−3/% by vol.)Type 1 < 5 > 2 ≤ 1, 300/18Type 2 < 50 > 50 1,300 - 1,700/18-42Type 3 < 10∗ > 100† ≤ 1, 500/30∗ Except immediately downstream of the outbreak where it can reach greater than 30%.† Can be a singular event in the case of a moraine dam or glacial breach.Table 1.1: Summary of debris-flood characteristics by type, adapted fromChurch and Jakob (2020).The watershed Melton ratio, or the watershed relief divided by the squareroot of watershed area (Melton, 1957), may be used to differentiate betweendebris-flood and debris-flow watersheds. Wilford et al. (2004) used a com-7bination of Melton ratio and straight-line watershed length to differentiatebetween primary fan processes (Table 1.2). Here, watershed length reflectsthe longest distance from the fan apex to a point on the watershed boundary.Holm et al. (2016) and Lau (2017) plotted the results of this classificationfor fans in Alberta and British Columbia. Using the watershed characteris-tics for Three Sisters Creek described in BGC Engineering Inc. (2020) theMelton ratio for the catchment is approximately 0.45. An approximate wa-tershed length of 4 km was measured from Google Earth. This plots theThree Sisters Creek catchment near the centre of debris-flood watershedswith some overlap into debris-flow watersheds (black square on Figure 1.3).Given the observed debris-flood dominance of Three Sisters Creek (BGCEngineering Inc., 2020), it is likely that any debris flows occurring the wa-tershed are diluted before reaching the fan apex. In addition, while fans thatare subject to debris flows may also experience debris floods, debris-floodfans are generally not susceptible to debris flows (Holm et al., 2016). Simi-lar distinctions were made by Blair and McPherson (1994) and Parker et al.Figure 1.3: Primary processes as a function of Melton ratio and watershedstream length using data from fans in Alberta and British Columbia (Holmet al., 2016; Lau, 2017). The black square shows the approximate watershedcharacteristics of Three Sisters Creek.8Process Melton Ratio Watershed Length (km)Floods < 0.3 AllDebris Floods 0.3 to 0.6 All> 0.6 ≥ 2.7Debris Flows > 0.6 < 2.7Table 1.2: Summary of watershed parameters used for fan process classifica-tion in Wilford et al. (2004) (after Holm et al., 2016).(1998a) between fluvial-dominated and debris-flow-dominated fans. This isbecause the watershed conditions generating debris flows are different fromthose that generate debris floods (Wilford et al., 2004). The experiments de-scribed herein are modelled after a debris-flood dominated catchment (BGCEngineering Inc., 2015) and focus on debris-flood and clearwater-flood pro-cesses, i.e. fluvial-dominated fans.1.3.2 Secondary ProcessesThe secondary processes described by Blair and McPherson (1994) encom-pass all activity that remobilizes or modifies sediment previously depositedby primary processes. These processes have been collectively referred toas fan degradation, however this is considered to be an over-simplificationgiven the complex reworking that may occur under secondary processes. Innature, these processes include surface and groundwater flow, weathering,wind erosion, plant rooting, animal burrowing etc. (Blair and McPherson,1994), although the predominant mechanism is fluvial transport with a sed-iment load below the channel’s transport capacity (Bowman, 2019).On alluvial fans, primary and secondary processes often occur on vastlydifferent temporal scales. Highly episodic runoff and hydrogeomorphic eventscomprise the majority of primary processes for some fans, while degradationby secondary processes acts over longer timescales (Blair and McPherson,1994). However, it is frequently secondary processes that dictate the sur-face morphology of alluvial fan landforms (de Haas et al., 2014) due tothe long recurrence intervals that characterize primary processes (Blair andMcPherson, 1994). Among the surface morphology features indicating thedominance of secondary processes are channel entrenchment, armouring,sediment redistribution, terracing, and down-fan migration of the incisionpoint.Bowman (2019) describes secondary processes as a stage of fan develop-9ment referred to as entrenchment: “when the main stage of fan depositionends, erosion becomes dominant by detachment and transport processes”.Entrenchment may be a temporary or permanent feature of fans, and itprovides a strong morphological indication for secondary process action. Inthe case of permanent entrenchment, large-scale allogenic processes such astectonism, isostacy, artificial base level lowering, climate change (and asso-ciated changes in runoff or sediment availability) or land-use changes maybe responsible. Short term fan entrenchment is often attributed to largeflood events with high sediment transport capacity or a series of moderateflow events with low sediment load (French, 1987).Irrespective of its longevity with respect to fan evolution, entrenchmentis most often controlled by fluvial action, wherein flow is directed into a con-fined channel, or channels, on the fan surface. A schematic representation offan entrenchment is shown in Figure 1.4. The initiation of entrenchment maybe brought on by: (i) a decreased sediment to water ratio, or (ii) oversteep-ening (Bowman, 2019). In the cases of debris flow activity, entrenchmentmay be initiated by the less viscous after-flow following the initial surge front(Iverson, 1997; Jakob and Hungr, 2005) and has been characterized exper-imentally on mixed-mode fans (Schumm et al., 1987). This phenomenon isdriven by the ability of water to move suspended sediment and fine-grainedbedload on lower gradients than debris flows (Hooke, 1967).Figure 1.4: Schematic showing the shift in depositional areas following fanentrenchment (a) untrenched alluvial fan before stream downcutting (b) en-trenched alluvial fan. The arrow shows the approximate location of the inter-section point. Adapted from Merriam-Webster (n.d.).10While entrenchment is the primary morphological feature associatedwith net degradation, the position of the fan intersection point, and thedegree of channel armoring are also markers of secondary processes. Theintersection point is defined as the point at which an incised channel reachesthe fan surface (Hooke, 1967; French, 1987; Clarke et al., 2010); and it marksthe threshold between channelization and dispersion of flow (Figure 1.4).The position of the intersection point may be used as a proxy for the extentof the fan surface that may be expected to be covered by flow (Clarke et al.,2010). Material deposited at the intersection point is generally coarser thanelsewhere in the channel, and a secondary fan may be superimposed on andextend beyond the larger fan below the intersection point (Hooke, 1967).French (1987) observed that for events which did not avulse, the location ofthe intersection point greatly directed the locus of sediment deposition.As secondary processes act to rework the fan channels, the flow is ableto remobilize finer sediments that were deposited by previous depositionevents. This selective material transport results in a phenomenon referredto as channel armouring, whereby coarse clasts are left behind on the channelbed (Bowman, 2019). These coarser clasts are often only one-grain deep butmay have a significant impact on overall bed stability (Harvey, 2010). Theprocess of armouring near the fan apex may act to shift channel degradationand entrenchment downstream (Colombera and Bersezio, 2011).Secondary processes have a profound impact on fan morphology. Pre-vious experimental work on delta environments has used variable dischargeto highlight the importance of secondary processes (Ganti et al., 2016; Pil-iouras et al., 2017; Esposito et al., 2018; Miller et al., 2019). In the words ofGanti et al. (2016) “unlike rivers upstream of the backwater zone, which canbe characterized by a single characteristic flood discharge that is responsi-ble for the most geomorphic work, the fundamental scale of deltas emergesonly under conditions of perpetual transient morphodynamic adjustment”.By comparison, much of the experimental work done on steep alluvial fanshas focused on primary processes only, often under constant discharge andsediment feed conditions (Hooke, 1968; Hooke and Rohrer, 1979; Schummet al., 1987; Zarn and Davies, 1994; Clarke et al., 2010) with a smallernumber of experiments including flood intermittency (Whipple et al., 1998;Parker et al., 1998a,b).111.4 Research Questions and Thesis StructureDespite the temporal importance of secondary processes in shaping alluvialfan morphology, their relevance to flood hazards on fans needs further re-search. In the case of steep alluvial fans, secondary processes have a greatercapacity to transport material over the fan surface even at relatively lowflow. The increased channelization and entrenchment of flow on fans thatoccur during secondary processes may act to contain consequent aggrada-tional events and shift flood hazards down-fan (Wasklewicz and Scheinert,2016). This study hypothesizes that secondary fan processes control debris-flood hazards on alluvial fans. My research investigates the role of secondaryprocesses in determining alluvial fan morphology and flood hazards, usingphysical modelling.The following questions will be addressed:1. Do longer durations of secondary processes on an experimental alluvialfan change fan morphology?2. Do longer durations of secondary processes reduce fan flood hazards,defined as avulsion frequency and flow dispersal over the fan surface?The following chapters are designed to answer these two questions. Chap-ter 2 presents an outline of the design of the alluvial fan experiments. Issuesof scaling are addressed and methods of data collection and analysis arediscussed.Chapter 3 summarizes broad morphological differences between the fansgenerated by the four experimental conditions described in Chapter 2. Theseresults consider the entire period of fan formation and the evolution of fangradient and fan area throughout.Chapter 4 looks specifically at the location and character of the chan-nel(s) on the fan surface. The binary channel maps described in Chapter 2are used to evaluate typical channel position and wet fraction on the fan,and estimate channel incision depth.Chapter 5 examines the critical role avulsion plays in alluvial fan for-mation. A manual analysis of avulsion frequency is first completed for thesecond phase of the experiments. This analysis is then cross-validated withan automated analysis. Avulsion frequency, timing, and type are discussedin detail.Chapter 6 summarizes the results of this study and proposes areas offuture work.12Appendix A supplies the complete results from the repeated run of Ex-periment 1.Appendix B supplies the complete results of the principal componentanalysis summarized in Chapter 4.13Chapter 2Experimental DesignPhysical models have long been used in alluvial fan research, with experi-mental studies taking place as early as the 1960s (Hooke, 1967, 1968). Phys-ical models are important tools in the observation of natural processes, andultimately seek to achieve predictive insight through analysis (Paola et al.,2009). Experimentation using physical models is particularly useful for allu-vial fan systems, as it allows for observations on temporal scales consistentwith fan evolution (Clarke et al., 2010; Harvey, 2010).Physical models may be classified in one of two ways, the first beingthe boundary conditions of the model (Schumm et al., 1987), and the sec-ond being the degree of model specificity (Peakall et al., 1996). Boundaryconditions may be either fixed-bed, in which the bed is non-erodible andno sediment transport occurs, or mobile-bed, in which sediment is free tomove within a constrained or unconstrained channel (Peakall et al., 1996).Fixed-bed models with non-erodible channel boundaries and no sedimenttransport may be used to examine processes outside of sediment transport,including wood movement (Braudrick and Grant, 2000; Bocchiola, 2011).Mobile-bed experiments may be used to examine key aspects of channelmorphodynamics, such as sediment transport and channel morphology (i.e.Malverti et al., 2008).Mobile-bed experiments may be further divided into constrained (fixedbanks) and unconstrained (mobile banks) channels. Experiments with con-strained channels, i.e. flumes, are often used to study channel transport anddeposition processes (Whiting and Dietrich, 1993; Hassan et al., 2006; Eatonand Church, 2009). Unconstrained channels are better suited to the charac-terization of channel patterns and their relation to sediment discharge or ex-perimental variables (Braudrick and Grant, 2000; Eaton and Church, 2004;Malverti et al., 2008). Mobile-bed experiments are much more common ingeomorphological models, and are often necessary when modelling alluvialfan processes (French, 1987). Most alluvial fan experiments employ mobile-bed and bank models (Clarke, 2015), while fixed-bank, one-dimensional fanstudies are the exception (Guerit et al., 2014; Booker and Eaton, 2020).The second type of model classification is the degree of model specificity14(Peakall et al., 1996), or the degree to which the model successfully repli-cates the prototype. Model specificity relates to the ability of the modelto retain geometric, kinematic, and dynamic similarity between itself andthe prototype. Yalin (1971) summarizes these three levels of similarity be-tween models (subscript m) and prototypes (subscript p) using the arbitraryconstants λL, λT , and λM :1. geometric similarity: pertains to similarity of form (French, 1987),wherein the dimensions of the prototype are preserved. Here, physicalproperties are scaled according to their relative lengths, L.λL =LpLm(2.1)2. kinematic similarity: pertains to motion across the model and proto-type, wherein paths of motion and ratios of velocities are preserved.Here, physical properties are scaled with the consideration of time, T .λT =TpTm(2.2)3. dynamic similarity: pertains to mass balance, wherein the ratios ofmasses and ratios of forces are preserved. Here, the movement ofsediment is scaled with the addition of mass, M .λM =MpMm(2.3)Peakall et al. (1996) describes three broad types of model specificity: one-to-one, scaled, or analogue (Figure 2.1), with one-to-one models having themost specificity and analogue models having the least specificity based onthe similarity criteria listed above.One-to-one models are not scaled and retain the dimensions of the proto-type. While one-to-one models are able to retain a high degree of specificityin replicating the prototype, there is a spatial limit on the phenomena thata one-to-one model can replicate. Virtually all mobile-bed models deviatefrom strict similarity criteria (Gaines and Maynord, 2001); even in one-to-one models, discrepancies may arise due to differences in temperature,viscosity, flow depth and boundary effects between the model and its pro-totype (Peakall et al., 1996). One-to-one models are typically reserved forhydraulic flume studies involving the observation of bed scale phenomena15Figure 2.1: Relationship between model scale (temporal or spatial) and modelspecificity, from Peakall et al. (1996).