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Modeling disturbance and channel evolution in mountain streams Davidson, Sarah 2016

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Modeling disturbance and channel evolution in mountainstreamsbySarah DavidsonB.Sc., McGill University, 2007M.Sc., The University of British Columbia, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Geography)The University Of British Columbia(Vancouver)August 2016c© Sarah Davidson, 2016AbstractResearchers and managers have sought for centuries to model the dynamics ofriver systems for hazard protection, water management, and ecological restoration.Models of channel dynamics generally assume that rivers adopt a constant geom-etry in response to a set of relatively static governing parameters. In this research,we develop two stochastic biogeomorphic models which we use to simulate therange of channel conditions associated with fluctuating governing conditions, in-cluding wood loading and discharge. We begin by developing a version of theReach Scale Channel Simulator (RSCS) that models the impact of riparian distur-bance on channel morphology at a range of channel scales, in a reach subject toan annual flood event of constant magnitude and duration. The simulations showthat small- to intermediate-sized channels are the most morphologically sensitive tofluctuations in wood loading. We then develop a STochastic CHannel AdjustmentSIMulator (STOCHASIM) that simulates the competition between bank erosionand vegetation colonization in a reach subject to variable annual floods. The modelproduces a dynamic channel geometry that adjusts in response to individual floods.The results challenge a major underlying assumption of most regime models bydemonstrating that the return period of the formative flow varies with watershedhydrology.Introducing variable floods and lateral migration has important implications forwood loading, as bank erosion increases wood recruitment and changes piece char-acteristics. In the final chapters, we use data from a series of flume experimentsto investigate the effects of piece characteristics on wood stability and transport.Rootwads – which are more common on wood pieces recruited through bank ero-sion than via toppling – increase piece stability while reducing travel distance. Weiiuse this research to further modify the RSCS model to account for wood inputsthrough bank erosion, as well as temporal changes in channel geometry and floodmagnitude. When lateral mobility is considered, bank erosion inputs dominatewood loading while piece stability and morphologic impact decreases. As thesestochastic models produce a range of channel conditions they are more likely toencompass the range of variability observed in natural systems than deterministicmodels of channel dynamics.iiiPrefaceSections of this dissertation have been published in peer-reviewed journals, aslisted below.Davidson, S.L., Eaton, B.C., 2015. Simulating riparian disturbance: Reachscale impacts on aquatic habitat in gravel bed streams. Water Resources Research51, 7590-7607. This paper is presented in Chapter 2 in essentially its publishedform. The paper builds on a model developed collaboratively by S. Davidson, B.Eaton, and M. Hassan. The modeling and analysis for this paper were conductedentirely by S. Davidson, with guidance from B. Eaton. The writing and figurepreparation were conducted by S. Davidson.Davidson, S.L., MacKenzie, L.G., Eaton, B.C., 2015. Large wood transportand jam formation in a series of flume experiments. Water Resources Research 51,doi:10.1002/2015WR017446. This paper is included in Chapter 4 in its entirety,with some modifications. The paper was written by S. Davidson, and figures wereproduced in collaboration with L. MacKenzie. The paper presents a re-analysis ofdata collected by S. Davidson in 2010-2011 for her M.Sc. thesis; all figures andanalyses presented in this work were generated in 2015-2016 solely for the PhDthesis and paper and were not presented in the earlier M.Sc. thesis work.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Modeling River Systems . . . . . . . . . . . . . . . . . . . . . . 11.2 Disturbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Moving from Morphology to Habitat . . . . . . . . . . . . . . . . 41.4 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Modeling Forest Disturbance and Aquatic Habitat at a Range of Scales 82.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.1 Base Scenario . . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 Fire Scenario . . . . . . . . . . . . . . . . . . . . . . . . 192.3.3 Harvesting Scenario . . . . . . . . . . . . . . . . . . . . 192.4 RSCS Habitat Module . . . . . . . . . . . . . . . . . . . . . . . 20v2.4.1 Jam Characteristics . . . . . . . . . . . . . . . . . . . . . 202.4.2 Pool Area . . . . . . . . . . . . . . . . . . . . . . . . . . 212.4.3 Sediment Storage . . . . . . . . . . . . . . . . . . . . . . 232.4.4 Bed Texture . . . . . . . . . . . . . . . . . . . . . . . . . 242.4.5 Side Channels . . . . . . . . . . . . . . . . . . . . . . . 252.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.5.1 Wood Load . . . . . . . . . . . . . . . . . . . . . . . . . 252.5.2 In-stream Habitat . . . . . . . . . . . . . . . . . . . . . . 292.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 Departures from Regime: Channel Evolution in a Laterally Unsta-ble Stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.3 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . 463.3.1 Model Overview . . . . . . . . . . . . . . . . . . . . . . 463.3.2 Erosion and Channel Adjustment . . . . . . . . . . . . . 473.3.3 Biogeomorphic Recovery . . . . . . . . . . . . . . . . . 543.3.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 573.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.4.1 Channel Evolution . . . . . . . . . . . . . . . . . . . . . 583.4.2 Long-term Channel Characteristics . . . . . . . . . . . . 623.4.3 Effective and Formative Discharge . . . . . . . . . . . . . 673.4.4 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . 713.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774 Large Wood Transport and Jam Formation in a Series of Flume Ex-periments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83vi4.3.1 Experimental Design . . . . . . . . . . . . . . . . . . . . 834.3.2 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . 864.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 904.4.1 Wood Stabilization . . . . . . . . . . . . . . . . . . . . . 904.4.2 Statistical Analysis of Mobility and Travel Distance . . . 964.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065 Modeling Wood Dynamics in a Laterally Active Reach . . . . . . . . 1075.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.3 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . 1095.3.1 Model Overview . . . . . . . . . . . . . . . . . . . . . . 1095.3.2 Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . 1185.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1185.4.1 Reach Characteristics . . . . . . . . . . . . . . . . . . . . 1185.4.2 Recruitment Mechanism . . . . . . . . . . . . . . . . . . 1225.4.3 Jam Dynamics . . . . . . . . . . . . . . . . . . . . . . . 1255.4.4 Rootwads and Piece Dynamics . . . . . . . . . . . . . . . 1255.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1285.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1326 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138A Model Description of the Reach Scale Channel Simulator . . . . . . 160A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160A.2 Reach Scale Channel Simulator . . . . . . . . . . . . . . . . . . . 160A.2.1 Riparian Forest Inputs . . . . . . . . . . . . . . . . . . . 162A.2.2 Small Wood Advection . . . . . . . . . . . . . . . . . . . 164A.2.3 Key Piece Identification . . . . . . . . . . . . . . . . . . 165A.2.4 LW Movement and Jam Growth . . . . . . . . . . . . . . 165A.2.5 Bed Material Sediment Storage . . . . . . . . . . . . . . 167viiA.2.6 In-stream Habitat . . . . . . . . . . . . . . . . . . . . . . 169A.2.7 LW Decay . . . . . . . . . . . . . . . . . . . . . . . . . 170B Fishtrap Creek Field Study . . . . . . . . . . . . . . . . . . . . . . . 172B.1 Study Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172B.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174B.2.1 Morphologic Survey . . . . . . . . . . . . . . . . . . . . 174B.2.2 Jam Survey . . . . . . . . . . . . . . . . . . . . . . . . . 178B.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180C Bank Erosion Data Comparison . . . . . . . . . . . . . . . . . . . . 183C.1 Historical Air Photo Analysis . . . . . . . . . . . . . . . . . . . . 183C.2 STOCHASIM Modeling . . . . . . . . . . . . . . . . . . . . . . 185C.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185D Additional Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189D.1 STOCHASIM Output . . . . . . . . . . . . . . . . . . . . . . . . 189D.2 Flume Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189D.3 Fishtrap Creek Field Data . . . . . . . . . . . . . . . . . . . . . . 189E Additional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201E.1 STOCHASIM Output . . . . . . . . . . . . . . . . . . . . . . . . 201E.2 Flume Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 201viiiList of TablesTable 2.1 Summary of variables used in the RSCS simulations. . . . . . . 12Table 2.2 The simulated reach characteristics associated with a range ofchannel sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Table 3.1 Parameters used in STOCHASIM sensitivity analyses . . . . . 58Table 3.2 Effective discharge for a range of flow variability values . . . . 67Table 3.3 Summary of differences between UBCRM and STOCHASIMpredictions of long-term channel width with increasing flowvariability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Table 4.1 Summary of the added wood load and time required to reachequilibrium for each experiment . . . . . . . . . . . . . . . . . 84Table 4.2 Wood characteristics and distribution in the model and proto-type systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Table 4.3 Parameters considered in logistic and linear regression analyses 88Table 4.4 Initial and final jam characteristics for four flume experiments . 93Table 4.5 Summary of logistic model for wood mobilization . . . . . . . 97Table 4.6 Summary of the linear regression model for transport distance . 100Table 5.1 Description of Reach Scale Channel Simulator (RSCS) versions 111Table 5.2 Riparian and hydrologic parameters included in the RSCS sim-ulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118Table 5.3 Wood loading and jam characteristics for four flow variabilityscenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119ixTable 5.4 Summary of piece characteristics according to recruitment mech-anism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Table 5.5 Jam characteristics at time of failure . . . . . . . . . . . . . . 127Table 5.6 Piece characteristics for each flow variability scenario . . . . . 128Table B.1 Jam size categories for Fishtrap Creek surveys . . . . . . . . . 178Table D.1 Erosion and channel mobility for five flow variability scenarios 189Table D.2 Erosion and channel mobility for five rooting depth scenarios . 190Table D.3 Erosion and channel mobility for five Shields number values . 190Table D.4 Erosion and channel mobility for five morphologic indices . . . 190Table D.5 Erosion and channel mobility for five vegetation rates . . . . . 191Table D.6 Morphologic characteristics surveyed in Fishtrap Creek . . . . 192Table D.7 Jam characteristics surveyed in Fishtrap Creek . . . . . . . . . 196xList of FiguresFigure 2.1 Examples of wood functionality classes and morphologic im-pacts from Fishtrap Creek, British Columbia . . . . . . . . . 16Figure 2.2 Schematic showing the effect of a channel-spanning jam onreach morphology . . . . . . . . . . . . . . . . . . . . . . . 22Figure 2.3 Variability in wood load over time for each scenario, as well asacross channel scales . . . . . . . . . . . . . . . . . . . . . . 27Figure 2.4 Functional wood load across a range of channel sizes for eachdisturbance scenario . . . . . . . . . . . . . . . . . . . . . . 28Figure 2.5 The effect of fire on pool area and deposit size across a rangeof channel sizes . . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 2.6 The effect of fire on deposit texture and side channel frequencyfor a range of channel sizes . . . . . . . . . . . . . . . . . . . 32Figure 2.7 2D histograms of pool and deposit areas in the fire and basescenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Figure 2.8 The impact of buffer size on morphologic response . . . . . . 35Figure 3.1 Schematic showing channel changes during a single year of amodel simulation . . . . . . . . . . . . . . . . . . . . . . . . 48Figure 3.2 Flood magnitude index (FMI) values for Pacific drainage Wa-ter Survey of Canada gauges and the flood frequencies for FMIvalues used in each scenario . . . . . . . . . . . . . . . . . . 49Figure 3.3 Time series plots showing variability in flood magnitude andchannel width for a range of flow variability values . . . . . . 60xiFigure 3.4 Changes in channel position over time for a range of flow vari-ability values . . . . . . . . . . . . . . . . . . . . . . . . . . 61Figure 3.5 Summary of the effect of flow variability on bank erosion andchannel width . . . . . . . . . . . . . . . . . . . . . . . . . . 63Figure 3.6 Summary of the effect of rooting depth on bank erosion andchannel width . . . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 3.7 Sediment rating curves and effective discharge for five flowvariability scenarios . . . . . . . . . . . . . . . . . . . . . . 68Figure 3.8 Sediment rating curves and effective discharge for five rootingdepth scenarios . . . . . . . . . . . . . . . . . . . . . . . . . 70Figure 3.9 Formative discharge for the range of channel widths generatedfor five STOCHASIM simulations . . . . . . . . . . . . . . . 71Figure 3.10 Boxplots showing results from sensitivity analyses . . . . . . 73Figure 4.1 Examples of wood piece types used in flume experiments . . . 86Figure 4.2 Wood travel over the entire duration of four experiments . . . 91Figure 4.3 Wood locations at the time of placement, after a single run, andat steady state in Experiment 3 . . . . . . . . . . . . . . . . . 92Figure 4.4 Radar plot showing the orientation of wood pieces accordingto jam membership . . . . . . . . . . . . . . . . . . . . . . . 94Figure 4.5 Radar plot showing the orientation of wood pieces accordingto rootwad presence . . . . . . . . . . . . . . . . . . . . . . . 95Figure 4.6 Boxplots summarizing the effect of piece characteristics ontravel distance . . . . . . . . . . . . . . . . . . . . . . . . . . 99Figure 5.1 Schematic of Version 3.0 of the Reach Scale Channel Simula-tor (RSCS) . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Figure 5.2 Tree height and diameter according to tree age . . . . . . . . 114Figure 5.3 Wood loading over time for four flow variability scenarios . . 120Figure 5.4 Wood loading from published research and unpublished dataworldwide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Figure 5.5 Boxplots of the effect of flow variability on riparian forestcharacteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 123xiiFigure 5.6 Wood piece length for four flow variability scenarios . . . . . 124Figure 5.7 Jam wood loading and frequency according to flow variabilityscenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Figure B.1 Map of Fishtrap Creek watershed and McClure fire area . . . 173Figure B.2 Landslide in a large glaciofluvial outwash terrace . . . . . . . 175Figure B.3 Morphologic classification example photographs . . . . . . . 176Figure B.4 Textural classification scheme . . . . . . . . . . . . . . . . . 177Figure B.5 Jam size class example photographs . . . . . . . . . . . . . . 179Figure B.6 Jam frequency and valley confinement . . . . . . . . . . . . . 181Figure B.7 Channel gradient and piece frequency for a range of channeltypes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182Figure C.1 Example of historic air photograph analysis . . . . . . . . . . 184Figure C.2 Comparison of modeled and predicted bank erosion for 40stream reaches . . . . . . . . . . . . . . . . . . . . . . . . . 186Figure C.3 Comparison of modeled and predicted erosion rates for a sub-set of stream reaches . . . . . . . . . . . . . . . . . . . . . . 188Figure E.1 Time series plots of flood magnitude and channel width forthree flow variability scenarios . . . . . . . . . . . . . . . . . 202Figure E.2 Critical discharge and the size of mobilized sediment over timeafter a large widening event . . . . . . . . . . . . . . . . . . 203Figure E.3 Wood position during Experiment 1 . . . . . . . . . . . . . . 204Figure E.4 Wood position during Experiment 2 . . . . . . . . . . . . . . 205Figure E.5 Wood position during Experiment 3 . . . . . . . . . . . . . . 206Figure E.6 Wood position during Experiment 4 . . . . . . . . . . . . . . 207xiiiAcknowledgmentsI would first like to thank Brett Eaton for his continued patience, guidance, andseemingly endless enthusiasm over the last seven years. Of all of the things you’vetaught me over this time, though, the most important lesson has been to have faithin myself. I’m also grateful to Marwan Hassan for providing continuing guidance,and to Jordan Rosenfeld for introducing me to another perspective on this research.I’d also like to thank Dan Moore for always keeping your door open and makingtime for me - your support along the way has been truly appreciated. Field as-sistance from Ariel Kettle, Lea Zhecheva, Ali Beamish and Lucy MacKenzie wasalso essential to this work. My time at UBC also wouldn’t have been the samewithout the amazing Geography department and Acadia Park communities. Thankyou to the many friends and neighbours who have provided me with laughs, freebabysitting, friendship, and wine over the years.This work wouldn’t have been possible without the support of my family. An-gus, I couldn’t have accomplished everything that I have without your love andsupport (and gentle nudging) - you’re my rootwad and my branch snags. My par-ents have also always been ready to help out in any way possible, no questionsasked; your last minute babysitting has saved me countless times and your subtleencouragement has not gone unnoticed. And last but not least, Austin. You and Ihave been in this together from the start - you took your first steps in Acadia Parkduring my first month of graduate school, almost seven years ago. I’m so proud ofthe little man that you’ve become, and I couldn’t have asked for anyone better totake this trip with.xivChapter 1Introduction1.1 Modeling River SystemsThroughout history, models have been developed to support and test a basic un-derstanding of our physical environment [Oreskes, 2003]. Models of river systemshave been used to inform the design of irrigation systems, predict and manage haz-ards, and to rehabilitate degraded ecosystems. Since the late nineteenth century, theconcept of river regime, or equilibrium, has been invoked in many of these models[Ackers, 1992]. Regime theory asserts that rivers exist in a state of dynamic equi-librium, adjusting channel gradient and texture to maintain a balance between sed-iment supply and transport. Streams with excess supply aggrade and fine, therebyincreasing transport capacity to match the imposed supply, while streams with ex-cess transport capacity degrade and armour, decreasing transport capacity in orderto restore a long-term sediment transport equilibrium [Lane, 1955]. This equi-librium condition produces predictable downstream patterns in some rivers. At thelandscape scale, there is a decrease in channel competence and transport capacity asgradient decreases moving downstream, which produces a pattern of downstreamfining [Hoey and Ferguson, 1994], as well as a predictable sequence of channelmorphologies in mountain streams [Montgomery and Buffington, 1997, Church,1992]. In small- and intermediate-sized mountain streams – which are character-ized by widths smaller than the largest riparian trees (i.e. 20-30 m) [Church, 1992]– there is a downstream progression from supply-limited ‘transport’ reaches, to1transport-limited ‘response’ reaches, with reach morphologies correlating stronglywith channel gradient [Montgomery and Buffington, 1997]. These morphologiesprovide a useful first order approximation of habitat quality.Watershed managers and engineers often also need to predict channel size, sta-bility, or migration rates in order to assess hazards to infrastructure. Over the lastseveral decades numerous regime models – both empirical and physically based –have been developed to relate average channel characteristics in rivers in regime(i.e. equilibrium) to the formative flow (see Ackers [1992] for a detailed review).Early empirical models were developed to support the design of irrigation canalsin India and Egypt in the early twentieth century and relate channel geometry todischarge according to a series of power equations. Hydraulic geometry equationsgrew out of attempts to apply regime concepts to natural alluvial rivers in the mid-twentieth century [e.g. Leopold and Maddock, 1953]. Empirical regime modelshave since expanded to consider the effect of rooted vegetation on channel dimen-sions [e.g. Millar, 2005], and a number of rational regime models have also beendeveloped [e.g. Eaton et al., 2004]. Rational regime models combine resistancelaws, bank stability criteria, and continuity equations to determine a range of pos-sible channel geometries. Optimality criteria (e.g. the maximization of transportcapacity) are then used to select a single, optimal channel configuration [Eatonet al., 2010b].In addition to the influence of live vegetation on bank stability, the presenceand abundance of dead in-stream large wood dictates morphology in many small-to intermediate-sized mountain streams. The influence of large wood on reachmorphology and longitudinal patterns in gradient and sediment size was first rec-ognized in the 1970s [e.g. Heede, 1972, Beschta, 1979, Keller and Swanson, 1979].In-stream wood interrupts the typical longitudinal sequence of reach types; wood-forced pools and gravel accumulations disrupt the broader longitudinal patternsdictated by channel competence [May and Lisle, 2012]. By increasing channelroughness, wood increases both longitudinal and lateral variability in shear stressand bed erosion; scour forms pools where flow is concentrated, while sediment de-posits in areas of decreased shear stress [e.g. Abbe and Montgomery, 1996]. Woodis a first order control on pool availability in many systems, especially in moder-ate gradient reaches where free-formed pools are rare [Montgomery et al., 1995,2Beechie and Sibley, 1997, Buffington et al., 2004]. While conceptual models havebeen developed to describe downstream patterns in wood loading and temporalvariability at the reach scale [e.g. Benda and Sias, 2003, Czarnomski et al., 2008,Wohl and Jaeger, 2009], relatively few models have been developed to explorenon-chronic wood loading. Even fewer models consider the effects of wood load-ing on stream morphology; as the use of large wood in stream restoration grows[e.g. Bernhardt et al., 2005, Kail et al., 2007, Nagayama and Nakamura, 2009]there is an increasing need for predictive models capable of describing the effectsof wood on channel morphology.1.2 DisturbanceThe models described above share two common underpinnings: they predict aver-age stream conditions, and they are largely deterministic. The conditions governingmost river systems, however, are not constant over time. Indeed, disturbance is sointegral to fluvial systems that the elimination of disturbance (e.g. fire suppression)can itself be understood as a form of disturbance [Resh et al., 1998, Nakamura andSwanson, 2003]. Disturbances such as forest fires or large floods can be conceivedof as governing variables in their own right, rather than as interruptions to ‘normal’equilibrium conditions, in many systems. Rivers subject to large fluctuations inwood loading or flood magnitude can not, for example, be modeled without con-sidering these disturbances and the morphologic cycle they produce. Similarly,formative flow-based regime approaches that predict average conditions based ona single flood magnitude fail to capture temporal variability at short to intermedi-ate time scales which may be relevant for both infrastructure and habitat quality.Despite the proven utility of many regime models [e.g. Eaton and Church, 2007],these models tend to underestimate channel dimensions in streams subject to highvariability in flood magnitude.Deterministic models, which produce a single estimate of wood loading orchannel geometry, also fail to replicate conditions observed in natural systems.Wood loading has been shown to vary by several orders of magnitude in sys-tems with similar riparian forest characteristics [Wohl and Beckman, 2014]. Byincorporating variability in governing parameters – including disturbance history –3stochastic models provide a range of channel conditions which are more likely toencompass the conditions observed in the field. Similarly, regime models that pre-dict an optimal channel geometry based on a single formative flow fail to capturethe variability in channel widths that results from channel widening, which is thedominant geomorphic response to flooding in many rivers [Magilligan et al., 2015].In these systems, the assumption that conditions observed in the field on a givenday should ‘reflect the most effective discharge’ [Pickup and Warner, 1976] overthe long-term is often violated, as channel geometry commonly reflects recent floodhistory rather than a time-averaged formative flood discharge. Stochastic modelsthat incorporate variability in discharge are therefore more likely to accurately de-scribe the range of conditions encountered in natural streams, which reflect bothlong-term average conditions and flood history.1.3 Moving from Morphology to HabitatWhile modeling channel migration rates or size may be sufficient to inform hazardassessment, restoration design requires that morphologic predictions be translatedinto some measure of habitat quality. To predict changes in aquatic habitat – bothin terms of quantity and quality – it is first necessary to define habitat require-ments [Van Horne, 1983]. Habitat requirements exist due to the biological needsof a species at each life history stage, and the degree to which these requirementsare met is reflected in the growth, probability of survival, and reproductive po-tential of a fish within a given habitat [Garshelis, 2000]. Currently, the dominantapproach to quantifying fish habitat quality is based on correlations between mi-crohabitat variables and habitat selection, which is often measured based on fishdensity [Nickelson et al., 1992, Beechie and Sibley, 1997]. The use of fish densityas a measure of habitat quality has been widely criticized, however, perhaps mostimportantly because limited testing of habitat models has not supported the un-derlying assumption that fish abundance is related to habitat quality, and changesin the availability of high density habitat are often unrelated to fish population size[e.g. Van Horne, 1983, Garshelis, 2000, Rosenfeld and Boss, 2001, Railsback et al.,2003, Beecher et al., 2010].In order to reliably predict the location or change in high quality habitat fol-4lowing environmental change it is necessary to develop a better understanding ofboth the biological processes that dictate stage-specific habitat requirements, andthe larger scale geomorphic processes that control habitat creation, maintenance,and distribution within the landscape. An alternative approach based on the avail-ability of geomorphically suitable habitat – sometimes referred to as the intrinsicpotential approach – offers a simpler means by which to evaluate the distributionand availability of potential habitat [Burnett et al., 2007, Busch et al., 2013]. In-stead of evaluating actual habitat use, which depends on both biological and an-thropogenic factors, the intrinsic potential approach yields estimates of potentialhabitat based on the geomorphic characteristics which determine habitat use. Ap-proximations using this approach therefore avoid many of the pitfalls associatedwith a selection-based approach, while also offering a mechanistic basis for ob-served fish distributions.1.4 Thesis ObjectivesModeling river systems is integral to the sound management of watersheds andcan be used to inform process-based restoration. An understanding of stream be-haviour is also necessary for the prediction and mitigation of hazards to humaninfrastructure. While a number of models exist to predict channel dimensions, aswell as processes associated with riparian disturbances, there is a strong need forbiogeomorphic models which integrate the effects of vegetation – both live ripar-ian vegetation and dead in-stream wood – on channel processes. Furthermore, it isnecessary to move beyond regime models based on a single formative flow, whichfail to capture the dynamics associated with erosion and floodplain creation in lat-erally active systems. The current work attempts to address these needs throughthe development of a series of stochastic, physically based models. These mod-els explicitly incorporate the influence of vegetation on channel processes, whilealso considering riparian and hydrologic disturbance. The models are not spatiallyexplicit and essentially represent a “black box” approach to modeling, whereinprocesses such as wood movement and subsequent trapping by jams are treatedprobabilistically.The primary objective of this thesis is to explore the role of disturbance in5shaping fluvial systems. We hypothesize that disturbance is a key governing factorcontrolling channel morphology in mountain streams, rather than a perturbation to‘natural’ conditions, and that cyclic wood loading and flooding create a morpho-logic life cycle in small- and intermediate-sized streams. Throughout the thesiswe develop a series of stochastic biogeomorphic models with an increasing de-gree of complexity to address the impacts of riparian disturbance and flooding onin-stream wood loading and channel morphology. The thesis is organized aroundthree primary objectives, as well as a number of research questions:1. Objective 1: Develop a stochastic, physically based model that links ri-parian disturbance to channel morphology and in-stream habitat avail-ability. We use the model to address the following research questions: Howdo changes in wood recruitment affect the amount of wood and the num-ber of jams in a laterally stable reach? Do changes in recruitment affect thevariability in wood loading and in-stream habitat?2. Objective 2: Develop a biogeomorphic model to simulate the changes inchannel geometry associated with variable flood magnitudes in a later-ally unstable stream reach. This research addresses the following ques-tions: How does increasing variability in flood size affect long-term averagechannel conditions, as well as year-to-year variability in channel size? Dothe return periods of the formative flood or the effective discharge changewith flow variability? Does erosion frequency of magnitude differ in streamscharacterized by low rooting depths compared with streams with high root-ing depths?3. Objective 3: Incorporate the effects of bank erosion on in-stream woodloading, jam formation, and piece movement. We begin by using datafrom flume experiments in Chapter 4 to address the following questions:How does rootwad presence affect piece mobility and transport distance?Do pieces with rootwads adopt different orientations than those without? Wethen modify the wood recruitment model presented in Chapter 2 to accountfor the effects of bank erosion on wood recruitment and in-stream dynamicsin an erodible reach. We use the model to explore the following research6questions: How does bank erosion affect wood loading? How do jam stabil-ity and abundance change in a reach subject to lateral instability? How is thestability of individual pieces affected?7Chapter 2Modeling Forest Disturbance andAquatic Habitat at a Range ofScales2.1 SummaryLarge wood governs channel morphology, as well as the availability of in-streamhabitat, in many forested streams. In this chapter we use a stochastic, physicallybased model to simulate wood recruitment and geomorphic response, in order toexplore the influence of disturbance history on the availability of aquatic habitat.Specifically, we consider the effects of fire on a range of stream sizes by varyingthe rate of tree toppling over time in a simulated forest characterized by a treeheight of 30 m. We also consider the effects of forest harvesting with various ri-parian buffer sizes by limiting the lateral extent of the riparian stand. Our resultsshow that pulsed inputs of wood increase the availability and variability of physi-cal habitat in the post-fire period; reach-averaged pool area and deposit area doublein small streams, while side-channels increase by over 50% in intermediate-sizedchannels. By contrast, forest harvesting reduces the availability of habitat withinthe reach, though the effects diminish with increasing buffer size or stream width;in laterally stable streams the effects are minimal so long as buffer width is large8enough for key pieces to be recruited to the reach. This research emphasizes theimportance of natural disturbance in creating and maintaining habitat heterogene-ity and shows that scenario-based numerical modeling provides a useful tool forassessing the historical range of variability associated with natural disturbance, aswell as changes in habitat relevant to fish. It can be also used to inform forestharvesting and management.2.2 IntroductionLarge wood promotes favourable habitat conditions for fish and other aquatic speciesby increasing the heterogeneity in channel hydraulics and morphology. Pool vol-ume and frequency are governed by wood loading in many small- and intermediate-sized streams [Fausch and Northcote, 1992, Montgomery et al., 1995, Richmondand Fausch, 1995, Buffington et al., 2002, Sweka and Hartman, 2006]. Fish abun-dance is in turn correlated to pool frequency, as pools damp the effects of flowfluctuations and provide rearing and refugia habitat [Hakala and Hartman, 2004,Lester and Boulton, 2008], and salmonids are often most abundant in pool-rifflemorphologies [Buffington et al., 2004]. Large wood also provides cover for fish,acts as a substrate for biofilm growth, and promotes the deposition of fine spawn-ing gravels upstream of wood obstructions [Floyd and Taylor, 2009, Nagayamaand Nakamura, 2009]. Channel spanning jams, which create discontinuities in thewater and bed surface along a stream profile, exert a disproportionate influence onstream morphology and habitat availability.Current conceptual models suggest that wood loading is scale-dependent. Woodload, defined as the volume of wood per unit area of bed, decreases predictablyin the downstream direction as stream size becomes sufficiently large that wood iseasily transported, and channel-spanning jams become rare [Fetherston et al., 1995,Gurnell et al., 2002, Naiman et al., 2002, Wohl and Jaeger, 2009]. Investigationsof the relationship between wood load and