(Peakall et al., 1996). For this reason, one-to-one models are rarely used inalluvial fan experiments (Clarke, 2015).Scale modelling attempts to maintain geometric, kinematic, and dynamicvariables to produce a miniature version of a field example or prototype. Inthe idealized case, scaled models would scale each model parameter perfectly.In reality, parameters such as gravity, fluid viscosity, density of sedimentand water are held constant between the model and prototype (Ashworthet al., 1994). Often, turbulent forces and associated phenomena (Reynoldsnumber) are relaxed within a certain range to allow for flexibility in modelscaling, while gravity forces and associated phenomena (Froude number) arescaled correctly (Paola et al., 2009). This type of model scaling is referredto as ‘Froude scaling’ (Peakall et al., 1996).The third type of model, analogue modelling, follows Hooke’s similarityof process criterion, defined in his 1967 paper as “the postulate that pro-cesses in the laboratory are similar to those in nature and that the morpho-logic effects of these processes are the same on both laboratory and naturalfans”. These models are often more flexible and have more expansive de-signs and applications than models created under the principles of classicaldynamic scaling (Paola et al., 2009). Analogue models are used to describe16general theory without achieving dynamic similarity (Peakall et al., 1996).They are commonly used to study form, process, and evolution as indepen-dent entities and may not make reference to a specific prototype (Peakallet al., 1996).2.1 Model ScalingThe experiments described herein follow Hooke’s (1967) similarity processcriterion and are thereby classified as mobile-bed, Froude-similar experi-ments. While the model is geometrically scaled, it does not abide by strictFroude-scaling due to the presence of transitional and laminar flow. Thisleads to a classification of Froude-similarity. For these experiments, the gra-dient of the fan and the width of the channels upon it were self-formed,with gradients typically falling between 0.06 and 0.12 m m−1. Therefore, itwas impossible to experimentally control the Froude number, mean channelwidth, or mean hydraulic depth for the experiments; they were consideredemergent properties1 of the experiments.At the fan apex, where the water surface width is constrained, the typicalhydraulic parameters were estimated using the criteria of similarity equa-tions below (Yalin, 1971; Peakall et al., 1996). The criteria used are the flowReynolds number (Re, Eqn. 2.4), the Froude number (Fr, Eqn. 2.5) and theparticle Reynolds number (Re∗, Eqn. 2.6). Here, µ and ρ reflect the fluiddynamic viscosity and density, respectively, U is the average downstreamvelocity, R is the hydraulic radius of the channel, D is the characteristicgrain size, and g is the gravitational constant.Re =ρRUµ(2.4)Fr =U√gR(2.5)Re∗ =ρU∗Dµ(2.6)The Froude Number at the apex during my experiments is estimated tohave been about 1.3, which is consistent with observations of super-criticalflow on fan surfaces made in the field by others (Beaumont and Oberlander,1971), but often fell below 1 further downstream as the flow spread out1Emergent properties are considered to be properties that appear only under the fullcomplexity of the given experimental conditions.17across the fan surface. This phenomenon would also be expected on naturalfans as channels widen at the fan apex thereby decreasing flow velocity(Eqn. 1.1), leading to a decrease in Froude number below the fan apex. Asa result, the model is most appropriately interpreted as a Froude-similarmodel, not a Froude-scaled model, even though the typical Froude numbersare consistent with the expected values for gravel-cobble fans in the field.The typical Reynolds number at the apex was approximately 1400, andthe typical Reynolds particle number at the apex was about 180, whichexceeds the threshold value of 15 proposed by Ashworth et al. (1994)2. Al-though this condition is met at the fan apex, the Reynolds number decreasesdown-fan as flow disperses and velocity decreases. Although the Re∗ in somedown-fan channels approximately conforms to the threshold value proposedby Ashworth et al. (1994), in others the flow may reach the transitionalzone between laminar and turbulent, which violates the requirement forstrict Froude scaling that the flow remain turbulent.The down-fan flow state closely approximates the conditions seen inmicro-scale models (Davies et al., 2003; Malverti et al., 2008). These mod-els typically have a small Reynolds number (Re ≤ 200) and display laminarflow (Davies et al., 2003). Although the mechanics of sediment transport andflow may differ from those at the field scale, it has been shown that distinctfluvial morphologies – including those of alluvial fans – may be replicatedunder purely laminar flow (Malverti et al., 2008). Schumm et al. (1987)also found that small scale analogue models of alluvial fans demonstratedmany of the same fundamental features and processes as natural fans. Theobserved consistencies between experimental and natural fans with differ-ing dimensionless numbers have been described as “unreasonably effective”(Paola et al., 2009). Paola et al. (2009) postulate that the scale indepen-dence of morphology is sufficiently robust to be more important and effectiveas an experimental method than classical dynamical scaling. Clarke (2015)underscores the concept that morphodynamics are scale independent andthat fan processes may be accurately modelled at a wide variety of scales.In summary, the Froude-similar approach used to generate alluvial fanmorphology in my experiments has a basis in micro-scale (Davies et al.,2003; Malverti et al., 2008) and process-similar (Hooke, 1967) modelling. Ibelieve that the broad morphologic processes present on natural fans arerepresented in my experiments. However, the length ratio of 1:128 thatis necessary to conduct experiments on fan evolution make it difficult toestablish dynamic similarity, which must be kept in mind when interpreting2Yalin (1971) proposed a threshold value of 70.18my results. Therefore, extrapolations of rates and volumes measured inmy model to a prototype fan are likely inappropriate without additionalsupporting information from the field.2.2 Model SetupExperiments were conducted using a physical model of a generic gravel-cobble fan, situated in the Biogeomorphic Laboratory at the University ofBritish Columbia, Vancouver. The experimental setup consisted of a 2.4 x2.4 x 0.3 m tiltable stream table - or fan simulator - with a 0.2 x 0.5 x 0.3m inlet at one corner (Figure 2.2). The table was set to an angle of 0.0002m m−1 (0.02%) with the inlet at the highest corner. This was the minimumangle required to allow for flow from the inlet to the drain.Figure 2.2: The idealized experimental setup, GCPs refer to ground controlpoints used to georeference images taken by the cameras. An image of atypical fan is shown in the background.19A sediment feeder was mounted above the inlet along with a constanthead tank from which flow was generated. Sediment and water were mixedin a funnel before entering the inlet. Water left via a drain in the corneropposite the inlet; sediment that reached the drain was caught by a finemesh. The water used in the experiments was dyed blue to allow photos tobe used for automated channel mapping.The base and walls of the table were roughened with coarse (2 mm)sand grains and Lego base plate sheets, respectively (Figure 2.3a). Theseroughness elements were used to produce walls with roughness characteris-tics similar to those of the alluvial bed. Lego was attached to base platesheets in the inlet in order to narrow it from 19.8 cm at the funnel to 7.1cm at the fan apex (Figure 2.3b). The zone upstream of this Lego structureacted as a mixing zone for sediment and water. Sediment was manuallyadded to this zone during Floods B and C of Phase 2, described below3.Figure 2.3: Photos of the experimental setup; (a) shows the complete experi-ment, with the inlet on the furthest side of the stream table from the camera,and the outlet closest to the camera, (b) shows a close-up of the fan inlet withthe Lego used as roughness elements.3The existing sediment feeder mounted on the stream table had a maximum sedimentfeed rate of 10 g/s. To achieve sediment feed rates in excess of 10 g/s, sediment wasmanually added at the stream table inlet.20The experiments used a mixture of sediment ranging between 0.25 –2.8 mm. A mixture was used to create more realistic looking channels(Hamilton et al., 2013), and because Booker and Eaton (2020) found thatnarrowly and widely graded mixtures with the same D50 produced differentmorphodynamics. The mixture represents a scaled distribution of sedimentsampled from the surface of Three Sisters Creek fan in Canmore, AB in July,20184 (Figure 2.4). The grain size distribution used in the experiments wastruncated at 0.25 mm to maintain a hydraulically rough boundary. Usinggeometric scaling relations, the length scale for this generic model is 1:128.The median size of the model bed material of 0.6 mm corresponds to aprototype value of 77 mm, and the model D84 of 1.3 mm corresponds toa prototype value of 166 mm. The experiments described herein producedfans with radii of up to approximately 1.4 m. Fan radius was calculatedby assuming an approximately concentric fan edge and using fan area tocalculate average fan radius.0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00020406080100Grain size (mm)Cumulative percent finer than (%)Three Sister's Creek scaled Wolman sampleExperimental grain size distributionFigure 2.4: Comparison of scaled field and experimental grain size distribu-tions.4Field data from the Three Sisters Creek fan was collected by lab group membersincluding: Emily Ballon, Deanna Shrimpton, Anya Leenman, Will Booker, Brett Eatonand Gabrielle Eaton.212.2.1 ExperimentsMy experiments may be divided into two distinct phases: fan formation(Phase 1) and fan flooding (Phase 2). In the first phase, alluvial fanswere generated using alternating primary and secondary process inputs (Ta-ble 2.1). Primary processes used a discharge of 100 ml/s and a sediment feedof 10 g/s. This reflects a sediment concentration of 10% which is typical ofwhat might be expected during a debris flood (Figure 1.2). Secondary pro-cesses used a discharge of 50 ml/s and no sediment feed. This reflects theminimum discharge at which sediment transport was observed on the fansurface. In the second phase, the fans generated during fan formation weresubjected to the sequence of floods summarized in Table 2.2. Both FloodsB and C reflect an increase in discharge from Phase 1, and Flood C alsoreflects an increase in sediment feed. Flood A is equivalent to the floodevents in Phase 1. Each of the three flood types was repeated three times.Secondary processes were run in between each flood for the same durationas during fan formation.An initial experiment (Experiment 0, Table 2.1) was conducted in whichonly primary process input was used at constant feed and flow for a totalduration of 120 mins. This duration was sufficient to observe processesof fan evolution, including numerous phases of channel avulsion, incisionand back-filling. Over the 120 minute period, a total of 72 kg of sedimentwas input into the fan. In order to allow for comparison between fans, allsubsequent experiments were run until a total of 72 kg of sediment had beeninput into the fan i.e. a total duration of 120 mins of primary processes.The preliminary experiment, Experiment 0, was used for the purposes ofvisual comparison only and results from this experiment were not includedin further analysis.Four subsequent experimental runs were completed with the same du-ration of primary process input and increasing durations of secondary pro-cesses. Experiment 1 had the shortest secondary process duration at 5 mins,while Experiment 4 had the longest secondary process duration at 40 mins5.Experiments 1, 2, 3, and 4 are the focus of all following analyses. Primaryand secondary process inputs to the fan for each of the five experimentalruns are summarized in Tables 2.1 and 2.2. Primary processes were run forperiods of 5 minutes for the same total duration (120 mins) in each of the5Experiment 1 had equal durations of primary and secondary processes – 5 minuteseach. The increasing duration of secondary processes (to 10, 20, and 40 minutes) insubsequent experiments aim to reflect the rarity of primary processes relative to secondaryprocesses.22experiments. In between each primary process interval, secondary processeswere run. The total length of the fan formation phase, Phase 1, varied basedon the duration of secondary processes (see Table 2.1 for total experimentdurations). In other words, experiments with longer durations of secondaryprocesses resulted in a longer total experiment duration.A summary of the complete sequence of floods run for two of the experi-ments is shown in Figure 2.5. In this comparison of Experiments 1 and 3, inorder to deliver the same amount of sediment to the fan, Experiment 3 lastsa total of 13 hrs 25 mins, while Experiment 1 lasts only 5 hrs 30 mins. Thelongest experiment, Experiment 4, lasted for a total of 24 hrs 5 mins. For ex-periments requiring over eight hours of run time, the experiment was pausedby halting flow, sediment feed and data collection. Prior to recommencingthe experiment, the fan was wetted under a flow of 5-10 ml/s to preventinfiltration of flow into the fan during the experiment6. Upon completion ofan experiment, the fan was drained and the material making up the fan wasmanually removed from the stream table and dried. The stream table wasthen dried using a fan and vacuumed before beginning a new experiment.Preliminary experiments sampled a range of secondary process discharges.Ultimately a discharge equal to 50% of the primary process discharge wasused, as it reflected the minimum discharge at which sediment transport ofbed material was observed on the fan surface. This discharge ratio is similarto those used in other fan-delta and river plume experiments (Chatanan-tavet and Lamb, 2014; Piliouras et al., 2017; Miller et al., 2019)7. The ratioof primary to secondary process inputs for the experiments described hereinwas, in part, based on these experiments.The model was scaled to represent Three Sisters Creek which producesdebris floods. For these experiments, primary process inputs were selected toreflect a debris-flood type event, based on a typical sediment concentration of10% from Figure 1.2. Using the experimental length scale, the primary pro-cess discharge of 100 ml s−1 corresponds to a prototype value of 19 m3 s−1.Flood discharge was run for periods of five minutes for each flood event;corresponding to a prototype time of just under one hour based on the6Due to the porosity of the experimental fan material, flows of 5-10 ml/s resulted insub-surface flow allowing the fan material to be wetted without alteration to surficial fanmorphology.7Discharge was halved and sediment feed was turned off during inter-flood periods inthe experiments of Miller et al. (2019). The experiments of Piliouras et al. (2017) used alow flow discharge equal to 40% of flood discharge with no sediment input. Chatanantavetand Lamb (2014) used a low flow of approximately half of high flow discharge and halvedthe sediment feed rate during low flow periods.23Primary Processes Secondary ProcessesExperiment Discharge Sed. Feed Duration Discharge Sed. Feed Duration Total DurationNumber (ml/s) (g/s) (mins) (ml/s) (g/s) (mins) (hours)0 100 10 120 0 0 0 21 100 10 5 50 0 5 42 100 10 5 50 0 10 63 100 10 5 50 0 20 104 100 10 5 50 0 40 18Table 2.1: Summary of experimental inputs for fan formation (Phase 1)Flood Discharge Sed. Feed Duration No. ofName (ml/s) (g/s) (mins) RepeatsA 100 10 5 3B 150 15 5 3C 150 20 5 3Table 2.2: Summary of experimental inputs for fan flooding (Phase 2)240 2 4 6 8 10 12 14Time (hrs)Sediment feed (g/s)0101520Sec. proc. (50 ml/s)Flood A (100 ml/s)Flood B (150 ml/s)Flood C (150 ml/s)Exp 1Exp 3Figure 2.5: An example of the flood sequence for two complete experiments, including Phase 1: fan formation andPhase 2: fan flooding. As per Table 2.1, Experiment 1 has 5 minute periods of secondary processes while Experiment3 has 20 minute periods of secondary processes. The dashed grey and black lines show the transition from Phase 1to Phase 2 for Experiments 1 and 3, respectively.25experimental length scale and Froude-similarity criteria. The return periodof the primary process event was 80 years based on estimated peak dischargesfor Three Sisters Creek (BGC Engineering Inc., 2020). This corresponds toa scaled prototype discharge of approximately 19 m3 s−1. For comparison,the secondary process discharge corresponds to a return period of approxi-mately 35 years, and a prototype discharge of approximately 9 m3 s−1 (BGCEngineering Inc., 2020). Although the return period of the secondary pro-cesses indicates they are rare themselves, the selected discharge is thoughtto represent the the suite of events that may occur between debris floods.The debris floods generated throughout these experiments most closelyresemble Type 1 and 2 debris floods from Church and Jakob (2020). Theevents generated substantial aggradation on the fan surface with smallerareas of degradation. The experimental sediment concentration for primaryprocesses was somewhere between those listed for Types 1 and 2. The pri-mary process return period corresponded most closely to the ranges listedfor Type 