channel width or drainage area, whichboth increase downstream, have largely corroborated this conceptual model of lon-gitudinal wood distribution [Lienkaemper and Swanson, 1987, Bilby and Ward,1991, Gippel, 1995, Bragg, 2000, Wohl and Jaeger, 2009].The effects of large wood on channel processes and reach morphology are9also scale-dependent. The strength of the relationship between wood abundanceand pool frequency decreases with increasing stream size, again because channel-spanning jams are infrequent in larger streams due to the small relative size ofwood pieces [Beechie and Sibley, 1997, Seo and Nakamura, 2009]. Wood-relatedsediment storage decreases with channel size, and pools are increasingly dictatedby fluvial processes rather than obstructions to flow such as boulders or wood,resulting in regular pool and riffle spacing [Fetherston et al., 1995, Thompson,1995, Montgomery and Buffington, 1997, Gurnell and Sweet, 1998]. The effectsof wood are also limited in small streams as an increasing proportion of pieces aresuspended on the channel banks; functional wood load – the proportion of the to-tal wood load located within the bankfull channel – and morphological impact aretherefore greatest in intermediate-sized streams [Wohl and Jaeger, 2009, Eaton andHassan, 2013].In small- to intermediate-sized streams governed by large wood, disturbancesto riparian forests alter channel morphology through changes in wood recruitment.Wildfires are the most significant natural disturbance in terms of affected land areaglobally, and are anticipated to increase in severity and intensity as a result of cli-mate change [Lavourel et al., 2007, Flannigan et al., 2013]. Forest fires fundamen-tally affect the timing and magnitude of streamflow through changes in intercep-tion, evapotranspiration, snowmelt rates, and soil structure. Disturbances (e.g. fireor insect infestation) also alter streams by changing the input rate of large wood.Systems driven by recurrent disturbances are subject to prolonged oscillations inwood recruitment, with wood loading at a given time reflecting disturbance historyrather than a chronic background recruitment rate [Bragg, 2000, Benda and Sias,2003, Wohl and Goode, 2008]. Given the role of wood as a governing control onchannel morphology, the cyclic pattern of wood recruitment may in turn create acycle of habitat availability [Lunetta et al., 1997, May and Lisle, 2012]. Anthro-pogenic disturbances such as forest harvesting, meanwhile, generally reduce woodloading relative to streams with older riparian stands, thereby limiting habitat het-erogeneity [Bilby and Ward, 1991, Bragg, 2000, Czarnomski et al., 2008].In this chapter, we use a stochastic, physically based model to investigate theeffects of natural and anthropogenic disturbances on wood recruitment, in-streamwood loading, and habitat availability. This research builds on the existing Reach10Scale Channel Simulator (RSCS) [Eaton et al., 2012, Eaton and Hassan, 2013]by introducing a habitat module and imposing variations in wood recruitment tosimulate disturbance. We use this modified RSCS version to simulate the effects offire through variations in tree toppling rates using a Monte Carlo approach. Forestharvesting, with a range of buffer sizes, is simulated by varying the size of theriparian corridor. The model results are then used to evaluate the effects of ripariandisturbance on the intrinsic habitat potential of the reach, defined as the availabilityof physical habitat [Burnett et al., 2007], at a range of channel scales.2.3 SimulationsThe Reach Scale Channel Simulator is a physically based model that simulates theprocesses of riparian wood addition, in-stream wood transport, and jam formation.The model uses a stochastic approach to account for natural variability by attribut-ing probabilities to each of the modeled processes. The RSCS tracks individualpieces recruited from the riparian corridor – with a lateral extent defined by thetree height (Htr) – as they travel through a reach with a length (Lch) equal to 15times the channel width (Wch). The model inputs include the size of the bed ma-terial (characterized by the D50 and D84), reach-averaged gradient (S), the median(i.e. 2-year flood) discharge (Q2), as well as the average tree rooting depth (H),mature tree size (Htr and Dtr), and the undisturbed riparian stand density (ρtr) (Ta-ble 2.1). Eaton et al. [2012] provided a detailed description of the model structure,as well as the equations describing the probabilities associated with each relevantprocess for a 10 m wide stream. The authors also presented sensitivity testing forkey parameters (e.g. forest density, breakage probability), and compared modelresults to data from similarly sized streams, as well as experimental findings fromDavidson and Eaton [2013]. Eaton and Hassan [2013] described an updated ver-sion of the model, which they applied to a range of stream sizes in order to assessdownstream patterns in wood loading, sediment storage, jam characteristics, andavulsion frequency.In this chapter, we adapt the model to evaluate the impacts of three distinctriparian forest scenarios on wood loading and in-stream habitat; a base scenariorepresents consistent, chronic wood inputs, while two disturbance scenarios rep-11resent the impacts of fire and forest harvesting. A complete description of allmodules contained in the model – including those described in the two previouspublications – is available in Appendix A. For each scenario we conducted 1000Monte Carlo simulations, each composed of 500 years of run time. In the two dis-turbance scenarios, the disturbance was introduced in year 300 in order to allow asteady state wood load and channel morphology to develop prior to the perturba-tion. The Monte Carlo simulations were conducted across a range of stream sizes,characterized by median discharges spanning an order of magnitude (from Q2 = 5to 50 m3/s). While median discharge can reliably be used as a surrogate for scalewithin a given region, the relation between discharge and channel size varies withhydrology and may need to be adjusted when applied to different locations.Table 2.1: A summary of variables used in the RSCS simulations. The valueof parameters which remained constant throughout all simulations areprovided, while values calculated during a model run are not shown.Variable Description ValueRiparian Forest CharacteristicsHtr Tree height 30 mDtr Tree diameter 0.4 mρtr Undisturbed riparian forest density 500 stems/haρtri Disturbed forest density in a given year —M Toppling (mortality) rate 0, 0.25, 2.8%/yearBtr Width of riparian buffer strip 0-30 mH Rooting depth 0.4 mReach CharacteristicsQ2 Median (2-year) discharge of the simulated channel 5-50 m3/sdch Depth of the simulated channel —Wch Width of the simulated channel —Lch Length of the simulated reach 15 WchAch Total bed area of the simulated reach —S Energy gradient of the simulated reach —12Variable Description ValueD50 Median diameter of the bed material 45 mmD84 Diameter of the 84th percentile of the bed material 128 mmQbm Bed material transport rate —In-Stream Large WoodDLW Diameter of in-stream wood piece —Kdecay Decay coefficient for calculating DLW 1%/yearLLW Length of in-stream wood piece —VLW Volume of individual wood piece —FLW Functionality class of wood piece 0.05, 0.5, 0.95Vjam Total volume of all jam members —d jam Jam height calculated from Vjam —Channel MorphologyWP Width of scour pool downstream of jam 0.25-0.75 WchLP Length of scour pool 2-4 d jamAP Surface area of individual scour pool —Ptot Total pool area normalized by bed area —Vsed Sediment volume stored by individual LW —VS Volume of sediment stored upstream of a jam —dS Depth of stored sediment upstream of a jam —AS Surface area of the sediment deposit —Dtot Total storage area normalized by bed area —SS Energy gradient upstream of a jam —Di Median grain size in sediment storage area —2.3.1 Base ScenarioThe base scenario represents a mature riparian forest with constant, chronic woodinputs to the stream. The simulated stand is intended to represent a mature montane13forest dominated by species such as lodgepole pine (Pinus contorta), Engelmannspruce (Picea engelmannii), and subalpine fir (Abies lasiocarpa), as this foresttype is typically subject to frequent fires. The stand also represents a forest that isat an equilibrium state, wherein chronic mortality (e.g. due to wind throw) is bal-anced by the maturation rate of younger trees, producing a constant forest densitythrough time. The simulated forest contains trees with a constant height (Htr) of30 m and diameter (Dtr) of 0.4 m, as well as a constant rooting depth (H) of 0.4m and undisturbed stem density (ρtr) of 500 mature trees per hectare (Table 2.1).These forest characteristics are consistent with those used by Eaton et al. [2012],based on the forest surrounding Fishtrap Creek, a mountain stream in the interiorof British Columbia. The modeled stand is generally representative of the montaneforests of the Interior Plateau of British Columbia, as well as parts of the UnitedStates such as Colorado and Wyoming [e.g. Bragg, 2000, David et al., 2009, Wohland Beckman, 2014]. Tree height is smaller than the height of 40 m which has pre-viously used to model forests of the Pacific Northwest [e.g. Benda and Sias, 2003,Czarnomski et al., 2008]; adjustments to tree size and stand density are necessaryto simulate more humid or lower elevation regions, which are dominated by largertree species and also characterized by longer fire intervals.The processes of wood toppling, input to streams, and subsequent breakageare described in detail in Eaton et al. [2012], as well as Appendix A. The topplingrate (M) in each year is randomly selected from a uniform distribution of valuesranging from 0.002 to 0.003 (or 0.2% to 0.3% of trees per year), with a meantoppling rate of 0.0025 (or 0.25% of trees per year). This rate, which is lower thanthe background rate of 0.5% per year used by Benda and Sias [2003], was selectedby calibrating the steady state wood loading produced by the model to observedpre-fire wood loading in Fishtrap Creek. The toppling rate and stem density areused to determine the number of trees that fall within the riparian area (i.e. thearea on either side of the stream within a distance of Htr from the bank) each year.Each of these trees is then assigned a location relative to the stream bank that israndomly selected from a uniform distribution from 0 to Htr, as well as a randomfall angle. Based on the distance and fall angle, the model determines the length oftree (LLW ) that intersects the stream channel.If a fallen tree intersects the stream, it is assigned a functionality class (FLW )14based on its position relative to the bankfull channel. Pieces that are suspendedabove the channel are given a value of 0.05, as they have limited influence onchannel morphology. Pieces that are ramped on one bank interact significantlywith a portion of the channel bed, and are assigned a value of 0.5, while pieceslocated entirely within the bankfull channel are assigned a functionality value of0.95 (Figure 2.1a). Piece functionality may remain low for a significant periodof time after wood recruitment, as wood remains suspended above the channelor ramped on one bank. The piece blockage ratio, which dictates the sedimenttrapping potential (i.e. the morphologic impact) of each piece, is scaled based onits functionality class.15Figure 2.1: Examples of wood functionality classes and morphologic impacts from Fishtrap Creek, British Columbia.a) A jam containing pieces with varied functional classes, b) A deposit area upstream of a channel-spanning jam,c) A scour pool downstream of a channel-spanning jam, d) A side channel (left arrow), triggered by a downstreamjam which deflected flow away from the main channel (right arrow).16Each year an individual piece may break, move within the system, or be ex-ported from the reach, depending on its shape and size. The diameter of all in-stream wood pieces (DLW ) decreases annually according to a decay rate (Kdecay) of1% per year, which produces a volumetric decay rate of 2% per year and is consis-tent with values reported in the literature [Benda and Sias, 2003, Bilby, 2003, Eatonet al., 2012]. As the diameter decreases relative to the piece length, the probabilityof breakage and subsequent movement increases, as does the likelihood of beingremoved from the reach entirely; pieces are exported when piece length is less than20% of the channel width (Wch), or when diameter is less than 0.1 m. Movementalso occurs when the key piece in a jam breaks, releasing all of the smaller piecesstored within the jam. The distance a piece moves is determined as a function ofits length and diameter, orientation, and the number of jams in the reach.The rate of sediment supply to the reach is assumed to equal to the bed materialtransport rate (Qbm), and therefore varies with channel size. The modeled channelproperties and transport rates for each scale are summarized in Table 2.2. Inputgrain sizes were selected based on field samples from Fishtrap Creek, consistentwith previous work by Eaton et al. [2012]. The input grain sizes (D50 = 45 mmand D84 = 128 mm) are held constant over the range of channel scales considered,while gradient varies according to the following empirical power function (derivedby Andrews [1984] for gravel bed streams in Colorado):S = 0.04Q−0.352 (2.1)17Table 2.2: A summary of the reach characteristics associated with a range of simulated channel sizes, as characterizedby median flood discharge.Median discharge (Q2) Slope (S) Width (Wch) Depth (dch) Bedload transport rate (Qbm)m3/s m/m m m m3/s5 0.023 5.8 0.49 0.001910 0.018 9.3 0.56 0.002915 0.016 12 0.61 0.003720 0.014 15 0.66 0.004325 0.013 18 0.69 0.005030 0.012 20 0.72 0.005535 0.012 22 0.75 0.006140 0.011 24 0.77 0.006645 0.011 26 0.80 0.007050 0.010 28 0.82 0.0075182.3.2 Fire ScenarioFire is simulated in the RSCS model by incorporating temporal variation into thetoppling rate of trees (M), as well as the stem density in a given year followingthe disturbance (ρtri), thereby altering recruitment to the fluvial system over time.Toppling rates cycle through three distinct states following a modified version ofthe conceptual model developed by Benda and Sias [2003]. In the 50 year periodfollowing a stand-replacing fire, we impose an elevated mean toppling rate (M) of0.028 (2.8% of standing snags per year), with the annual toppling rate randomlyselected from a uniform distribution ranging from 0.025 to 0.03. This produces adecrease in the stem density over time (t) according to:ρtri = ρtr · e−M·t (2.2)The magnitude of the post-fire toppling increase is supported by research instreams in British Columbia, which has shown that fires increase the recruitmentrate by an order of magnitude or more [King et al., 2013], and is conservative rela-tive to toppling rates measured by Bendix and Cowell [2010]. The period of pulsedwood increase is followed by a 50 year period in which no toppling or riparian re-cruitment occurs as the re-generating forest matures. In this period the maturingtrees are too young to die naturally and are therefore not yet subject to toppling.Finally, 100 years after the fire the forest again reaches the steady equilibrium stateassociated with the base scenario, with a tree height of 30 m, a stem density of 500trees per hectare, and a mean toppling rate of 0.25% per year.2.3.3 Harvesting ScenarioForest harvesting is simulated by reducing both forest density and recruitment dis-tance, while maintaining a constant chronic toppling rate. Forest density is firstreduced according to the ratio of buffer size (Btr) to tree height (Htr):ρtri =BtrHtrρtr (2.3)As the toppling rate and forest density are used to determine the number of treesthat fall within the riparian corridor, the decrease in forest density reduces the num-19ber of trees that fall each year. Harvesting limits the lateral extent of the riparianarea, so the distance from which a tree may fall is also randomly selected from a re-duced uniform distribution ranging from 0 to Btr. Forest harvesting thus decreasesthe number of stems entering the stream while simultaneously increasing the meanpiece length, as trees fall exclusively from areas nearer to the stream.We use the RSCS model to simulate a series of 16 buffer sizes, ranging from0 m to 30 m wide at 2 m intervals. Given the tree height of 30 m, a buffer size of30 m represents an undisturbed riparian forest, and has no effect on wood loading;tree height dictates the size of the undisturbed riparian corridor, as wood can not berecruited from a distance that exceeds tree height. A buffer size of 0 m, meanwhile,represents complete removal of the riparian forest. It is assumed that 100 yearsafter the harvesting occurs a mature forest has regenerated and the original pre-harvesting riparian extent and forest density from the base scenario are restored.2.4 RSCS Habitat ModuleThe RSCS provides a useful tool for linking riparian processes to channel morphol-ogy and in-stream habitat. Channel-spanning log jams affect channel morphologyby introducing discontinuities in water and bed elevation, and increasing the het-erogeneity in channel hydraulics and morphology within a reach. In addition toaltering the riparian inputs, we have therefore also developed a habitat module,which can be used to explore the effects of log jams on important aquatic habitatcomponents at the reach scale. Specifically, we focus on the effects of channel-spanning jams on pool area, sediment storage and texture, and the formation ofsecondary channels (Figure 2.1). The components of the habitat module are de-scribed in detail below.2.4.1 Jam CharacteristicsJams are defined in the model as individual pieces or assemblages of pieces thatcontain at least one key member. In this sense, the term indicates more about themorphological effectiveness of the wood than classifications based on the numberof pieces a jam contains, and includes log steps. Key members (i.e. large stablepieces capable of trapping and retaining smaller ones) have variously been defined20based on length, diameter, and stability [Abbe and Montgomery, 2003, Mannersand Doyle, 2008, Vaz et al., 2013]. We define key members as pieces that block atleast 75% of the channel width (Wch), taking into consideration the functional class(FLW ), essentially limiting the definition of jams to those that span the channel.Jam volume is determined by adding the individual volumes (VLW ) of all pieces ina jam, with the volume of each piece scaled by its functionality:Vjam = Σ(VLW ·FLW ) (2.4)Using simplifying assumptions about jam shape, jam height (d jam) is calculatedbased on the volume of wood in the jam and the width of the channel (Figure 2.2):d jam =√VjamWch(2.5)2.4.2 Pool AreaWhile research has repeatedly shown that in-stream wood reduces pool spacing andincreases pool surface area in a reach [e.g. Richmond and Fausch, 1995, Mont-gomery et al., 1995, Buffington et al., 2002], pool geometry depends on factorssuch as wood orientation, bed texture, and channel gradient, and has proven dif-ficult to model [Thompson, 2012]. In order to enable comparisons of reach scalepool area between simulations, we therefore adopt a simplified model of pool for-mation that assigns pool size based on channel width and the vertical height of thechannel obstruction, and is conceptually consistent with empirical findings [Rich-mond and Fausch, 1995, Buffington et al., 2002]. The pool area formed by local-ized scour downstream of each jam is calculated according to a set of probabilisticrules in each year (Figure 2.2). Pool width (WP) is randomly selected from a uni-form distribution ranging from 0.25 to 0.75 times the channel width, while the poollength (LP) is randomly selected from a uniform distribution of 2 to 4 times the jamheight:WP = [0.25−0.75] ·Wch (2.6)21d S = D842 Wchdjam2 djam4 djamdbfWchdSAPASFigure 2.2: Schematic showing the effect of a channel-spanning jam on reachmorphology. The upper panel shows a side view of the sediment accu-mulation upstream of a channel-spanning jam, and pool scour down-stream. The deposit area represents the portion of the accumulationarea where sediment depth exceeds the size of the D84. The lower panelshows the plan view of the deposit area and pool area produced by thechannel spanning jam.LP = [2−4] ·d jam (2.7)The pool area (AP) for each individual pool is then simply the product of the poollength (LP) and width (WP). Finally, a total pool area for the reach (Ptot), nor-malized by the bed area of the reach (where Ach =Wch ·Lch), is recorded for eachyear:22Ptot =ΣAPAch(2.8)2.4.3 Sediment StorageEmpirical studies suggest that a large proportion of sediment storage is attributableto large wood, and that the volume of sediment stored is determined by piece sizeand structure [e.g. Nakamura and Swanson, 1993, Thompson, 1995, Abbe andMontgomery, 2003]. Sediment storage by individual pieces in the RSCS model,described in detail by Eaton et al. [2012], is calculated based on the continuity-derived rate of sediment supply, the relative blockage ratio of the piece, and atrapping efficiency parameter determined through calibration with empirical ob-servations and flume experiments [Eaton et al., 2012, Davidson and Eaton, 2013].The volume of sediment stored upstream of each jam is simply the sum of thesediment stored by each individual piece within the jam (VS = ΣVsed).All of the sediment is assumed to be stored within a rectangular area upstreamof the jam, with a width equal to the channel width, and a maximum length of twochannel widths upstream of the jam. This results in a maximum storage area of 2Wch2. From the side view, the deposited sediment forms a triangular wedge (Figure2.2), so the depth of the sediment at the jam face (dS) is given by:dS =2VSWch ·2Wch =VSW 2ch(2.9)The area of the sediment accumulation that is significantly altered by deposi-tion (AS) is then calculated using the D84 value as a threshold:AS = (2Wch− D84WchdS )Wch (2.10)This threshold was selected because the D84 has been shown to represent the depthof the active layer [Wilcock et al., 1996, Haschenburger and Church, 1998, Devries,2002], and we assume that deposits with thicknesses less than the active layer depthrepresent transient changes in sediment texture. Finally, a normalized sedimentdeposit area for the reach is recorded in each year, where:23Dtot =ΣASAch(2.11)In some cases, the sum of all storage area and pool areas within the reach aregreater than the actual bed area of the reach. In these cases, the storage area for thereach is calculated by subtracting the total pool area from the total bed area. Thisessentially represents an assumption that pools scour within storage areas, ratherthan storage areas infilling pools.2.4.4 Bed TextureIn the absence of wood, the channel is assumed to follow a typical riffle spacing of5 Wch, with a constant gradient between riffles during bankfull flow conditions. Thedepth of the sediment accumulation can therefore be used to determine the changein energy gradient – and thus the change in sediment texture – within each storagearea, AS (Figure 2.2). The original slope of the bed (S) is reduced upstream of thejam by the depth of the sediment stored at the jam face (dS), enabling a calculationof the modified gradient upstream of the jam (SS):SS = S− dS5Wch (2.12)The ratio of the gradient of the sediment storage area to the channel gradientis then multiplied by the median grain size to estimate the size of the depositedsediment (Di):Di =D50 ·SSS(2.13)The grain size in the storage patch can also be normalized according to the originalgrain size of the underlying bed, with the result that:DiD50=SSS(2.14)242.4.5 Side ChannelsSide channels form when an avulsion occurs during high flows and persists overtime, either by scouring a new channel on the floodplain or by re-occupying anabandoned location, diverting flow from the main channel. Avulsions may be trig-gered by a number of mechanisms including flooding, flow obstruction by wood,and bank erosion at meander bends [Slingerland and Smith, 2004]. Regardlessof the specific trigger, avulsions occur when a gradient advantage develops, andare therefore most common in aggradational systems where deposition causes thechannel bed to become perched above the floodplain [Slingerland and Smith, 2004,Tal and Paola, 2010]. We model avulsion and side channel formation as a functionof the sediment depth relative to the bank height; when sediment accumulation up-stream of a jam forces a sufficient increase in bed elevation, an avulsion occurs ashigh flows can no longer be contained within the channel banks. Avulsion occurswhen the sediment accumulation at the jam face reaches a threshold depth relativeto the channel depth, dch. As with the other model elements, random variationaround the threshold value is incorporated to simulate the stochasticity inherent tothe process; on average avulsion occurs when the sediment deposition at the jamface is 80% of the channel depth, but the actual threshold is uniformly distributedbetween 60% to 100% of the flow depth. These values are largely consistent withprevious research that has shown that a height of aggradation equal to 60-110% ofthe bankfull flow depth is necessary to trigger an avulsion [Mohrig et al., 2000].Side channels are then maintained so long as a jam retains this threshold amountof sediment. The RSCS records the side channel frequency, which is simply theproportion of the total run time during which at least one of these jam-induced sidechannels is active in the reach.2.5 Results2.5.1 Wood LoadIn the base scenario, which represents chronic wood inputs in the absence ofdisturbance, a steady state wood load is reached after approximately 200 years.Large variability in wood loading nevertheless persists beyond this initial period,25as demonstrated by the sample of Monte Carlo simulations presented in Figure2.3a. This variability is a direct result of the stochasticity incorporated into themodel, and represents the range of different stream conditions that may developunder a constant set of exogenous forcings. The disturbances imposed in the fireand harvesting scenarios at year 300 dramatically alter the wood load in the stream(Figure 2.3a). The increased toppling rate in the 50 year period following the firecauses a sharp increase in wood loading, followed by a more gradual decrease inthe subsequent 50 years as in-stream wood decays. Renewed chronic toppling oftrees 100 years after the fire restores the base level of wood loading.While wood load increases in the post-fire period for all channel sizes, themagnitude of the effect depends on channel scale. In both the base and disturbancescenarios there is a decreasing trend in total wood load with increasing channelscale (Figure 2.3b). Functional wood load, which represents the total wood loadscaled by the functional class of each piece, peaks in channels characterized by amedian flood discharge of 10-20 m3/s (Figure 2.4a). At this channel size, thereremains a high ratio of bank length to bed area, but there are fewer suspendedpieces than in smaller channels. The magnitude and variability of both total andfunctional wood load is higher in the fire scenario across all scales as a result ofthe greater toppling rate in the post-fire period. Despite the upward shift in woodload as a result of fire, the effects of scale on wood load are consistent; functionalwood load in the fire scenario also peaks in streams with a median flood dischargeof 10-20 m3/s (Figure 2.4a).In the base scenario, trees located within a distance equal to the tree height(30 m) from the channel banks are capable of contributing wood to the stream.By reducing the width of the this riparian corridor, forest harvesting decreaseswood load during the post-harvesting period (Figure 2.3a). Recruitment is con-sistently reduced by the decrease in contributing area until 100 years after thedisturbance, when a mature forest has re-established. The effects of buffer sizeon functional wood loading are greatest in small- to intermediate-sized channels(Q2 = 5-25 m3/s) where wood is most abundant. As in both the base and fire sce-narios, the peak functional wood load occurs in streams characterized by a medianflood discharge of 10 m3/s, regardless of buffer size.The effects of harvesting decrease as buffer size increases; at a buffer width26200 250 300 350 400 4500.000.040.08Time (years)Total Wood Load (m3m2 ) BaseFire8m Buffera10 20 30 40 500.000.040.08Median Flood (m3 s)Total Wood Load (m3m2 ) 95th Fire50th Fire5th Fire50th BasebFigure 2.3: Variability in wood load over time for each scenario, as well asaccross channel scales is shown. a) Variability in the total wood loadover time in a channel with a median flood discharge (Q2) of 10 m3/sis shown for 10 simulations from each riparian forest scenario (dashedlines show period where disturbance affects wood recruitment), and b)the total wood load for a range of channel scales (characterized by bank-full discharge) is shown for the base and fire scenarios (grey polygonrepresents the range from 5th to 95th percentile for the base scenario).2710 20 30 40 500. Flood (m3 s)Functional Wood Load (m3m2 )95th Fire50th Fire5th Fire50th Basea10 20 30 40 500.0000.0050.0100.015Median Flood (m3 s)Functional Wood Load (m3m2 )8m Buffer16m Buffer24m BufferBase ScenariobFigure 2.4: Functional wood load across a range of channel sizes for eachdisturbance scenario. a) Functional wood load for the same range ofchannel scales is shown for the base and fire scenario, and b) the func-tional wood load in the harvesting scenario varies according to bothchannel scale and buffer size.of 24 m, or 80% of the tree height, there is no discernible effect of harvesting onfunctional wood load at any scale (Figure 2.4b). The size of the pieces recruited to28a reach is a function of both the distance of the tree from the stream bank and its fallangle, and the largest pieces of in-stream wood are derived from the trees nearestto the stream bank. At a distance of 24 m, even those trees that fall perpendicularto the stream contribute at most a 6 m long piece of wood. Thus, harvesting inthis area of the riparian zone (≥ 24 m from the stream) has limited potential toinfluence wood loading in a laterally stable (i.e. non-erodible) stream, especiallyas the channel scale increases.2.5.2 In-stream HabitatBase ScenarioThe results of the habitat model show that the impacts of large wood on channelmorphology also vary with channel scale. Pool area is greatest in small streams(Q2 = 5-10 m3/s; Figure 2.5a), where jams are small but frequent; wood load ishigh due to the high ratio of bank length to channel bed area, but wood is notsufficiently mobile (due to the large size of pieces relative to the channel width) toform large jams. In some cases, large wood forces the development of scour poolsthat cover nearly 30% of the channel bed. The proportion of the bed covered byjam-related sediment deposits is also greatest in small streams, peaking in streamscharacterized by a median flood discharge of 10 m3/s (Figure 2.5b). The extent offining upstream of individual jams, which occurs in response to decreased channelgradient and transport capacity, is greatest in intermediate-sized channels wherethe median flood discharge is 20-25 m3/s (Figure 2.4a). Similarly, the frequencyof avulsion and side channel development is greatest in intermediate streams withmedian discharges of 15-20 m3/s (Figure 2.6b). The intermediate scale is the scaleat which jam size is greatest, as there are both large channel spanning key pieces,and smaller mobile pieces which can accumulate to increase the jam size [Wohl andJaeger, 2009]. Increased jam size (and thereby jam height) at this scale enables agreater depth of sediment to deposit at the jam face, causing greater alteration ofchannel gradient.2910 20 30 40 500. Flood (m3 s)Pool Area (m2m2 )95th Fire50th Fire5th Fire50th Basea10 20 30 40 500.00.40.8Median Flood (m3 s)Deposit Area (m2m2 ) 95th Fire50th Fire5th Fire50th BasebFigure 2.5: The effect of fire on pool area and deposit size across a range ofchannel sizes. a) Pool area from year 300 to 500, normalized by thechannel bed area, is shown for a range of channel sizes in both the fireand base scenarios (grey polygon represents the range from 5th to 95thpercentile for the base scenario), and b) deposit area, again normalizedby the channel bed area, is shown for this same 200 year period.30Fire ScenarioThe addition of wood following the simulated fire at 300 years increases the me-dian value of all of the habitat metrics. Scale remains an important control onin-channel habitat, however, as the disturbance does not influence the channel sizeat which each habitat metric is optimized. Pool area and deposit area both approxi-mately double in small and intermediate streams (Q2 = 5-15 m3/s) in the post-fireperiod (Figure 2.5a and 2.5b). The reach also experiences extensive fining, withthe greatest textural change occurring in large channels characterized by a medianflood discharge of 30 m3/s (Figure 2.6a). At this scale, however, channel spanningjams are rare and the deposit size is generally low, though deposits may occasion-ally occupy up to 20% of the bed area. Thus, in terms of areal coverage, fining isactually greatest in smaller channels. The pulsed additions of wood associated withfire also increase the side channel frequency in small and intermediate streams byapproximately 50% (Figure 2.6b).In addition to increasing the median value of all habitat metrics in small andintermediate streams in the post-fire period, fire also increases the variability inhabitat. While the minimum values remain nearly constant, the 95th percentileincreases dramatically for each habitat metric, suggesting that a wider range ofconditions occur in reaches subject to fire than in those with chronic tree mortality.Figure 2.7 shows that the range of potential combinations of pool and deposit areaincreases in the 200 year period following the fire, suggesting greater heterogeneityin the channel bed.In the base scenario, the reach generally exhibits a low areal coverage of bothpools and sediment deposits, indicating that the majority of the reach displays arelatively featureless, plane bed morphology [Montgomery and Buffington, 1997].In the fire scenario, however, the reach often contains abundant pool and depositareas, signifying a shift toward a pool-riffle morphology. Fire has little apparent ef-fect on either habitat availability or morphologic variability in large streams, wherethe median flood discharge exceeds 30-35 m3/s. In these streams, the frequency ofchannel spanning jams is so small – due to a lower ratio of bank length to bed area,as well as increased piece mobility – that the addition of wood is inconsequentialin terms of habitat, and side channels never form as a result of wood. Most wood,3110 20 30 40 500.00.40.8Median Flood (m3 s)Deposit Texture (DiD50) 95th Fire50th Fire5th Fire50th Basea10 20 30 40 500. Flood (m3 s)Side Channel Frequency Fire ScenarioBase ScenariobFigure 2.6: The effect of fire on deposit texture and side channel frequencyfor a range of channel sizes. a) The deposit texture represents the grainsize in a sediment deposit normalized by the original median grain sizeof the reach, and b) the side channel frequency represents the proportionof the time that at least one side channel is present in the reach.320.000.250.500.751.000.0 0.1 0.2 0.3 0.4Pool Area (m2/m2)Deposit Area (m2 /m2 )400080001200016000count0.000.250.500.751.000.0 0.1 0.2 0.3 0.4Pool Area (m2/m2)Deposit Area (m2 /m2 )200040006000countFigure 2.7: 2D histograms of pool and deposit areas in the fire and base sce-narios. a) Pool and deposit area from year 300 to 500 in the base sce-nario shows the number of years (counts) in which the 10 m3/s channeldisplays a given combination of the two parameters, and b) the same isshown for the fire scenario in the 10 m3/s stream.33regardless of the input mechanism, is exported from larger streams and thereforehas little influence on bed morphology. At this scale fluvial processes, rather thanwood, govern the channel morphology.Harvesting ScenarioIn the harvesting scenario, habitat again reflects jam frequency and spacing, whichare in turn a function of both the channel scale and the buffer width. In order toexplore the effect of the buffer size clearly, the results are shown for the streamscharacterized by median floods of 10 and 20 m3/s (Figure 2.8). These channel sizeswere selected because they represent the scale at which habitat is most abundant,and these streams are therefore the most responsive to disturbance. Pool and de-posit area are greatest in 10 m3/s streams, while fining and side channel frequencyare greatest in 20 m3/s channels. Deposit area increases in both channel sizes withincreasing buffer width (Figure 2.8a). The deposit area at a 30 m buffer width rep-resents an undisturbed condition; when buffer size is equal to tree height (30 m),harvesting does not influence the riparian contributing area or wood recruitment.A closer examination of Figure 2.8a suggests that deposit area is comparable tothe undisturbed values beyond a buffer size of approximately 20 m in the 10 m3/schannel, but decreases dramatically in the clearcut scenario even relative to a 2 mwide buffer. The deposit area is relatively unaffected by harvesting beyond a buffersize of 10-15 m in the 20 m3/s channel, but deposits are completely absent belowa buffer width of 6 m. As anticipated, side channel frequency is greater in the 20m3/s for all buffer sizes. Again, an examination of the inflection points in Fig-ure 2.8b shows that side channel frequency is relatively unaffected by harvestingbeyond a buffer size of approximately 15-17 m in both the 10 m3/s and 20 m3/schannels, though the pattern is less clear than in Figure 2.8a. These results suggestthat harvesting has little effect on reach morphology and habitat formation whenbuffer size exceeds about 50% of the tree height, though the exact size depends onboth channel scale and the habitat metric under consideration.The diminishing effect of harvesting on in-stream habitat is related to the im-portance of large, key pieces in habitat formation. The largest pieces of in-streamwood (i.e. those that block at least 75% of the channel width) are derived from the340 5 10 15 20 25 300. Size (m)Deposit Area (m2m2 )10 m3 s20 m3 sa0 5 10 15 20 25 300. Size (m)Side Channel Frequency10 m3 s20 m3 sbFigure 2.8: The impact of buffer size on morphologic response. a) The effectof buffer size on the median deposit area from year 300 to 500 is shownfor two channel sizes, and b) the effect of buffer size on side channelfrequency is shown for two channel sizes.trees nearest to the stream. In a stream with a median flood discharge of 10 m3/s,35characterized by a width of 9.3 m (Table 2.2), the furthest distance from the banksfrom which a key piece can be recruited is 23 m. When buffer size exceeds this dis-tance, harvesting therefore has no effect on the number of jams in the reach, thoughit does have a limited effect on jam size by reducing wood loading. In a stream witha median discharge of 20 m3/s and a channel width of 15 m (Table 2.2), the piecelength needed to produce a jam increases in proportion to the increased channelwidth such that a key piece can only be recruited from trees falling within a dis-tance of 19 m of the stream bank. So long as buffer width exceeds this distance,harvesting does not influence jam frequency, and only minimally influences habitatthrough its effects on jam size.2.6 DiscussionThe simulation results contribute to a greater understanding of the longitudinaltrends in wood loading and habitat availability that result from changes in channelsize, as well as the effects of disturbances which interrupt these broad underlyingpatterns. As shown by Eaton and Hassan [2013], the total wood load in the basescenario is negatively related to channel size, characterized here by median flooddischarge (i.e. 2-year flood magnitude). This pattern, which is supported by empir-ical data [e.g. Lienkaemper and Swanson, 1987, Bilby et al., 1989, Gurnell et al.,2002, Wohl and Jaeger, 2009], results from two primary factors. First, as streamwidth and bed area increase, the length of the bank from which wood is recruitedremains constant resulting in lower wood recruitment per unit area of the streambed. Second, decreasing piece size relative to channel width and depth leads toincreased wood mobility and export [e.g. Braudrick and Grant, 2000, Bocchiolaet al., 2006]. Functional wood load depends on both the total wood load and thefunctionality class of the wood pieces, and reaches a maximum value in slightlylarger streams (Q2 =10-15 m3/s) regardless of the disturbance scenario. At thisscale the trade-off between decreasing total wood load and increasing wood func-tionality (due to a decreasing proportion of suspended and ramped pieces) producesan optimal, morphologically effective wood load. The variability in both total andfunctional wood loading also decrease with stream size. Eaton and Hassan [2013]attribute this pattern to the increase in reach length, which is scaled to reach width;36because recruitment occurs through the random death and toppling of trees, vari-ability decreases as the number of trees in the population increases.The intrinsic habitat potential of the reach – which describes habitat in terms ofmorphological suitability rather than actual use [Burnett et al., 2007] – also varieswith channel scale and is greatest in small- to intermediate-sized streams. Thissupports previous studies on jam distribution, which have shown that morpholog-ically effective jams are most frequent in intermediate-sized streams where woodis sufficiently small relative to the channel dimensions to move within the reachand join jams created by immobile key members, but wood retention and woodload remain high [Wohl and Jaeger, 2009, Beckman and Wohl, 2014]. Accordingto our results, pool area is greatest in small streams (Q2 = 5-10 m3/s) where jamsare small but frequent. The spatial coverage of pools at this scale, however, whichrarely exceeds 10% of the reach area in the base scenario, is low relative to empir-ical values of 10-30% observed in similar streams [Richmond and Fausch, 1995].This discrepancy likely arises from our modeling approach, which considers onlyplunge or scour pools downstream of channel spanning jams. While scour is thedominant pool-forming mechanism related to wood obstructions, dammed poolsmay account for as much as a quarter of all wood-related pools [Richmond andFausch, 1995, Buffington et al., 2002]. Including additional pool-forming mecha-nisms in the model may improve future estimates of pool coverage, but would notlikely influence our interpretation of the relative effects of disturbance on habitatavailability.Sediment storage is greatest in intermediate-sized streams (Q2 = 10-15 m3/s).The spatial coverage of deposit areas is large relative to pool area, covering upto 50% of the bed in the base scenario and nearly 90% of the bed when fire isconsidered. While wood has been shown to drastically increase sediment storage[e.g. Megahan, 1982, Nakamura and Swanson, 1993, May and Gresswell, 2003],the model does not explicitly consider the effect of slope, which may limit depositsize [Nakamura and Swanson, 1993]. The effects of slope are indirectly included,however, through the imposition of a threshold sediment depth equal to the D84of the bed. In our model, there is a slope-invariant maximum deposit area (AS =2W 2ch), but only the portion of this deposit region where the depth of accumulatedsediment exceeds the D84 is included in the calculation of the total reach deposit37area. The size of sediment deposit areas can therefore be restricted by imposinga larger grain size distribution (D50 and D84) when modeling small, high gradientstreams, which are often characterized by coarser bed material.The effects of wood on channel roughness and shear stress partitioning are in-corporated through the partitioning of slope in the model, which induces sedimentdeposition and fining in the deposit areas upstream of channel spanning jams. Thedegree of fining produced by individual jams peaks in somewhat larger channelsthan deposit area (Q2 = 20-30 m3/s), but considering that total deposit area is lowin these larger channels, these fine deposits are relatively infrequent and occupyonly a small proportion of the bed in large streams. Thus, large jams may producea greater degree of textural modification, but textural heterogeneity will be greatestin smaller streams where sediment size is locally reduced by more frequent ob-structions. The extent of the fining produced by the model may also be exaggeratedin large channels, as negative feedbacks which limit the textural response are notconsidered. While wood increases roughness and decreases transport capacity atthe reach scale [Shields and Gippel, 1995, Brooks et al., 2004], the decreased grainsize upstream of wood obstructions increases the relative submergence of grains,reducing grain resistance and locally increasing transport capacity [Buffington andMontgomery, 1999, Manga and Kirchner, 2000, Wilcox et al., 2006, David et al.,2011]. Furthermore, reach-scale aggradation induced by in-stream wood has beenshown to increase the average bed gradient, thereby increasing transport capacityand limiting textural response [Davidson and Eaton, 2013].Side channel formation, which occurs in response to aggradation in the de-posit area upstream of channel-spanning jams, is maximized in intermediate-sizedstreams and rarely, if ever, occurs in large channels (Q2 > 30-40 m3/s). This ap-pears to contradict the presence of side channels observed in field studies on largestreams [e.g. Abbe and Montgomery, 2003], and likely occurs because the modeldoes not consider a number of additional mechanisms for side channel formationnot related to large wood, such as channel bifurcation due to mid-channel bar for-mation. Although avulsion may still be triggered by large wood jams in large chan-nels, the frequency of wood-induced side-channels decreases with channel size.The simulated disturbances dramatically alter the functional wood load at agiven scale. The modeled increases in wood loading following fire, as well as the38decreases following harvesting, are largely in agreement with previous conceptualmodels [e.g. Bragg, 2000, Benda and Sias, 2003, Czarnomski et al., 2008], de-spite differences in the exact timing and magnitude of the wood recruitment. Themodel proposed by Bragg [2000] to simulate fire, for example, produces two dis-tinct peaks in wood loading, while the model developed by Benda and Sias [2003]exhibits a lag in wood recruitment following a fire, as well as a period where woodload decreases below the base loading between fires. The influence of disturbancein natural systems may explain the greater variability in wood loading typicallyobserved in empirical data relative to model predictions [Eaton and Hassan, 2013].Debris flows, which have been shown to increase by as much as 42% in the post-fireperiod and deliver large volumes of wood from outside of the riparian area [Mayand Gresswell, 2003], may further increase this variability. These changes in woodloading translate into changes in the availability of habitat following disturbance.Our model shows that fire approximately doubles the availability of pools, whichare important rearing habitat and refugia, as well as sediment deposits which pro-vide spawning substrate. It is also associated with a 50% increase in side channels,which provide critical habitat for many life stages.The effects of disturbance-induced variations in wood loading on habitat arehighly scale-dependent. The positive morphologic impacts associated with fire aregreatest at that scale where a given habitat feature is typically most abundant, andbecome negligible in large streams exceeding 30-35 m3/s median flood discharge,where channel-spanning jams are rare and most individual wood pieces are ex-ported from the reach. The negative effects of harvesting on in-stream habitat arealso fundamentally related to the width of the riparian buffer. When buffer sizeexceeds the distance from which key pieces are recruited, which ranges from ap-proximately 50-80% of the tree height, the impacts of harvesting on wood load andwood-related habitat rapidly diminish. The negative relation between stream sizeand required buffer width, however, only applies to streams that are laterally sta-ble. Previous research suggests that bank stability in gravel bed streams is relatedto the type and density of bank vegetation [e.g. Eaton and Millar, 2004, Millar,2005]; where rooting depth equals or exceeds the bankfull channel depth, the bankstrength provided by root networks prevents lateral migration. Beechie et al. [2006]specified a threshold channel size of 15-20 m, corresponding to a discharge of 1039m3/s, in forested streams of the Pacific Northwest. Eaton and Giles [2009] found asimilar threshold width of 11-16 m (Q2 = 10 m3/s) in Fishtrap Creek, suggestingthat the threshold channel size may decrease slightly in drier montane forests. Instreams larger than this threshold size for lateral migration, a larger riparian bufferis needed in order to ensure that key pieces are still recruited to the stream as chan-nel position shifts. In addition, wider buffers will be needed in regions with largertrees, such as the Pacific Northwest, in order to maintain reference levels of keypiece recruitment and in-stream wood loading.The morphologic benefits of increased wood loading following fire may bepartially offset by inputs of fine sediment, which often occur as a result of soilhydrophobicity or increased debris flow frequency [May and Gresswell, 2003].Fine sediment input causes sedimentation in spawning gravels, and may limit theanticipated increases in pool area during the post-fire period. Road construction as-sociated with forest harvesting also contributes substantial fine sediment to streamnetworks both through altering runoff patterns and the de-stabilization of hillslopes[e.g. Bilby et al., 1989, Motha et al., 2003, Hassan et al., 2005a, Sheridan andNoske, 2007]. However, because the simulated channel is competent to transportthis fine material, the effects of fine sediment addition will be short-lived relative tothe underlying morphologic adjustments resulting from changes in wood loading.Empirical research supports this assertion, as the effects of fire on fine sedimentconcentrations have been shown to vary markedly between systems and events,and to cause only transient morphologic changes [Benda et al., 2003, Smith et al.,2011]. The magnitude of the fine sediment loading also likely depends on post-firemeteorological conditions [Warrick et al., 2012, Owens et al., 2013].Riparian disturbances may also have additional, non-morphologic impacts onin-stream habitat. As riparian shading moderates stream temperature, the loss ofshading due to fire or forest harvesting may increase stream temperature and alteraquatic assemblages [Kiffney et al., 2003]. Loss of evapotranspiration and changesin flow routing from both fire and harvesting may also alter stream hydrology, re-sulting in larger peak flows prior to forest regeneration [Jones and Grant, 1996,Scott, 1997]. While many of these effects occur only in the years immediately fol-lowing the disturbance, even short term increases in stream temperature, suspendedsediment load, and peak flows have the potential to decimate aquatic populations.40This highlights the importance of the spatial and temporal scale of disturbance; ifimportant morphologic benefits are to be realized, disturbances must occur overa small enough area that fish are able to leave the reach when conditions are un-favourable, and later re-colonize to take advantage of improved physical habitat.To our knowledge, this research represents the first attempt to simulate the ef-fects of disturbance on in-stream habitat availability using a stochastic, physicallybased numerical model. Our results highlight the importance of natural disturbancein maintaining habitat heterogeneity. By simultaneously increasing the availabilityof both spawning and pool habitats, the additional wood loading due to fire enablesa transition from a relatively featureless plane bed to a pool-riffle morphology,which often provides the greatest availability of habitat for salmonids [Buffingtonet al., 2004, Moir et al., 2009, May and Lisle, 2012]. The heterogeneity associatedwith pool-riffle morphologies creates spatial complementarity and increases theoverall quality of the habitat, as habitats required for different life stages are avail-able in close proximity, thus limiting the dispersal distances for aquatic species[Fausch et al., 2002, Le Pichon et al., 2009, Kim and Lapointe, 2011].Fire also creates temporal heterogeneity in a reach. A fire cycle, characterizedby a mean recurrence interval that is dictated by climatic and stand characteristics,produces a ‘morphologic life cycle.’ Rather than displaying a consistent morphol-ogy defined by the median annual flood, equilibrium sediment supply, and chronicwood inputs, forested streams subject to fire may display oscillatory morphologiesas periods of high wood loading and habitat heterogeneity are followed by periodsof wood and habitat depletion. Due to the patchiness of natural wildfires, water-sheds are likely composed of a mosaic of sub-basins characterized by varied phys-ical habitat complexity and quality. Climate change and fire suppression, whichare projected to increase the spatial extent of future wildfires, may counteract thepositive influence of natural fires on channel morphology and habitat heterogeneityby exceeding the dispersal limits of many aquatic species [Flannigan et al., 2013,Owens et al., 2013].412.7 ConclusionsThis research uses a physically based numerical model to simulate the effects ofriparian disturbance on a range of channel scales, and highlights the potential forscenario-based numerical modeling to inform watershed management. Our resultsshow that the habitat associated with channel-spanning log jams is most abundantin small- to intermediate-sized streams, and that the effects of disturbance are alsogreatest at this scale. Wildfires increase habitat availability within the reach byincreasing wood recruitment, while the effects of harvesting depend largely on theability of the riparian corridor to supply key pieces to the reach, which in turninitiate jams, and decrease with increasing buffer size. The large oscillations inchannel conditions produced by the fire simulations show that regions adapted tofrequent fires may have historically experienced highly variable wood loading, andhighlight the role of stochastic modeling in assessing the historical range of vari-ability at sites where reference conditions are unavailable. Other potential modelapplications include harvesting planning, fire management, prioritization of sitesfor restoration or conservation, and climate change adaptation.42Chapter 3Departures from Regime:Channel Evolution in a LaterallyUnstable Stream3.1 SummaryRegime models were developed to predict the dimensions of irrigation canals insediment transport equilibrium, and generally assume that channel geometry ad-justs to convey a single formative discharge. The modeling presented in Chapter 2employs a regime model to predict average channel dimensions based on a forma-tive discharge equal to the median (2-year return period) flood. Most stream chan-nels, however, are subject to variability in annual flood magnitude, and unconfinedchannels above a threshold size of 10-15 m also tend to be laterally unstable. Inthis chapter we develop a physically based biogeomorphic model called STochasticCHannel SIMulator (STOCHASIM) to simulate the competition between episodicwidening during floods and vegetation colonization during the post-flood recoveryperiod. We use the model to explore the effects of flow variability and rootingdepth on long-term channel geometry and erosion rates. The modeling shows thatin highly variable systems the channel conditions are determined by two distinctpopulations of floods: relatively frequent effective floods which transport the most43sediment over time and rare flood events which determine channel size. The in-crease in flow variability also produces higher long-term erosion rates and a widerchannel geometry due to both greater erosion magnitude and frequency. Changesin rooting depth have little effect on long-term erosion rates, but influence thepattern of erosion; simulations with low rooting depths are characterized by highmagnitude-low frequency erosion, while those with high rooting depths experiencethe opposite.3.2 IntroductionAdjustments in channel geometry, often accompanied by lateral migration acrossthe floodplain, pose challenges for maintaining infrastructure such as roads, pipelines,and urban centres. The need to understand channel response to imposed flows pro-vided the impetus for the development of predictive models of channel adjustment.The Reach Scale Channel Simulator (RSCS) presented in Chapter 2 employs arational regime model to predict the average channel dimensions. This approachrelies on the fundamental assumption that average channel dimensions can be pre-dicted based on a single formative discharge, which is assumed to equal the me-dian (i.e. 2-year return period) flood. The formative discharge concept originallyemerged from seminal work by Wolman and Miller in 1960. The authors proposedthat the formative discharge, or the flow that exhibits the best statistical correla-tion with the reach-average channel dimensions, is equal to the effective discharge,or the flow that transports the most sediment over time. Since then the prevailingparadigm has asserted that a river reach in regime is adjusted to efficiently exportthe sediment supplied to the reach, and that bankfull channel dimensions are ad-justed to approximately convey the effective discharge [Wolman and Miller, 1960,Pickup, 1976, Andrews, 1980, Tal and Paola, 2010, Church and Ferguson, 2015].It is generally believed that the formative flow that dictates channel size is approxi-mately equal to the effective or bankfull discharge, and occurs every 1-2 years [e.g.Wolman and Miller, 1960, Harvey, 1969, Pickup and Warner, 1976].The idea that average channel dimensions can be predicted based on a singleformative flood magnitude – approximately equal to the bankfull flood or the ef-fective discharge – has become entrenched in the geomorphic literature. However,44while regime models based on a single flood discharge yield meaningful predic-tions of average conditions in many systems [e.g. Eaton and Church, 2007], forma-tive flow and effective discharge diverge in some circumstances [e.g. Pickup andWarner, 1976, Hassan et al., 2014]. Rare floods become increasingly importantin determining channel capacity in small watersheds that exhibit significant vari-ability in flood magnitudes [e.g. Pickup and Warner, 1976, Baker, 1977, Williams,1978, Andrews, 1980]. The growing importance of larger floods may also resultin a slight increase in effective discharge, as well as a larger increase in the pro-portion of the total sediment load transported by flows exceeding this relativelymodest flow [Sholtes et al., 2014]. Headwater streams with small watershed ar-eas also often lack a well-defined floodplain, further complicating the definition offormative flow in terms of the bankfull channel capacity. Thus mountain streamscharacterized by high flow variability and coarse bed material, are generally shapedby formative flows that occur less often than the effective discharge [Hassan et al.,2014], and may be poorly represented by regime models [Church and Ferguson,2015].Approaches based on a single formative flow also provide little insight intointermediate-term variability in channel form in mountain streams [Hassan et al.,2014]. Changes in channel geometry at intermediate time scales, however, haveobvious relevance for hazard prediction, as channel widening is the most commongeomorphic response to flood events worldwide [Magilligan et al., 2015]. Fur-thermore, the effects of land use practices and riparian disturbances on aquatichabitat quality typically manifest over intermediate (101 to 103 yrs) time scales[Fausch et al., 2002, Eaton et al., 2004]. A second related limitation concernschannel migration, or bank erosion, which is also an important consideration forstream managers over intermediate time scales; even streams with relatively con-sistent channel width typically move across the floodplain unless fully stabilizedby vegetation [Beechie et al., 2006, Eaton and Giles, 2009] or resistant bank mate-rial. While regime models may produce reasonable estimates of channel width instreams with relatively consistent geometry, they yield no insight into the rate ofchannel migration.These limitations suggest that new conceptual and predictive models are neededto describe bank erosion and channel change in streams that adjust to relatively in-45frequent formative flows. Current bank stability models primarily apply to the low-magnitude, high-frequency progressive erosion typical of low-gradient streamswith cohesive banks [e.g. Darby and Thorne, 1996b, Darby et al., 2007], whereerosion is balanced by deposition, and channel width remains approximately con-stant over time. These models also require detailed knowledge of bank compo-sition and geometry [e.g. Darby and Thorne, 1996a, Simon and Collison, 2002].While such models are useful for exploring the stability of banks over small spa-tial scales, there is a need for reach-scale biogeomorphic models that consider theeffects of the interdependent processes of erosion and vegetation colonization onchannel evolution [Church and Ferguson, 2015]. Although reach-scale biogeomor-phic modeling of channel evolution has been attempted [e.g. Asahi et al., 2013], ithas continued to focus on bank erosion and meander development in low-gradientstreams characterized by cohesive banks.The primary objective of this chapter is to address this gap by developing astochastic, physically based biogeomorphic model to simulate the competition be-tween the episodic channel widening associated with large floods, and vegetationcolonization of exposed bars during the post-flood recovery period. We use themodel to explore temporal variability in channel geometry, as well as the influ-ence of flow variability and rooted bank vegetation on channel characteristics. Themodel is also used to test the hypothesis that formative flow varies with flow vari-ability.3.3 Model Description3.3.1 Model OverviewThe STOchastic CHannel Adjustment SIMulator (STOCHASIM) is a biogeomor-phic model that simulates the interplay between erosion resulting from a randomsequence of flood events, and the colonization of exposed bars by vegetation. Theinitial channel geometry is simulated based on the first flood in the randomly gener-ated flood sequence using the UBC Regime Model (UBCRM) developed by Eatonet al. [2004], such that the starting conditions vary randomly between runs withineach simulation. In each subsequent year, the model simulates two competing pro-46cesses: i) a flood event with the potential for erosion, and ii) vegetation colonizationwhich narrows the channel (Figure 3.1). At the beginning of each year, the reachwidens if the shear stress associated with the annual flood exceeds a bank erosionthreshold (τbank). Based on experimental evidence we define this threshold as thecritical shear stress associated with full mobility of the coarse fraction (D84) of thebed material [Eaton and MacKenzie, 2016 in review]. During the second part ofthe year the reach experiences moderate flows (equal to the mean daily discharge),and narrows as vegetation colonizes exposed bar surfaces. Throughout each modelrun erosion occurs along the same channel bank, while vegetation consistently col-onizes the opposite bank. Each of the modules contained in STOCHASIM is de-scribed in detail below.3.3.2 Erosion and Channel AdjustmentAnnual Peak FlowsThe first module in STOCHASIM randomly generates a sequence of peak annualflood events (i.e. the largest daily flow that occurs over the course of a singleyear) equal in length to the number of years in the simulation. The floods arelog-normally distributed, based on user-specified values for the median (log(Q2),where Q2 is the 2-year return period event) and standard deviation. We use the stan-dard deviation of the log-transformed flow values as an index of the year-to-yearvariability, which we refer to as the Flood Magnitude Index (FMI) [after Beard,1975, Baker, 1977]. The model uses a default FMI of 0.4, which is approximatelyequal to the mean value of 0.35 measured from Water Survey of Canada (WSC)peak flow data for all gauged watershed in the Pacific drainage from 1980 to 2010(Figure 3.2a). Reducing the FMI decreases the range of annual peak flow values,while increasing the FMI has the opposite effect. As the FMI increases, the mag-nitude of the extreme flood events relative to the median flood increases (Figure3.2b). Arid regions are typically characterized by high FMI values, while humidregions have lower values; Baker [1977] recorded values as low as 0.19 in humidcoastal lowland of Louisiana, and as high as 0.9 in central Texas, Arizona, andsouthern California (Figure 3.2a).47Figure 3.1: Schematic showing possible channel changes during a single yearof a model simulation. The channel width (Wch) and depth (dch) adjustas a result of erosion along the right bank (WBE) during large floods.Over time the left bank moves toward the right, narrowing the channelin response to vegetation colonization (Wrv) along the left bank. The lowflow channel width is defined by WMAD, and the size of the exposed bar(Wexp) available for colonization is a function of the difference betweenthe channel width and the low flow width.48FMIFrequency0.0 0.2 0.4 0.6 0.8 1.0 1.2020406080HumidMedianMeanArida2 5 10 20 50 10012510Return interval (years)QQ 2FMI = 0.2FMI = 0.4FMI = 0.6FMI = 0.8FMI = 1.0bFigure 3.2: a) A histogram shows FMI values for all 287 WSC gauges activein the Pacific drainage between 1980 and 2010; dashed lines show themean and median values, as well as the extreme values for humid andarid regions presented in Baker [1977], and b) the relative flood mag-nitude associated with events ranging from the 2- to 100-year flood ispresented for all of the modeled FMI values; recurrence intervals werecalculated based on a simulated 300-year flood sequence.49Flow CharacteristicsThe boundary shear stress associated with the annual flood varies as a function ofboth the flood magnitude and the channel geometry. Reach-averaged shear stress(τ0) is a function of hydraulic radius of the flow (R) and the channel gradient (S),and is calculated for each flood according to:τ0 = γRS (3.1)where γ is the unit weight of water. While the gradient remains constant throughoutthe simulation, the hydraulic radius (R) varies with channel geometry:R =AP(3.2)where A is the cross sectional area of the flow and P is the wetted perimeter. Thehydraulic radius, and thus shear stress, also varies with flow resistance (ℜ), whichis calculated in the model using Ferguson’s continually varying power law:ℜ=a1a2(R/D84)√a21+a22(R/D84)(3.3)where a1 and a2 are constants (6.5 and 2.5, respectively), and D84 represents thecoarse fraction of the bed surface material.Finally, flow resistance is related to flow velocity (U), and thus discharge (Q),according to:U =ℜ√gRS (3.4)and:Q = A ·U (3.5)where g represents gravitational acceleration. The hydraulic radius associated witha given flood discharge can therefore be solved iteratively by changing the flowdepth while maintaining the original channel width and geometry (i.e. trapezoidheight, vertical bank height, and side slope angle). The same flood discharge may50produce a shear stress below the critical value if the channel has recently widened,but above the critical value if the channel geometry is narrow. The decrease inshear stress for a given discharge also leads to a concomitant decrease in trans-port capacity, promoting aggradation in the post-flood period. While this aggra-dation is not explicitly considered in the model, we assume that sediment depositspreferentially on exposed bars, due to higher roughness provided by encroachingvegetation [Asahi et al., 2013]. This leads to an increase in the elevation of the de-veloping floodplain, while the bed elevation within the active channel is unaffectedby aggradation during the recovery period.Sediment TransportFor each flood the model also calculates the sediment transport rate associatedwith the flow, prior to widening, using the sediment transport equations describedin Eaton and Church [2011]. This method invokes an excess stream power relation,rather than one formulated on excess shear stress, such that sediment transport isproportional to excess stream power, (ω −ωc)3/2. Research has shown that thestream power per unit bed area is both a better predictor of bedload transport andless dependent on bed slope than excess shear stress [Parker et al., 2011]. However,as the sediment flux predicted by the model is best understood as a scale represen-tation of transport, rather than a true estimate, the choice of sediment transportformulation is not critical [Eaton et al., 2004].Following Eaton and Church [2011] we first define the dimensionless streampower (ω∗) according to:ω∗ =ωρ[g(ρs−ρwρw)D50]3/2 (3.6)where ρ and ρs are the water and sediment density, respectively, and D50 is the me-dian grain size. Stream power (ω) is simply equal to γQSW , where W is the averagechannel width. The critical stream power (ω∗c ) is then calculated using:ω∗c =ℜ ·θ 3/2c (3.7)Because the resistance (ℜ) varies with changes in relative roughness, RD84 , the crit-51ical stream power also varies throughout a run. As we are interested in bedloadentrainment rather than bank erosion, the model uses the critical dimensionlessshear stress for entrainment (θc) as the threshold value, rather than the bank ero-sion threshold which will be defined in Section 3.3.2. Finally, Eaton and Church[2011] used an empirical dataset to relate a dimensionless transport parameter (E∗)to the ratio of ω∗ω∗c:E∗ =[0.92−0.25√ω∗cω∗]9(3.8)Using this relation, the dimensional sediment transport rate (Qb) for each flood iscalculated according to:Qb =E∗QSg(ρs−ρ) (3.9)Bank ErosionPrevious research suggests that the coarse fraction of the bed material constrainsthe mobility of the bed surface and subsurface [Nanson and Hickin, 1986, Olsenet al., 1997, Emmett and Wolman, 2001], and that erosion of the cohesionless banktoe in turn controls the rate of bank retreat, even where a cohesive upper layer ispresent [e.g. Eaton, 