2 debris floods (Table 1.1). Secondary process discharges may beconsidered clear-water flood events, occurring in the absence of the sedimentinputs required to generate a Type 1 or 2 debris flood.It should be noted that throughout this thesis, the terms flood and pri-mary process may be used interchangeably. In addition, secondary processesmay be described as an inter-flood period – referring to the suite of flows afan may experience between debris flood events. When referencing locationson the experimental fans, the fan apex is considered to be at end of the nar-rowed inlet. The upper and lower fan are proximal and distal to the inlet,respectively. The left and right sides of the fan refer to the perspective ofan observer looking downstream from the inlet.2.3 Data Collection and AnalysisFan topography and flow patterns were monitored using an adaptation ofStructure from Motion (SfM) photogrammetry. SfM has been used for a va-riety of geoscientific approaches, and has recently seen use in physical models(Morgan et al., 2017; Leduc et al., 2019). Photographic data were collectedusing nine digital single-lense reflex (DSLR) cameras positioned over theexperimental setup (Figure 2.2). Eight of the cameras were positioned atequally spaced intervals around the perimeter of the stream table, and theninth camera was mounted face down above the experiment. The camerascollected synchronous images of the experimental fan at one minute inter-vals. To reduce data quantities for the longer experiments, Experiments 326and 4, were processed at five minute intervals instead of one minute through-out Phase 1. For Phase 2, all four experiments were processed at one minuteintervals to allowed for detailed analysis of flood impacts. The following dataprocessing and analysis steps were completed using code generously suppliedby Anya Leenman.The resulting images were georeferenced to a local coordinate system ateach time step using eight ground control points (GCPs) on the stream tablewalls. The images were then processed in AgiSoft Photoscan (AgiSoft, 2018)to produce point clouds (∼ 28 points per cm2) and orthomosaics (1 mmresolution). The topographic point clouds were used to generate digital el-evation models (DEMs). In order to generate DEMs with 1 mm resolution,topographic point clouds were interpolated using a k-nearest neighbours ap-proach (number of neighbours = 2), combined with inverse distance weight-ing (power = 2). DEMs were cropped to 1 cm from the edges of the table toremove any edge effects. The DEM processing and analysis was completedin R (R Core Team, 2019) using functions from the lidR package (Rousseland Auty, 2020).Using functions from the raster package (Hijmans et al., 2020), the initial(t = 0) DEM was subtracted from each subsequent DEM. This produced asurface of elevation change relative to the initial, empty table. To determinethe extent of the fan at each time step, the output was thresholded at 6 mm.With the largest grains in the experiment ranging between 5.8 and 8 mm,this threshold was used to differentiate between portions of the fan tablewith, and without, sediment buildup between the timestep of interest andt = 0. Cells with > 6 mm of elevation increase were assigned a value of 1,while those with < 6 mm of increase were assigned a value of 0, to producea map of the fan area. An error threshold of 2 mm was used for topographicchange detection8. Previous work by Anya Leenman indicates that the 90%confidence interval for elevation values varied by less than + 1.3 mm, -1.2 mm within a 20 minute period (Leenman and Eaton, 2020).The orthomosaics generated in AgiSoft Photoscan were used to generatemaps of flow distribution over the fan (i.e. the location of flow/channels onthe fan surface). The fan channels were then picked out from the ortho-mosaics based on their colour. First, each orthomosaic was masked to thecorresponding map of fan area (described above). Because the water in theexperiment was dyed blue, flow had high reflectance in the blue and greenbands, and low reflectance in the red band. Consequently, a colour index8This vertical error threshold is not to be confused with the horizontal resolution ofthe DEM grid which is 1 mm.27was developed to delineate channels. The index for each cell was calculatedas:colour index =blue+ green− redblue+ green+ red(2.7)For each cell, the colour index was normalised by the sum of all blue,green and red reflectance, to account for spatial variations in lighting. Foreach image, a threshold was set at 5% above the mean colour index for thewhole image. This meant the threshold changed depending on whether theimage as a whole was more or less “blue-green”. This was important, as theconcentration of blue dye was not held constant between experiments, andtherefore a single threshold could not be used throughout. Values greaterthan the threshold were assigned a value of 1, and those less than or equalto the threshold were assigned a value of 0, resulting in a binary map ofchannel vs non-channel locations. There was some noise, so patches smallerthan 10 cm2 were removed.The initial flow maps did not have smooth channel boundaries. Conse-quently, the flow maps were smoothed with a 7× 7 cell majority filter 9. Inaddition to this, for some of the subsequent analyses, channels that were notconnected to the channel network were removed and both sets of flow mapswere smoothed with the 7×7 majority filter. Subsequent analyses describedherein used the map with disconnected (seepage) channels removed as theinput dataset.Fan radius and gradient were calculated for 88 profiles from apex to toe,at intervals of ∼ 1 degree; profiles at the table walls were excluded. For eachprofile, fan radius from the fan area map was calculated. To calculate fangradient, elevations were extracted from the DEM at 1 mm intervals alongeach profile. Gradient was then calculated as the slope of a linear regressionbetween x and y coordinates along the profile. The results of these stepswere DEMs, colour orthomosaics, and binary channel maps (smoothed andunsmoothed). An example of each of these data types is shown in Figure2.6. These outputs were used in subsequent analyses to characterize fan be-haviour and morphology. Where additional data manipulation or processingwere required, the steps have been detailed in the following sections.9The majority filter uses the focal function within the raster package in R (Hijmanset al., 2020). The function uses a moving window of set dimensions around the cell inquestion. In the case of this analysis, a 7 cell by 7 cell moving window with equal cellweighting was used. The mean value of the cells within this moving window was thenapplied to the cell in question.28Figure 2.6: An example of the three data types used in subsequent analyses(a) shows a smoothed DEM masked to the fan area, (b) shows an orthomosaicof the fan surface, and (c) shows a smoothed binary channel map, where whitepixels indicate the fan channel locations. Each of these data types were takenfrom Experiment 3 at t = 10.5 hours.2.3.1 Channel EntrenchmentThe degree of channel entrenchment, or channel incision depth, was mea-sured over Phase 2 – the fan flooding phase following fan formation – ofthe experiments. The analysis was limited to Phase 2 in part to reduce the29data quantity, and in part to ensure that data was available at one minuteintervals for all four experiments. To determine the incision depth of thechannel, the DEM and smoothed channel maps were used. Measurementsof incision were taken along a cross-section at a specified distance of 0.5 mfrom the fan apex. The cross-sections were taken at this location to reducethe effects of temporary incision below the fan apex. In addition, 0.5 m fromthe fan apex was generally located above the fan intersection point.Once the cross-section elevation values had been extracted from theDEM, spurious data points were removed from the edges of the cross-sectionwhere the fan abutted the stream table walls. Spurious data were identifiedas sudden (i.e. near vertical) increases in elevation occurring adjacent to thestream table walls. A smoothing filter was applied to the cross-sections toreduce noise in the data. Finally, the binary channel maps were used todetermine the position of the channels along the cross-sections. An exampleof a smoothed cross-section with channels overlain is shown in Figure 2.7.Figure 2.7: Cross-section of an experimental fan 0.5 m downstream of thefan apex, with x = 0 at the left edge of the fan. Distance along the fansurface reflects the number of points in the smoothed data set and not actualdistance measurements. Grey values represent dry portions of the fan, whileblue values reflect fan channels. Elevations are recorded in meters below thestream table walls, resulting in negative values for fan elevation. The left andright banks and the channel thalweg are indicated. These cross-section datawere captured at t = 18 h 02 m during Experiment 4.30The edge of each channel was marked as either a left bank or a right bank,and the minimum channel elevation was recorded. The bank elevations weremeasured by averaging over 10 points from each bank. Incision was thenmeasured as the difference in elevation between the bank elevations andthe channel ‘thalweg’, i.e. the minimum in-channel elevation. The incisiondepth was calculated for each of the channels in a given cross section, andthe maximum value was used to reflect incision for each time step. Themaximum incision value was assumed to reflect incision in the primary fanchannel.2.3.2 Avulsion AnalysisFor the manual avulsion analysis, channel patterns were observed through-out the nine flood events occurring in Phase 2. For each flood event, asequence of six images taken at one minute intervals were analysed. Five ofthe images captured the flood sequence and the sixth image captured theconditions on the fan in the minute prior to the onset of flooding. The sixphotos representing each of the nine flood periods for the four experimentsresulted in a total of 216 photos being manually inspected to identify avul-sions. Orthomosaics from the same time steps were used to determine thenumber of channels present on the fan and identify avulsion events. Theminute-to-minute DEMs of Difference (DoDs) were overlain on the ortho-mosaics to determine where incremental erosion and deposition occurred onthe fan surface. These images were used to characterise the types of avulsionand triggers leading to avulsion.The number of channels on the fan surface was characterized at approx-imately 0.25 m from the fan apex. The number of channels at this locationwas used a proxy for avulsion frequency. Avulsions were characterized bychannel bifurcations – the separation of channelized flow into two or morechannels – and rapid changes to channel position. A location 0.25 m fromthe fan apex was determined to be far enough from the fan apex that chan-nel bifurcation could be observed. In addition, flow on the lower portionof the fan tended to disperse resulting in a number of undifferentiated shal-low channels. The location selected for channel identification was both farenough from the fan apex for distinct channels to be observed, and abovethe typical channel intersection point. This resulted in more clearly definedchannels and allowed for uncomplicated channel characterization. In caseswhere a primary channel carried most (approximately > 70%) of the flow,and a single secondary channel carried the remainder of flow, the number ofchannels was characterized as 1.5 instead of rounding.31An automated avulsion analysis was used to validate the results of themanual analysis. For the automated avulsion analysis, the binary channelmaps described in Chapter 2 were used to characterize avulsion frequencyover Phases 1 and 2. To identify instances of avulsion, successive channelmaps were compared (labelled t1 and t2). Channel map comparisons wereused to determine the area of new flow (channel present in t2 and not t1) andthe area abandoned by the flow (channel present in t1 and not t2). Thesevalues were then normalized by fan area in order to allow for comparisonbetween experiments with fans of differing dimensions. The normalizedvalues were used to extract avulsions, defined as new flow area in excess ofa specified threshold. The selection of the threshold and the results of theseanalyses are detailed in Chapter 5.32Chapter 3Fan MorphologyAs described in Chapter 2 the four experiments used what were referredto as primary and secondary process inputs. The only difference betweenthe experiments was the duration of the secondary process intervals. Thesecondary process durations were 5, 10, 20, and 40 minutes for Experiments1, 2, 3, and 4, respectively (Table 2.1). In other words, Experiment 1 had theshortest secondary process durations, while Experiment 4 had the longestsecondary process durations. In this chapter, I examine the importance ofsecondary process duration in controlling overall fan morphology. The focusof this chapter is the fan evolution stage of the experiments, Phase 1.3.1 Fan GradientThe gradient of an alluvial fan is determined by sediment grain size, deposi-tional processes, and water discharge (Clarke, 2015). Fan gradient dictatesthe capacity of the fan to transport sediment; in other words, fan gradi-ent is inversely related to the efficiency of the sediment transport system(Bowman, 2019). The fans generated in each of the four experiments werecompared on the basis of mean fan gradient. Figure 3.1 shows the meangradient for the four experiments plotted over time. In all four experiments,fan gradient was initially variable before achieving a dynamic equilibrium.Following this initial decrease in gradient, it was clear that mean fan gradi-ent both decreased over time and was greatest for Experiment 1 (approx. 0.1m m−1) and least for Experiment 4 (approx. 0.06 m m−1). In other words,fan gradient achieved a lower equilibrium value with longer durations ofsecondary process action.In addition, Figure 3.1 indicates that mean fan gradient is closely tiedto flood and inter-flood periods. A sawtooth pattern was visible in themean fan gradient for each of the four experiments. The peaks (i.e. highergradient periods) in this pattern correspond approximately to flood periodswhere sediment was actively being added to the fan, while the lows (i.e.lower gradient periods) of the pattern correspond more closely to inter-floodperiods of reworking. Although the sawtooth pattern was visible in all four331 2 3 4 50.060.100.14Experiment 12 4 6 80.060.100.14Experiment 22 4 6 8 10 120.060.100.14Experiment 35 10 15 200.060.100.14Experiment 4Mean fan gradient (m/m)Time (hrs)Figure 3.1: Mean fan gradient over time for each of the four experiments. The dashed black lines show the approximatepoint of transition from Phase 1 to Phase 2. The grey polygons represent flood periods.34experiments, the pattern was most regular and most consistently linked withflood periods in Experiment 4. This points to the importance of secondaryprocess duration as an allogenic (i.e. external) forcing on fan morphology.Figure 3.1 shows that the total duration of the four experiments varieswidely, from 5.5 hours for Experiment 1 to approximately 24 hours for Ex-periment 4. To better compare fan morphology across the different experi-ments, fan gradient was plotted over normalized time, t∗ (Figure 3.2). Foreach experiment, time was divided by the total duration of the experimentgiving normalized time, which reflects a percentage of the total experimentduration (i.e. 0.5 = 50% of total experiment duration). The use of nor-malized time facilitated comparison between Phases 1 and 2 of the variousexperiments, and subsequent plots of fan area (Figure 3.4) and fan wet frac-tion (Figure 4.1) were also plotted using normalized time.Figure 3.2 compares the four experiments on the basis of normalizedtime. Fan gradient remained generally between 0.06 and 0.12 m m−1 forall four experiments, and fan gradient decreased in the initial stages of fanformation before asymptotically approaching a dynamic equilibrium. Fangradient measurements taken in the first 20% of the experiment duration(t∗ < 0.2) show higher gradients. As material was deposited at the fan apexnear the beginning of the experiments the mean fan gradient was high. Itis only as material was transported down-fan through time that