2006, Darby et al., 2010]. According to experiments by Eatonand MacKenzie [2016 in review], bank stability decreases when the D95 of the bedmaterial along the toe of the bank is entrained, which approximately correspondswith full mobility of the D84 of the bed material. The model therefore assumes thatthe channel widens when the D84 of the material comprising the bank toe is fullymobilized, as the coarse material that accumulates at the base of the bank controlsthe rate of bank undercutting and subsequent retreat [Nanson and Hickin, 1986,Darby et al., 2010, Eaton and MacKenzie, 2016 in review].This approach to bank stability is analagous to the relative bed stability criteriaoutlined by Olsen et al. [1997], which defines bed stability in terms of the ratio ofboundary shear stress to the critical value for entrainment – rather than full mobil-ity – of the D84 of the bed surface. The proposed bank erosion threshold is alsosimilar to the relative bed stability criteria described by Kaufmann et al. [2008] in52terms of the ratio between observed mean particle diameter and the flow compe-tence (i.e. the mean particle size entrained) during the bankfull flow. Accordingto their stability criteria, Kaufmann et al. [2008] found that only 16% of streamswere stable during bankfull conditions. As large-scale instability and erosion isgenerally related to relatively infrequent floods, our more conservative approach –which assumes that erosion occurs during rare floods that fully mobilize the bedmaterial D84 – appears justified.To determine the bank erosion threshold the model first calculates the criticalshear stress for entrainment of the median grain size (τc50) according to the bedmaterial grain size and the critical Shields number (θc):τc50 = θcg(ρs−ρw)D50 (3.10)The critical Shields number is equivalent to the dimensionless shear stress at whichthe sediment is entrained, and generally varies between 0.02 and 0.06 for gravel-bed rivers [Haschenburger and Wilcock, 2003, Church, 2006]. Research has alsoshown that the critical Shields number increases with channel slope, in part dueto the effect of higher relative roughness – due to both larger particle sizes andshallower flows – on velocity profiles and the intensity of near-bed turbulence [e.g.Mueller et al., 2005, Lamb et al., 2008, Recking, 2009, Parker et al., 2011, Prance-vic et al., 2014, Prancevic and Lamb, 2015], and decreases with the sand contentof the bed surface [Wilcock and Crowe, 2003, Church and Ferguson, 2015]. Weadopt a value of 0.04 as a default value and present sensitivity testing on the effectsof variations in the critical Shields number on erosion and channel size.The critical shear stress for entrainment of the surface D84 of the bank toe (τc84)is calculated based on the ratio of the D84 to the D50 in the reach, according to workby Wilcock and Crowe [2003]:τc84 = τc50 ·(D84D50)0.67(3.11)The bank erosion threshold (τbank) is reached when the surface D84 of the banktoe is fully mobilized. According to flume experiments conducted by Wilcockand Mcardell [1993], full mobility occurs at two times the shear stress required to53entrain material of a given size, such that:τbank = 2 · τc84 (3.12)If the bank erosion threshold is exceeded, a new channel width is calculatedusing the flood discharge as the formative flow value in the UBCRM. Consistentwith experimental evidence [Pitlick et al., 2013, Eaton et al., 2016 in review], thesize of the new channel adjusts to the imposed flood magnitude; erosion progressesuntil the reach-averaged boundary shear stress is reduced to the threshold value.Flume experiments conducted by [Pitlick et al., 2013, Eaton and Mackenzie, 2016in review] suggest that this erosion can occur rapidly – within a single day of flowin a prototype system – as eroded material deposits in the centre of the channelleading to sedimentation of the channel bed.3.3.3 Biogeomorphic RecoveryLow Flow Channel WidthEach year vegetation colonizes the exposed bar surface along one side of the chan-nel, reducing the channel width. STOCHASIM estimates the wetted width of thechannel for the mean annual discharge (i.e. the average daily flow throughout theyear) in order to determine the exposed bar area available for vegetation coloniza-tion each year. The exposed bar area therefore depends on two factors: i) the meanannual discharge, and ii) the bed morphology. Together these factors determine thewetted width of the channel during the period of vegetation colonization.The mean annual discharge (MAD) is calculated based on an empirical regres-sion (r2 = 0.96) between the median flood size and the FMI value for the 286Pacific draining WSC stations used in the FMI analysis:log(MAD) = 1.03 · log(Q2)−0.95 ·FMI−1.70 (3.13)Mean annual discharge is positively related to the median flood size, but negativelyrelated to the FMI value. As flow variability increases the magnitude of the medianflood relative to the mean annual discharge increases. Streams with high FMI val-54ues, which are typical of mountain headwater systems or arid regions, experiencerelatively low base flows punctuated by large floods.The model then calculates the wetted width associated with the mean annualdischarge using the At-a-Station Hydraulic Geometry Simulator (ASHGS), whichis described in detail by McParland et al. [2014]. While most models calculate theregime geometry associated with a formative discharge, ASHGS can be used tosimulate hydraulic conditions at flows below bankfull. The inputs to the model aresimilar to STOCHASIM, with the addition of a morphologic index, b. This index,sometimes referred to as a shape factor, describes the variability in the channeldepth within a reach and ranges from 0-1 [Ferguson, 2003]. Low b-values arecharacteristic of plane bed channels with low amplitude bars [Montgomery andBuffington, 1997, McParland et al., 2014], while streams with values greater than0.4 generally exhibit pool-riffle morphologies with high amplitude bars [Ferguson,2003, McParland et al., 2014]. The morphologic index is calculated according to:b = 1− d2dmax(3.14)where d2 is the mean channel depth associated with the 2-year flood discharge anddmax is the maximum depth in the reach. The morphologic index is also a reflectionof sediment supply, as increased supply in pool-riffle response reaches generatesgreater variability in channel depth and a higher morphologic index.The channel morphology dictates the width of the low flow channel (WMAD)relative to the long-term average (i.e. regime) channel width. In a rectangularplane-bed channel (b = 0), the entire channel bottom is occupied regardless of theflow magnitude, and there is no difference between the low flow width and thelong-term average channel width. As the depth distribution becomes increasinglyskewed due to the formation of pools and bars, however, low flows are confined toa decreasing proportion of the channel bed, resulting in a reduced wetted low flowwidth. To account for annual variability in low flows, the actual low flow width(WMAD) in each year is randomly selected from a normal distribution centred onthe mean value generated by ASHGS.55Vegetation ColonizationBased on previous research on vegetation colonization rates, we assume that ap-proximately 10% of the exposed bar surface is colonized by vegetation in a givenyear [Konrad, 2012]. This produces a negative exponential trend in channel widthover time, which is consistent with previous field and experimental work [e.g. Per-ona et al., 2009, Tal and Paola, 2010]. Stochasticity is incorporated into the modelby randomly varying the vegetation colonization rate according to a normal distri-bution with a mean equal to 10% and a standard deviation of 3.3% to reflect annualvariability in growth conditions.The exposed bar surface available for colonization is equal to the differencebetween the total width of the channel (Wch) in a given year, and the channel widthduring low flow width (WMAD). As described in Section 3.3.3, the size of the ex-posed bar relative to the total channel width is controlled by channel shape; pool-riffle channels with high variability in channel depth have a smaller low flow width(and a larger proportion of the bed exposed) than plane-bed reaches, which arecharacterized by a rectangular channel geometry. The size of the exposed bar –and therefore the absolute rate of revegetation – varies throughout a simulation asthe channel width changes in response to the flood history. The width colonized inany year (Wrv) is:Wrv = 0.1 · (Wch−WMAD) (3.15)Colonization reduces both the top and bottom width of the channel by the dis-tance Wrv (Figure 3.1). The channel narrows each year, so long as the channelwidth exceeds the low flow channel width; the low flow channel width thereforeconstrains the extent of channel narrowing, and is asymptotically approached dur-ing successive years with small or moderate flood peaks. By decreasing the channelwidth – and therefore increasing the depth and hydraulic radius associated with aflood of any given magnitude – colonization increases the likelihood of bank ero-sion in subsequent years. Interactions between flow variability and the colonizationrate are not considered in the model, but may influence channel evolution. Asahiet al. [2013] have shown, for example, that increasing flow variability can leadto the development of lower sinuosity, braided planforms as increasingly frequent56large floods prevent vegetation establishment on exposed bars.3.3.4 SimulationsWe use the model to conduct a series of Monte Carlo simulations for a stream reachcharacterized by a median flood magnitude of 20 m3/s. The associated channelwidth is slightly larger than the observed channel width in Fishtrap Creek, the pro-totype stream described in Chapter 2 and in Appendix B. This channel size wasselected as it exceeds the minimum threshold for lateral mobility of approximately11 m [Eaton and Giles, 2009], which is set by the typical rooting depth of bank veg-etation; in streams smaller than this size roots fully penetrate the channel bank, pre-venting bank instability. Of the range of channel sizes above this threshold whichwere modeled in Chapter 2, the selected channel scale of 20 m3/s also experiencesthe highest wood loading and the greatest morphologic response to wood inputs.We therefore use this channel scale for all simulations in the remaining chapters.Each simulation includes 400 runs, each lasting 300 years. Simulations wereconducted for five flow variability scenarios, with FMI values ranging from 0.2 to1.0. We also conducted simulations for five rooting depth values, ranging from 0 to0.8 m. As channel migration is limited when roots fully penetrate the channel depth[Beechie et al., 2006, Eaton and Giles, 2009], this represents the range of rootingdepths over which erosion and lateral migration are expected to occur (d2 =0.73).As in Chapter 2, the channel gradient was calculated based on the median floodaccording to a modified empirical relation from Andrews [1984], resulting in agradient of 0.014 m/m. The effective discharge for each simulation was determinedby categorizing the flood magnitudes for all years into constant 0.5 m3/s classes[Sholtes et al., 2014], and multiplying the duration of each flow category by itsmean sediment transport rate (Qb), in order to determine the total bed load transportrate. We defined the effective discharge as the mid-point of the class with thehighest bed load transport [Pickup, 1976, Andrews, 1980].A second series of Monte Carlo simulations were also conducted to investigatethe model sensitivity to variations in the critical Shields number (θc), re-vegetationrate (Cv), and channel morphology (b). Specifically, we focused on the impactsof changes in these governing parameters on the length of stability intervals (i.e.57the time between bank erosion events), and the long-term average erosion rate andchannel width. In each case only the parameter of interest varied, while all otherparameters were set equal to the default values shown in Table 3.1. The sensitivityanalysis for each parameter included a sequence of simulations, each comprised of400 runs lasting 300 years.Table 3.1: Parameters considered in STOCHASIM sensitivity analyses, aswell as the default values for each parameter.Parameter Description Default value Rangeθc Critical Shields number 0.04 0.02-0.06Cv Vegetation colonization rate 10% 5-25%b Morphologic index 0.2 0-0.8Finally, we conducted simulations for 40 stream reaches across western Canadausing data obtained from BGC Engineering Inc. The model results are comparedwith actual bank erosion rates measured from historical air photographs in Ap-pendix C, and show that STOCHASIM produces a reasonable upper estimate oflong-term erosion rates for a large range of stream types.3.4 Results3.4.1 Channel EvolutionChannel geometry varies over time for all simulations in response to episodic ero-sion as well as progressive narrowing between floods. Figure 3.3 shows the tempo-ral variability in flood magnitude and channel width for three of the simulated flowvariability scenarios. These results highlight the large range of possible channelgeometries in any given year, despite constant governing conditions (e.g. mediandischarge, grain size, gradient), and represent the potential spatial variability withina system. A separate set of simulations conducted with the same flood sequencefor all 300 runs in each scenario, presented in Figure E.1, show that channel ge-ometry varies between runs even when the same flood series is used. In additionto variations in channel geometry, the stream position shifts throughout the runs.58Channel migration occurs in response to erosion, which removes material fromthe one bank, as well as floodplain creation resulting from vegetation coloniza-tion along the opposite bank. The result is a progressive movement of the channelacross the floodplain (Figure 3.4a).590 20 40 60 80 10004080Time (years)Discharge (m3s) FMI = 0.2FMI = 0.4FMI = 0.6Median flooda0 20 40 60 80 1005152535Time (years)Top Width (m) WidthMedian widthRegime widthbFMI = 0.20 20 40 60 80 1005152535Time (years)Top Width (m) WidthMedian widthRegime widthcFMI = 0.40 20 40 60 80 1005152535Time (years)Top Width (m) WidthMedian widthRegime widthdFMI = 0.6Figure 3.3: Time series plots of flood magnitude and channel width for arange of scenarios. a) A single flood sequence from each of three flowvariability scenarios. Channel width for the first 100 years for b) a lowflow variability scenario, c) a moderate flow variability scenario, d) anda high flow variability scenario. Grey polygons show the range of widths(1st to 99th percentile) in each year.600 20 40 60 80 100 120−1.5− (m)Elevation (m)Original geometryFMI = 0.2FMI = 0.6FMI = 1.0a0 10 20 30−1.5− (m)Elevation (m) Colonization Bank erosiont=0t=5 t=10 t=15Pre−wideningPost−widening5 years10 years15 yearsbFigure 3.4: a) The channel position at 50 and 100 years is compared with the original channel location for three of theflow variability scenarios, and b) the widening and subsequent narrowing associated with a large erosion eventis shown for a single run from the default (FMI = 0.4) flow variability scenario. The position of the left bank isshown after 5, 10, and 15 years of vegetation colonization.61Figure 3.4b shows a single cycle of erosion and recovery for the default flowvariability scenario (FMI = 0.4). Following an initial adjustment in channel geom-etry, width progressively decreases over time during the recovery period throughcolonization along the left bank, asymptotically approaching the low flow chan-nel width until it is interrupted by a subsequent erosion event. As we assume thatflood flows are distributed over the entire channel bed, sediment transport rates andflow competence decrease as a result of reduced flow depths immediately followingchannel widening, and increase progressively throughout the recovery period. Thestreams with the greatest flow variability are subject to the most dramatic erosion,and therefore experience the largest decreases in shear stress and flow competenceafter widening. In the absence of large floods, wider reaches require a longer periodof biogeomorphic recovery to narrow sufficiently to produce further bank erosion(Figure E.2).3.4.2 Long-term Channel CharacteristicsLong-term channel channel geometry and erosion rates vary with both flow vari-ability and rooting depth. The results from the five flow variability scenarios aresummarized in Table D.1. The length of the stability interval between erosionevents changes with flow variability; as fluctuations in flood magnitude increase,the stability interval between erosion events decreases more than four-fold (Fig-ure 3.5a). The median erosion magnitude (i.e. the amount of erosion associatedwith a single erosion event, WBE) also nearly doubles over the range of FMI valuesconsidered and the variability in bank erosion rates increases dramatically (Figure3.5b). The combined effects of greater erosion magnitude and frequency producedan order of magnitude increase in the long-term average bank erosion rate betweenthe lowest and highest flow variability scenarios (Figure 3.5c). Furthermore, asflow variability increases, the range of potential channel widths in any given yearalso increases. In other words as floods become more variable, confidence in pre-dictions of channel width based on a single formative discharge value decrease, aschannel size at a given time increasingly reflect the flow history.620.2 0.4 0.6 0.8 11020304050FMIStability Interval (years)a0.2 0.4 0.6 0.8 1.025102050FMIErosion Magnitude (m) 25th percentileMedian75th percentileb0.2 0.4 0.6 0.8 Erosion Rate (m/yr)c0.2 0.4 0.6 0.8 1.010203040FMIWidth (m)25th percentileMedian75th percentileRegime widthdFigure 3.5: The effect of FMI on a) the average interval between erosion events, b) the average magnitude of individualerosion events, c) the long term mean bank erosion rate, and d) channel width. Grey polygons show the 1st to99th percentile for the parameter and red boxes indicate the default value.63The median channel width also changes with flow variability – approximatelydoubling in value between the lowest and highest variability scenarios – despite aconsistent median flood size for all simulations (Figure 3.5d). The median channelwidth of 12.4 m produced by the UBCRM using a single formative flow equal tothe median flood is intermediate between the widths generated by STOCHASIMfor the two lowest variability scenarios (Table D.1; Figure 3.5d). In the simu-lation with a flow variability parameter of 0.4, which is approximately equal tothe median value for all WSC Pacific drainage streams, the width predicted by theUBCRM is equal to the 10th percentile of the estimates produced by STOCHASIM(Figure 3.5d). At flow variability values greater than 0.4, which are typical ofarid regions or small drainage areas, the regime model significantly under-predictschannel widths relative to STOCHASIM estimates.Variations in the rooting depth (H) – a proxy for bank strength – also affectchannel mobility and long-term average geometry (Table D.2). Increasing therooting depth to 0.8 m produces a five-fold decrease in the length of stability in-tervals relative to the 0 m rooting depth scenario, which represents a cohesionlessbank with a resistance to entrainment equivalent to that of the bed material (Figure3.6a). As rooting depth increases, however, the extent of the widening associatedwith each erosion event declines (Figure 3.6b). By providing apparent cohesion tothe banks, high rooting depths produce relatively narrow channels (Figure 3.6c).The high rooting depth scenarios generate a high-frequency, low-magnitude ero-sion regime; the narrow channel geometry reduces the threshold flow required toinitiate erosion, while the bank cohesion provided by tree roots limits the extentof the channel adjustment. The low rooting depth scenario, meanwhile, producesa low-frequency, high-magnitude erosion regime as a result of the comparativelylow bank cohesion and wide channel geometry (Figure 3.6d). Widening eventsoccur rarely because the wide channel geometry limits the depth – and thereforeerosive capacity – of the flood flows. When widening does occur, however, themodel generates a relatively wide and shallow post-flood channel geometry therebyproducing dramatic bank erosion. As a result of the competing influences of bankcohesion on erosion frequency and magnitude, the time-averaged bank erosion rateis relatively consistent for all rooting depths. UBCRM predictions, which accountfor the effect of rooting depth on channel geometry, provided similar estimates to64STOCHASIM for the low rooting depth scenarios characterized by low erosionfrequency, but underestimate channel widths relative to STOCHASIM estimatesfor reaches with high rooting depths and frequent, low-magnitude erosion.650 0.2 0.4 0.6 0.810203040Rooting Depth (m)Stability Interval (years)a0.0 0.2 0.4 0.6 0.8251020Rooting Depth (m)Erosion Magnitude (m) 25th percentileMedian75th percentileb0 0.2 0.4 0.6 Depth (m)Bank Erosion Rate (m/yr)c0.0 0.2 0.4 0.6 0.851015202530Rooting Depth (m)Width (m)25th percentileMedian75th percentileRegime widthdFigure 3.6: The effect of rooting depth on a) the average interval between erosion events, b) the average magnitude ofindividual erosion events, c) the long term mean bank erosion rate, and d) channel width. Grey polygons showthe 1st to 99th percentile for the parameter .66Table 3.2: Effective discharge values are shown for a range of flow variability(FMI) values.FMI Effective discharge Qe f f /Q2 Return periodm3/s years0.2 20.25 1.0 2.10.4 21.25 1.1 2.30.6 23.25 1.2 2.50.8 24.75 1.2 2.51.0 35.25 1.8 Effective and Formative DischargeRegime models such as UBCRM use a single formative discharge – often assumedto equal the median flood – to predict long-term average channel characteristics.Research in humid regions has often supported the Wolman and Miller [1960] prin-ciple, showing that the formative discharge is similar in magnitude to the effectivedischarge, or the flow that transports the largest amount of sediment over time[Baker, 1977]. Our results show, however, that flow variability influences the mag-nitude and return period of both the effective and formative discharge. For thelowest flow variability scenario, the effective discharge is approximately equal tothe median discharge (Table 3.2). The effective discharge nearly doubles betweenthe lowest and highest flow variability scenarios, and the return period for the ef-fective flow increases to 3.5 years (Table 3.2). These increases are small, however,compared with the changes in the shape of the frequency-magnitude distributions,which becomes more positively skewed with increasing flow variability. Figure3.7b shows that the importance of large floods in long-term sediment transportincreases dramatically with increased flow variability, despite the comparativelysmall increases in the effective discharge. In other words, as flow variability in-creases, the fraction of the total sediment load transported by flows exceeding theeffective discharge increases, and the tail of the distribution become heavier.We also estimated the effective discharge for each of the five rooting depthscenarios. The sediment rating curve (i.e. the rate of sediment transport for a67llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll0 100 200 300 400 5000. (m3 s)Sediment Flux (m3s)lllllllllllllllllllllll llllllllll l ll l llllllllllllFMI = 0.2FMI = 0.4FMI = 0.6FMI = 0.8FMI = 1.0allllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll0 10 20 30 40 50 60 700.00000.00040.00080.0012Discharge (m3 s)Frequency−magnitude Product FMI = 0.2FMI = 0.4FMI = 0.6FMI = 0.8FMI = 1.0bFigure 3.7: a) Sediment rating curves for the range of FMI values consideredin the five flow variability scenarios, and b) the product of flow durationand sediment transport rate for the range of discharges simulated in eachflow variability scenario. Dashed lines indicate the effective dischargefor each flow variability value.68given discharge) increases slightly with rooting depth due to the reduced channelwidth, which produces higher stream power per unit bed area for a given discharge(Figure 3.8a). The effective discharge, however, remains approximately constantfor the five scenarios (Figure 3.8b). The effective discharge for all rooting depthvalues (Qe f f ≈ 22 m3/s) is slightly greater than the median discharge of 20 m3/sbecause of the moderate flow variability (FMI = 0.4) which was used as the defaultvalue for the simulations.While the formative flow is often assumed to occur every 1-2 years, we hypoth-esize that the return period of the formative flow should instead increase with flowvariability, as large floods exert an increased influence on long-term channel ge-ometry in highly variable systems. In order to assess this effect we determined theformative flow (Q f ) required to produce the STOCHASIM-derived channel widthsusing the UBCRM (i.e. with constant annual floods) for each flow variability sce-nario. For the lowest flow variability scenario the UBCRM and STOCHASIMmodels produce comparable channel widths, suggesting that the formative flow isapproximately equal to the median flood when variability is low and conditionsare similar to those present in the irrigation canals where regime theory originated(Table 3.3; Figure 3.9). In the highest variability simulation, however, the me-dian width produced by STOCHASIM is more than twice the value generated bythe UBCRM using the median flood as the formative flow (Table 3.3). The for-mative flow required to generate this width using the regime model is three timesthe median flood magnitude, with a return period of more than seven years (Table3.3), and also significantly larger than the effective discharge estimated for the highvariability simulation. Thus, while the effective and formative flows are similar forlow variability scenarios, the flows diverge with increasing flow variability. Theformative flow – which relates to channel stability – increases more rapidly thanthe effective discharge as the variability in flood magnitude increases. The returnperiod of the formative flow can be predicted from the FMI value according to theregression (r2 = 0.95):RP = 6.85 ·FMI+0.65 (3.16)69lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llll l ll0 20 40 60 80 1000. (m3 s)Sediment Flux (m3s)lllllllll llll lllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllH = 0H = 0.2H = 0.4H = 0.6H = 0.8alllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll0 10 20 30 40 50 600e+002e−044e−046e−04Discharge (m3 s)Frequency−magnitude Product H = 0H = 0.2H = 0.4H = 0.6H = 0.8bFigure 3.8: a) Sediment rating curves for the range of rooting depths consid-ered, and b) the product of flow duration and sediment transport rate forthe range of discharges simulated for each rooting depth. The verticalgrey polygon indicated the range of effective discharge values for thefive rooting depth scenarios.700 10 20 30 40 50 6005101520253035Qf (m3 s)Width (m)FMI = 0.2FMI = 0.4FMI = 0.6FMI = 0.8FMI = 1.0Figure 3.9: Formative discharge is shown for the range of channel widthsgenerated for five STOCHASIM simulations. The black line representsthe regime channel width produced by the UBCRM for a range of flows,and dashed lines indicate the formative discharge required to producethis channel width using the UBCRM for each flow variability scenario.3.4.4 Sensitivity AnalysisWe conducted sensitivity analyses to assess the influence of variations in three ad-ditional input parameters (Table 3.1) on channel stability, long-term average bankerosion rates, and channel width. The results are summarized in Tables D.3, D.4,and D.5. Increasing the critical Shields number (θc), a representation of the dimen-sionless critical shear stress required to entrain material, produces a dramatic in-crease in the median stability interval (Figure 3.10) by increasing the bank erosionthreshold (τbank) and decreasing the mobility of the material at the toe of the bank.Increasing the critical Shields number generates a proportional increase in the flowdepth – and therefore the flood magnitude – required to erode the cohesionless toe71Table 3.3: Summary of differences between UBCRM and STOCHASIM pre-dictions of long-term channel width with increasing flow variability. Themagnitude of the formative discharge Q f (i.e. the flow required byUBCRM to produce widths that match STOCHASIM estimates) is alsoshown.FMI Median width W/W2 Q f Q f /Q2 Return periodm m3/s years0.2 11.6 0.93 17.9 0.9 1.40.4 14.6 1.2 25.9 1.3 3.90.6 17.3 1.4 33.9 1.7 5.30.8 20.3 1.6 43.4 2.2 6.01.0 24.3 2.0 59.7 3.0 7.2of the bank and produce widening. The average erosion rate and channel widthdecrease approximately linearly as the critical Shields number increases betweenthe five scenarios.720.02 0.04 0.06050100150200250300Shields NumberStability Interval (years)5 10 15 20 255101520Revegetation Rate (%)Stability Interval (years)0 0.2 0.4 0.6 0.85101520Morphologic IndexStability Interval (years)0.02 0.04 NumberBank Erosion Rate (m/yr)5 10 15 20 Rate (%)Bank Erosion Rate (m/yr)0 0.2 0.4 0.6 IndexBank Erosion Rate (m/yr)0.02 0.04 0.0651015202530Shields NumberChannel Width (m)5 10 15 20 25510152025Revegetation Rate (%)Channel Width (m)0 0.2 0.4 0.6 0.8510152025Morphologic IndexChannel Width (m)Figure 3.10: Boxplots are shown for sensitivity analyses of the critical Shields number (θc), revegetation rate (Cv), andmorphologic index (b). The red boxes indicate the default scenario for the modeled parameter and the dashedblack line shows the regime width (W2) generated by the UBCRM with the median flood (Q2) as the formativeflow.73Variations in the revegetation rate (Cv) also directly impact channel migrationand geometry. Increasing the revegetation rate decreases the stability interval whileincreasing the average erosion rate (Figure 3.10). By increasing the rate of nar-rowing, higher revegetation rates reduce the critical discharge required to initiateerosion more rapidly after widening, and increase the bed and bank mobility. Thehigher rate of narrowing is also accompanied by a decrease in the median channelwidth (Figure 3.10), as exposed bars are more rapidly colonized and converted intofloodplain. Varying the channel morphology via the morphologic index (b), hasa similar effect on the reach geometry and lateral mobility; moving from a plane-bed to a pool-riffle morphology [sensu Montgomery and Buffington, 1997] resultsin shorter periods of stability and a higher long-term bank erosion rate, while de-creasing the channel width (Figure 3.10). Similar to raising the revegetation rate,the increase in morphologic complexity increases the size of the exposed bar in anygiven year, leading to more rapid colonization and narrowing.3.5 DiscussionSTOCHASIM is a stochastic biogeomorphic model that can be used to explorehow variations in the accepted processes controlling channel dynamics affect thereturn period of the formative flow. The increasing importance of relatively in-frequent flows with rising flow variability demonstrated by our results is consis-tent with early conceptual and empirical research [e.g. Wolman and Miller, 1960,Pickup and Warner, 1976]. The model output shows that the formative and ef-fective discharge diverge as flow variability increases, and support the notion thatchannel form is related to two separate populations of flows: i) moderate effectivedischarges which dictate the bed texture, and ii) larger formative flows which deter-mine channel capacity [Pickup and Warner, 1976]. As the bankfull and formativedischarge are closely correlated [Andrews, 1980], these results may provide a phys-ical explanation for high observed variability in bankfull discharge return periodsin natural streams [Williams, 1978]. Further, these findings explain the improve-ments in regime model predictions achieved by using larger discharge values, suchas the five-year return period flood, as the formative flow in some regime modelapplications [e.g. Eaton and Church, 2007].74While STOCHASIM is a relatively simple biogeomorphic model, it accuratelyreproduces the range of erosion rates reported in a number of river systems. Therange of long-term averaged erosion rates produced by the model (with medianvalues ranging from 0.06 m/yr to 1.9 m/yr) is broadly consistent with previous em-pirical work, which has recorded average migration rates ranging from 0.05 m/yrto nearly 2.5 m/yr [Allmendinger et al., 2005, Hooke and Yorke, 2010], and is con-sistent with the rates of 0.01 to 0.5 m/yr invoked in conceptual models of channelevolution [Benda and Sias, 2003]. The rates also compare favourably with erosionrates measured in 40 streams across western Canada (Appendix C), which rangedfrom 0.05 to 3.5 m/yr. Perhaps most importantly though, by simulating a distribu-tion of flows and incorporating stochasticity throughout the model, STOCHASIMyields a statistical distribution of channel widths and erosion rates, rather than asingle deterministic value. Similar to the RSCS model presented in Chapter 2,STOCHASIM output can be used to explore the effects of changes to driving pa-rameters such as flood variability on the range of predicted channel conditions. Inaddition to providing estimates of long-term migration rates, the stochastic model-ing can be used to assess the historical range of variability in channel conditions[Wohl and Beckman, 2014], and in turn to inform restoration targets and hazardmitigation. Perhaps most importantly, these results suggest that in systems subjectto variable floods, field measurements should be interpreted with caution; observedchannel conditions may reflect channel adjustment to the recent flood history ratherthan a long-term formative flow.The results presented in this chapter can be used to elaborate a simple modelof channel evolution. As a run progresses, the reach experiences periods of widen-ing related to erosion events and subsequent periods of narrowing, or recovery,due to vegetation colonization. The channel response to any flood is historicallycontingent; the probability of the channel eroding or narrowing in a given year is afunction of both the magnitude of the randomly generated flood event and the exist-ing channel geometry. The processes of erosion and colonization, or widening andnarrowing, are intimately linked in the model by a negative feedback loop: imme-diately after an erosion event, channel widening reduces the reach-averaged shearstress by decreasing the flow depth associated with a given flood, thereby reducingflow competence and sediment transport. This is consistent with observations from75natural systems, where widening associated with large floods has been shown todecrease the proportion of the bed with a potentially mobile coarse fraction (D84) –and thus susceptible to erosion and bank retreat – by up to 50% [Tamminga et al.,2015], as well as experimental observations [e.g. Pitlick et al., 2013]. Over time,narrowing progressively increases the shear stresses experienced by the boundary,as well as the mobility of the bed and banks, thereby increasing the probability ofchannel widening. As flow variability increases, the reach experiences more fre-quent and higher magnitude erosion, producing higher rates of lateral migrationand a wider channel geometry, and more frequently interrupting the simple modelof channel evolution described above.Erosion and channel migration also vary with