fan gradi-ents begin to decrease and stabilize after t∗ > 0.2. The higher variability ingradient measurements for t∗ < 0.2 is likely a result of increased measure-ment error when the fan was very small, i.e. at or near the 2 mm thresholddescribed in Section 2.Experiment 1 showed a decrease in gradient at approximately t∗ = 0.58(Point A Figure 3.2). This decrease is the result of a blockage in the sed-iment feeder that was recorded in the experimental notes, and does notreflect an autogenic, i.e. internal, fan process. The blockage lasted for ap-proximately 5 minutes (the duration of a single flood cycle) before beingcorrected. Although the reduction in sediment feed at this stage of the ex-periment was unintentional, it illustrates the sensitivity of the experimentalfans to changes in inputs, even over short time periods. In addition, thefan gradient slowly climbed back to levels equal to those recorded beforethe blockage. This shows the resiliency of the fan morphology to short termchanges in inputs, and highlights the overall importance of secondary processduration in dictating the fan structure.While the transition from Phase 1 to Phase 2 (dashed black line in Fig-ure 3.2) does not impact the mean gradient for Experiments 3 and 4, thereis a notable decrease in mean gradient for Experiments 1 and 2. Point B35Figure 3.2: Mean fan gradient over normalized time for each of the four ex-periments. The dashed black line shows the approximate point of transitionfrom Phase 1, fan formation, to Phase 2, fan flooding.on Figure 3.2 indicates the decrease in gradient corresponding with Phase 2flooding for Experiment 1. This decrease occurs precisely at the onset ofPhase 2 and may be a related to the recommencement of the experiment atthis point. The mean gradient for Experiment 1 rebounds later in Phase 2,but does not reach the typical gradients observed in Phase 1. For Experi-ment 2, a decrease in gradient occurs at Point C, after approximately 25%of Phase 2 had elapsed. Again, an increase in mean gradient is observed forExperiment 2, with values similar to those seen in Phase 1 re-obtained nearthe end of Phase 2.3.1.1 Fan Gradient by AzimuthIn my experiments, fan gradient – measured from the fan apex to the fantoe – was measured over an 88 degree range from the left flank of the fanto its right flank10. Previous work by Hooke and Rohrer (1979) found thatalluvial fan gradient varied by azimuth. In both experimental and naturalfans, fan gradient was steepest on the fan flanks and gentlest along the fanaxis. In their experiments, the fan axis was defined as the orientation of the10Fan gradient was calculated for 88 profiles from apex to toe, at intervals of ∼ 1degree; profiles at the table walls were excluded. Gradients measured along the left andright fan flanks were at azimuths of 1 and 88 degrees, respectively, and a measurementalong the fan axis reflected an azimuth of 45 degrees.36primary source channel above the fan apex.For each of the 88 fan profiles along which fan gradient was calculatedfor these experiments, the gradient was averaged over the duration of theexperiment. These time averaged values allowed for comparison of gradientsat a given azimuth across the four experimental fans. The mean valueof gradient for each of the profiles is shown for the four experiments inFigure 3.3. Here profile azimuth, or orientation, was measured startingfrom one degrees at the left side of the fan to 88 degrees along the right sideof the fan. The figure shows that the results of these experiments are inagreement with the work of Hooke and Rohrer (1979). For each of the fourexperiments, fan gradient was highest near the flanks of the fan and gentlestalong the fan axis, resulting in a concave gradient profile. The concavity ofthe profile appears to be most exaggerated for Experiments 3 and 4.0 20 40 60 800.060.080.100.12Profile orientation (degrees)Mean fan gradient (m/m)Right flankLeft flank AxisExp 1Exp 2Exp 3Exp 4Figure 3.3: Mean gradient along each of the fan profiles. Profile orientationin degrees is measured from the left flank of the fan. Note that some spuriousgradient measurements may exist near the edges of the fan.3.2 Fan AreaFan area increased consistently as sediment was added throughout the ex-periments (Figure 3.4). It is clear that Experiments 3 and 4 had greaterareas than Experiments 1 and 2. In addition, the experiments appear tobe grouped in that the fan areas are very similar for Experiments 1 and372 and for Experiments 3 and 4. This grouping is remarkable in the caseof Experiments 3 and 4 where secondary processes were run for a full 20minutes longer between each flood period in Experiment 4 as compared toExperiment 3.Figure 3.4: Mean fan area over time for each of the four experiments. Tofacilitate comparison between experiments of different durations, time hasbeen normalized to fraction of the total experiment duration. The dashedblack line shows the approximate point of transition from Phase 1 to Phase 2.A slight uptick in fan area is visible for Experiment 1 around t∗ = 0.58(Point A Figure 3.4). This may be related to the aforementioned sedimentblockage. However, the impact on fan area appears to be less severe thanthat on fan gradient. There is a clear increase in fan area for Experiment 1starting in Phase 2 (Point B Figure 3.4). Again, this is likely related tothe recommencement of the experiment at this point. There is a slightincrease in fan area for Experiment 2 in Phase 2; however, the change isnot as apparent and does not occur immediately, but after a delay (Point CFigure 3.4). As with fan gradient, the timing of this change to fan areaoccurs at the onset of the higher magnitude Phase 2 debris floods. Thesefloods likely achieved greater sediment mobility, thereby lowering the fangradient and extending the fan boundary.The increase in fan area for Experiment 2 which occurs at approx.t∗ = 0.7 is related to the fan geometry. Prior to the onset of floodingat this point, the fan channels were bifurcated at the apex and sedimenthad been deposited near the fan flanks, with little sediment deposited atthe fan margin along the fan axis. The flood event which occurred at ap-38prox. t∗ = 0.7 resulted in a centralized channel which rapidly transportedsediment along the fan axis to the margin. This quickly filled in the areawhich had previously been devoid of sediment and resulted in a marked in-crease in fan area. It is unclear what caused this unique fan geometry; itis assumed to be a result of the stochastic nature of channel position andsediment deposition on fans.3.3 DiscussionThe differences in secondary process duration across the four experimentsresulted in clear changes to fan gradient and area. In comparing Experi-ments 1 through 4 using normalized time, the following broad morphologicaldifferences are apparent:1. The gradient of the fan generally decreased with increasing secondaryprocess duration i.e. fan gradient was greatest in Experiment 1 andleast in Experiment 4 (Figure 3.2).2. The area of the fan generally increased with increasing secondary pro-cess duration i.e. the area of the fan in was greatest in Experiment 4and least in Experiment 1 (Figure 3.4).These results corroborate previous studies. It has been known sincethe earliest days of alluvial fan research that fan gradient increases withincreased sediment concentration, and decreases with increasing discharge(Bull, 1977; Hooke and Rohrer, 1979; French, 1987). With the same amountof sediment input to the four fans, the area of the fans in Experiments 3and 4 was approximately 12% greater, and the gradient 25% gentler than forExperiments 1 and 2. The grouping of Experiments 1 and 2 and Experiments3 and 4 is especially notable in the fan area data. The grouping of theexperiments may indicate that a threshold exists between Experiments 2and 3. Further experiments with secondary process durations between 10and 20 minutes would be needed to evaluate the presence of a threshold.These fan morphologies are resilient to allogenic forcings, as evidencedby the impacts of the sediment blockage in Experiment 1 at Point A (Fig-ures 3.2 and 3.4). While fan gradient and area were initially impacted bythe blockage, both returned to their pre-blockage levels over a period of ap-proximately 40 minutes, or four flood cycles. Experiment 1 was repeated toisolate the impact of the sediment blockage. The results, referred to as Ex-periment 1B, are shown in Appendix A. The results did not show a decrease39in gradient or an increase in area similar to those identified at Point A inFigures 3.2 and 3.4, suggesting that changes to gradient and area startingat approximately t∗ = 0.58 in Experiment 1 were most likely related to thesediment blockage, and not to other autogenic or allogenic forcings. In ad-dition, with the exception of the sediment blockage period, the fan gradientand area between Experiment 1 and Experiment 1B were similar through-out the experimental duration. This suggests that the gradients and areasachieved during these experiments are repeatable under equivalent inputconditions.The decrease in fan gradient observed at the onset of Phase 2 for Ex-periment 1 is thought to be related to recommencement of the experimentat this point. The first flood, Flood A, run during Phase 2 is equivalent tothe primary processes used throughout Phase 1 (Table 2.1 and 2.2). There-fore, the disruption of the dynamic equilibrium achieved during Phase 1 isthought to be a result of under-wetting of the fan prior to recommencing theexperiment. A partially wetted fan is likely to experience greater sedimentmobility during flooding and may explain the sudden decrease in gradientseen at the onset of Phase 2 for Experiment 1. In addition, no decrease ingradient was seen at the onset of Phase 2 for Experiment 1B (Appendix A),thereby lending support to the idea that the early decrease in gradient forExperiment 1 was related to the recommencement of flow on a drier fan.The decrease in fan gradient occurring later in Phase 2 for Experi-ments 1B and 2 may be attributed to the onset of larger magnitude debris-flood events (Floods B and C). This flood sequence was likely able to achievegreater sediment mobility by transporting sediment from the upper reachesof the fan to the lower reaches, thereby lowering the fan gradient. That Ex-periments 3 and 4 were not impacted by these debris-flood events points tothe resilience of fans with longer durations of secondary processes to changesin input conditions. The greater area and gentler gradient of fans formedunder extended secondary process action appear to exhibit a higher degreeof stability under changing flood conditions. Indeed, Schumm et al. (1987)found that fan morphology was an important control on flow behaviour.Thus, the fan morphologies formed during Phase 1 may determine the flowcharacteristics in Phase 2.Fan Gradient by AzimuthThe mean gradients by azimuth in Figure 3.3 show a clear trend of increasedgradient near the fan edges, and decreased gradient proximal to the fanaxis. However, the results do not follow Hooke and Rohrer’s theory that40increased fan curvature would be expected for steeper fans. Here, increasedfan curvature relates to the difference in gradient between the fan flanks andthe fan axis. Figure 3.3 indicates that curvature is greatest for Experiments3 and 4, which have gentler mean fan gradients than Experiments 1 and2. It should be noted that comparisons between Hooke and Rohrer’s andmy experiments may be limited as Hooke and Rohrer used fans with a 180degree extent, as compared to the 90 degree fan extent in my experiments.For my experiments, the differences in fan gradient by azimuth are thoughtto be a result of variation in typical flow paths under different sedimentconcentrations.Characteristic fan channel flow paths are discussed in more detail inChapter 4, but in general, fan channels were diverted towards the edgesof the fan at the onset of flooding, and gradually re-centralized over thecourse of secondary process action. Re-centralization and straightening offan channels increase channel efficiency (Pacheco-Ceballos, 1984; Graf andBlanckaert, 2002). Longer durations of secondary processes allowed for thecreation of a more efficient, straighter channel path. In turn, the efficienciesof these centralized channels allowed for the transport of additional sed-iment, thereby reducing fan gradient along the axis and leaving gradientsalong the fan flanks unaltered. In other words, primary processes dominantlyacted along the fan flanks, depositing sediment, while secondary processesdominantly acted along the fan axis, eroding sediment. This centralizationof flow through secondary processes is thought to be the driver of increasedcurvature in the Experiment 3 and 4 profiles (Figure 3.3).41Chapter 4Channel BehaviourTypical channel behaviour was assessed on each of the four experimentalfans. First, the wet fraction of the fan and characteristic channel patternswere assessed using the smoothed binary channel maps described in Chap-ter 2. Then, fan channel incision depths were examined using high-resolutiontopographic data from the DEMs.4.1 Fan Wet FractionThe wet area of the fan was measured from the binary channel maps de-scribed in Chapter 2, which indicate the location of water-bearing channelson the fan surface. The wet area data were normalized by fan area to createthe wet fraction, thereby accounting for the different fan dimensions acrossexperiments. The wet fraction of the fan was plotted for Experiments 1through 4 using data from the smoothed binary channel maps. Figure 4.1ashows the wet fraction of the fans for each of the four experiments plottedover normalized time (t∗). The trend lines indicate that the wet fractiondecreased over time for all four experiments. Experiment 4 had a slightlylower wet fraction than the other experiments. However, given the noise inthe data sets, the trend lines rely on a weak correlation between t∗ and wetfraction; the R2 values for the four trend lines range from 0.22 to 0.39.To directly compare the experiments, the wet fractions were separated,or clustered, into four groups; one for each experiment. These clusters werethen plotted as a box plot (Figure 4.1b). A one-way ANOVA test showedthat there was a significant difference between the group means for at leastone of the experiments11. A Tukey multiple pairwise-comparison12 indicatedthat Experiment 4 was significantly different from each of the other threeexperiments and that the remaining three experiments were not significantly11For this ANOVA test, the value of the test statistic and the degrees of freedom wereequal to 9.86 and 3, respectively.12Tukey’s multiple pairwise-comparisons determine which means differ significantlyfrom the rest among a set of means. It is used when comparing more than two groups asit compares between each set of means while adjusting for the effects of multiple testing.420.0 0.2 0.4 0.6 0.8 1.00.00.10.20.30.4Normalized time (t*)Wet fraction (% of fan area)Exp 1 Exp 2 Exp 3 Exp 4(a)l llllllExp 1 Exp 2 Exp 3 Exp 40.150.200.250.300.35Wet fraction (% of fan area)(b)Figure 4.1: (a) Wet fraction of the fan by normalized time t∗, with trend linesfor each experiment overlain. The dashed black line indicates the approximatetransition from Phase 1 to Phase 2. (b) Box plot of wet fraction over the entireexperiment duration for each of the four experiments. The boxes delineate theinter-quartile range, while the whiskers reflect the minimum and maximumvalues excluding outliers; outliers are represented as open circles.different from each other. The box plot shows that the median wet fractionwas lowest for Experiment 4, and the spread of wet fraction data was greatestfor Experiment 4. While statistical differences exist between Experiment 443and the other experiments, no broad conclusions may be drawn about fanwet fraction from these data. It is believed that the influence of decreasingwet fraction over time may obscure any inter-experimental relationships.The decrease in wet fraction is in part an artifact of increasing fan areawith time i.e. the same amount of water routed over a larger fan results ina decreased wet fraction.4.1.1 Phase 2 Wet FractionTo minimize the effects of decreasing wet fraction over experimental time,the wet fraction was assessed over Phase 2 of the experiments. The wet frac-tion of the fan is shown in relation to flood events over Phase 2 (Figure 4.2).Here, debris flood events, or primary processes, are shown as grey bars,while inter-flood periods, or secondary processes, are shown with a whitebackground. It is clear that wet fraction increases during flood periods anddecreases during inter-flood periods for all four of the experiments. For eachof the experiments, the maximum wet fraction over Phase 2 is approx. 0.3,or 30% of the total fan area. The minimum wet fraction is approx. 20% ofthe total fan area for Experiments 1 and 2. For Experiments 3 and 4, theminimum wet fraction is as low as 15% of the total fan area. For each ofthe four experiments wet fraction data were taken at one-minute intervals;differences in data density are a result of the varied experimental durations.The initial decrease in fan wet fraction following flooding is attributedto a decrease in discharge as the input conditions change from primary tosecondary processes. Any decrease in fan wet fraction in excess of this initialchange may then be attributed to flow channelization events. It should benoted that the sharp decrease in wet fraction at the beginning of the thirdinter-flood period – circled with a dashed black line – in Experiment 3 doesnot reflect a channelization event. The photograph at this time step captureda partially wetted fan resulting in an erroneously small wet fraction.While all experiments show a decrease in wet fraction following flood-ing, not all experiments show evidence of channelization; Experiment 1 doesnot exhibit channelization characteristics. Experiment 2 shows evidence ofchannelization near the end of the fourth, fifth, and sixth inter-flood periods.Experiment 3 shows evidence of channelization in the third, seventh, andeighth inter-flood periods. For Experiment 4, evidence of flow channeliza-tion is observed in each inter-flood period and in the fourth and fifth inter-flood periods, multiple potential channelization events may be observed. Inaddition, there is a clear downward trend in wet fraction throughout allinter-flood periods for Experiment 4 that is not consistently observed for44Figure 4.2: Fan wet fraction over Phase 2 for each of the four experiments. Grey polygons represent flood periods.The vertical dashed black lines represents the transition from Phase 1 to Phase 2. Potential channelization eventsare indicated by orange arrows. The dashed circle highlights the false channelization event.45any of the other experiments. Each of the potential channelization eventslisted above have been indicated with orange arrows on Figure 4.2.Many of the channelization events seen in Figure 4.2 occur near the end ofthe inter-flood period. For Experiments 2 and 3, channelization events occurdirectly prior to the following flood period. For Experiment 4, decreases inwet fraction are observed as early as half-way through the inter-flood period.Clearly the increased duration of secondary processes in Experiment 4 leadsto continued channelization over the inter-flood period. Throughout thefour experiments, flow channelization was observed to occur more frequentlyduring experiments with longer secondary process durations. These resultsare consistent with visual observations of the experiments.For Experiment 4, a single channel was formed over the course of theinter-flood periods through which the entirety of the discharge was routed.While channelization was occasionally observed during the inter-flood pe-riods for Experiments 2 and 3, it was only Experiment 4 that routinelyexperienced flow channelization resulting in the formation of a single fanchannel. It is postulated that the minimum wet fraction observed for Ex-periment 4 (approx. 15%) reflects an absolute minimum value for the givendischarge. Given the single channel geometry, the corresponding flow areais not likely to be decreased further without a reduction in discharge i.e.a single channel is assumed to represent a minimum wet fraction for thesefans.To visualize the differences between Phase 2 wet fractions for the fourexperiments, the data were grouped by experiment and separated into floodand pre-flood values. A box plot showing wet fraction prior to flooding andduring flooding is shown for each experiment in Figure 4.3. ‘During flood’values were averaged over the complete five minute flood duration for eachof the nine flood events in Phase 2. ‘Pre-flood’ values were taken from theminute prior to the onset of flooding. Although the during flood wet frac-tions do not differ significantly across the four experiments, there is a visibledifference between the pre-flood wet fractions for the four experiments. Ex-periments 1 and 2 have similar pre-flood wet fractions, clustered around20-25% of the fan area. Meanwhile Experiment 3 has a lower pre-flood wetfraction; closer to 20% of the fan area. Experiment 4 has a pre-flood wetfraction ranging from 15-20% of the fan area.46llllllllll0.100.150.200.250.300.35Wet fraction (% of fan area)Exp 1 Exp 2 Exp 3 Exp 4Pre−flood During floodFigure 4.3: Box plot showing the differences in wet fraction for the pre-floodand flood time-steps for the four experiments. The boxes delineate the inter-quartile range, while the whiskers reflect the minimum and maximum valuesexcluding outliers; outliers are represented as open circles. The wet fractiondata used to generate this plot were taken from Phase 2 only.4.2 Channel PatternPrincipal component analysis (PCA) is a statistical analysis method whichreduces the dimensionality of large datasets while retaining the maximumpossible variance in the dataset. The result is a summary of the dataset madeup of uncorrelated variables, called principal components (Hsieh, 2009).PCA was used to rapidly and objectively characterize temporal changesin the fan channel pattern. This was done using the binary channel mapsdescribed in Chapter 2 showing the locations of channels on the fan sur-face (Figure 4.4). In the case of the channel maps, the rasterPCA package(Leutner et al., 2019) was used to calculate principal components using theprincomp function built into R (R Core Team, 2019). To increase the ef-ficiency of the calculations, the package uses a random sample of pixels(nSamples = 5,000) from the channel maps were used to calculate the PCA,and then predicted for the full raster.Figures 4.5 and 4.6 show a representative example of the PCA results,taken from Experiment 3. The shaded blue and red images are the eigenvec-47Figure 4.4: Example of binary channel maps taken from Experiment 4 at (a)t = 21 h 05 m at the end of a secondary process period and (b) t = 21 h 10m at the onset of flooding (primary processes). White portions of the imageindicate the locations of the fan channels – ‘wet’ areas – while black portionsof the image reflect ‘dry’ areas.tors, which represent the spatial patterns in the data containing the mostvariance. The principal components (PCs) – graphs with blue lines – showthe temporal coefficients which reflect the strength of the eigenvector pat-tern over time. The eigenvalues for each mode are shown in Appendix B. Forthis analysis, the eigenvectors show the typical channel pattern, while theircorresponding PCs indicate the strength of the channel pattern in time. Forthe eigenvectors shown below, blue cells indicate a strong positive signal,while red cells indicate a strong negative signal. When the value of the PCis positive, it indicates that one would expect to find channels at the eigen-vector locations shown in blue. When the PC is negative, one would expectto find channels at the locations shown in red in the eigenvector maps. Es-sentially, together the eigenvectors and PCs indicate the most common fanchannel locations over time for each experiment.In general, the first eigenvector for each of the experiments had positive(blue) values near the fan inlet. This indicates that throughout the exper-iments, flow was present immediately down-fan of the apex. This is unsur-prising, and corresponds well with the results of Zarn and Davies (1994),who found that flow frequency was highest near the fan apex for their ex-periments. For each of the experiments, modes 2 (PC2) and 3 (PC3) showedopposing patterns of channel bifurcation and channel centralization. Thisindicates that two of the most common channel configurations throughoutthese experiments were a single centralized channel and two fan channelsbifurcated near the fan apex. This can be seen in Figure 4.5 where the pos-48Figure 4.5: Raster PCA results for Experiment 3 channel maps showing thefirst four modes (Mode 1 - top left, Mode 2 - top right, Mode 3 - bottom left,and Mode 4 - bottom right) and their principal components. For each of thefour modes, blue and red values correspond to positive and negative signalsfor channel position, respectively. Grey polygons on the PC plots correspondto flood (primary process) periods.itive and negative eigenvector values reverse between modes 2 and 3. Therewas no clear pattern across the experiments for modes with values greaterthan four.In examining the eigenvectors and PCs for Experiment 3 more closely,we see there is a clear temporal signal in the PC (Figure 4.6). This signalcorresponds well with flood and inter-flood periods, shown as grey polygonson the PC graph. The pattern has a strong positive signal (i.e. centralizedchannel) during inter-flood periods and has a strong negative signal (i.e. bi-furcated channel) during flood periods. A similar temporal pattern was alsoobserved for the other experiments, in which fan channels were centralizedduring inter-flood periods and bifurcated during flood periods. This chan-nel pattern was alluded to in Chapter 3, where it was used to explain thesteeper gradients near the edges of the fan (Figure 3.3).49Figure 4.6: Raster PCA results for Mode 2 in Experiment 3. The amplitudeof the PC signal illustrates how strongly the pattern on the right is reflectedon the fan surface at any given point in the experiment. Grey polygons onthe PC plot correspond to flood (primary process) periods. Note the strongtemporal PC signal and its relation to flood periods.4.3 Channel EntrenchmentChannel entrenchment is an indication that stream power (Bull, 1979) hasincreased to the point where discharge capacity exceeds the available sedi-ment load. The increased stream power in entrenched channels results fromincreasing water depth and mean shear stresses. Additional stream powerincreases the transport capacity of the stream, allowing it to move more ma-terial and incise further (Bowman, 2019). This results in a positive feedbackloop following the onset of channel incision. This process may continue un-til the channel gradient is sufficiently lowered to reduce transport capacity,or allogenic forcings disrupt erosive processes. As described in Chapter 1,short term fan entrenchment is attributed to large scale flooding events withgreater sediment transport capacity or as a series of moderate flow eventswith low sediment load (French, 1987).The secondary processes in the experiments described herein reflect flowevents with low sediment load having the capacity to erode the fan surfaceand create an entrenched channel. They represent the suite of events whichmay occur between debris flood – or primary process – events. It was hy-50pothesized that experiments with longer secondary process durations wouldexperience greater channel incision.Using the methodology outlined in Chapter 2, maximum incision depthswere plotted in relation to primary and secondary process periods (Fig-ure 4.7). This methodology involved the combination of the binary channelmaps with the DEMs. The binary channel maps were used to determinethe position of the channel(s) along each DEM cross-section. The incisionvalue was then recorded as the maximum difference in elevation between thechannel banks and the minimum in-channel elevation. In general, maximumincision values occurred during secondary process - or inter-flood - periods,with some exceptions. The measurements of incision were taken at oneminute intervals for all four experiments. Differences in data density are areflection of the varied experimental durations. Data gaps reflect time stepswhere the channel(s) was located near the stream table walls and accuratebank elevations could not be obtained.These results indicate that the fan channels experienced more incision4.0 4.5 5.0 5.50.0000.0040.008Experiment 16.0 6.5 7.0 7.5 8.00.0000.0040.008Experiment 210 11 12 130.0000.0040.008Experiment 317 18 19 20 21 22 23 240.0000.0040.008Experiment 4Elevation difference (m)Time (hrs)Figure 4.7: Maximum values of channel incision measured 0.5 m from fanapex. Measurements were recorded at one minute intervals throughout Phase2. The dashed black line shows the approximate point of transition from Phase1 to Phase 2. The grey polygons represent flood periods.51during Experiment 4 than any other experiment with maximum incisiondepths on the order of 0.01 m, or 1 cm. This aligns with the hypothesisthat experiments with longer secondary process durations would experiencegreater channel incision. However it should be noted that at least one mea-surement of incision depth greater than 0.5 cm was recorded in all fourexperiments. In addition, while the greatest incision values were measuredin Experiment 4, incision did not reach 1 cm in each inter-flood period. Thisdoes not reflect visual observations of the fan channels during experimenta-tion. Based on observation of the experiments in real time, channel incisionin excess of the values shown in Figure 4.7 was observed; in particular atthe end of the secondary process periods for Experiment 4. While nominalvalues of incision were observed for Experiments 1 and 2, deeper and moreextensive incision was observed in Experiments 3 and 4.Figure 4.8 gives a representative photo of observed incision for each ofthe four experiments. The images were taken at the end of a secondaryprocess period, when the fans were each subject to a discharge of 50 ml/s.Flow is progressively more channelized with increasing secondary processduration. In other words, flow in Experiments 3 and 4 is almost entirelyconfined to a single channel while Experiments 1 and 2 show more diluteflow paths. In addition, in Experiment 4 terraces have formed on the banksof the fan channel; flow depth is below bank height. These observations ofchannel behaviour strongly indicate that the incision depths in Figure 4.7are underestimates.Figure 4.8: Photo of characteristic channel incision for (a) Experiment 1, (b)Experiment 2 , (c) Experiment 3, and (d) Experiment 4. Photos were takenat the end of the first secondary process period in Phase 2.524.4 Discussion4.4.1 Fan Wet FractionThe wet fraction data clearly indicate that inter-flood periods for Experi-ment 4 (i.e. longest secondary process duration) are subject to increased andmore consistent channelization events. Although Experiments 2 and 3 showsome evidence of channelization events (Figure 4.2) and decreased pre-floodwet fraction (Figure 4.3), Experiment 4 is an outlier in all respects. Notonly did Experiment 4 experience channelization in each of its eight sec-ondary process periods, but multiple channelization events were observedduring some of these periods. By comparison, Experiments 2 and 3 each ex-perienced only three channelization events. In addition, Experiment 4 hada significantly different pre-flood wet fraction than the other experiments(Figure 4.2).There is no clear evidence from these experiments to indicate a gradual,progressive transition towards increased channelization and decreased wetfraction. The transition in behaviour from Experiment 3 to Experiment 4remains abrupt. Therefore, it is thought that this change in wet fractiondynamics reflects a threshold change. However, at 20-30 minutes into theinter-flood period the unique dynamics of Experiment 4 reveal themselves.Although the scope of this research was limited to the four experimentsdescribed herein, running additional experiments of 25, 30, and 35 minutesecondary process durations would be required to prove or disprove thisthreshold theory.Despite differences in the pre-flood wet fraction, the wet fraction duringflooding was similar across all four experiments (Figure 4.2). This camein spite of evidence for increased channel incision depth with increasingsecondary process duration described in the previous section. Clearly