rooting depth, a proxy for bankcohesion. STOCHASIM generates fairly consistent moderate bank erosion ratesacross the range of rooting depths despite a marked difference in the erosion regime;reaches with low rooting depths are characterized by low-frequency, high-magnitudeerosion, while those with high rooting depths exhibit high-frequency, low-magnitudeerosion. While STOCHASIM is limited to gravel-bed streams with cohesion pro-vided by vegetation rather than silts or clays, the erosion pattern produced by highrooting depths is similar to that of meandering streams with cohesive banks. Bycontrast, reaches with very low rooting depths are characterized by infrequent, dra-matic widening. Because bank strength is low, the wide and shallow channel ge-ometry limits the shear stress associated with a given flood event in these systems,but when erosion does occur, erosion is relatively unconstrained by bank strengthresulting in a wide post-flood geometry. The impacts of the differences in migra-tion rates associated with these different channel patterns are reflected in foreststand ages in natural systems [Beechie et al., 2006], as well as observed migra-tion rates [e.g. Allmendinger et al., 2005]. Simulations with intermediate rootingdepths typical of sparse forest cover produce the highest migration rates, as chan-nel widths are sufficiently narrow to produce relatively frequent erosion, but theextent of widening remains high.STOCHASIM may be especially relevant in the context of climate change,which is anticipated to affect precipitation and runoff patterns, and thereby flowvariability, globally. While the magnitude of the predicted change in precipitationand annual runoff is regionally specific and subject to large uncertainty [Herricks76and Bergner, 2003], rising winter temperatures in temperate latitudes are expectedto decrease the proportion of precipitation falling as snow. Many regions will there-fore experience changes in runoff timing, even in the absence of changes in totalprecipitation. As a result, many streams will shift from nival to hybrid regimes,characterized by earlier freshets and more frequent rain-on-snow events [Loukasand Quick, 1999]. Based on the model results we anticipate that these changeswill increase both channel migration rates and channel widths. As aquatic ecosys-tems are adapted to hydrologic characteristics, changes in peak flow timing andmagnitude may also affect the likelihood of egg scour [Goode et al., 2013] and theavailability of refuge during high flows, providing an interesting avenue for futureresearch. The model also provides a useful tool to for assessing channel responseto disturbances that affect rooting depth, such as wildfire, forest harvesting, andinsect infestation. While the habitat model presented in Chapter 2 addressed theimpacts of such disturbances on in-stream wood loading and associated habitat fea-tures, the effects of endogenous changes in bank strength on channel geometry cannow be investigated through changes in the rooting depth parameter. Followingtree death, root strength (i.e. rooting depth) decreases gradually before rebound-ing as new vegetation colonizes the riparian zone [Sidle, 1992, Benda and Dunne,1997]. Based on our sensitivity analyses, we anticipate that the decrease in rootstrength following a disturbance will lead to larger erosion magnitudes, increasingchannel widths.3.6 ConclusionsThis chapter presents output from a series of Monte Carlo simulations using theSTOchastic CHannel Adjustment SIMulator (STOCHASIM). The biogeomorphicmodel describes channel evolution in intermediate-sized gravel-bed streams bysimulating the competing influences of bank erosion and vegetation colonizationof exposed bars. The model is particularly well suited to gravel-bed streams withmoderate to high flow variability, which are poorly described by traditional regimemodels. The results presented in this chapter show that channels exhibit a widerange of conditions over time, and that channel geometry at a given time maytherefore be poorly described by regime estimates. Furthermore, our results show77that formative flow can not be described by a single return period, and is not thesame as effective discharge. While these assumptions may be valid in humid re-gions where most research is conducted, the return period of the formative flowincreases with flow variability. The dimensions of channels characterized by highflow variability – which is typical of arid watersheds, small mountain streams, orregions with thunderstorm-generated flood events – are best predicted by using for-mative discharge values that are several times larger than the effective discharge,and the median flood. Cutting-edge regime approaches such as the UBCRM, whichcaptures the effect of variations in rooting depth on channel size, can therefore befurther improved by incorporating the effects of flow variability on the magnitudeof the formative flow. At the simplest level, this can be achieved by adjusting theformative flow based on a regression between the FMI value and the return periodof the formative discharge.These findings have important implications for empirical work in highly vari-able systems, and highlight the importance of historical contingency. As flow vari-ability increases, the variability in channel geometry also rises. Thus the commonlyheld assumption that field observations on a given day should “reflect the most ef-fective discharge more than any other” loses traction [Pickup and Warner, 1976],as channel conditions increasingly reflect the legacy of the most recent large floodevent. Historical contingency also dictates channel response to individual floodevents: a flood of a given magnitude is more likely to induce erosion in a narrowchannel than in a channel that has recently widened in response to an earlier floodevent. Predictions of hazard probability, as well as interpretations of field measure-ments, therefore require knowledge of both the magnitude of the formative floodand the recent flood history. Channel geometry can not be used to infer formativeconditions independent of the historical context.78Chapter 4Large Wood Transport and JamFormation in a Series of FlumeExperiments4.1 SummaryBank erosion in laterally unstable reaches introduces wood containing rootwads tothe channel, which influences wood stability and subsequent transport. At present,however, the scientific understanding of the factors affecting wood mobilizationand travel is incomplete. This chapter presents results from a series of four flumeexperiments in which wood was added to a reach to investigate the piece and reachcharacteristics that determine wood stability and transport, as well as the time scalerequired for newly recruited wood to self-organize into stable jams. Our resultsshow that wood transitions from a randomly distributed newly recruited state, toa self-organized, or jam-stabilized state, over the course of a single bankfull flowevent. Statistical analyses of piece mobility during this transitional period indi-cate that piece irregularities, especially rootwads, dictate the stability of individualwood pieces; rootwad presence or absence accounts for up to 80% of the vari-ance explained by linear regression models for transport distance. Furthermore,small pieces containing rootwads are especially stable. Large ramped pieces pro-79vide nuclei for the formation of persistent wood jams, and the frequency of thesepieces in the reach impacts the travel distance of mobile wood, as modeled inthe Reach Scale Channel Simulator (RSCS). This research suggests that recruitedwood rapidly organizes into persistent, stable jams, and characterizes the time scalefor this transition. The results can be used to modify the RSCS to account for theeffects of rootwads on the stability of pieces recruited via bank erosion.4.2 IntroductionThe quantity and distribution of wood in streams is a function of recruitment pro-cesses, as well as subsequent mobilization, transport, and deposition [Benda andSias, 2003, Hassan et al., 2005b, Czarnomski et al., 2008, Wohl and Jaeger, 2009].As shown in Chapter 2, the amount of wood delivered to streams varies with dis-turbance type and history; fire increases the amount of wood delivered to a streamthrough toppling, for example, while forest harvesting reduces wood delivery. Asthe RSCS model only considers wood input through toppling, wood is assumed tofall at random angles and the effects of rootwads are ignored. Previous researchshows, however, that inputs due to bank erosion may far exceed inputs from top-pling in laterally unstable forested streams [e.g. Benda and Sias, 2003]. Woodinput through bank erosion also has different stability and transport characteristicsthan those presented in Chapter 2 and Appendix A for wood input via toppling dueto: i) non-random fall angles oriented preferentially toward the channel, and ii) theincreased presence of rootwads.While considerable research has been dedicated to identifying the benefits oflarge wood on aquatic habitat, the factors affecting wood stability and transporthave received less attention [Macvicar and Pie´gay, 2012, Schenk et al., 2014].Over the preceding two decades, researchers have attempted to explain wood en-trainment and transport in terms of piece and reach characteristics, using both lab-oratory experiments and field surveys of in-stream wood. Numerous studies havesuggested that piece mobilization occurs when water depth is sufficiently large,relative to piece diameter, to cause instability [Braudrick et al., 1997, Braudrickand Grant, 2001, Bocchiola et al., 2006, Manners and Doyle, 2008]. The ratioof flow depth to diameter required to mobilize a wood piece has been shown to80vary with piece shape, size, and orientation [Braudrick et al., 1997, Braudrick andGrant, 2000, Bocchiola et al., 2008]. In unsteady flows, drag and lift forces alsovary over time, such that pieces are more easily mobilized early in the rising stageof a high-flow event when the forces acting on the wood are greatest [Shields andAlonso, 2012]. Flume experiments show that rolling and pivoting allow wood tomove to areas with deeper flow where flotation is possible, enabling mobilizationbelow the critical water depth [Braudrick et al., 1997].Once mobilized, travel distance may vary with channel pattern and reach-scalewood loading, both of which influence the probability of encountering an obsta-cle during transport [Dixon and Sear, 2014]. Independent wood pieces tend tore-deposit in positions that minimize drag force, often with pieces aligned parallelto the dominant flow direction [Gippel et al., 1996, Braudrick and Grant, 2001,Webb and Erskine, 2003, Bocchiola et al., 2006, Manners and Doyle, 2008]. Bychanging piece orientation and decreasing its blockage ratio (i.e. the proportion ofthe cross sectional area occupied by a wood piece) the mobilization and depositionof large wood minimizes its morphological and hydraulic impact, while increasingpiece stability [Gippel et al., 1996]. Thus, a large proportion of wood movementoccurs during the first large flow event following recruitment, when piece stabilityis low [Wallerstein et al., 2001, Sweka and Hartman, 2006]. In natural systems,large wood often accumulates into jams, which amplify the hydraulic and morpho-logical effects of the wood and increase piece stability [Nakamura and Swanson,1993]. Over time, a reach with unstable, newly recruited wood thereby transitionsto a lower mobility, jam-stabilized state. Piece mobilization nevertheless occurs,but often requires higher magnitude floods to mobilize key pieces enabling thebreak-up of jams. Previous studies have shown that mobilization of stable, in-stream wood may be achieved by flows that overtop the bankfull channel [Iroume´et al., 2015] and that flashy flow regimes cause greater mobility [Cadol and Wohl,2010], especially during the rising limb of unsteady flows [Macvicar and Pie´gay,2012, Shields and Alonso, 2012]. Despite the development of general models ofjam formation and evolution [e.g. Manners et al., 2007, Manners and Doyle, 2008,Bocchiola et al., 2008] and the important influence of jam formation on piece sta-bility, the formation of stable jams has rarely been attempted in experimental work.A better understanding of in-stream wood dynamics, as well as the factors in-81fluencing the formation of stable jams, is necessary to inform an improved modelof wood recruitment that accounts for bank erosion. As wood mobilization andtransport generally occur during discrete high flow events [Schenk et al., 2014],and often immediately after wood recruitment, it is difficult to directly to observeor measure wood movement at the relevant flows [Braudrick and Grant, 2001, Man-ners et al., 2007]. As a result, field studies are generally based on surveys of ex-isting in-stream wood [e.g. Wohl and Merritt, 2008, Merten et al., 2010, Dixonand Sear, 2014, Schenk et al., 2014, Iroume´ et al., 2015], which has typically beensubjected to a number of prior flood events, and is thus relatively stable comparedwith newly recruited wood. Flume studies offer an opportunity to directly observewood dynamics immediately after recruitment during high flow events, and pro-vide a useful complement to field observations of wood transport. Most laboratorystudies conducted to date, however, have employed cylindrical dowels, which lackthe complexity of natural in-stream wood [e.g. Braudrick et al., 1997, Braudrickand Grant, 2001, Bocchiola et al., 2006, 2008, Bocchiola, 2011, Schmocker andWeitbrecht, 2013]. Research involving greater piece complexity (e.g. rootwads)has primarily been conducted using individual pieces, ignoring the effects of inter-actions between pieces [e.g. Braudrick and Grant, 2000, Wallerstein et al., 2001,Shields and Alonso, 2012].In this chapter, we build upon this previous work through a series of flume ex-periments conducted in 2010-2011 in which a number of complex wood pieces,designed to represent segments of whole trees, were added to a reach to producea range of wood loadings characteristic of natural systems. The experiments sim-ulate the simultaneous addition of wood to a reach during a large widening event.The primary objectives of this chapter are to: i) constrain the time scale over whichhighly mobile, newly recruited wood transitions to a lower mobility, jam-stabilizedstate, and ii) identify the piece and reach characteristics that influence wood mo-bilization and transport during this transitional period. This analysis will then beused in Chapter 5 to develop a modified RSCS model that accounts for wood re-cruitment through bank erosion.824.3 Methods4.3.1 Experimental DesignA series of four experiments were conducted with varying wood loads (Table 4.1)in order to examine the time scale required to achieve a self-stabilized wood con-figuration after initial recruitment, as well as the piece and reach characteristicsthat influence wood stability and transport during this transitional period. The ex-periments were performed in a 7 m long by 0.9 m wide flume designed to representa low sinuosity reach in Fishtrap Creek, which is located in the interior of BritishColumbia, Canada [Eaton et al., 2010a,c], and is described in detail in Appendix B.Fishtrap Creek has an average channel width of approximately 10 m, and is definedas an intermediate-sized stream as the channel width is significantly larger than thegrain diameter but similar to the size of wood pieces, resulting in frequent jams[Church, 1992, Wohl and Jaeger, 2009]. The wood loads used in Experiment 1 and2 (Table 4.1) were selected to approximately represent the pre- and post-fire woodloads surveyed in Fishtrap Creek in 2008. The higher wood loads used in Exper-iment 3 and 4 were chosen to represent the potential wood loading in the decadesafter the fire.The physical model represents an approximate 1:30 Froude-scaled model ofthe prototype, with non-erodible banks constructed from Styrofoam. The channelcontained a mobile bed, composed of a 0.08 m thick layer of sand, with a sizedistribution scaled to the bed material surveyed in Fishtrap Creek. Each experimentwas composed of a series of five hour runs, with each run representing a single dayof the 2-year return period flood in the prototype stream. Water was pumped intoa head pond at the top of the flume at a constant discharge of 1.6 L/s (equivalentto the mean annual peak flow of 7.5 m3/s in the prototype) and was delivered tothe channel through a Plexiglass weir with the same dimensions as the channel.Sediment was input at a rate of 55-60 g/min into the channel using a rotating feeder,and sediment output was dried and used as input for the subsequent run. Channelmorphology was recorded using a laser profiling system at the end of each run [seeDavidson and Eaton, 2013, for a detailed description]. In order to account for anyboundary effects at the inlet, data was only collected in the lower 4.5 m of the flume83(i.e. at least one channel width downstream of the weir).Table 4.1: Summary of the wood load added in each experiment, as well asthe time required to return to steady state sediment transport.Experiment Wood load Prototype equivalent Time to equilibrium(m3/m2) (m3/m2) (hr)1 4.8 x 10−4 1.4 x 10−2 302 7.0 x 10−4 2.1 x 10−2 353 9.8 x 10−4 2.9 x 10−2 454 1.2 x 10−3 3.7 x 10−2 50Experiments were first conducted without wood until the system reached asteady state sediment transport condition, wherein the rate of sediment output ap-proximately matched the input rate and a stable morphology had developed. Woodpieces were then added at low flow (0.4 L/s) at randomly selected cross sections,representing the input of a discrete pulse of wood. The experimental design mimicsa large widening event as all wood enters the reach simultaneously from directlyadjacent to the channel, with the rootwad end remaining at the base of the channelbank. The orientation and the bank side from which each piece entered the channelwas randomly selected for each piece. If a piece was long enough to reach the op-posite bank, one end was left suspended on the opposite bank creating a ‘ramped’piece. The wood pieces used in the experiments were scaled geometrically (1:30)to the three major size classes surveyed in Fishtrap Creek in 2006-2008 (Table 4.2).The 16-32 m size class, which amounted to only 2% of the large wood surveyedat Fishtrap Creek, was excluded from the experiments as pieces of this size (witha dimensionless piece length > 1.5) would be ramped on one bank regardless oftheir angle of entry. It was therefore assumed that these long pieces serve a simi-lar purpose as ramped 0.41 m pieces. Including these larger pieces may, however,have slightly increased the number of ramped pieces in the reach. Key members,which have previously been defined based on piece length, diameter, or stability[Abbe and Montgomery, 2003, Manners and Doyle, 2008, Vaz et al., 2013], aredefined as pieces that block at least 75% of the channel width. Thus only the 0.41m pieces, which have a dimensionless piece length of approximately 1.2, may act84as key pieces.Table 4.2: Comparison between the length classes and frequencies of largewood in the prototype stream and those used in the experiment. Variabil-ity in the length of modeled pieces in a particular size class relates to thepresence or absence of a rootwad.Prototype ModelLength (m) Frequency (%) Length (m) L/Wch Frequency (%)3 27 0.10-0.11 0.29-0.32 30-346 36 0.20-0.21 0.59-0.62 35-3612 35 0.40-0.41 1.2.1 32-3424 2 - - -Wood pieces were designed to represent mature lodgepole pine trees, contain-ing both a rootwad and branch snags (Figure 4.1). Rootwads were simulated byjoining two square wood pieces (approximately 0.038 m by 0.038 m wide, and0.006 m thick), rotated 45 degrees relative to one another, to the base of the woodpiece. Branches were modeled using four 0.025 m long cylindrical dowels insertedthrough the upper 0.1 m of the wood piece, creating eight 0.006 m long branchsnags. The largest size class represent mature trees that remained intact followingtheir introduction to the channel while the smaller size classes represent maturetrees that have broken during recruitment or subsequent transport in the channel.The 0.2 m pieces each represent half of a full tree; 50% of all 0.2 m pieces con-tained a rootwad and the remaining 50% contained branch snags. For the smallestpieces, 25% contained a rootwad, 25% contained branch snags, and the remaining50% had neither. Although previous studies have employed cylindrical dowels tosimulate large wood [e.g. Braudrick and Grant, 2001, Bocchiola, 2011], we usedwood with a square cross section (0.013 m by 0.013 m) and a density of approxi-mately 700 kg·m−3 to minimize rolling and flotation. Wood location and orienta-tion was surveyed at the end of each five hour run, and the location of jams, whichwe define as accumulations of at least three pieces of wood, were also recorded.Five hour runs were conducted until a new steady state sediment transport con-dition with wood was achieved, and experiments ranged in length from 30 to 5085hours, representing a prototype equivalent of 6 to 10 flood events (Table 4.1).Figure 4.1: Examples of the six piece types used in the experiments, rangingin length from 0.10 m to 0.41 m. Pieces were designed to representsegments of entire trees surveyed in the prototype stream.4.3.2 Statistical AnalysisLogistic and linear regression analyses were used to assess the importance of var-ious piece and reach characteristics on the probability of piece mobilization andsubsequent travel distance immediately after recruitment. In order to determinethe factors influencing wood dynamics during the transition from the highly mo-bile newly recruited state to the jam-stabilized configuration, only mobilizationand travel during the first five-hour experimental run were considered. Beyond thistime scale additional factors such as piece burial become increasingly important,and wood mobility is limited by piece orientation and jam membership.For each analysis we differentiated between piece movement (i.e. a non-zerotravel distance) and substantial movement, which we define as a travel distance ofat least 0.3 m, or approximately one channel width. While wood may move small86distances during pivoting and initial stabilization, substantial travel is a more rele-vant metric when assessing potential risk to downstream infrastructure. The initialmodels for the logistic and regression analyses considered both piece and reachcharacteristics (Table 4.3), including several of the morphologic parameters pre-sented in Davidson and Eaton [2013]. As most post-addition morphologic changesoccurred over numerous experimental runs (i.e. numerous 2-year return periodflood events) following wood addition [Davidson and Eaton, 2013], the morpho-logic conditions measured immediately prior to wood addition were used in thestatistical analyses.87Table 4.3: Reach and piece characteristics included in the statistical analyses.Variable Description ValuesPiece characteristicsOrientationa Oblique/perpendicular at time of addition 0, 1Rampinga Absence/presence of suspension on a channel bank 0, 1Rootwad Absence/presence of a rootwad 0, 1Branching Absence/presence of branch snags 0, 1Length Total dimensionless piece length 0.29 - 1.21Reach characteristicsWood load Prototype-equivalent wood load 1.4 - 3.7 x 102 m3/m2Ramped frequencyb Number of ramped pieces per channel width 0.076 - 0.53Depth variability Mean standard deviation in depth for all cross sections 4.9 - 6.5 mmRoughness Manning’s roughness coefficient 0.02 - 0.022Pool frequency Number of pools per channel width 0.23 - 0.68Percent pool Percent of length occupied by pools 41-71 %Gradient Water surface gradient 1.44 - 1.48 %a indicates variables only considered in the logistic modelb indicates variables only considered in the linear regression88The logistic regression analyses included all 103 pieces added in the four ex-periments, and were used to determine which characteristics affect the probabilityof a newly recruited piece becoming mobilized, or moving a substantial distance(at least 0.3 m) in the first five hours after wood addition. A backward stepwiseprocedure was used to select a final model for both travel distances (i.e. all mo-bilization and substantial mobilization) based on Akaike’s Information Criterion(AIC) – a measure of goodness-of-fit that penalizes a model based on the num-ber of parameters it contains – using the open-source software, R (R core team,2015). The relative importance of each predictor variable was assessed based onits absolute Wald z score, as well as its odds ratio, which represents the change inthe probability of mobilization associated with a one unit increase in the predictorvariable. To assist in interpretation of the regression coefficients and odds ratios,all continuous predictor variables were scaled to a mean value of 0, and a standarddeviation of 1.A linear regression analysis was then conducted to determine the influence ofthe piece and reach characteristics on travel distance during the first five hours fol-lowing recruitment. The linear regression analysis of all travel distances includedthe 64 pieces that were mobilized during this period, while the second analysis ofsubstantial movement considered only the 34 pieces that moved a distance of atleast 0.3 m. The natural logarithm of the response variable, travel distance, wasused in order to meet the assumptions of linear regression. The relative importanceof each predictor variable included in the final model was calculated using themethod of Lindeman et al. [1980], who proposed averaging the sequential sums ofsquares (which vary in size based on the ordering of variables in the model) of thelinear model over all potential variable orderings. Relative importance was alsoevaluated by determining the contribution of each variable when included eitherfirst or last in the model.894.4 Results4.4.1 Wood StabilizationThroughout the duration of the four experiments 74% of all pieces were mobi-lized, with the largest proportion of total travel consistently occurring in the firstfive hours following wood addition (Figure 4.2a). The largest percentage of pieceswere also mobile during this initial period, with 62% of all pieces mobilized duringthe first flood event (Figure 4.2b). Following this initial period of elevated mobil-ity, the total travel distance of wood pieces decreased, and a lower proportion ofwood pieces moved during subsequent runs. The mean travel distance of mobilizedwood pieces, however, remained relatively consistent throughout the experimentalruns suggesting that the decrease in total travel distance over time was primarily at-tributable to decreased piece mobilization in the jam-stabilized state (Figure 4.2c).Mobilized pieces generally continued to travel downstream until an obstacle wasencountered, though some pieces also deposited on shallow bars. As interactionswith other pieces impose key limits on travel distance, experiments that do notallow wood interactions to occur may over estimate travel distance for mobilizedpieces.Jams formed during the first flood following recruitment (i.e. the first fivehour run) in all but the lowest wood load experiment. Existing jams generallyincreased in size as the experiments progressed by trapping mobile wood (Figure4.3), though one jam formed in a later run in Experiment 3 and two in Experiment4. Of the jams that developed during the first five hours of Experiments 2, 3, and4, two eventually failed. Wood position from the remaining experiments is shownin Appendix E. The gradual failure of a small jam in Experiment 4 caused a slightincrease in wood transport approximately 10-15 hours after wood addition, whilethe sudden failure of a large jam in Experiment 3 resulted in a punctuated increasein piece mobilization and transport (Figure 4.2a and b).905 10 15 20 25 30 35 40 45 5000.Σ Distance Travelled (m) a) Experiment 1Experiment 2Experiment 3Experiment 4End of Experiment*5 10 15 20 25 30 35 40 45 50020406080% Pieces Movingb)5 10 15 20 25 30 35 40 45 50Hours Since Wood Addition00. Distance (m/piece) c)Figure 4.2: Summary of wood travel over the entire duration of the four ex-periments. a) The total travel distance of all wood pieces present in thereach during each five hour run for each experiment, b) the percentageof all wood pieces that were mobilized during each five hour run, andc) the mean travel distance of each mobile piece during each five hourrun. The color of the dashed line corresponds to the end of a givenexperiment.9100.5Initial Locationa) Wood Piece00.5After 5−hr Runb)0 1 2 3 400.5Distance Downstream (m)Distance Across (m)Steady Statec)d)e)Figure 4.3: The location of wood pieces in the flume, plotted based on wood surveys conducted after each run, is shownfor Experiment 3: a) when wood was first added to the reach at low flow, b) after the first five hour run, and c)at steady state after 45 hours. A large jam located at the downstream end of the reach in Experiment 3 is alsoshown: d) five hours after addition, and e) at steady state 45 hours after addition. Rootwads are indicated by aperpendicular line.92Jam frequency varied between the experiments from 0 to 0.45 jams per channelwidth (Table 4.4), and was related to the number of ramped pieces in the reach(P= 0.053), though not to the wood load. While jam frequency remained relativelyconsistent throughout the experiments, the number of pieces in jams and the meanjam size increased as mobile pieces racked on to stable jams, and piece burialincreased the stability of some jam members (Figure 4.3).Table 4.4: Summary of jam characteristics for the four experiments after thefirst five hours, and at equilibrium.Experiment Frequency Percent Mean size(jams/wc) in jams (piece/jam)Initial Final Initial Final Initial Final1 0 0 0 0 0 02 0.23 0.23 71 86 5 63 0.15 0.15 40 50 6 7.54 0.38 0.45 70 87 5.2 5.3All of the jams present at the end of the experiments contained at least onekey member (0.41 m piece), and 9 of the 11 jams contained a ramped piece. Theinitial position of these ramped key pieces appeared to exert a strong control onthe location of jams throughout the reach (Figure 4.3). Notably, the two jams thatfailed in Experiments 3 and 4 did not contain ramped pieces. Based on the classi-fication presented by Abbe and Montgomery [2003], the jams containing rampedpieces represent combination jams, composed of stable in situ key members. Onceformed, these jams all remained stable for the remainder of the experiments, thoughtheir size varied over time through the shedding and subsequent trapping of mobilepieces. The jams that did not contain ramped pieces are best classified as transportjams [Abbe and Montgomery, 2003], as the key members were transported somedistance downstream prior to jam formation.In addition to moving downstream, pieces also changed orientation throughoutthe four experiments. Similar to wood travel and jam formation, the majority ofre-orientation occurred in the initial five hour period after wood addition as woodtransitioned from the newly-recruited state to a stable configuration (Figure 4.3).93Jam membership was an important determinant of piece orientation across the ex-periments. At the conclusion of the four experiments, 37% of pieces remainedindependent, and of these pieces nearly 65% were oriented parallel to the flow di-rection (Figure 4.4a). Of the 63% of pieces located in jams at the conclusion ofthe experiments 82% were oriented oblique or perpendicular to the flow direction(Figure 4.4).0!10!20!30!40!50!0!45!90!135!180!225!270!315!In jams (63%)!Individual (37%)!Density (%)!Orientation!