thepre-flood channel incision depth did not determine the degree to which thefan was wetted during subsequent debris flood events. However, it will beseen in Chapter 5 that pre-flood fan channel conditions did have an impacton avulsion behaviour during flooding.4.4.2 Channel PatternWhile the use of PCA allowed for rapid and objective differentiation be-tween channel patterns across flood and inter-flood periods, it should benoted that the first four modes of this analysis accounted for less than 40%of the total variance in the wet binary maps. This indicates that the fanchannel pattern is ultimately chaotic, and cannot be fully predicted using53these results. For this reason, the results of the PCA were not used forfurther analysis. However, the results indicate that for all four experiments,channel bifurcation is most common during flood periods while a central-ized channel is common during inter-flood periods. This typical pattern ofchannel flood behaviour was observed for all four experiments and may ex-plain the regularity of wet fraction changes between primary and secondaryprocess periods (Figure 4.2). In addition, the insights provided by the PCAaided understanding of channel behaviour and informed further analyses.4.4.3 Channel EntrenchmentDespite the visual differences between the channels across the four experi-ments, main channel incision depth was not easily captured using the DEMdata. This was in part due to complex fan flow paths resulting in numerouspaleochannels on the fan surface. Work by Reitz et al. (2010) indicates thatactive channels on alluvial fans are never completely erased and may appearas relict floodplain scars in fan topography. These paleochannels resultedin fan profiles with significant topographic relief outside of the wet portionof the fan (i.e. the current channel). The complex profile of the fan surfaceobscured the topographic signal of the channel banks. Channel banks weretherefore assumed to be adjacent to the wet portions of the fan surface. Thismethod may have resulted in underestimates of incision depth for channelswith bank heights well above water surface (i.e. terraced banks).In addition, the presence of water on the fan may have artificially de-creased channel depth estimates. Previous work on the concepts behindtwo-media photogrammetry indicates that systematic error occurs when el-evations are corrupted by refraction at the air-water interface (Butler et al.,2002). Refraction occurs according to Snell’s law:sin(r)sin(i)=hhA= n (4.1)where i is the angle of incidence of a light ray, r is the angle of the refractedray, h is the actual water depth, hA is the apparent water depth, and n isthe refractive index. The result of this effect is to produce an image withelevations that appear shallower than they are in reality, i.e. hA < h.In order to determine the impacts of Snell’s Law on the experimentsherein, dry DEMs from the end of a secondary process period were comparedto the subsequent wet DEMs for the same experiment. A simple subtractionof the DEMs indicated that error exists primarily within the wet portionsof the fan, with differences in measured depths reaching as much as 1.5 cm54(0.015 m). This means that the measurements recorded in Figure 4.7 mayunder-report channel incision by up to 1.5 cm. The measurement errorbetween the wet and dry DEMs ranged from 0.1 to 1.5 cm. This initialanalysis did not constitute enough data to calculate a reliable estimate ofthe systematic error produced by DEM measurements taken on the wetfan. In addition, these measurements could not be corroborated by manualmeasurements taken at the fan surface during the experiment. In conclusion,while it is assumed that incision in Figure 4.7 is underestimated, not enoughdata exist to reliably account for this measurement error.Future work on this dataset should include an analysis of potential cor-relation between water colour and water depth based on elevation differ-ences observed between wet and dry DEMs. Methods employed in shallowstreams, such as the work of Dietrich (2017), may be impacted by the pres-ence of dye in the water as they rely on a clear view of the channel bed.Future experiments should include draining of the fan surface throughoutexperiments to capture dry DEMs reflecting a complete range of channeldepths and dimensions. Only with a larger dataset can a reliable correctionfactor be applied to estimate channel incision depth.55Chapter 5AvulsionAvulsions are critical for understanding fan evolution and flood hazards sincethey determine the distribution of fan deposits in space and time (de Haaset al., 2018a). The triangular or conical nature of a fan is a result of shiftingchannel position over time. This repeated shifting of the active channel toa new path is referred to as avulsion (Bowman, 2019). The point at whichthe channel shift or bifurcation occurs is referred to as the avulsion node.Alluvial fans are more prone to avulsion than other river systems (Clarke,2015). Despite their ubiquity, definitions of avulsion vary across fan andfluvial literature alike.While channel lateral migration refers to the gradual shifting of channelposition over time, avulsions are characterized by “sudden abandonment”of the channel position (Allen, 1965). Ganti et al. (2016) simply describeavulsions as an abrupt change in river course. In the case of experimentaldebris flow fans, avulsions have been characterized as a predictable cycleof channel plugging, backstepping13, avulsion and channelization (de Haaset al., 2018a). Bryant et al. (1995) describe avulsions on their experimentalfans as the formation of a new channel carrying at least 50% of the dischargefrom the previous channel. However, their experiments involved high sedi-ment concentrations (ranging from 7% to 23%) and avulsions were primarilydriven by channel superelevation resulting from differential deposition, re-sulting in more ‘catastrophic’ avulsions.Following the definitions of Allen (1965) and Ganti et al. (2016), avul-sions have been characterized herein as sudden changes in channel position,as it is these kinds of abrupt channel changes that may increase the poten-tial for flood damage and building impact (French, 1987; Federal EmergencyManagement Agency, 2000; BGC Engineering Inc., 2015). For my experi-ments, a channel was considered to be any continuous wet portion of thefan surface whose source was traceable to the fan apex.13Backstepping is the process by which channels retreat from their previous position,i.e. move up-fan and away from the fan toe, in response to in-channel sediment deposition.The process of progressive backstepping continues until avulsion occurs and a new channelis established.565.1 Manual AnalysisA manual analysis of avulsion frequency was conducted over Phase 2 of thefour experiments. Additional detail on the methods used may be found inChapter 2. The manual analysis was limited to Phase 2 in part to limit thescope of the analysis and in part to compare avulsion characteristics acrossthe different Phase 2 flood events. Avulsions were characterized visuallyat one-minute intervals using the orthomosaics. Avulsions occurring in theupper 10% of alluvial fans – determined based on the fan radius – havebeen termed “apical avulsions” by Bryant et al. (1995) and were used tocharacterize avulsion frequency on their experimental fans. The fans createdin these experiments were larger than those of Bryant et al. (1995), whichreached a maximum radius of 0.8 m. As such, for the experiments describedherein, avulsions were characterized within 0.25 m of the fan apex, i.e. thetop 35 - 50 % of the fan by radius.As described in Chapter 2, a location 0.25 m from the fan apex wasdetermined to be far enough from the fan apex that channel bifurcationcould be observed. In addition, this location was above the typical channelintersection point and resulted in more clearly defined channels, allowingfor more consistent channel characterization. Using this methodology, atotal of 65 avulsions were recorded throughout Phase 2 for all four of theexperiments. The characteristics of avulsions occurring during Phase 2 aresummarized in Table 5.1.The results of the manual analysis indicate that a total of 20 avulsionsoccurred during Experiment 1, while only 12 avulsions occurred during Ex-periment 4. In addition, the time at which the avulsions first occurred wasearliest for Experiment 1 and latest for Experiment 4. In other words, avul-sion occurred both sooner after the onset of flooding and more frequently inexperiments with shorter secondary process duration. Given that the dataused for avulsion characterization were captured at intervals of one-minute,there is some uncertainty associated with avulsion timing. However, theavulsions in Experiment 4 occurred on average 46 seconds later than avul-sions in Experiment 1, which exceeds the margin of error for avulsion timingof ± 30 seconds.The four experiments all had an average of approximately two channelsduring flooding, although the average number of channels for Experiment4 was the lowest at 1.9. The number of fan channels increased as floodingprogressed and in many cases, the number of channels could be used as aproxy for avulsion timing. Prior to the onset of flooding Experiments 1 and2 had an average of 1.7 channels, while Experiments 3 and 4 had an average57Exp.No.Avg. No.of ChannelsAvg. AvulsionTiming (mins)Avg. FanWet FractionAvulsion Type Flood cycle AvulsionCountDep. Ero. Reocc. Unc. A B C1 2.1 2.6 25.9% 13 3 2 2 4 7 9 202 2.1 2.7 26.4% 9 3 1 5 3 7 8 183 2.1 3.1 25.2% 11 0 1 3 4 6 5 154 1.9 3.4 25.4% 9 1 0 2 4 4 4 12Table 5.1: Summary of the manual avulsion assessment completed over Phase 2. The average number of channelsrefers to the average number of channels measured 0.25 m from the fan apex during flooding, as described in Chapter2. Avulsion timing refers to the minute of flooding in which avulsion first occurs, where t = 0 is the onset of floodingor primary processes. Information regarding the wet fraction of the fan was taken from the wet fraction analysisdescribed in the Chapter 4 Section 4.1. For avulsion types ‘Dep.’ refers to depositional avulsions, ‘Ero.’ refers toerosional avulsions, ‘Reocc.’ refers to reoccupation avulsions, and ‘Unc.’ refers to unclassified avulsions. Flood cycleinputs for Phase are summarized in Table 2.2.58of 1.2 and 1.0 channels, respectively. That flow in Experiment 4 was con-sistently confined to a single channel prior to flooding is an indicator ofthe power of secondary processes in determining pre-flood conditions. Thegreatest number of channels observed prior to flooding was 3, and the max-imum number of distinct channels observed during flooding was 4.While avulsions occurred during each of the three flood sequences, theavulsion count was highest for Flood C (Table 5.1) which had the great-est input sediment concentration (∼ 13%). This aligns with previous worksuggesting that avulsion frequency is proportional to sediment concentration(Bryant et al., 1995; Ashworth et al., 2004; Reitz et al., 2010; De Haas et al.,2016). While Experiments 1 and 2 had the greatest number of avulsions dur-ing Flood C, Experiment 3 had the greatest avulsion count during Flood Band Experiment 4’s avulsions were equally distributed across all three floodtypes. Although it is difficult to conclude much from these limited data, itis plausible that longer durations of secondary processes in Experiments 3and 4 countered avulsion tendency under increased sediment concentration.The avulsion type, or trigger, is divided into four categories in Table 5.1.These avulsion types are described in more detail in the following section.5.1.1 Avulsion TypeThe process of avulsion is composed of two steps (Mohrig et al., 2000;de Haas et al., 2018b) involving a setup and/or a trigger phase. In caseswhere bankfull flow is not exceeded, the setup phase involves the accumu-lation of sediment, resulting in blockages due to local sediment deposition,and the trigger phase refers to the short term event causing channel aban-donment - typically flooding (Mohrig et al., 2000). Thus avulsion frequencyhas been shown to be related to sediment flux (Clarke, 2015). Avulsionnode locations may be determined by topographic controls on alluvial fans(Ganti et al., 2016). In particular, a decrease in gradient within a fan chan-nel would reduce shear stresses allowing for the selective deposition of largegrains within the channel. An increase in channel width would result in asimilar decrease in shear stress and subsequent local sediment deposition(Eqn. 1.1).Following this understanding of avulsion mechanisms, the high resolutiontopographic data provided by the DEMs of Difference (DoDs) were used toidentify likely causes of avulsion based on the loci of erosion and depositionon the fan surface. Four broad types of avulsion mechanism were identi-fied based on the DoDs: depositional, erosional, channel re-occupation, andunclassified. A schematic of the three primary avulsion types is shown in59Figure 5.1: Hypothetical channel cross-sections showing the three primarytypes of avulsion: (a) depositional, (b) erosional, and (c) reoccupation. Thetop cross-sections show the initial channel geometry, and the lower cross-sections show the post-avulsion channel geometry. The blue arrows representthe direction of flow following avulsion. The channel geometry is approximateand is not meant to reflect the true geometry of the experimental fan channels.Figure 5.1 and examples of the different avulsion types are shown in Figures5.2 through 5.5.As per Figure 5.1, depositional avulsion was the result of sedimentationin the initial channel, which resulted in bank over-topping causing avulsion.The second avulsion type was the result of erosion of the initial channelbanks, resulting in redirection of subsequent flow towards the site of ero-sion. The third avulsion type occurred when a previous fan channel wasreoccupied following over-topping of the initial channel’s banks. The finalavulsions were unclassified, and may be the result of a combination of theabove mechanisms. These avulsion types are described in more detail, withexamples from the DoDs, below.The first avulsion type involved deposition in the initial channel andmay be referred to as “depositional avulsion” (Figure 5.2). Often the siteof deposition was located precisely at the avulsion node. Although deposi-tion may have occurred elsewhere on the fan, deposition occurring at theavulsion node was generally a continuous patch with a minimum area of 100cm2. The deposition depth was generally less than 2 cm. In other cases,deposition was more widespread at the fan apex and appeared to result inbroad channel instability. Deposition was typically observed in same time60Figure 5.2: Depositional avulsion occurs at t = 22h 33m. Note the in-channeldeposition in the previous time step (t = 22h 32m) and the widespread depo-sition at the fan apex at t = 22h 33m. The red circle indicates the depositionalpatch that is assumed to have caused the avulsion.step as avulsion, or during the time step preceding avulsion. However, depo-sition also occurred at time steps where avulsion was not observed. In thesecases, the deposition often happened on the lower portion of the fan or hada smaller areal extent. Depositional avulsion accounted for 42 avulsions ofthe total 65 avulsions observed throughout Phase 2.For some depositional avulsions, the deposition assumed to trigger avul-sion was observed in the time-step prior to the avulsion occurring. In thecase of the depositional avulsion example shown in Figure 5.2, depositionwas observed both in the time step preceding avulsion and the time stepin which the avulsion occurred. At t = 22h 32m both deposition and ero-sion are observed in the channel near the avulsion node. At t = 22h 33mdeposition is observed near the fan apex. Deposition and erosion occurringdown-fan of the avulsion node are not considered to impact avulsion timing.The second type of avulsion mechanism may be referred to as “erosionalavulsion” (Figure 5.3). In this avulsion type an area of erosion was observedin the DoDs at the head of a newly formed channel. Although the erosiondepth was often less than 2 cm there were cases where erosion reached upto 5 cm. Erosional avulsion was difficult to classify, as in many cases itwas difficult to determine if observed erosion caused the avulsion, or if theerosion commenced following the establishment of the new channel. In thecase of the avulsion shown in Figure 5.3, scattered erosion and depositionare observed near the avulsion node at t = 7h 16m and erosion is observed61Figure 5.3: Erosional avulsion occurs at t = 7h 17m. Erosion occurs on theright side of the channel present at t = 7h 16m, directing flow to the right att = 7h 17m. The red circle indicates the erosional patch that is assumed tohave caused the avulsion.in this same location at t = 7h 17m. It is possible that the depositionoccurring along the left bank at t = 7h 17m helped to push flow to the rightand allow for erosion and occupation of the secondary channel. Erosionalavulsion was a less common avulsion type, accounting for 7 avulsions of thetotal 65 avulsions observed throughout Phase 2 of the four experiments.The third avulsion type involved the reoccupation of paleochannels (Fig-ure 5.4). This avulsion type was applied when a paleochannel was clearlyvisible in the orthomosaic prior to the avulsion and little erosion or depo-sition were required for flow to reoccupy the paleochannel following floodonset. Paleochannels such as these have been referred to as areas with anincreased probability of diversion in the experiments of Hooke and Rohrer(1979). In Figure 5.4 there is a paleochannel visible near the fan axis att = 5h 20m. Although it is difficult to see without the full resolution ofthe orthomosaic, it may be identified primarily by its bank structures andthe dominantly finer material present on its bed. This channel is reoccu-pied at t = 5h 21m. “Reoccupation avulsion” accounts for 4 of the total65 avulsions observed throughout Phase 2. It is possible that reoccupationavulsion occurred more frequently, as its classification relied upon the visualidentification of paleochannels from the orthomosaics. Paleochannels thatwere not wide or deep enough to be visible in the orthomosaics may haveresulted in an unclassified avulsion classification.The final 12 avulsions remain unclassified, as there was no clear topo-62graphic trigger for their occurrence in the DoDs (Figure 5.5). This typeincluded avulsion sequences where both erosion and deposition were ob-served in the vicinity of the avulsion node. This is the case in Figure 5.5,where both erosion and deposition are observed near the fan apex. In otherexamples of unclassified avulsion, little erosion or deposition were observed.Figure 5.4: Channel reoccupation avulsion occurs at t = 5h 21m. A paleochan-nel is faintly visible at t = 5h 20m proximal to the fan axis. This channel isreoccupied at t = 5h 21m. The red dashed lines indicate the approximatelocation of the banks of the paleochannel.Figure 5.5: An avulsion with an unclear cause occurs at t = 12h 34m. Botherosion and deposition are observed at the fan apex.635.2 Automated AnalysisI completed an automated analysis of avulsion to validate the findings of themanual method, and ensure they were not the result of any bias on the partof myself, the observer. The automated analysis was completed over bothPhases 1 and 2 using the binary channel maps and cross-validated with theresults of the manual avulsion assessment. I used the binary channel mapsto determine channel locations through time and map changes to channelpattern. Channel pattern changes in excess of a certain threshold wereclassified as avulsions. The methodology is described in greater detail inChapter 2. Figure 5.6 shows the types of channel pattern changes identifiedby the automated method: new channel area, abandoned channel area andcombined new and abandoned channel area. I determined that time stepswith only abandoned channel area (Figure 5.6b), do not represent fan floodhazards. Therefore, only time steps with new channel area were used in thetotal avulsion count.Figure 5.6: Types of channel pattern change identified using the thresholdmethod: (a) new channel area in t2, (b) abandoned channel area in t2, and(c) a combination of both new and abandoned channel area. The yellow andpurple polygons show the location of the fan channels in the first minute (t1)and second minute (t2), respectively. The darker purple sections representzones of overlap between the t1 and t2 channel locations.64New channel area normalized by fan area was plotted over time for eachof the four experiments. Figure 5.7 shows normalized new channel area withrespect to flood sequences for each of the experiments. The link betweenavulsion events and flood periods is increasingly apparent for experimentswith longer secondary process duration (Experiments 3 and 4). A thresh-old was selected for the four experiments that sought to isolate ‘abnormal’increases in new channel area, i.e. avulsions. From observation of the nor-malized new flow area data a threshold of 0.11, or 11% of fan area wasselected. Using this threshold, the automated method identified 76, 64, 82,and 78 avulsions over the complete duration of Experiments 1, 2, 3, and 4,respectively.While the total number of avulsions identified by the automated analysiswas similar across the four experiments, the avulsion frequency for Experi-ment 4 was much lower than for Experiment 1. The mean inter-event timefor avulsions was 3.6, 5.8, 8.5, and 14.7 minutes for Experiments 1, 2, 3,and 4, respectively. This indicates that increasing secondary process dura-tions decreased the avulsion frequency. To determine the periodicity of theavulsion sequence, the Kim and Jo (2016) burstiness parameter An was ap-plied. The burstiness parameter is used to characterize time series in whichevents occur in rapid succession followed by long periods of inactivity. Anscales from -1 for periodic time series to 0 for random time series and 1 for‘extremely bursty’ time series. The burstiness parameter for the four exper-iments ranged from -0.25 to 0.1514, indicating that the avulsion frequencyfor the experiments was aperiodic, or random.The results of the automated method were then calibrated against theresults of the manual avulsion analysis. In general, the manual selectionsaligned with automated threshold selections. However, on average the auto-mated method identified between 2 and 2.5 times as many avulsions as themanual method. In part, this was due to the manual method recording asingle avulsion ‘event’ for a rapid sequence of channel changes, each of whichwas characterized as an avulsion in the automated method. In some casesup to six clustered avulsions were recorded in the automated method for asingle manually identified avulsion. In other words, the automated methodwas more sensitive to channel shifting than the manual method.Figure 5.8 compares the normalized new and abandoned channel areawith the results of the manual avulsion analysis over Phase 2. The manually14The burstiness parameter was calculated using a ratio of the standard deviation (σ)and mean (µ) of the inter-event time (r = σ/µ) and the number of events n. In the caseof my experiments, the inter-event time refers to the time between avulsion events.651 2 3 4 50.000.100.20Experiment 12 4 6 80.000.100.20Experiment 22 4 6 8 10 120.000.100.20Experiment 35 10 15 20 250.000.100.20Experiment 4New channel area normalized by fan area (% fan area)Time (hrs)Figure 5.7: New flow area between each flow map pair, normalized by fan area. The horizontal dashed line (orange)indicates new fan area in excess of the threshold of 0.11. The vertical dashed lines indicate the approximate transitionfrom Phase 1 to Phase 2. Grey polygons represent flood periods.66Figure 5.8: New (dark blue) and abandoned (light blue) flow area between each Phase 2 flow map pair, normalizedby fan area. Red points indicate avulsions mapped manually. Horizontal dashed line indicates new fan area in excessof the automated avulsion analysis threshold (0.11). Vertical dashed lines indicate the approximate transition fromPhase 1 to Phase 2. Grey polygons represent flood periods.67mapped avulsions corresponded closely to automated analysis peaks. Incases where a manually selected avulsion does not exceed the automatedavulsion threshold (> 0.11) the event often corresponds with a spike inabandoned channel area. This comparison lends credence to the automatedavulsion method when paired with manual validation. In addition, the au-tomated method was applied to data taken at 5-minute intervals for Ex-periments 3 and 4, while the manual method was completed at one minuteintervals for all four experiments. This may account for some of the dis-crepancies between the two methods. Despite these discrepancies, the man-ual and threshold methods identified many of the same avulsion events (±5 minutes).5.3 Discussion5.3.1 Predicted Avulsion FrequencyIt is probable that the avulsion mechanisms described above work in con-cert to achieve channel abandonment. For example, erosional avulsion maybe the result of compensating erosion following in-channel deposition fromprevious time steps. The purpose of this classification is to indicate thatin-channel deposition is not the sole driver of fan channel avulsions in theseexperiments and that sediment input alone may not effectively predict avul-sion frequency. In addition, while the DoDs provide high resolution temporaldata, they do not reflect the conditions of sediment deposition or erosion atthe precise moment when avulsion occurs. As such, the avulsion mechanismsdescribed herein reflect an estimate of the most likely cause of avulsion giventhe data temporal resolution.The experiments of Reitz et al. (2010) showed that avulsion followed apredictable frequency following conservation of mass. Deposition progradedfrom the fan toe up the channel to the fan apex thereby decreasing the fangradient. Their experiments indicated that avulsion frequency is tied to fanradius and may be predicted by estimating the time required to fill a channelof a certain width and depth under a given sediment feed rate.TA(t) =hwr(t)Qs(5.1)where TA is the characteristic avulsion frequency, h is the typical depth ofa channel, w is the average wetted width, r(t) is the mean fan margin posi-tion, or fan radius, over time and Qs is the sediment feed rate (or sediment68transport rate in natural streams). In my experiments, the mean fan mar-gin position was back-calculated using the fan area, assuming the fan wasperfectly semi-circular. The mean fan margin position was calculated atone- or five-minute intervals depending on the data density of the relevantexperiment.Equation 5.1 was applied to the four experimental fans and characteristicavulsion frequency was averaged over Phase 2. The results give character-istic avulsion frequencies of approximately 150 seconds for Experiments 1and 2 and 170 seconds for Experiments 3 and 4. The characteristic avulsionfrequency started at values as low as 60 seconds near the beginning of the ex-periments, and increased progressively as fan area increased. These resultsused a standard channel width and depth of 20 cm and 0.24 cm, respec-tively. The channel width of 20 cm was based on measurements of typicalfan channel dimensions from the orthomosaics. The channel depth was anaverage value of channel depth taken from the channel incision analysis inChapter 4.Using the characteristic avulsion frequencies predicted above, one wouldexpect 18 avulsions to occur during Phase 2 for Experiments 1, and 2 and16 avulsions to occur during Phase 2 for Experiments 3 and 4. These pro-jected values for avulsion closely predict the observed avulsions mappedmanually throughout Phase 2 for the four experiments (Table 5.2). Theover-prediction of avulsion events for Experiments 3 and 4 indicates thatthe decrease in avulsion frequency for Experiment 4 cannot be explainedentirely by the increased fan area.Experiment Predicted Observed Percent ChangeNo. Avulsions Avulsions Observed vs. Predicted1 18 20 + 10%2 18 18 0%3 16 15 - 7%4 16 12 - 33%Table 5.2: Summary of predicted vs. observed avulsions throughout Phase 2for each of the four experiments. Percent change reflects the percentage ofobserved avulsions in excess of or fewer than predicted avulsions.695.3.2 Links to Fan GradientThe experiments of Bryant et al. (1995) found that avulsions would be ex-pected to occur more frequently on steeper fans. This may be related to adecrease in channel depth with increasing gradient (Parker, 1978). Underthis paradigm, the difference in avulsion frequency across the four experi-ments may be attributed to differences in overall fan gradient. However, thefans in Bryant et al.’s (1995) experiments formed under differing sedimentfeed conditions. The steepest fans, with gradients of 0.130, formed under asediment feed of 34.5 cm3/s while those with gradients of 0.076 were formedwith a sediment feed of 15.8 cm3/s. It is therefore not possible to attributethe increase in avulsion frequency to increased fan gradient alone.5.3.3 SummaryAvulsions in my experiments were correlated with primary process periods.A study of channel pattern changes revealed that increases in normalizednew channel area represented a good proxy for avulsion timing. However,my automated analysis tended to count multiple avulsions for each manuallyidentified avulsion. While the automated avulsion method may be used forinitial characterization of avulsion frequency, it should not be utilized inthe absence of manual verification. This manual verification is crucial forselecting an appropriate avulsion threshold.The results of the manual avulsion analysis indicate that longer durationsof secondary processes resulted in fewer avulsions during flood sequences. Inaddition, the first avulsion in the flood sequence was delayed for experimentswith longer durations of secondary processes. The decrease in avulsion num-ber was higher than predicted based upon fan morphology from Eqn. 5.1.This indicates that alterations made by secondary processes during inter-flood periods have an important effect on avulsion frequency.70Chapter 6ConclusionsDespite several decades of alluvial fan experimentation and research, thefocus has remained on primary process events. The role of inter-event, orsecondary, processes on fan evolution and behaviour has been largely ig-nored. The objective of this study was to advance understanding of theimportance of secondary processes on steep alluvial fans. This has beenachieved through a series of four experiments designed to isolate the im-pacts of varying secondary process duration. The results presented hereinyield insight into the emergent properties of the fan system under differentsecondary process conditions.6.1 Impacts to Fan MorphologyThe duration of secondary processes was found to have a profound impacton both fan morphology and fan flood behaviour. Each of the four fanswas created with the same volume of sediment, with no sediment addedduring the secondary process periods. The only difference between the fourexperiments was the duration of secondary processes run between each floodevent. Secondary processes were run for periods of 5, 10, 20, and 40 minutesfor Experiments 1, 2, 3, and 4, respectively.An increase in fan area and a corresponding decrease in gradient wereobserved for experiments with longer durations of secondary processes. Sed-iment transport occurring during the secondary process periods accountedfor the larger extent and gentler gradient of the fans in Experiments 3 and4. Interestingly, Experiments 1 and 2 and Experiments 3 and 4 appearedto be grouped in terms of both gradient and area. The grouping was espe-cially remarkable for Experiments 3 and 4, given the difference in secondaryprocess duration between the two. The grouping of the experiments mayindicate that a threshold exists between Experiments 2 and 3. Furtherexperiments with secondary process durations between 10 and 20 minuteswould be needed to evaluate the presence of such a threshold.In addition, the fans exhibited gentler gradients along the fan axis andsteeper gradients proximal to the fan flanks. The differences in fan gradi-71ent with azimuth were most pronounced for Experiments 3 and 4. Thesedifferences were thought to be the result of secondary process action be-ing concentrated near the fan axis. As discussed throughout the channelbehaviour sections, typical flow patterns included the formation of a singlecentralized channel during secondary process periods and the subsequentbifurcation of flow during primary process periods.A sediment blockage