(degrees)!UPSTREAM!DOWNSTREAM!a)! b)!Flow Direction!Figure 4.4: a) A radar plot showing the orientation of individual wood piecesand those located in jams for the aggregated data set including all fourexperiments, and b) an image showing the typical orientation of manyindependent pieces with rootwads.The orientation of both independent pieces and jam members also varied basedon rootwad presence or absence. Independent pieces with rootwads generally piv-oted around the stable rootwad to align parallel to the flow direction with the root-wad upstream, and developed a crescentic scour pool around the rootwad end (Fig-ure 4.4b). At the conclusion of the four experiments, over 70% of independent94pieces with rootwads were oriented parallel to the flow (Figure 4.5a), and of theseparallel pieces 80% were positioned with the rootwad end upstream. A significantproportion of independent pieces without rootwads were also oriented parallel tothe flow direction, but nearly half of the pieces adopted and oblique orientationcompared with only 29% of the pieces containing rootwads (Figure 4.5a). Simi-larly, pieces without rootwads located in jams were more likely to adopt obliqueorientations (70% of pieces) than those with rootwads (Figure 4.5b). Nearly a quar-ter of pieces with rootwads in jams remained parallel to the flow direction, thougha larger percentage of these pieces were also oriented perpendicular to the flow(Figure 4.5b).0	  10	  20	  30	  40	  50	  60	  0	  45	  90	  135	  180	  225	  270	  315	  0	  5	  10	  15	  20	  25	  0	  45	  90	  135	  180	  225	  270	  315	  No rootwad!Rootwad!Density![%]!Orientation![degrees]!DOWNSTREAM!INDIVIDUAL! IN JAM!DOWNSTREAM!Figure 4.5: a) A radar plot showing the orientation of individual wood piecesfor the aggregated data set including all four experiments, and b) a radarplot showing the orientation of pieces in jams.954.4.2 Statistical Analysis of Mobility and Travel DistanceBackward stepwise regression produced a logistic model for piece mobilization(AIC = 117.42) that included four of the predictor variables: wood load, depthvariability, rootwad presence, and ramping (Table 4.5). The Nagelkerke’s andTjur’s r2 values for the model, which represent pseudo r2 rather than actual mea-sures of goodness-of-fit, were 0.34 and 0.26, respectively. Ranking the variablesbased on the absolute Wald z values and odds ratios presented in Table 4.5, rootwadwas the most important variable in restricting mobilization, followed by ramping.Conversely, reach-scale wood loading and variability in flow depths were positivelyrelated to the probability of mobilization. When the threshold for substantial move-ment (i.e. travel of at least one channel width downstream) was used, the backwardstepwise regression produced a logistic model (AIC = 97.17) with Nagelkerke’sand Tjur’s r2 values of 0.51 and 0.40, respectively. The model for substantial mo-bilization included additional piece characteristics – branch presence and dimen-sionless piece length – while wood load was eliminated in the stepwise procedure(Table 4.5). Based on the absolute Wald z score and the odds ratios, rootwad wasagain the most important variable.96Table 4.5: Summary of the variables included in the final logistic model for wood mobilization for all travel distances.The final model for piece mobilization has an AIC of 117.42, and Nagelkerke and Tjur’s r2 values of 0.34 and 0.26,respectively. The final model for piece mobilization greater than 0.30 m has an AIC of 97.17, and Nagelkerke andTjur’s r2 values of 0.51 and 0.40, respectively.Variable Estimate Odds Ratio St. Error Wald z P valueAll mobilizationIntercept -1.89 - 0.46 4.11 < 0.001Rootwad present -1.69 0.18 0.55 -3.07 0.0022Ramped -1.72 0.18 0.73 -2.35 0.019Wood load 0.38 1.47 0.24 1.61 0.11Depth variability 0.37 1.45 0.24 1.57 0.12Substantial mobilizationIntercept 3.67 - 1.30 2.84 0.0045Rootwad present -4.91 0.0073 1.28 -3.84 < 0.001Branches present -2.54 0.078 1.02 -2.51 0.012Dimensionless length 1.78 5.91 0.74 2.39 0.017Depth variability 0.63 1.88 0.29 2.22 0.026Gradient 0.49 1.64 0.28 1.80 0.072Ramped -17.26 3.20 x 10−8 1588.57 -0.011 0.9997Linear regression for all of the mobilized pieces produced a final model fortransport distance (r2 = 0.46) that contained five of the input variables: wood load,ramped piece frequency, branch presence, rootwad presence, and dimensionlesslength (Table 4.6). The effect of the three piece characteristics on travel distanceare shown in Figure 4.6. While travel distance generally decreased with dimension-less piece length when all pieces were considered, the shortest pieces containingrootwads (with a dimensionless length of 0.32) moved significantly shorter dis-tances than any other piece size (Figure 4.6). Rootwad presence accounted for44-51% of the variance explained by the linear regression model, regardless of themethod used. The relative importance of the remaining four predictor variablesvaried depending on the method used. When only pieces that moved a substantialdistance (0.3 m) were included, dimensionless piece length was eliminated fromthe final model (r2 = 0.29; Table 4.6). Rootwad presence accounted for 59-78% ofthe variance explained by the model, while the importance of the remaining threepredictor variables again varied according to the method used.98ll llll0.29 0.59 Piece Lengthln(Travel Distance)llllll0 Presenceln(Travel Distance)lll0 Presenceln(Travel Distance)Figure 4.6: Boxplots show the effect of each of the three piece characteristicsincluded in the linear regression model for all travel distances. Redboxes indicate pieces containing rootwads.99Table 4.6: Summary of the variables included in the final linear regression model for wood transport distance. The finalmodel for all travel distances has an r2 of 0.46 and an adjusted r2 of 0.42. The final model for substantial travel(i.e. greater than 0.30 m) has an r2 of 0.29 and an adjusted r2 of 0.20.Variable Estimate St. Error t value P valueAll travel distancesIntercept 1.04 0.15 7.16 < 0.001Rootwad present -0.76 0.16 -4.68 < 0.001Branches present -0.47 0.13 -3.45 0.0011Ramped frequency -0.45 0.17 -2.56 0.013Wood load 0.38 0.17 2.19 0.033Dimensionless length 0.20 0.091 2.17 0.035Substantial travel distancesIntercept 0.93 0.087 10.63 < 0.001Rootwad present -0.40 0.13 -3.13 0.0040Wood load 0.34 0.22 1.56 0.13Branches present -0.16 0.11 -1.53 0.14Ramped frequency -0.33 0.22 -1.48 0.151004.5 DiscussionWhile the addition of large wood enhances morphological complexity and habitatquality [e.g. Brooks et al., 2004, 2006, Nagayama and Nakamura, 2009], newlyrecruited wood is often unstable and may pose a risk to downstream infrastructure.Our experiments simulate the sudden addition of wood to a reach by bank erosionduring a large widening event. The experiments show that highly mobile newlyrecruited wood can transition to a self-organized, jam-stabilized state, over thecourse of a single flood. While the overall proportion of pieces mobilized through-out the duration of the four experiments is consistent with previous field studies[e.g. Sweka and Hartman, 2006, Dixon and Sear, 2014], the proportion of piecesmobilized during the first flood event after wood addition (i.e. the first five hour ex-perimental run) is high relative to previously reported values [e.g. Cadol and Wohl,2010, Schenk et al., 2014, Iroume´ et al., 2015]. The precipitous decrease in woodmobility and transport over time coincided with the development of stable jams;a large but highly variable proportion of initially mobile pieces became trapped injams, most of which formed during this first five hour run. This highlights a chal-lenge with using surveys of in situ wood stored within a stream channel to inferthe stability or probability of mobilization of newly recruited pieces, as wood sur-veyed in field studies has generally been ‘primed’ by exposure to high flows, andhas adopted a more stable configuration. Thus, field studies likely underestimatethe mobility of newly recruited wood during the transitional phase immediatelyafter recruitment.Newly recruited wood self-organized into a series of stable jams in all exceptthe lowest wood load experiment, often around a ramped key piece. Indeed, jamfrequency was significantly related to the number of ramped pieces in the reach.The observed jam frequencies were relatively consistent with the reported valueof approximately 0.12 jams per channel width recorded in Fishtrap Creek in 2008[Andrews, 2010], though the average number of pieces per jam was lower in ourexperiments than in the prototype reach. At the time of the 2008 survey, FishtrapCreek had an overall wood loading similar to the moderate wood loading exper-iment. The jam frequencies for the four experiments were within the range ofthe values surveyed in 2013 which ranged from approximately 0 to 1.2 jams per101channel width (Appendix B). The consistency in jam frequency between the flumeexperiments and the field survey suggests that the experiments accurately capturethe transition to the jam-stabilized state commonly observed in natural streams.Jam formation during the experiments followed the first two stages of the con-ceptual jam evolution model proposed by Manners and Doyle [2008], with piecesforming a framework around stable key members, and gives further insight into thetemporal scale of jam development. Although wood pieces were trapped by, andoccasionally shed from, these jams throughout the duration of the experiments, astable and persistent jam framework was established during the first flood eventafter wood recruitment. The absence of small wood, as well as the finite durationof the experiments, limited the extent of jam growth and prevented the reduction inporosity that characterizes later-stage jam evolution [Manners and Doyle, 2008].Thus, while the jam framework establishes during the relatively short transitionto a jam-stabilized state, jam size may continue to increase over time through thecapture of mobilized wood. In addition to stabilizing wood in the reach and reduc-ing subsequent transport, jam formation also enabled a greater proportion of piecesto orient oblique or perpendicular to the flow, likely increasing the hydraulic andmorphological impact of the added wood.As shown, wood mobility is greatest during the transition to a jam-stabilizedconfiguration, which occurs immediately after recruitment. The statistical analysesconducted during the first flood after wood addition therefore offer insight into thepiece and reach characteristics that dictate wood stability – and thus the potentialrisk to infrastructure of added wood – during the period of greatest instability. Ourresults show that rootwad presence, which has been found to influence piece sta-bility in previous work [Braudrick and Grant, 2000, Merten et al., 2010, Schenket al., 2014], is the most important determinant of both mobilization and travel dis-tance. This effect appears to be related to the greater piece complexity, rather thanthe added piece length or volume, as pieces with rootwads travelled significantlyshorter distances than other pieces of comparable size. Rootwads may decreasethe mobility of newly recruited wood by lifting pieces above the bed and reduc-ing the proportion exposed to the flow, and the buoyant force acting on the piece[Merten et al., 2010, Shields and Alonso, 2012], though the development of a scourhole around the rootwad end may limit this effect over time [Braudrick and Grant,1022000]. Independent pieces with rootwads were often oriented parallel to the flowwith the rootwad end upstream, reducing the hydraulic forces exerted on the wood[Gippel et al., 1996, Braudrick and Grant, 2001, Bocchiola et al., 2006, Shields andAlonso, 2012]. Branch presence also decreased both the probability of mobiliza-tion and the travel distance. The branches modeled in these experiments representrelatively low complexity branch systems, typical of coniferous trees, rather thanthe complex branching often present in broadleaf species [Dixon and Sear, 2014],and the importance of branches in this study suggests that the presence of large (i.e.branch diameter > 0.05), sturdy branch snags may significantly increase piece sta-bility. Greater branching complexity, which was not a significant determinant ofpiece stability in several previous studies [e.g. Hygelund and Manga, 2003, Mertenet al., 2010], is often attributable to small branches which break easily during highflows and are the first to decay [Shields and Alonso, 2012, Merten et al., 2013] andwere not included in these experiments. These results suggest that branch presencemay be a more reliable metric than branching complexity in future studies.Dimensionless length, defined as the size of the piece relative to the channelwidth, also influences piece mobilization and transport. The general decrease intravel distance with increasing length observed in the four experiments appearsconsistent with previous research that has shown that piece length is an importantdeterminant of mobilization [e.g. Sweka and Hartman, 2006, Merten et al., 2010,Dixon and Sear, 2014, Schenk et al., 2014] as well as deposition [e.g. Bocchiolaet al., 2008, Schmocker and Weitbrecht, 2013]. These results must be interpretedwith caution, however, due to the high multicollinearity between branching, root-wad presence, and piece length inherent in the study design (i.e. all of the longestpieces contain rootwads and branches). While this piece design may realisticallysimulate the characteristics of pieces input through bank erosion, the decreasingtrend in travel distance is largely attributable to the increasing presence of root-wads, rather than piece length. Indeed, according to the linear and logistic mod-els, the probability of mobilization, and overall travel distance, actually increaseswith piece length. This pattern is most evident when only those pieces with root-wads are considered, as the smallest pieces with rootwads are the most stable of allpiece types, with the exception of large ramped pieces. Larger pieces integrate awider range of depths and velocities, reducing the importance of local conditions103[Braudrick and Grant, 2000]; shorter pieces have a greater probability of becomingtrapped in low depth or velocity areas [Wohl and Merritt, 2008]. Once in transport,larger pieces also have more momentum than smaller pieces, and are less likely tobecome trapped during encounters with banks or obstacles [Braudrick and Grant,2000]. The high stability of small pieces with rootwads has important implica-tions for stream restoration, as the crescentic scour pools that characteristicallyform around the rootwad end may provide high quality habitat. Similar to previousresearch, ramping (or bracing) was an important determinant of individual piecestability [Cadol and Wohl, 2010, Merten et al., 2010], as only a quarter of rampedpieces moved in the first five hours after wood addition, and none far enough tofully enter the channel.Several reach characteristics, including reach morphology, wood loading, andramped piece frequency, also influenced piece mobilization and transport duringthe transition to the jam-stabilized state. The average cross sectional variability inchannel depth was included in both logistic models for wood mobilization, whilethe water surface gradient was a significant predictor of substantial mobilization.As pieces integrate the range of depths they encounter, the probability that someportion of a piece will encounter a part of the channel with a depth exceedingthe buoyant depth for the piece increases with the bed variability, in addition tothe piece length [Braudrick et al., 1997, Braudrick and Grant, 2000]. Thus, in amore variable reach, the initiation of floatation along some part of a wood piece ismore likely. This small initial movement, combined with scour, may increase thelikelihood that a piece will pivot or roll toward the thalweg and travel further down-stream. Water surface gradient, which varied only slightly between the four exper-iments, influences water velocity and thus the drag and lift forces acting on thepiece [Shields and Alonso, 2012]. None of the morphologic variables consideredin the analyses were included in either model for travel distance, likely becausepieces in motion travel along the deepest part of the channel, which generally ex-ceeded the buoyant depth for the piece regardless of the overall variability in depthwithin the reach [Braudrick and Grant, 2001]. While depth variability may influ-ence the likelihood of encountering a shallow bar, interactions with other piecesexerted a greater influence on deposition, as many of the mobile pieces rackedon to existing jams. Wood loading, which varied between the four experiments,104also exerted a significant control on both mobilization and travel distance. Theexperiments demonstrated semi-congested transport [Braudrick et al., 1997] char-acterized by frequent piece interactions, and the greater potential for interactionsbetween pieces with increasing wood load promoted mobilization and increasedtravel distance. Trapping of mobile pieces, meanwhile, was governed by the num-ber of large, ramped pieces in the reach, and the frequency of these pieces restrictedthe mean travel distance. For individual pieces, however, the probability of joininga jam increased with travel distance. Thus, while the frequency of obstructionslimited the mean travel distance, the probability of an individual piece racking onto an existing jam increased the further it travelled.The modest predictive power of many existing statistical models of wood mo-bilization and travel reflects the stochasticity inherent in wood transport, and theinability of models based on reach averaged parameters to capture the hydraulicconditions operating on individual pieces. Furthermore, important predictors suchas piece burial are difficult to directly quantify and therefore not considered inmany studies. The high degree of variability between the parameters included inthe statistical models presented in this and previous studies [e.g. Braudrick andGrant, 2000, Wallerstein et al., 2001, Merten et al., 2010, Dixon and Sear, 2014,Schenk et al., 2014], meanwhile, highlights the need for consistent metrics in themeasurement and modeling of large wood [Wohl et al., 2010]. Metrics such asramping, branching complexity, key piece size, and even stability (i.e. the thresh-old distance for mobilization) vary between studies [e.g. Wohl and Merritt, 2008,Merten et al., 2010, Dixon and Sear, 2014, Schenk et al., 2014].While the present research yields insight into the importance of numerous pieceand reach characteristics in determining wood stability immediately after recruit-ment, several important variables were not included in the models. Piece burial,which enhances piece stability leading to decreased re-mobilization of pieces overtime [Merten et al., 2010], was observed during the experiments but not directlyquantified, though its importance is likely limited during the initial period after re-cruitment when mobility is greatest. While differences in wood diameter, as wellas wood density and type, may also affect entrainment and transport [Dixon andSear, 2014], variability in these parameters was not included in the experiments.The large proportion of jams containing ramped key members also suggests that105the initial location of these pieces is a key determinant of jam location. Finally, asthese experiments model only the 2-year flood events, the de-stabilizing effects oflarge flows on key pieces is not represented.4.6 ConclusionsThe wood dynamics observed during four flume experiments, which employed asteady flow rate approximately equal to the median or 2-year return period flood,demonstrate that a physically-based model can be used to realistically reproducethe transition from newly recruited, highly mobile wood to the self-organized, jam-stabilized state typical of many natural systems. According to our experiments, thistransition occurs during a single flood after recruitment, as ramped key pieces formnuclei for the development of stable jams which trap mobile pieces. Independentpieces tend to pivot and align parallel to the flow direction during this transitionalperiod, increasing piece stability by minimizing the forces acting on the piece.Wood mobilization and transport during this initial period is dictated by bothpiece and reach characteristics. Field studies of wood transport generally fail tocapture wood dynamics during this highly mobile period immediately after recruit-ment, and thereby underestimate the mobility of newly recruited wood. Our resultsdemonstrate the importance of piece complexity, and especially rootwads, in gov-erning mobility during the transition a stabilized configuration. Jam formation,which depends primarily on the number and location of large ramped pieces, alsoexerts an important influence on piece mobility. Increased wood loading, mean-while, increases piece mobility and travel distance, likely through interactions be-tween stationary and mobile wood pieces. These results have important implica-tions for future experimental research, as most prior studies have employed simplecylindrical dowels or individual wood pieces. These findings also have valuableimplications for modeling wood recruitment through bank erosion in laterally ac-tive streams, as they show that rootwad presence dominates piece stability as wellas subsequent travel distance, while also influencing piece orientation.106Chapter 5Modeling Wood Dynamics in aLaterally Active Reach5.1 SummaryWood recruitment in laterally unstable streams occurs through both toppling andbank erosion. Modifications to the Reach Scale Channel Simulator (RSCS) areneeded to account for additional inputs due to bank erosion, as wood recruitedfrom the stream banks contains rootwads, which alter piece stability and transport.Vegetation colonization along the non-eroding bank also incorporates wood fromthe channel into long-term floodplain storage. In this chapter we present a modifiedversion of the RSCS which incorporates the effects of rootwads on piece dynam-ics based on the experiments presented in Chapter 4, while also accounting for theeffects of variable flood magnitudes and channel dimensions on in-stream wooddynamics. We use output from three of the STochastic CHannel Adjustment SIM-ulator (STOCHASIM) flow variability scenarios presented in Chapter 3 as inputto the modified RSCS model to explore the effects of flood variability on woodloading and jam characteristics. Our results show that the introduction of bankerosion increases wood loading by an order of magnitude. As flow variability –and channel width – increase, wood loading rises due to the increase in the numberof pieces recruited to the reach, as well as an increase in the average piece size.Greater erosion rates and increasing channel size are also associated with reduced107piece stability; in highly variable reaches jams fail often due to frequent episodicwidening, limiting jam size and increasing piece mobility. The modeling presentedin this chapter highlights the importance of incorporating bank erosion and flood-plain creation in recruitment models for erodible reaches. The inclusion of bankerosion is especially necessary in reaches subject to high flow variability, which istypical of arid regions and small watersheds.5.2 IntroductionWhile in-stream large wood has been shown to influence floodplain processesthrough avulsion and side channel creation, floodplain dynamics also directly influ-ence recruitment processes and wood loading. Chronic wood recruitment occursthrough two primary mechanisms: toppling and bank erosion [Benda and Sias,2003, Czarnomski et al., 2008]. The Reach Scale Channel Simulator (RSCS) ver-sion presented in Chapter 2 accounts for the influence forest disturbances on top-pling rates in a laterally stable channel, but does not account for inputs throughbank erosion in a laterally active channel. This modeling approach is primarilyapplicable to systems where bank erosion is limited either by bank cohesion orapparent cohesion provided by tree roots. In forested streams with rooting depthsthat exceed the bank height – generally channels less than 10-20 m – bank erosionis limited or prevented entirely [Beechie et al., 2006, Eaton and Giles, 2009] andrecruitment is dominated by toppling inputs. As shown in Chapter 3 and AppendixC, bank erosion rates may reach up to 2 m/yr in some laterally active streams, andthe erosion rate increases with flow variability. In laterally active systems, woodinputs from bank erosion can exceed inputs from toppling by an order of magnitudeor more [Benda and Sias, 2003].In this chapter, we develop a new version of the RSCS model presented inChapter 2, which accounts for wood recruitment through both bank erosion andtoppling. In this modified RSCS model the stability and transport distances ofpieces vary as a function of rootwad presence based on the flume experimentspresented in Chapter 4. Output from the STOCHASIM simulations presented inChapter 3 is used to generate channel widths and flood magnitudes, which varyeach year. Annual bank erosion values generated by STOCHASIM are used to108drive wood recruitment in the RSCS, while floodplain colonization each year de-termines wood removal from the reach. Combined, these models simulate woodrecruitment and channel morphology in a reach with erodible banks and variableannual flood magnitudes. In combination these biogeomorphic models account forthe influence of both live and dead vegetation on the evolution of channel morphol-ogy and highlight the importance of incorporating bank erosion into recruitmentmodels for laterally migrating reaches.5.3 Model Description5.3.1 Model OverviewThe STOCHASIM model presented in Chapter 3 models channel migration acrossthe floodplain, which occurs through a combination of erosion along the retreat-ing bank during large floods and vegetation colonization along the opposite bankbetween flood events. Output from STOCHASIM can be used to generate annualflood magnitudes, channel dimensions, and wood input volumes in a laterally stablereach, but requires modifications to the existing RSCS model; both bank erosionand floodplain creation (i.e. vegetation colonization) affect the amount and charac-teristics of the wood recruited to the reach. The modeling presented in this chapterbuilds on previous versions of the RSCS by incorporating the effects of erosionand floodplain creation on wood recruitment and in-stream processes (Figure 5.1).Table 5.1 describes each of the RSCS versions.109Figure 5.1: A schematic of the RSCS model (V. 3.0). Bank erosion increasesthe rate of recuitment along the the right bank, as well as the proportionof trees falling toward the channel. Vegetation colonization reduces theforest age – and therefore the average tree height and the toppling rate– along the left bank (adapted from Eaton and Hassan [2013]).110Table 5.1: Description of the RSCS version developed to date.Name Source DescriptionVersion 1.0 Eaton et al. [2012] Stochastic physically based model of wood recruitment,movement, and jam formation. Uses a Monte Carlo modelingapproach to simulate variability in wood loading and jamcharacteristics.Version 1.1 Eaton and Hassan [2013] Modifies the original version of the RSCS to account for arange of channel scales using an empirical relation betweenslope and discharge.Version 2.0 Chapter 3, Appendix A, Incorporates variability in recruitment to simulate disturbance.Davidson and Eaton [2015] Adds a habitat module to translate morphologic impacts of woodto physical habitat.Version 3.0 Chapter 5 Models wood movement in a stream with temporalvariability in stream discharge and channel width. Incorporateswood addition via bank erosion as well as wood removal throughfloodplain incorporation.111Wood recruitment through bank erosion affects piece characteristics, therebyaltering wood mobility and transport. Wood input through bank erosion includes arootwad, and is therefore subject to a lower probability of mobilization than piecesinput through toppling. Pieces containing rootwads also travel shorter distancesonce entrained, increasing the residence time of wood recruited through bank ero-sion. Vegetation colonization along the non-eroding bank, meanwhile, reduces theaverage height of the riparian vegetation. Assuming that chronic mortality is lowin non-mature forests [e.g. Benda and Sias, 2003], vegetation colonization also re-duces the inputs of wood through toppling along the newly formed riparian zone.Finally, as new floodplain forms through a combination of aggradation (acceleratedby the reduced transport rate in the widened channel) and vegetation growth, in-stream wood is incorporated into long-term storage within the floodplain. Figure5.1 shows a modified version of the wood recruitment model presented in Eatonand Hassan [2013] which accounts for many of these factors.Riparian Stand CharacteristicsIn addition to the STOCHASIM output described above, it is also necessary thatSTOCHASIM record riparian stand characteristics in each year, as the riparian for-est is affected by channel migration. At the outset of each simulation, the riparianforest is the same along either bank. As the simulation progresses, vegetation es-tablishment decreases the average age of the vegetation along the colonizing bank.Trees that colonize the bar surface are assigned an age of 0 years in the STochasticCHannel Adjustment SIMulator (STOCHASIM) presented in Chapter 3 and thevegetation age increases by 1 year during each modeled time step. This producesa sequence of increasing forest age with distance from the newly forming channelbank.Each year STOCHASIM calculates the average age for the riparian forest alongthe colonizing bank. An average tree size is then calculated using published growthcurves describing the change in lodgepole pine height with years since the treeattained breast height (ytb):ytb = 5.6+42.64SI(5.1)112where SI is a site index that describes the tree height at 50 years breast height age(Aytb), which represents the number of years since the tree attained breast height[Thrower et al., 1994]. Site index is essentially a measure of site productivity; inhigh productivity sites a tree will attain breast height in a shorter period of timethan in a lower productivity site. The height associated with a given breast heightage, Aytb, is then:Htri = 1.3+(SI−1.3) ·b1b2(5.2)whereb1 = 1+ exp[7.815−1.285 · ln(50)−1.007 · ln(SI−1.3)] (5.3)andb2 = 1+ exp[7.815−1.285 · ln(Aytb)−1.007 · ln(SI−1.3)] (5.4)The growth model was calibrated by adjusting the site index in order to producea tree height of 30 m (i.e. the mature tree height along the eroding bank) 100 yearsafter colonization (Figure 5.2a). This requires a site index of 23.5 m, such that thetree achieves breast height in 7.4 years and 23.5 m 50 years later. This site index isrelatively high compared to the site indices for interior lodgepole pine presented inThrower et al. [1994], which range from 6 to 22 m at 50 years, and require 10 to 150years to attain breast height. The high site index may nevertheless be a reasonableestimate for the riparian zone, where growing conditions are generally favourable.Tree diameter (Dtr) increases linearly with tree age, reaching a diameter of 0.4 mafter 100 years (Figure 5.2b).Wood RecruitmentBank erosion and vegetation colonization influence the rate of wood recruitmentto the reach, as well as the characteristics of the recruited wood. Wood may enterthe channel either by toppling, which is described in detail in Appendix A andChapter 2, or by bank erosion. Toppling along the advancing bank is influencedby the process of colonization in the RSCS (V. 3.0), which reduces the average1130 20 40 60 80 1000. Age (years)Relative Height0 20 40 60 80 1000. Age (years)Relative DiameterFigure 5.2: a) Tree height (relative to the mature tree height) increases be-yond the breast height age (ytb), which is represented by a dashed line,and b) tree diameter (relative to the mature tree diameter) increases lin-early with tree age.114stand age. This in turn affects the average tree dimensions, as described in theprevious section, as well as the toppling rate. The base toppling rate (M) – whichis randomly selected from a uniform distribution of values ranging from 0.002 to0.003 (or 0.2% to 0.3% of trees per year) with an average value of 0.0025 – isscaled along the colonizing bank by the ratio of the average tree height (Htri) to themature tree height (Htr). The mortality rate therefore reflects the stand age, withthe base mortality rate of 0.25% of trees per year reached only when the stand isfully mature along both banks, with an average age of 100 years.Bank erosion introduces mature trees to the channel; for simplicity we assumethat erosion occurs along a consistent retreating bank throughout the simulationperiod, and that colonization always occurs along the opposite bank. This resultsin a consistent direction of lateral migration, and ensures that the channel erodesinto mature riparian forest. The riparian zone along the retreating bank is thereforesubject to the base toppling rate, which averages 0.25% of trees per year.The number of trees recruited as a result of channel widening in any given yearis simply:NBE = ρtr · Lch ·WBE10000 (5.5)where ρtr represents the mature forest density. Unlike toppling, which can occuranywhere within the riparian stand (i.e. up to a distance of Htr from the chan-nel), trees recruited via bank erosion enter immediately adjacent to the stream andfall toward the channel. As the channel widens, an increasing proportion of entiremature trees (Htr = 30 m) enter the stream channel. As trees recruited via bank ero-sion generally fall towards the channel [Murphy and Koski, 1989], each fallen treewithin the eroded section is randomly assigned a fall angle (Θtr), from a uniformdistribution ranging from 0 to 180 degrees.Trees that reach the opposite channel bank (i.e. 30 · sinΘtr > Wchi) are short-ened through breakage (LLW →Wchi/sinΘtr). These trees remain ramped on theopposite bank, and are assigned a piece functionality, FLW , of 0.5. If the channelwidth exceeds 30sinΘtr, entire trees may enter the channel without breaking onthe opposite bank. These trees are assigned a functionality class of 0.95.115Rootwad EffectsWood entering a reach via bank erosion includes a rootwad, by definition. Theresearch presented in Chapter 4 shows that rootwad presence is the most impor-tant factor governing piece stability and travel distance; pieces with rootwads areless likely to become mobilized than those without rootwads, and travel shorterdistances when mobilized. To reflect these differences we have modified the prob-ability of piece movement such that only 18% of potentially mobile pieces withrootwads – as determined by piece orientation, length, and diameter relative to thelocal flow depth – are mobilized, based on the logistic modeling presented in Chap-ter 4. Based on the results of the regression analysis of piece movement, mobilepieces with rootwads move only 1/8 of the distance predicted based on the relativepiece length and diameter.The experimental results presented in Chapter 4 also show that individual woodpieces containing rootwads are more likely to orient parallel to the flow directionthan pieces without rootwads. The orientation a piece adopts after movement istherefore modified to account for the presence or absence of a rootwad; followingpiece movement, approximately 75% of pieces with rootwads are assigned ori-entations parallel to the flow direction, compared with only 50% of non-rootwadpieces. The remainder of pieces deposit with an oblique orientation. Followingpiece breakage we assume that the portion of the piece containing the rootwaddoes not change position, while the non-rootwad end adopts a new orientation.Again, we assume that 50% of these pieces orient parallel to the flow direction,and the remaining 50% deposit in a skewed or oblique orientation.Channel WideningChannel widening throughout a run affects the piece size relative to the channelwidth and depth, as well as the functional class of wood pieces. Following an ero-sion event, the functional class of all pieces is re-evaluated and suspended pieces(FLW = 0.05) which no longer extend across the channel banks are assigned aramped functional classification (FLW = 0.5). Approximately half of all rampedpieces recruited through toppling are assumed to fully enter the channel whenwidening occurs and are assigned a piece functionality of 0.95. For ramped pieces116recruited through bank erosion we assume that the non-rootwad end is suspendedon the opposite (i.e. colonizing) bank, and the functional class is therefore notimpacted by further erosion along the retreating bank.Key pieces are defined as pieces that block at least 75% of the channel width(Wch), taking into consideration the functional class (FLW ). By reducing relativepiece size and the number of key pieces in the reach, widening de-stabilizes jams.In the year following an erosion event the model re-identifies all key pieces in thereach according to the piece length relative to the new channel width. The modelthen searches for any jams that no longer contain a key member and redistributes allwood pieces in the failing jam. Jam age, size, and failure mechanism are recordedat the time of failure.Floodplain IncorporationEach year, a subset of the wood pieces in the reach are moved into long term storagewithin the developing floodplain. We assume that wood is evenly distributed acrossthe channel bed, and that the volume of wood removed from the bankfull channelthrough this mechanism is proportional to the reduction in the channel width due tovegetation colonization. The reduction in wood volume (Vf p) in any year is thus:Vf p =VLW ·WrvWch (5.6)where VLW and Wch are the total wood load and the width of the channel prior tovegetation colonization, respectively, and Wrv is the width that is colonized thatyear.In order to achieve this reduction in wood loading, individual pieces are re-moved randomly from the reach until a volume equal to Vf p has been removed. Ifa key piece is selected, all of the pieces in the jam are also removed. Again thejam age and size at the time of removal are recorded. The removal of entire jamssimulates the process of avulsion, which can lead to the abandonment of in-channeljams as the river adopts a new course on the floodplain, as well as the developmentof patches of floodplain upstream of large jams [Fetherston et al., 1995, Collinset al., 2012].1175.3.2 ScenariosThe RSCS model (V. 3.0) is used to explore wood loading in a reach characterizedby a median discharge of 20 m3/s that is subject to variable flood magnitudes. Thisrepresents a channel size that is sensitive to morphologic change due to wood load-ing, but also large enough to experience lateral instability. Output from three of theSTOCHASIM simulations presented in Chapter 3 is used as input to the modifiedRSCS model (V. 3.0) to explore the effects of flow variability on wood loading andjam formation. Increasing flow variability leads to more frequent and higher mag-nitude erosion events, increasing the long-term average channel width and lateralmigration rate for a given median flood size. The high variability simulations areintended to represent channel dynamics in arid regions or small drainages, both ofwhich are subject to more variable flows [Baker, 1977]. We compare these simu-lations with the base scenario presented in Chapter 2, which represents a laterallystable reach with a consistent annual flood of 20 m3/s. In this base scenario all ofthe wood in the channel is recruited via toppling (Table 5.2).Table 5.2: Summary of the riparian and hydrologic conditions considered inthe modeled scenarios. Text in bold represents the scenario that was pre-viously modeled in Chapter 2.Scenario Median FMI Input mechanism No. runswidth (m)Base 12.4 0 Toppling 400Low variability 11.6 0.2 Toppling/Erosion 400Moderate variability 14.6 0.4 Toppling/Erosion 400High variability 17.3 0.6 Toppling/Erosion 4005.4 Results5.4.1 Reach CharacteristicsThe effects of flow variability on the amount of in-channel wood and the numberof jams present in the reach are summarized in Table 5.3. As flow variability in-118creases, both the frequency of erosion events and the long-term average channelwidth increase. Increased input of wood via bank erosion leads to a dramatic risein the volume of in-stream wood in Scenarios 1 to 3 relative to the base scenario.The volume of wood in the reach increases from 35.3 m3 to 119 m3 with the in-troduction of bank erosion in the lowest variability scenario, and increases by anorder of magnitude in the highest variability scenario relative to the base simulation(Figure 5.3; Table 5.3).Table 5.3: Median wood loading and jam characteristics in year 300 for eachof the flow variability scenarios.Scenario Volume Wood load No. jams Wood load in jamsm3 m3/m2 m3/m2Base 35.3 0.015 1.1 0.0072 (47%)1 119 0.054 11 0.019 (35%)2 280 0.10 15 0.027 (27%)3 431 0.13 15 0.031 (24%)While wood loading also increases with higher flow variability, the increase ismitigated by the larger bed area associated with the higher variability scenarios.Both wood load and volume are highly variable over time, even within a singlerun (Figure 5.3). Similar to the fire inputs modeled in Chapter 2, the volume ofin-stream wood increases significantly in response to individual disturbances (i.e.erosion events), before decreasing over time during the recovery period as wooddecays and is exported from the reach. While the number of jams in the reach in-crease rapidly with the initial introduction of bank erosion in the lowest variabilityscenario, the proportion of the total wood load trapped in jams declines as flowvariability increases (Table 5.3).The wood load produced by the base scenario is similar to the pre-fire woodloading in Fishtrap Creek (Figure 5.4). The model results also compare favourablyto wood loadings measured globally for the low variability scenario, but typicallyexceed observed values for the moderate and high variability scenarios. Figure5.4 highlights the large range of variability in natural systems, with wood load-ing varying by three orders of magnitude in the 27 streams surveyed. The large1190 50 100 150 200 250 3000200400600Time (years)Wood Volume (m3 )BaseFMI = 0.2FMI = 0.4FMI = 0.6a0 50 100 150 200 250 3000.000.100.20Time (years)Wood Load (m3m2 ) BaseFMI = 0.2 FMI = 0.4FMI = 0.6bFigure 5.3: The median a) wood volume, and b) wood load are shown overtime for each of the four flow variability scenarios. Light grey linesrepresent wood volume and wood load over time for a single run.120variability produced during a single run (Figure 5.3) suggests that the large rangeof wood loadings likely represents both spatial and temporal variability in woodrecruitment. High variability in wood loading is also a reflection of differencesin anthropogenic legacy, as historic wood removal has dramatically reduced woodloads in many streams worldwide [e.g. Wohl, 2013].lllllll0 5 10 15 (m)Wood Load (m3m2  x 10−2 )llllllll lllll lllllllllllBritish ColumbiaWorldFishtrap CreekBaseFMI = 0.2FMI = 0.4FMI = 0.6Figure 5.4: Wood loadings reported from studies throughout BritishColumbia (unpublished data) and globally [Andreoli et al., 2007, Bragg,2000, Cadol et al., 2009, Nakamura and Swanson, 1993, Richmond andFausch, 1995, Wohl and Jaeger, 2009] are shown for a range of channelsizes. Pre- and post-fire wood loadings for Fishtrap Creek, measuredduring a 2008 survey by Andrews [2010], are also shown. Dashed linesindicate the predicted median wood load for each flow variability sce-nario.1215.4.2 Recruitment MechanismFlow variability also affects the characteristics of the wood pieces recruited to thereach. In the highest variability scenario, more than 98% of pieces in the reachwere recruited via bank erosion, due to a combination of higher erosion rates anda decrease in the contribution from toppling; as erosion rates increase the age andmortality rate of wood along the colonizing bank decreases, leading to a decline inthe number of pieces recruited through this mechanism (Table 5.4 and Figure 5.5).Table 5.4: Summary of the piece characteristics associated with each re-cruitment mechanism. Values in brackets represent dimensionless piecelengths.Name Base 1 2 3Number of piecesAll 119 178 245 300Toppling 119 28 9 5Bank erosion - 150 237 295Median piece length (m)All 4.4 (0.35) 7.0 (0.60) 9.6 (0.66) 11.4 (0.66)Toppling 4.4 5.8 7.2 8.1Bank erosion - 7.4 9.7 11.5Mean residence time (yrs)All 22 17 12 10Toppling 22 11 7 5Bank erosion - 18 12 10Despite a decrease in mean stand age and tree height, the size of in-streamwood pieces actually increases with flow variability for both recruitment mech-anisms. Recruited pieces that fully span the channel are forced to break at theopposite bank, limiting piece length based on both the tree fall angle and the chan-nel width. Thus as channel size increases with greater flow variability and erosionfrequency, the median piece size also increases (Figure 5.6). Pieces recruited viabank erosion are consistently longer for all scenarios than those input via toppling,1221 2 302060100ScenarioRiparian Stand Age (years)1 2 305152535ScenarioRiparian Stand Height (m)Figure 5.5: Boxplots showing a) the decrease in riparian stand age, and b)the decrease in stand height associated with increasing flow variabilityin Scenarios 1 to 3. The red dashed lines indicate the characteristicsassociated with a mature riparian forest (i.e. no flow variability).as wood input through this mechanism is necessarily located along the channelbank, while pieces that topple toward the channel may be up to a distance of Htrfrom the stream (Table 5.4).123LLWProbability0 5 10 15 20 25 300.000.100.20Base scenarioaLLWProbability0 5 10 15 20 25 300. = 0.2bLLWProbability0 5 10 15 20 25 300.000.040.08FMI = 0.4cLLWProbability0 5 10 15 20 25 300.000.040.08FMI = 0.6dFigure 5.6: Histograms of the length of in-stream wood pieces are shown for each scenarios. Red dashed lines indicatethe median piece length.1245.4.3 Jam DynamicsThe effects of flow variability on jam dynamics are more complex. The mediannumber of jams in the reach increases dramatically between the base and low vari-ability scenario due to a large increase in wood volume (Figure 5.7), as well as agreater number of key pieces with rising dimensionless piece length (Table 5.4).The two highest flow variability scenarios have approximately equal jam frequen-cies, however, despite the continued increase in wood volume (Figure 5.7a). Thisstagnation is partially attributable to the dimensionless piece size, which remainsconstant between the two scenarios, despite an increase in the absolute piece size,due to channel widening (Table 5.4).Increased rates of jam failure with greater flow variability compound this effect,reducing the proportion of wood trapped in jams (Figure 5.7b; Table 5.3). As flowvariability increases, greater variability in channel width increases the frequencyof jam failures as key pieces are no longer able to span the channel. Failure dueto channel widening increases from 0% in the base scenario, to 59% of all failuresin the highest variability scenario (Table 5.5), and leads to large fluctuations inthe number of jams present in the reach over time (Figure 5.7a). An increasingnumber of jams are also incorporated into the floodplain as channel variability –and the rate of floodplain creation through revegetation – increases. The averagejam size and age at failure both decrease with rising flow variability (Table 5.5),indicating that highly variable systems are characterized by the frequent formationand failure of small, transient jams.5.4.4 Rootwads and Piece DynamicsThe base and variable flow scenarios produce differences in piece functionalityand mobility. Overall the average functionality of wood pieces decreases withincreasing flow variability (Table 5.6). While functionality simply represents theproportion of the piece located within the bankfull channel, it is a useful proxy forits potential morphologic impact. The change in piece functionality is primarilyattributable to the greater number of newly recruited pieces in the reach as the rateof bank erosion increases, as new pieces tend to be ramped on one channel bank.The effect is mitigated, however, by the increased frequency of widening events1250 50 100 150 200 250 3000.000.020.04Time (years)Wood Load (m3m2 ) BaseFMI = 0.2 FMI = 0.4FMI = 0.6a0 50 100 150 200 250 30005102030Time (years)Number of JamsBaseFMI = 0.2FMI = 0.4FMI = 0.6bFigure 5.7: The median a) wood load in jams and b) number of jams in thereach are shown over time for each of the four flow variability flow variability increases; channel widening increases the functional class ofall pieces suspended across the channel banks, as these pieces become ramped as126Table 5.5: The characteristics of jams at the time of failure are summarizedfor each scenario and failure mechanism.Name Base 1 2 3Number of failuresAll 15 212 545 749Widening - 79 288 437Decay 15 81 124 131Floodplain incorporation - 52 132 181Age of jam at failure (yrs)All 16 15 11 10Widening - 23 13 11Decay 16 11 8 6Floodplain incorporation - 12 10 9Jam size at failure (no. pieces)All 21 5 4 3Widening - 4 3 2Decay 21 7 6 5Floodplain incorporation - 6 5 5the banks shift. Meanwhile approximately half of all ramped pieces that enteredthe reach via toppling fully enter the channel during a widening event. Pieceswith rootwads (i.e. pieces that enter via bank erosion), however, fall toward thecolonizing bank and therefore remain ramped during widening events. As a resultthese pieces have consistently lower functionality than pieces without rootwads forall of the variable flow scenarios, reducing their capacity to alter bed morphology.Pieces with rootwads differ significantly from those without rootwads in termsof their stability, as well as their potential for morphologic impact. Piece residencetime (i.e. the number of years that a piece has been at its present location) decreasessystematically with increasing flow variability due to both higher rates of woodinput, and a greater frequency of jam failure. Higher piece mobility with increasedflow variability is evident from the decrease in the residence time of pieces inputthrough toppling, which falls from 22 years in the base scenario to just 5 years in127Table 5.6: Piece characteristics are summarized by piece type for each of thefour flow variability scenarios.Name Base 1 2 3Number of piecesAll 119 178 245 300Rootwad - 56 103 138No rootwad 119 122 142 161Mean residence time (yrs)All 22 17 12 10Rootwad - 26 18 15No rootwad 22 12 8 6Mean orientation (◦)All 94 99 104 114Rootwad - 121 121 115No rootwad 94 97 101 105the highest variability scenario (Table 5.6). While the residence time of pieces withrootwads also decreases with greater flow variability, these pieces are consistentlymore stable than pieces without rootwads (Table 5.6).5.5 DiscussionThis chapter presents the results of simulations that combine the STOCHASIMchannel evolution model presented in Chapter 3 with a modified version of theRSCS wood recruitment model presented in Chapter 2. Together these models pro-vide a comprehensive biogeomorphic simulator that incorporates the influence ofboth live and dead vegetation on channel dynamics in a laterally active stream. Theimposition of variable flows produces a channel with a variable width and dramati-cally increases wood recruitment by introducing a second recruitment mechanism:bank erosion. The ten-fold increase in wood volume between the laterally stablebase scenario and the highest variability scenario is consistent with the increasein wood volume modeled by Benda and Sias [2003] with the inclusion of bank128erosion.The results of the biogeomorphic simulations provide insight into the effect ofincreasing flow variability – and increased lateral instability – on wood dynamics.As flow variability increases, both the average channel width and the variability inwidth (i.e. the bank erosion rate) increase. This leads to a higher rate of recruitmentvia bank erosion, while simultaneously decreasing the contribution from topplingby reducing the average forest age, tree size, and mortality rate. Wood volume in-creases approximately linearly with flow variability due to both the increased rateof wood recruitment and an increase in piece size, as pieces input by bank erosionare assumed to enter from the bank immediately adjacent to the active channel.The size of pieces input through toppling also increases, despite a decrease in av-erage tree dimensions in the riparian zone; channel width limits the size of newlyrecruited wood through breakage, such that piece length increases with increasedchannel width in the variable flow scenarios.Piece functionality also reflects recruitment mechanism and therefore variesbetween the four scenarios, limiting the potential morphologic impact of newlyadded wood. While bank erosion leads to an increase in wood recruitment, a largerproportion of the wood input through this mechanism is long enough to reach theopposite bank, and therefore remains ramped on the colonizing bank until a subse-quent breakage occurs as the piece decays. As a result, pieces input by bank erosionhave greater residence times – and lower mobility – than pieces input through top-pling. Piece input through toppling are also more likely to fully enter the channelduring widening events.The results also indicate a significant shift in jam dynamics with increasinglateral instability and wood loading. The base scenario produces a reach character-ized by relatively large, stable jams, similar to those which developed in the flumeexperiments presented in Chapter 4. Jam age at failure systematically decreases asflow variability increases, however, signifying an overall decrease in jam stability.The increase in failure rates is largely driven by channel widening – which reducesthe number of key pieces in the reach by decreasing relative piece length – withmore than 50% of all failures resulting from widening in the highest variability sce-nario. Jam size also decreases dramatically with the introduction of bank erosion;as lateral instability rises, the reach is increasingly characterized by small, transient129jams. These jams fail frequently as the channel size fluctuates, producing pulsedwood recruitment but also temporarily reducing relative piece size. As channel mi-gration drives floodplain creation, high lateral instability also increases the numberof jams that are incorporated into the floodplain over the course of a simulation.Jam removal by this mechanism effectively simulates the large wood floodplaincycle proposed by Collins et al. [2012]; jams induce deposition upstream leadingto island growth, which eventually incorporates the stabilizing jam in to the flood-plain, while also increasing the probability of avulsion [Fetherston et al., 1995].The presence of buried log jams in historical floodplain deposits [e.g. Abbe andMontgomery, 2003] support this theory, as well as the model formulation.Piece mobility is affected by increased lateral instability in a number of com-plex, interacting ways. Increased jam instability contributes to greater overall piecemobility with increasing flow variability, largely because jam failure releases alltrapped pieces. For a given channel geometry, higher piece mobility should alsooccur during floods that exceed the median flood, leading to pulses of high mo-bility which reduce residence times relative to the base scenario. This effect iscomplicated, however, by the variability in channel geometry. Following erosionpiece mobility is affected by the competing influences of the increase in the di-mensionless piece diameter (i.e. the diameter relative to the flow depth) due tochannel widening, which decreases the probability of entrainment [Braudrick andGrant, 2000], and a reduction in the dimensionless piece length, which has beenshown to increase the likelihood of entrainment in some research [e.g. Merten et al.,2010, Dixon and Sear, 2014, Schenk et al., 2014]. Dimensionless piece length didnot, however, definitively influence piece mobility in the experiments presented inChapter 4. Finally, the addition of wood by bank erosion in the variable flood sce-narios leads to the introduction of pieces containing rootwads, with an increasingproportion of all pieces containing rootwads as flow variability rises. The higherstability of pieces with rootwads relative to those without partially compensates forthe increased piece mobility associated with high lateral instability.While wildfire is not explicitly included in this modeling, it is clear that su-perimposing additional riparian disturbances would further increase the long-termaverage wood load, as well as the temporal variability in wood loading due to in-creased toppling rates. Bank erosion may also increase following wildfire due to130the loss of apparent cohesion as roots decay. Previous research suggests that rootdecay follows a negative exponential function, reaching a minimum value approx-imately 5-10 years after tree death [Sidle, 1992, Benda and Dunne, 1997]. Basedon the modeling presented in Chapter 3, the decrease in rooting depth following afire would produce increased rates of erosion, as the amount of widening predictedfor a given flood would increase. Indeed, accelerated bank erosion was observedin Fishtrap Creek four years after the 2003 fire, and has been attributed to the de-creased post-fire rooting depth [Eaton et al., 2010c]. The threshold for erosionhowever – which is a function of grain size – would remain constant, and ero-sion frequency should therefore not change. The increase in wood volume due tohigher erosion rates would also be mitigated by the decreased forest density duringthe period of accelerated toppling after a fire.Overall these results outline a realistic model of channel evolution in whichhigher rates of bank erosion lead to a higher volume of in-stream wood, while si-multaneously reducing jam size and stability, as well as piece functionality. How-ever, while the wood loads produced by the model compare favourably with woodloadings measured globally for the base scenario and the lowest variability sce-nario, the predicted loading exceeds wood loads observed in most natural streamsfor the higher variability scenarios. This discrepancy partly reflects interrelation-ships between flow variability and forest characteristics which are not accountedfor in the models. Arid regions, which are typically characterized by higher flowvariability [Baker, 1977], may also have reduced riparian tree density and growthrates, limiting the density of bank vegetation and the volume of wood recruited bybank erosion. The lack of vegetation in truly arid watersheds may partially or en-tirely prevent vegetation growth and channel recovery after widening events [Wol-man and Gerson, 1978]. According to the modeling presented in Chapter 3, thiswill limit the rate of channel narrowing, thereby reducing or eliminating long-termerosion rates and producing a near constant channel geometry. Finally, researchsuggests that historical wood loading vastly exceeded the wood loads currentlyobserved in many streams, including those believed to reflect natural conditions[Wohl, 2013]. Thus the high wood loadings predicted by the model relative toobserved wood loading may reflect the legacy of anthropogenic wood removal inmany river systems worldwide [Nagayama and Nakamura, 2009].1315.6 ConclusionsA comprehensive biogeomorphic model of channel evolution must consider theimpacts of both live and dead vegetation on channel dynamics. This work presentsa modified version of the Reach Scale Channel Simulator (RSCS) that accountsfor both chronic wood inputs due to toppling, and episodic wood inputs throughbank erosion. The model also incorporates variability in channel dimensions usingthe channel geometry and erosion rates produced by the STOchastic CHannel Ad-justment SIMulator (STOCHASIM) developed in Chapter 3. The model thereforeconsiders the effect of variations in channel width – produced by erosion duringlarge flood events and subsequent revegetation – on wood functionality and stabil-ity.The model results show that reaches subject to bank erosion experience anorder of magnitude increase in wood loading relative to those with non-erodiblebanks. As flow variability and channel size increase, however, piece mobility in-creases. This increase is partially attributable to a decrease in jam stability, ashighly variable reaches are characterized by the frequent failure of relatively smalljams due to episodic widening. Piece characteristics are also affected by chan-nel variability; as flow variability increases a greater proportion of pieces containrootwads, and piece length increases. These changes lead to greater piece stabil-ity, partially counteracting the effects of flooding and channel widening on relativepiece size. While the model produces reasonable estimates of wood loading andjam frequency for the low variability scenarios, the wood loads generated by thehigh variability scenarios exceed those observed in many natural systems. This dis-parity likely reflects both the legacy of anthropogenic wood removal from streams,as well as interrelationships between flow variability and forest density that are notcaptured by the current model.132Chapter 6ConclusionSmall- to intermediate-sized mountain streams are highly dynamic systems subjectto forcings that vary through both space and time. Throughout recent history, peo-ple have reduced the variability in key drivers such as flood magnitude and woodloading in order to exploit natural resources, while also limiting threats to humaninfrastructure. Large wood, which increases morphologic complexity, has been re-moved from rivers worldwide to increase navigability and reduce flooding, as wellas indirectly through beaver trapping and fire suppression [Abbe and Montgomery,1996, Wohl and Beckman, 2014, Wohl et al., 2015]. Meanwhile, over 60% ofthe world’s rivers have been fragmented by hydrologic alteration, largely for thepurposes of flood control, irrigation, and power generation [Graf, 1999, Tharme,2003]. The effect of human alterations to river systems – which date back severalcenturies in North America – are so extensive that the archetypal ‘natural’ mean-dering stream often used as a reference condition for restoration projects is likelya relic of valley filling and subsequent incision related to mill dams [Walter andMerritts, 2008, Wohl et al., 2015].Prior to the hydrologic and ecological alteration that accompanied Europeansettlement, many natural streams were anabranching systems with extensive wet-land complexes [Walter and Merritts, 2008]. In order to better predict channeldynamics and to set useful restoration targets, it is therefore necessary to developan understanding of the historical range of variability in natural streams prior to hu-man alteration [Wohl and Beckman, 2014]. Existing models of fluvial dynamics,133however, are largely deterministic and assume that rivers adopt an optimal config-uration based on relatively constant forcings. Regime models, for example, weredeveloped in the late nineteenth and early twentieth century to determine the opti-mal dimensions of stable irrigation canals in India and Egypt [Ackers, 1992]. Thefundamental underlying premise of these models is that rivers adjust to efficientlyconvey the imposed sediment supply with the available discharge, and that channeldimensions can therefore be predicted based on a formative discharge.Stochastic modeling provides an avenue with which to explore the range inchannel conditions associated with variability in key governing parameters, whilealso incorporating uncertainty into model predictions. Stochastic models can beused to assess the relative influence of changes in governing conditions, as wellas to estimate the historical range of variability prior to human alteration. Fur-thermore, predictions from stochastic models are more likely to capture the rangeof conditions observed in natural systems than single values generated by deter-ministic models, as many stream processes such as jam failure and even sedimententrainment are inherently stochastic [Church and Ferguson, 2015]. This thesispresents stochastic models of wood loading and channel migration, which togetherprovide an integrated, physically based biogeomorphic model of channel evolution.The version of the Reach Scale Channel Simulator (RSCS) developed in Chap-ter 2 builds upon earlier work by [Eaton et al., 2012] and [Eaton and Hassan,2013] to incorporate the effects of variability in wood recruitment – due to bothanthropogenic and natural riparian disturbances – on in-stream wood loading. Themodeled wood loading is then used to estimate the impact of various riparian sce-narios on channel morphology, and by extension aquatic habitat availability. Theresults suggest that the morphologic impacts of wood are greatest in small- tointermediate-sized streams characterized by a median discharge of 5 to 25 m3/s.Wood loading is highest in streams characterized by flows of 10 to 15 m3/s, as thestream is wide enough for wood to be transported but narrow enough that channel-spanning jams remain common. Beyond a channel size of about 30 m3/s woodhas little impact on channel morphology, which is instead determined by fluvialprocesses.The modeling presented in Chapter 2 also shows that pulsed inputs of woodincrease the availability and variability of physical habitat in the post-fire period;134reach-averaged pool area and sediment storage double in small streams, while side-channels increase by over 50% in intermediate-sized channels. Forest harvesting,meanwhile, reduces the availability of habitat within the reach, though the effectsdiminish with increasing buffer size or stream width; in laterally stable streams theeffects of harvesting are minimized so long as buffer width is large enough for keypieces to be recruited to the reach. This research emphasizes the importance ofnatural disturbance in creating and maintaining habitat heterogeneity, and providesa useful tool for assessing the historical range of variability associated with naturaldisturbance.While Version 2.0 of the RSCS model introduces disturbance to the modeledreach, it relies on the formative discharge approach and can not be applied to lat-erally unstable streams. Chapter 3 therefore introduces a STOchastic CHannelAdjustment SIMulator (STOCHASIM), which incorporates the effects of variableflood magnitude on channel geometry. Unlike regime models, which yield predic-tions of long-term average conditions, STOCHASIM generates a variable channelgeometry. The model simulates the interplay between erosion, which occurs in re-sponse to mobilization of the material forming the bank toe, and floodplain creationthrough vegetation colonization. Channel geometry is historically contingent, as isthe geomorphic response to a flood event; similar to field observations a flood ofa given magnitude produces lower shear stresses in the years following an erosionevent [Tamminga et al., 2015], and the channel is therefore less likely to undergofurther erosion.We use STOCHASIM to simulate channel evolution in a reach characterizedby a median flood discharge of 20 m3/s, for a range of flow variability scenarios.This channel size has been selected as it is wide enough to experience lateral insta-bility (i.e. deeper than the typical rooting depth), but also highly morphologicallysensitive to wood inputs. The modeling shows that as flow variability increases, thereach experiences greater erosion magnitude and frequency, resulting in increasedlong-term erosion rates and average channel width. The size of channels character-ized by high flow variability – which is typical of arid watersheds, small mountainstreams, or regions with thunderstorm-generated flood events – are therefore bestpredicted by formative discharge values that are several times larger than the ef-fective discharge, and the median flood. Furthermore, the increase in formative135discharge far exceeds the rise in effective discharge. This suggests that channelconditions in highly variable systems are determined by two distinct populationsof floods: relatively frequent effective floods which transport the most sedimentover time and rare flood events which determine channel size. Changes in root-ing depth have little effect on long-term erosion rates, but do impact the nature ofchannel erosion; streams characterized by high rooting depths experience frequent,low magnitude erosion while those characterized by low rooting depths are subjectto infrequent, high magnitude widening events.In order to model wood recruitment in laterally active channels it is necessaryto consider wood recruitment through the process of bank erosion, which intro-duces large pieces containing rootwads to the channel. Chapter 4 presents analysesfrom a series of four flume experiments which are used to assess the effects ofreach and piece characteristics on wood mobilization and transport distance. Thestatistical analyses of piece mobility indicate that piece irregularities, especiallyrootwads, dictate the stability and transport of newly recruited wood pieces. Largeramped pieces, meanwhile, provide nuclei for the formation of persistent woodjams which form during a single flood event after recruitment. Piece orientation,which affects morphologic impact, also differs according to piece type as piecescontaining rootwads are more likely to orient parallel to the flow.In the final chapter we integrate the stochastic recruitment and channel adjust-ment models outlined in Chapters 2 and 3 to create a comprehensive biogeomor-phic model of channel evolution that accounts for the effects of both live riparianvegetation and dead in-stream wood. The model development is informed by theanalysis of wood stability presented in Chapter 4, and also considers the effectsof widening events on piece functionality and relative piece size, as well as theincorporation of wood into long-term storage within the floodplain. The resultingsimulations describe changes in channel geometry and wood loading over time inresponse to variable flood magnitude. The simulated channel responds to episodicflooding through rapid widening, which in turn introduces large pulses of woodto the channel but also leads to frequent jam failure. Thus while wood loadingincreases by an order of magnitude in the high variability scenarios relative to thebase simulation from Chapter 2, jam size declines and piece mobility increases.Furthermore, while Chapter 2 shows that the addition of wood increases the avail-136ability of aquatic habitat by generating morphologic complexity, the decreasedfunctionality of wood recruited through bank erosion limits its effectiveness. Whilethe wood loading generated in the low variability scenario appears reasonable com-pared with data reported from wood surveys, the wood loads generated by the highvariability scenarios exceed those observed in most natural systems. This disparitymay reflect historical wood removal from streams, but also arises from correlationsbetween flow variability and forest density that are not captured by the currentmodel.Stochastic modeling can be used to estimate of the range of historic variabilityin wood loading and channel geometry in natural systems in the absence of anthro-pogenic alteration, as well as to better understand uncertainty around model predic-tions. Stochastic approaches can therefore be used to inform restoration planning,as well as hazard prediction and mitigation, as they provide more information re-garding channel behaviour than deterministic predictions, or comparison with ref-erence reaches which were often themselves subject to significant alteration Walterand Merritts [2008]. The stochastic models developed in this work can also beused for scenario testing; in future work the combined biogeomorphic model willbe used to explore the effects of increased flow variability due to climate change,which is anticipated to alter hydrologic timing in British Columbia [Loukas andQuick, 1999, Schnorbus et al., 2014], on channel morphology, wood loading, andhabitat availability. These models also provide a means with which to investigatethe relative impacts of different management scenarios, such as harvesting bufferwidth or bank protection, on in-stream processes.137BibliographyT. B. Abbe and D. R. Montgomery. Large woody debris jams, channel hydraulicsand habitat formation in large rivers. Regulated Rivers: Research &Management, 12:201–221, 1996. → pages 2, 133T. B. Abbe and D. R. Montgomery. Patterns and processes of wood debrisaccumulation in the Queets river basin, Washington. Geomorphology, 51(1-3):81–107, Mar. 2003. 