occurred during Experiment 1, resulting in a de-crease in gradient and subsequent increase in fan area. While fan gradientand area were initially impacted by the blockage, both returned to their pre-blockage levels over a period of approximately 40 minutes. Experiment 1 wasrepeated to isolate the impact of the sediment blockage. Experiment 1B didnot experience similar changes to fan area or gradient, which indicated thatchanges to Experiment 1 were indeed the result of allogenic forcing on thepart of the sediment blockage. With the exception of the sediment blockageperiod, the fan gradient and area between Experiment 1 and Experiment 1Bwere similar throughout the experimental duration. This suggests that thegradients and areas achieved during these experiments are repeatable underequivalent input conditions.Both Experiments 1B and 2 experienced changes in fan area and gradientduring Phase 2. The timing of these changes occurred at the onset of thehigher magnitude Phase 2 debris floods. These floods likely achieved greatersediment mobility, thereby lowering the fan gradient and extending the fanboundary. Following the initial decrease in fan gradient, both experimentsunderwent a subsequent increase until the gradient matched those observedthroughout Phase 1. Importantly, Experiments 3 and 4 did not exhibitsimilar changes to fan area or gradient during Phase 2. That Experiments 3and 4 were not impacted by these debris-flood events points to the resilienceof fans with longer durations of secondary processes to changes in inputconditions.6.2 Channel BehaviourThe wet fraction of the fan increased predictably with the onset of flooding,and during flood periods the fan wet fraction was approximately equal acrossthe four experiments. The wet fraction of the fan prior to flooding decreasedwith increasing secondary process duration. In the case of Experiment 4,secondary process periods ended with the formation of a single, centralizedfan channel. This process of channelization during inter-flood periods wasechoed in the characteristic channel patterns identified using PCA. The72analysis revealed that a single, central channel was most common duringsecondary processes, while bifurcated flow and multiple channels were morecommon under primary processes.Experiment 4 experienced channelization – further reductions in fan wetfraction – in each of its eight secondary process periods, and multiple chan-nelization events were observed during some of these periods. By compari-son, Experiments 2 and 3 each experienced only three channelization events.Experiment 4 also had a significantly different pre-flood wet fraction thanthe other experiments. The experiments do not show evidence of a gradualtransition towards this increased channelization and decreased wet fraction.The transition in behaviour from Experiment 3 to Experiment 4 remainsabrupt and is thought to reflect a threshold change. Again, further experi-ments would be needed to determine whether this change reflects a thresholdor gradient change.Despite differences in the pre-flood wet fraction, the wet fraction dur-ing flooding was similar across all four experiments. This came in spite ofthe evidence for increased channel incision depth with increasing secondaryprocess duration. Clearly the pre-flood channel incision depth did not deter-mine the degree to which the fan was wetted during subsequent debris floodevents. While some of the similarity in wet fractions during flooding may beattributed to the limitations of the binary channel mapping, it ultimatelypoints to the chaotic nature of flood events on steep alluvial fans. Despitedecreases in avulsion frequency for experiments with longer secondary pro-cess duration, avulsions and subsequent lateral spreading of flow occurredduring flooding for all four experiments.Channel incision depth was measured from the DEM data. While theresults indicated that channel incision for Experiment 4 was greatest, withdepths up to 1 cm, these results are considered to be underestimates dueto the error inherent in two-media photogrammetry. Observation of theexperiments and an initial error analysis suggest that incision depths forExperiment 4 may be as high as 2.5 cm. Future work is required to bettercharacterize this error and correct the recorded depth measurements.6.3 AvulsionsExperiments with longer durations of secondary process action showed botha decrease in the number of avulsions and a delay in the first onset of avulsionfollowing flooding. These changes cannot be solely attributed to increasedfan area or fan gradient, and are thought to be a result of the flow chan-73nelization and incision resulting from prolonged secondary process action.In addition, the number of channels present on the fan prior to floodingwas lowest for Experiment 4. That flow in Experiment 4 was consistentlyconfined to a single channel prior to flooding is an indicator of the power ofsecondary processes in determining pre-flood conditions.The results of a manual avulsion analysis were compared against minute-to-minute DoDs to determine the avulsion trigger mechanism. Avulsionswere classified into four types: depositional, erosional, reoccupational, andunclassified. Avulsions in my experiments were correlated with primaryprocess periods. This is unsurprising, given that a majority of avulsionevents were attributed to deposition. Although each avulsion was assigneda single type, it is more likely that a combination of these mechanisms actedin concert to trigger channel changes.The avulsions manually identified during Phase 2 of the experiments werevalidated with an automated analysis that identified anomalies in new chan-nel area. Changes to normalized new channel area in excess of a thresholdof 11% were classified as avulsion events. Correlation between the manualand automated analyses was generally good, although the automated analy-sis tended to count multiple avulsions for each manually identified avulsion.While the automated avulsion method may be used for initial characteriza-tion of avulsion frequency, it should not be utilized in the absence of manualverification.These findings indicate that alterations made by secondary processesduring inter-flood periods have an important effect on both avulsion fre-quency and the timing of avulsion. It is possible that these changes may beexplained by increased channelization prior to flooding. Under these condi-tions, additional sediment deposition may be required to force flow outsideof the initial channel. In other words, the fan morphology prior to floodinghas a role in determining the fan flood response.6.4 SummaryLonger durations of secondary processes generate larger and less steep fans.They also tend to concentrate flow near the fan axis, where a single channelmay form following secondary processes. These fan channels tend to be moreincised under longer secondary process durations. Channel incision andthe restriction of flow on the fan surface are the likely causes of decreasedavulsion frequency, and delayed avulsion timing during subsequent floodperiods.74Figure 6.1 summarizes the differences in fan and channel morphologyunder differing durations of secondary processes. The fan on the left wasformed under shorter durations of secondary processes (Experiment 1) whilethe fan on the right was formed under longer secondary process durations(Experiment 4). The fan on the left has a smaller areal extent and is steeper.Numerous channels are present on the fan surface. In addition, the primarychannel on the fan surface is barely incised – if at all. The intersection pointis located approximately half way down-fan from the apex. The fan on theright is larger and has a shallower gradient. It has a single channel which isentrenched, and the intersection point is located in the bottom third of thefan.The larger area and lower gradient of the fan on the right results ingreater potential for energy dissipation under flood events. In addition, thesingle channel geometry allows for greater channelization of flood eventsand may serve to delay avulsion onset and decrease avulsion frequency. Theresults of this research indicate that the fan in Figure 6.1b is better able toFigure 6.1: Summary of secondary process effects on fan morphology with twofans formed under (a) shorter and (b) longer durations of secondary processes.The primary fan channel on each of the fans is indicated by a dashed orangeline and a hypothetical cross-section for each of these channels is shown abovethe fans.75manage flood events and does not experience significant changes to overallgradient and area when subjected to flooding. However, it should be notedthat despite these differences in flood response, a similar fraction of the fanmay become wetted during a flood event.6.4.1 Links to Climate ChangeClimate exerts a strong influence over the recurrence interval of primaryprocesses (Jakob, 1996; Webb et al., 2008). Changes in rainfall patternsand intensity will occur within this century as a result of climate change. Inmany places, these changes in precipitation are predicted to increase the fre-quency and magnitude of catastrophic hydrogeomorphic events (Jakob andLambert, 2009; Turkington et al., 2016). The increased recurrence intervalof these events may decrease the time over which secondary processes areable to act on alluvial fans, potentially shifting the balance of aggradationand entrenchment on fan surfaces in the future.For fans situated in watersheds which are sediment supply unlimited15,climate change will result in a greater proportion of events being primaryprocesses – rather than clearwater flows. An increase in primary processevents would shift the fan type towards the one shown in Figure 6.1a. Bycomparison, for fans existing within a sediment supply limited watershed,more clearwater flows will occur under a climate change scenario. Thisincrease in clearwater flows will push the fan in the direction of Figure 6.1b16.The results of this study indicate that pre-flood conditions are impor-tant determinants of fan flood hazards associated with primary processes.The shift towards fans shown in Figure 6.1a may result in increased avulsionfrequency, earlier avulsions, and changes to fan morphology. These resultshighlight the importance of secondary processes in creating fan morphologicstructure and improve understanding of how secondary processes act to de-lay avulsions and decrease overall avulsion frequency. An understanding ofantecedent fan conditions during a flood event is important in determiningthe overall flood impact.15Watersheds which are supply unlimited are those in which sediment is perpetuallyavailable to contribute to hydrogeomorphic events. Supply limited watersheds requiresome amount of ‘recharge’ time in order to deliver additional sediment to the drainagenetwork.16It should be noted that the entire range of climate change impacts on alluvial fanwatersheds have not been considered, and these shifts may only be observed under certainwatershed conditions and where precipitation frequency and magnitude are predicted toincrease.766.5 Future WorkFuture studies could examine the impacts of secondary processes on channelarmouring. Evidence of channel armouring was observed throughout the ex-periments described herein, however, higher resolution photographs wouldbe required to characterize the channel bed. In addition, unpublished workby Leenman and Eaton (Leenman and Eaton, 2020) suggests that the floodhydrograph has an important effect on fan behaviour. Future experimentscould include varied flood hydrographs for comparison with constant flow.As mentioned previously, the development of a water depth correction fac-tor would allow for more accurate measurements of channel incision. Anyadditional studies wishing to characterize channel or water depth could ap-ply a similar method. Additional experiments are required to determine ifa threshold exists between Experiments 3 and 4.While these experimental results suggest a basic link between secondaryprocess duration and fan morphology and behaviour, work on prototype fansis required to determine how these processes play out in natural systems.Further experimental studies would be bolstered by field measurements andobservations.77BibliographyAgiSoft (2018). AgiSoft PhotoScan Professional.Allen, J. R. (1965). A Review of the Origin and Characteristics of RecentAlluvial Sediments. Sedimentology, 5(2):89–191.Ashworth, P. J., Best, J. L., and Jones, M. (2004). 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The grey polygons represent floodperiods.871 2 3 4 50.060.100.14Time (hrs)Mean fan slopeExp 1B2 4 6 80.060.100.14Time (hrs)Mean fan slopeExp 22 4 6 8 10 120.060.100.14Time (hrs)Mean fan slopeExp 35 10 15 200.060.100.14Time (hrs)Mean fan slopeExp 4Figure A.2: Mean fan gradient over time for each of the four experiments, with Experiment 1B. The dashed blacklines shows the approximate point of transition from Phase 1 to Phase 2. The grey polygons represent flood periods.880.0 0.2 0.4 0.6 0.8 1.00.00.51.01.5Normalized Time (t*)Fan area (m2 )Exp 1BExp 2Exp 3Exp 4Figure A.3: Mean fan area over time for each of the four experiments, withExperiment 1B. To facilitate comparison between experiments of different du-rations, time has been normalized to fraction of the total experiment duration.The dashed black line shows the approximate point of transition from Phase1 to Phase 2.89Appendix BPrincipal ComponentAnalysisThe results of the principal component analysis (PCA) are shown for Ex-periments 1, 2, and 4 in this appendix. The PCA results for Experiment 3are shown in Chapter 4. For each experiment the first four PCA modes andprincipal components are shown. Mode 1 for all four experiments shows flownear the fan apex (bottom left). Meanwhile, the second and third modesgenerally show bifurcated flow below the fan apex. The fourth mode doesnot exhibit a clear pattern across experiments. The grey polygons on thePCA plots indicate flood periods. Correlation between the strength of thePCs for modes two and three and the flood periods may be observed.The eigenvalues corresponding to each of these PCA modes are sum-marized by experiment in Table B.1. The first eigenvector for the four ex-periments represented between 21% and 28% of the total variance and thesecond, third, and fourth eigenvectors accounted for approximately 3-6% oftotal variance. This indicates that the PCA results shown herein explainless than 40% of the total variance in channel pattern. In other words, thereis a great deal of variance in fan channel position which is not explained bythis analysis. This should be considered when interpreting my results.Exp. No. Mode 1 Mode 2 Mode 3 Mode 41 0.278 0.056 0.039 0.0342 0.278 0.060 0.034 0.0313 0.274 0.060 0.049 0.0364 0.210 0.061 0.055 0.030Table B.1: Eigenvalues for each of the first four PCA modes by experiment.90Figure B.1: Raster PCA results for Experiment 1 channel maps showing the first four modes (Mode 1 - top left,Mode 2 - top right, Mode 3 - bottom left, and Mode 4 - bottom right) and their principal components. For each ofthe four modes, blue and red values correspond to positive and negative signals for channel position, respectively.Grey polygons on the PC plots correspond to flood (primary process) periods.91Figure B.2: Raster PCA results for Experiment 2 channel maps showing the first four modes (Mode 1 - top left,Mode 2 - top right, Mode 3 - bottom left, and Mode 4 - bottom right) and their principal components. For each ofthe four modes, blue and red values correspond to positive and negative signals for channel position, respectively.Grey polygons on the PC plots correspond to flood (primary process) periods.92Figure B.3: Raster PCA results for Experiment 4 channel maps showing the first four modes (Mode 1 - top left,Mode 2 - top right, Mode 3 - bottom left, and Mode 4 - bottom right) and their principal components. For each ofthe four modes, blue and red values correspond to positive and negative signals for channel position, respectively.Grey polygons on the PC plots correspond to flood (primary process) periods.93
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eng
Geography
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
The importance of secondary processes on alluvial fan morphology, channel behaviour, and flood hazards
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