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Magnitude and Frequency of Forces inGeomorphic Processes. The Journal of Geology, 68(1):54–74, 1960. → pages44, 67, 74159Appendix AModel Description of the ReachScale Channel SimulatorA.1 IntroductionThe Reach Scale Channel Simulator (RSCS) uses a stochastic modeling approachin which specified event probabilities are used to estimate the volume of largewood (LW), the number of jams, and the effects of large wood on the channelmorphology in a reach. The initial version of the RSCS was described in detail byEaton et al. [2012], who used the model to analyze a 10 m wide reach and testedthe model output against field data from Fishtrap Creek, British Columbia [Eatonet al., 2010a,c], as well as other similar field sites. Eaton and Hassan [2013] usedthe model to investigate wood loading and jam characteristics across a range ofchannel scales by coupling the RSCS with the regime model proposed in Eaton[2006]. Individual RSCS model runs produce a realistic but highly variable set ofestimates for the modeled time period: numerous runs (i.e Monte Carlo modeling)are used to estimate the distribution of estimates.A.2 Reach Scale Channel SimulatorThe RSCS has seven separate modules that are run in sequence during each yearof the simulation. Each module adds, modifies, or removes data stored in a ma-160trix that contains an entry for each individual LW piece in the stream. The datarecorded in the matrix includes: LW piece length (LLW ); LW diameter (DLW ); LWorientation (ΘLW ); time since the piece last moved (tx); functional class (FLW ); jamidentification number (if the piece is associated with a jam); volume of sedimentstored by the individual piece (Vsed); and the total sediment storage capacity for thepiece (Vpot). Using this data, estimates are made for each year in the simulation ofthe reach-average total wood load (and the wood load for each functional class),the volume of stored sediment, the volume of wood incorporated into jams, and thesediment stored in association with jams. In a separate data storage matrix, addi-tional information is collected on individual jams once they reach their maximumsize, including the jam age, the number of LW pieces in the jam and the volume ofsediment stored by the jam. The model also characterizes and records the in-streamhabitat associated with each jam, including the surface area of scour pools, the sizeand extent of textural modification within sediment deposits, and the probability ofside-channel formation.The seven modules in the RSCS are:• Module 1: Riparian Forest Inputs• Module 2: Small Wood Advection• Module 3: Key Piece Identification• Module 4: LW Movement and Jam Growth• Module 5: Bed Material Sediment Storage• Module 6: In-stream Habitat• Module 7: LW DecayThe modules are run in the sequence that they are listed. The details of each moduleare presented below. The reader is referred to Eaton et al. [2012] and Eaton andHassan [2013] for a discussion and rationale for the modeling approach.Before running the RSCS model, both the model domain and the boundaryconditions need to be specified. To do this, the user specifies Q2, S, D50, D84, and161the typical rooting depth of the riparian forest (H), which is used to parameterizebank erodibility. The regime model uses these inputs to calculate the channel di-mensions (Wch and dch), as well as the steady state bed material supply to the reach,Qbm, assuming that the river is at the formative discharge for 1 day each year. Thelength of the reach (Lch) is assumed to be 15 times the channel width.The user also specifies the average height and diameter of the trees in the ri-parian forest (Htr and Dtr, respectively), as well as the undisturbed (steady state)riparian forest density (ρtr), and the length of time for which to run the simulation.The time required to reach steady state wood load from an initial condition with noin-stream wood is about 200 years, so most simulations run for several centuries.The user may also select a either a fire or harvesting disturbance scenario, in whichcase it is also necessary to specify the year in which the disturbance occurs andthe size of the riparian buffer, if applicable. Both disturbance scenarios influencewood loading and channel morphology by altering riparian forest inputs throughthe mechanisms detailed below.A.2.1 Riparian Forest InputsThe first module estimates the annual input of LW to the stream channel. Thenumber of tree mortalities in any given year (Nmortality) is calculated by first de-termining the total number of trees that could potentially contribute wood to thestream reach based on a tree mortality rate. The toppling rate (M) in each yearis randomly selected from a uniform distribution of values ranging from 0.002 to0.003 (or 0.2% to 0.3% of trees per year), with a mean toppling rate of 0.0025(or 0.25% of trees per year). Forest density remains constant as fallen trees areassumed to be immediately replaced by newly matured ones.In the 50 years after a stand-replacing fire, however, all trees are immediatelykilled and the toppling rate shifts to a mean annual value of 0.028 (2.8% of trees peryear), with the annual toppling rate randomly selected from a uniform distributionranging from 0.025 to 0.03. It is assumed that the forest requires 100 years after afire or harvesting to generate mature trees, so post-fire toppling results in a decreasein forest density over time (t), such that the forest density in a given year (ρtri) is:162ρtri = ρtr · e−M·t (A.1)The period of elevated post-fire toppling is followed by a 50 year period with notoppling – and thus a constant forest density – as the forest regenerates. Finally,100 years after a fire the chronic mortality rate of 0.002 resumes, and forest densityagain remains constant at the specified initial value of ρtr.In the case of forest harvesting, the forest density assumes a reduced valueduring the 100 year regeneration period – determined according to the ratio of thebuffer size (Btr) to the tree height (Htr) – while the toppling rate is unchanged:ρtri =BtrHtrρtr (A.2)Using the appropriate mortality rate and forest density for a given year, thenumber of trees that fall in each year (Nmortality) is calculated according to:Nmortality = M ·ρtri ·2Htr ·Lch (A.3)In order to determine wood inputs to the stream, a total of Nmortality trees arethen assigned positions relative to the edge of the stream (Xtr). The position Xtr fora given tree is chosen randomly from a uniform distribution from 0 to Htr. In thecase of forest harvesting, the position is instead selected from a random uniformdistribution from 0 to Btr. Each tree is assumed to fall to the ground immediately,and is assigned a fall direction (Θtr) that is randomly distributed from 0 to 360◦.Once the tree position and fall direction are known, the model determines howmuch (if any) of the tree will intersect the stream channel, and calculates the lengthof the LW piece that enters the stream (LLW ) as follows:LLW =Htr · sinΘ−XtrsinΘ(A.4)If the tree reaches the other side of the channel (i.e. LLW · sinΘtr >Wch), thenthe LW piece is shortened (LLW →Wch/sinΘtr). LW that spans the channel in thisway is assigned to the “Spanning LW” functional class, for which it is assumedthat only 5% of the piece interacts with the stream, modifying streamflow andaffecting sediment storage in the channel, so that FLW = 0.05. All other LW pieces163are assumed to be suspended on the stream bank at one end, and are assigned to the“Hanging LW” functional class. For hanging pieces, 50% of the piece is assumedto affect sediment storage in the stream (FLW = 0.5).Since many LW pieces break when they fall into a stream, the RSCS evalu-ates the probability that an LW piece from a single tree will break into two pieces(Pb−tr). The probability is estimated using a scaled error function, such that piecesthat are only 5 m long are very unlikely to break (Pb−tr = 0.039), 10 m long pieceshave a reasonable chance of breaking (Pb−tr = 0.36), and 15 m long pieces are verylikely to break (Pb−tr = 0.86). The equation for estimating the probability is:Pb−tr = 1+erf(0.2LLW −2.25)2(A.5)If a random number drawn from a uniform distribution (0 to 1) falls belowPb−tr, then the LW piece is broken into two pieces at a point randomly selectedsomewhere between 25% and 75% of the initial LW length. One piece is assignedto the “Hanging” functional class, the other is assigned to the “In-channel LW”class, for which it is assumed that 95% of the LW piece interacts with the streamprocesses (FLW = 0.95); both are assigned orientations that are identical to the treefall direction. At this stage, the residence time (tx) for each piece is set to zero.A.2.2 Small Wood AdvectionOnce wood has been added to the channel, the RSCS examines the LW piece di-mensions to ensure that the piece is large enough to be retained in the channel. AllLW pieces with lengths less than 20% of the channel width are removed from thedata matrix, since such pieces are much more likely to be transported through thereach without being re-deposited than larger pieces. While pieces larger than thiscan and do move, any pieces leaving the reach are assumed to be compensated byinputs of similar wood from upstream. Since piece mobility is strongly dependenton the length of the piece relative to the width of the channel, it is assumed that thesmall wood entering from upstream is not trapped within the reach. Similarly, oncethe LW diameter decreases below 0.1 m, the LW piece is removed from the matrix.See module 7 for the details on how LW diameter is modified by the RSCS.164A.2.3 Key Piece IdentificationThe next step in the simulation is to identify any LW pieces that could act as keypieces triggering the formation of an LW jam. All pieces that span more thansome critical proportion of the channel are identified as potential key pieces. Thedefault threshold is 75%, so that key pieces have the property that LLW · sinΘLW >0.75 ·Wch. Any new LW pieces (tx = 0) that are identified as key members areassigned a unique identification number that is used to associate other, smaller LWpieces with the key piece and thus form LW jams.A.2.4 LW Movement and Jam GrowthAt the next stage, LW pieces that are in the channel but not part of a jam are movedrandomly, according to a probability of movement that depends on the dimensionsof the piece relative to the channel dimensions. The first step is to determine ifthe diameter of the piece, DLW , is likely to limit the piece mobility. Generally,entrainment is thought to be possible so long as the water depth is at least half theLW diameter. The RSCS randomly chooses a local water depth (dlocal) to associatewith each LW piece from a normal distribution with a mean equal to dch and astandard deviation equal to dch/3. If the ratio dlocal/DLW > 0.5, then entrainmentis deemed to be possible, and the RSCS proceeds to the next step.Even when dlocal/DLW > 0.5, entrainment is most strongly controlled by therelative length (Lch/Wch) and orientation of the LW piece. The probability ofmovement (Pmove) is calculated by first estimating the probability of movementfor perpendicular pieces (PLmove) as a function of LLW/Wch, then multiplying it bya second term that represents the effect of orientation on mobility (PΘmove). Theseprobabilities are estimated using scaled conjugate error functions that represent thequalitative behaviour observed by Davidson [2011] during a set of experiments onwood mobility and sediment storage. The relevant equations are:PLmove =12erfc(3LLW/Wch−0.5) (A.6)PΘmove =12erfc( |ΘLW |−9045)(A.7)165Pmove = PLmove ·PΘmove (A.8)If the piece moves (i.e. a random number falls below the estimate of Pmove),then the RSCS next considers whether or not it is likely to interact with one of thekey pieces or jams in the reach. The model again uses a random number and anestimate of the probability that the piece will be trapped (Ptrap) to decide whetherthe piece is trapped or not. The probability depends on the predicted distancethat the LW will travel (Ltravel), the length of the reach (Lch), and the number ofpotential jam locations (NJ) in the reach. The equation is:Ptrap = 1−(1− LtravelLch)NJ(A.9)The term NJ is related to the number of key pieces in the reach, but also to theproportion of the piece in the channel. LW that is in the channel is more likely todevelop into a jam than a piece suspended above the channel. Therefore, NJ is thesum of number of key pieces, weighted by their functional class. If Ltravel > Lch,then Ptrap = 1 automatically (i.e. the piece will inevitably be trapped).The travel distance (scaled by the channel width) is estimated using data onwood movement from Mack Creek as described by [Eaton et al., 2012]. However,since the initial version of the RSCS was used to consider streams with dch/DLWto similar to Mack Creek, we have added a scaling term (φ ) that increases thenormalized travel distance (Ltravel/Wch) for relative water depths larger than that ofMack Creek and decreases it for smaller ratios.LtravelWch= 10.33 · e−3.824(LLW /Wch) ·φ (A.10)Without information to constrain the behaviour of the scaling term φ , we haveassumed that it is a linear function of dlocal/DLW , such that φ = α ·dlocal/DLW . Forα ≈ 1 the relation conforms to the Mack Creek data, since dlocal ≈ DLW in thatsystem, as it is in Fishtrap Creek.If an LW piece moves, it releases any sediment that it may have stored, andtakes up a new orientation within the stream. For pieces that do not interact witha jam, the piece will take up an orientation that is nearly parallel to the streamflowdirection 2/3 of the time (between 150◦ and 180◦, where 180◦ corresponds to the166direction of stream flow), and will be skewed across the stream 1/3 of the time(between 120◦ and 150◦). The pieces that do interact with a jam are assignedan identification number given to one of the existing key pieces, and assigned anorientation that is close to perpendicular to the flow (between 75◦ and 105◦); theyare also prevented from moving in the future until the key piece that trapped thembreaks.A.2.5 Bed Material Sediment StorageThis module links the wood load to channel morphology by storing a fraction of thebed material sediment supplied to the reach in association with each LW piece inthe system. The rules are based on experimental observations made by Davidsonand Eaton [2013] and have been validated against field observations from Fish-trap Creek by Eaton et al. [2012]. The initial version of the RSCS assumed thatbed material sediment trapping efficiency dropped off exponentially with time asthe storage capacity behind each LW piece was progressively filled with sediment.That approach is only valid for systems with bed material sediment supply ratesthat are similar to Fishtrap Creek and to the Froude-scaled experiments conductedby Davidson and Eaton [2013]. In order to make the RSCS more general, we havemodified the trapping efficiency function so that it depends on the volume of sed-iment stored behind each piece (Vsed) relative to the maximum available sedimentstorage volume for the piece (Vpot). The equations relating the trapping efficiencyto Vsed/Vpot were calibrated by choosing a set of coefficients that produced sedi-ment storage volumes for a simulation of Fishtrap Creek that were similar to thosereported by Eaton et al. [2012]. This removes time from the equation, and allowsthe model to describe systems with much higher and much lower bed material sup-ply rates than Fishtrap Creek.The first step is to calculate the maximum potential trapping efficiency of thewood in the reach, which was shown by Davidson and Eaton [2013] to be func-tionally related to the reach-average wood load. In this version of the RSCS, weweight the contribution of each LW piece to the wood load by the functional class;suspended pieces contribute relatively little to the functional wood load, while in-channel pieces dominate the functional wood load. The bed material sediment trap-167ping efficiency is assumed to be relatively linear for low wood loads, but reaches amaximum value for high wood loads. It is estimated using the same scaling func-tion published in Eaton et al. [2012], which conforms to experimental data reportedby Davidson and Eaton [2013].ζbm = erf(FLW ·LLW ·D2LW0.056 ·Wch ·Lch)(A.11)The term ζbm is the reach-average trapping efficiency that would be observedif all of the wood were placed in the channel at the same time, which correspondsto the methodology used by Davidson and Eaton [2013].This potential bed material trapping efficiency is distributed between all of theLW pieces in the reach, based on the ratio B/∑B, where B is the area of each pieceprojected across the channel (weighted by the functional class).B = FLW(DLW ·LLW |sinΘ|+D2LW |cosΘ|)(A.12)Then, the volume of sediment trapped by an individual LW piece is calculated,considering the volume of sediment that it currently stores (Vsed) relative to the totalpotential sediment storage volume (Vpot), which is calculated from the projectedarea, B, the piece diameter, DLW , and the reach-average channel gradient, S:Vpot =B ·DLW2S(A.13)The annual volume of sediment trapped by each LW piece (∆Vsed) is deter-mined by applying the scaled trapping efficiency to the bed material sediment sup-ply rate, Qbm, assuming that the trapping efficiency drops off exponentially as theavailable sediment storage space is filled with sediment.∆Vsed = Qbm ·ζbm Bn∑i=1Bieβ ·Vsed/V pot (A.14)The term β is a rate constant; when β = 50, the equation above produces sim-ilar sediment trapping behaviour to the time-based equations published in Eaton168et al. [2012]. By making the dependence of the actual trapping efficiency on thevolume of stored sediment explicit, the model becomes more generally applicable.A.2.6 In-stream HabitatThis module uses the jams identified in module 3, as well as the sediment stor-age calculated of individual pieces in module 5, to assess the effects of channel-spanning jams on several key reach-scale habitat metrics. The first step involvescalculating the vertical height of channel-spanning jams (d jam), based on the vol-ume of wood in each jam (Vjam), by assuming a simplified jam geometry. Therelevant equations are:Vjam = Σ(VLW ·FLW ) (A.15)d jam =√VjamWch(A.16)The size of scour pools – which form downstream of each channel-spanningjam – are then determined based on a set of probabilistic rules. Pool width (WP)is randomly selected from a uniform distribution ranging from 0.25 to 0.75 timesthe channel width, while the pool length (LP) is determined based on a uniformdistribution of 2 to 4 times the jam height (d jam).Next, the volume of sediment stored upstream of each jam (VS) is calculatedbased on the total amount of sediment stored by each individual piece (Vsed) withinthe jam. It is assumed that all sediment is stored in a rectangular area upstream ofthe jam that is defined by the channel width (Wch) and extends a maximum distanceof 2 Wch upstream. It is also assumed that the sediment deposits in a triangularwedge, such that the depth of sediment at the jam face (dS) is described by:dS =VSW 2ch(A.17)The final size of the deposit area is limited to the portion of the deposit zone inwhich the depth of the sediment exceeds the D84 of the bed, and may thereforevary from 0 to 2 W 2ch based on the amount of accumulated sediment.Textural modification within the deposit area is then determined by calculating169the effect of the stored sediment on the channel gradient. In the absence of wood,the channel is assumed to have a consistent riffle spacing of 5 Wch, with a constantgradient between riffles during bankfull flow conditions. The original slope of thebed (S) is reduced upstream of the jam by the depth of the sediment stored at thejam face, enabling a calculation of the reduced gradient within the sediment deposit(SS):SS = S− dS5Wch (A.18)The slope modification reduces the channel competence, resulting in a decreasedmedian grain size in the deposit area (Di):Di =D50 ·SSS(A.19)Finally, the model determines the probability of avulsion – which creates side-channel habitat – based on the ratio of the depth of sediment at the jam face (dS)to the bankfull flow depth (dch). The mean threshold is set at 80%. As with othermodel elements, random variation around the threshold value is incorporated sothat the actual threshold is uniformly distributed between 60% to 100% of the flowdepth. Before proceeding to the final module, the model records key habitat metricsin each year. These include the pool and deposit area associated with each jam, thesediment texture, and whether an avulsion will results. In some cases, the sum ofall deposit areas and pool areas within the reach is greater than the actual bed area.In these cases, the total storage area for the reach is calculated by subtracting thetotal pool area from the total bed area.A.2.7 LW DecayThe final module in the RSCS modifies the diameter of each LW piece, using anexponential decay model that modifies DLW as a function of the piece age (tLW ).DLW = Dtr · e−Kdecay·tLW (A.20)The default decay constant, Kdecay, is 0.01, which translates to a volumetric decayrate of 0.02.170Once DLW is determined, the shape (LLW/DLW ) is used to estimate the proba-bility that the piece will break using the following equation:Pbreak = Kbreak · LLW/DLW100 (A.21)The default value of the coefficient Kbreak is 0.10; the equation is based on theassumptions that (a) the shape of the piece determines how likely it is to break,and that (b) a piece for which LLW/DLW = 100 has a 10% chance of breakingin a given year. Without data to constrain the model, we have assumed that therelation is linear. It is worth noting that this breakage rule, combined with thebreakage rules for wood that falls into the channel, produce exponential LW piecedistributions that are similar to those observed in the field and those specified byother (deterministic) LW models such as Benda and Sias [2003].If a piece that is in the channel or hanging (rather than suspended) breaks,part of the piece is assumed to move downstream and adopt a new orientationsimilar to the orientations randomly imposed on moving pieces in module 4. Itis also assumed that a proportion of the sediment stored by the initial LW pieceis released, based on the length of the moving LW piece relative to the originaltotal piece length. The other part of the original LW piece retains the originalorientation. Both pieces are assigned to the in-channel functional class.When pieces that are suspended above the channel break for the first time, onlythe functional class is changed (to hanging instead of suspended). The second timeone of these channel-spanning pieces breaks, it generates two separate LW pieces,which move downstream releasing all sediment stored by the piece. Most of thesepieces also form the nucleus of a larger LW jam; any smaller LW pieces associatedwith the jam are also moved and release their stored sediment. All pieces areassigned a new orientation following the procedure described for module 4.Once this module is complete, the data in the storage matrix are interrogated tomake reach-average estimates of the various parameters for the given year of thesimulation. The RSCS then returns to module 1 and the sequence is repeated.171Appendix BFishtrap Creek Field StudyB.1 Study AreaFishtrap Creek is an intermediate-sized tributary to the North Thompson River,located in the British Columbia interior plateau near the town of Barriere (FigureB.1). The watershed is nival, with a mean annual peak flow of 7.5 m3/s measuredat the gauge occurring almost exclusively during the freshet in April through June[Eaton et al., 2010a] . The lithology of the watershed is primarily of volcanicorigin, but glacially derived surficial deposits cover all but the steepest parts of thewatershed [Phillips, 2007]. Surveys performed by the Department of Fisheries andOceans and the Ministry of Environment suggest that a number of fish species arepresent in the Fishtrap Creek watershed. The fish species include resident sculpin,rainbow trout, dolly varden, and brook trout, as well as anadramous Coho salmon.It is not currently clear where within the watershed the observations of fish and/orspawning habitat were made, and therefore remains uncertain whether anadramousCoho are able to migrate beyond the Water Survey of Canada stream gauge weir tothe upper portion of the drainage basin.In August 2003, 62% of the 158 km2 watershed was burned by a high inten-sity fire, resulting in nearly complete mortality throughout the affected area (Fig-ure B.1). A number of research projects have been undertaken in Fishtrap Creeksince 2003 to investigate the effects of the fire on stream hydrology [e.g. Leachand Moore, 2010, 2011], suspended sediment loading [e.g. Petticrew et al., 2006,172Owens et al., 2013], and channel morphology [e.g. Eaton et al., 2010a,c]. The ma-jority of this research has focused on a small reach directly upstream of the WaterSurvey of Canada gauge; a 130 m long study reach was established in 2004, andwas subsequently expanded in 2006 to include a total stream length of 440 m. Asegment of this study reach has also been used as a prototype for a number of ex-periments conducted using a Froude-scaled physical model [Davidson and Eaton,2013].Figure B.1: Fishtrap Creek watershed (dark) and the area burned by the 2003McClure fire. The 440 m reach used in previous morphologic studies islocated within the black circle. Map created by Eaton et al. [2010b].As a result, the morphologic characteristics of this study reach have been welldescribed in previous research [e.g. Andrews, 2010, Eaton et al., 2010a,c]. Com-pared to the watershed as a whole, the study reach has a low gradient (1.5-2.0%)173with a relatively fine bed (D50 = 50-55 mm and D95 = 128 mm), and a low de-gree of valley confinement. The average bankfull width of the channel in the studyreach is approximately 10-12 m, suggesting a high potential for wood retention.According to the most recent wood inventory conducted in 2008, the study reachhad a jam frequency of 1.25 jams per 100 m (equivalent to an average jam spacingof 6.7 channel widths), and an average wood load of 0.0206 m3/m2. Comparisonwith earlier inventories dating back to 2004 shows that the wood load increased by38% (from 0.0128 m3/m2) in the 5-year period following the fire [Andrews, 2010].During this period, the study reach largely shifted from a plane-bed to a riffle-poolmorphology due to the increased wood recruitment (Montgomery and Buffington,1997; Eaton et al., 2010).The current work increases the scale of the study area to include the entire 7 kmsegment of the stream from Skull Creek to the confluence with the North Thomp-son river. By expanding the study area, we aim to investigate the variations in woodloading and habitat availability that occur between different reach types. The 440m study reach, which has been extensively studied in the past, is not representativeof the majority of the lower watershed; the reach is located atop the outwash plainof a much larger glacial meltwater channel, which was likely deposited proximalto a large glacier which previously occupied the North Thompson valley. Down-stream of the reach, the stream is incising into these glacial deposits, resulting inclose hillslope coupling (and significant inputs from mass wasting) and channelconfinement throughout much of the watershed (Figure B.2). Thus, the remainderof the watershed is generally steeper, coarser, and more confined than the studyreach.B.2 MethodsB.2.1 Morphologic SurveyA morphologic survey was completed in October, 2013 along a 7 km segment ofFishtrap Creek. Progressing in the downstream direction, a series of reaches weredefined based on the classification scheme presented in Montgomery and Buff-ington [1997]. Each homogenous reach was classified as either boulder-cascade,174Figure B.2: Northeast oriented photograph showing a landslide scar in thelarge glaciofluvial outwash terrace located in the lower Fishtrap Creekwatershed.step-pool, plane bed, or pool-riffle (Figure B.3). Where wood was present andinfluencing channel morphology, a fifth category of forced pool-riffle was used.The boundaries of each morphologic unit were recorded using a handheld GPS,as well as the upstream and downstream locations of all stream segments with amulti-thread channel pattern. The distance to the upstream end of the reach wasalso recorded using a hip chain.175Figure B.3: An example of each morphologic classification is shown in photographs from Fishtrap Creek taken in Julyand October, 2013. The classifications include a) pool-riffle, b) plane bed, c) step-pool, and d) cascade.176Within each reach we recorded channel gradient and width at a minimum ofthree locations using a laser range finder. A characteristic grain size was also es-timated based on the methodology of Buffington and Montgomery [1999]. Usingthis method, each reach was assigned a dominant grain size as well as a maxi-mum of two sub-dominant facies, listed in order of increasing availability (FigureB.4). Where possible, the dominant facies was also assigned a size classification.The approximate median grain size of each grain size category was then calibratedbased on a series of Wolman counts performed in July, 2013. The diameter of thelargest five grains was also measured for each reach, as well as the relative degreeof valley confinement.Figure B.4: The textural classification scheme used to delineate the majortextural classes is based on a series of ternary diagrams (adapted fromBuffington and Montgomery [1999]).177B.2.2 Jam SurveyA survey of wood jams was also completed throughout the same 7 km segment.Each jam was photographed and classified by size according to the number ofpieces, as shown in Table B.1. Examples of each size class are shown in FigureB.5. The location of each jam was recorded using a handheld GPS.Table B.1: Size categories for jams based on visual estimates of piece num-ber.Jam Size Number of PiecesSmall 3-10Medium 11-20Large 21-40Very large > 40178Figure B.5: An example of each jam size class is shown in photographs from Fishtrap Creek taken in July and October,2013. The size classes include a) small, b) medium, c) large, and d) very large jams, as defined in Table B.1.179B.3 ResultsBased on the morphologic survey the 7 km study segment was divided into 70reaches. Characteristics of the 135 jams identified in the reach are presented inTable D.7. Based on the field surveys, jam frequencies in the 70 surveyed reachesin Fishtrap Creek varied from 0 to 11.4 jams/100 m, with a median jam frequencyof 2.7 jams/100 m (or approximately 0.25 jams per bankfull channel width). Afield survey in 2008 revealed a jam frequency of approximately 1.25 jams/100m [Andrews, 2010]. The average jam frequency in this same reach in 2013 was4.8 jams/100 m. Jam frequency did not vary systematically with confinement, butlarger jams – and therefore higher piece frequencies – were recorded in un-confinedreaches (Figure B.6).The reach characteristics recorded during the field survey are presented in Ta-ble D.6 in Appendix D. The only pool-riffle reaches identified in the study segmentappeared to be forced by large wood and were classified as forced-pool-riffle. Asshown by [Montgomery and Buffington, 1997], plane-bed, step-pool, and cascadereaches were associated with progressively higher gradients (Figure B.7a). Forcedpool-riffle reaches were associated with a wide range of gradients (up to 6%) sug-gesting that wood has the capacity to change reach-scale morphology across abroad spectrum of mountain streams. Forced pool reaches were generally asso-ciated with reaches containing large jams, and the median piece number in thesereaches is over 40 pieces/100 m (Figure B.7b).180lConfined Semi−confined Un−confined0246810No. jams/100m)llConfined Semi−confined Un−confined02060100No. pieces/100mFigure B.6: Boxplots show the a) jam frequency and b) piece frequency as-sociated with varying valley confinement.181llC F−PR PB SP12345678Gradient (%)lC F−PR PB SP02060100No. pieces/100mFigure B.7: Boxplots show the a) gradient and b) piece frequency associatedwith a range of channel types. C represents cascade reaches, fPR isforced-pool-riffle, PB is plane-bed, and SP is step-pool.182Appendix CBank Erosion Data ComparisonC.1 Historical Air Photo AnalysisThe STOCHASIM model introduced in Chapter 3 is used here to predict rates oflateral migration in streams with diverse bed textures and gradients. As bank ero-sion poses a threat to infrastructure, the prediction of stream migration rates hasnumerous applications in industry. We test the model by comparing bank erosionrates generated by STOCHASIM against bank erosion data provided by BGC En-gineering Inc. (BGC) for 40 stream reaches in British Columbia, Alberta, andSaskatchewan. The data was originally collected to assess erosion rates at pipelinecrossings located within each reach.BGC measured the magnitude of bank erosion for each reach using a series ofhistorical air photos (Figure C.1). BGC selected pairs of air photos that bracketedlarge flood events on streams containing Water Survey of Canada (WSC) gauges.Each pair of air photos was then georeferenced and used to estimate the reach-averaged bank erosion, as well as the maximum bank erosion, between the succes-sive photos. This erosion was attributed to the largest flood during the air photointerval, and used to build a relation between flood magnitude and erosion distancefor each site.We have re-analyzed the data provided by BGC to calculate an average erosionrate over time for each reach. In 38 of 40 reaches, the air photo pairs covered theentire range from the year of the first to last air photo in the series (e.g. six photos183Figure C.1: Bank outlines mapped from a number of historical air photos aresuperimposed on the 2014 google earth imagery. The bank is advancingtoward point A, while the stream is also avulsing on to the floodplainat point B. The red line represents a pipeline crossing. The area ofbank change measured between each pair of historical photos was usedto calculate an average erosion width throughout the reach [Robergeet al., 2016].covering the complete 59-year period from 1951 to 2010 in the Wapiti River), whilethe remaining two sites had gaps of 2 and 9 years in the air photo sequence. Theaverage erosion rate for each site was calculated by dividing the total measuredreach-average erosion for all air photo intervals by the number of years covered byall air photo pairs.184C.2 STOCHASIM ModelingIn order to validate our model, we ran STOCHASIM simulations for each of the 40sites. The recorded flow data – rather than a synthetically generated flood sequence– were used as the hydrologic input. Peak annual flows (i.e. the largest daily floweach year) were obtained from the nearest WSC gauge at each site for the entiregauge history and prorated to yield a flood series for each reach according to:Qsite = QWSC ·(AdsiteAdWSC)0.75(C.1)Data inputs which were not included in the original data provided by BGC(e.g. grain size and rooting depth) were estimated from photographs, as well asdetailed hydrotechnical reports completed by BGC, which were available for eachsite. Rooting depth was estimated based on the type of vegetation present on thechannel banks, with a maximum value of 1.07 m for trees and a minimum valueof 0.53 assigned to sites with grass banks. Grain size values from reports werechecked against Wolman counts based on site photograph where possible usingthe Linecut program in MATLAB. Bankfull channel widths were estimated fromgoogle earth imagery along each reach and used as the starting width for the simu-lations.C.3 ResultsSTOCHASIM produced bank erosion rates ranging from 0 to 39.8 m/yr, with amedian rate of 2.3 m/yr. The measured rates for the 40 reaches, meanwhile, rangedfrom 0.05 to 3.2 m/yr, with a median rate of 0.37 m/yr. When normalized bybankfull width, this represents a median rate of 0.9% of the bankfull width eachyear. A comparison of modeled and predicted erosion rates is shown in Figure C.2.STOCHASIM is best suited to gravel-bed reaches, as the entrainment of sandparticles is affected by bedform characteristics rather than grain size alone, andincreased particle hiding increases the critical Shield’s number. When only gravel-bed reach were considered, the predictions ranged from 0 to 7.1 m/yr with a medianvalue of 2.27 m/yr (Figure C.3a). These values were more similar to the averagevalues measured from air photos, but still significantly over-predicted erosion rates185llllllllllll ll lllllllllllllllllll llll0.05 0.20 1.00 5.00 erosion rate (m/yr)Measured erosion rate (m/yr)lllllAnastamosedMeandering − High SinuosityMeandering − Low SinuosityMeandering − Moderate SinuosityWanderingFigure C.2: Modeled and predicted bank erosion rates are shown for all 40reaches considered in the analysis. All predicted and erosion rates wereincreased 0.05 m/yr to enable plotting of zero values on the logarithmicaxes. The dashed grey line indicates the 1:1 most cases; the median erosion rate measured in gravel bed streams was 0.38m/yr, or 0.7% of the bankfull width each year.Finally, we used google earth imagery to identify and remove all deeply incisedreaches from the dataset. The original dataset contained 13 such reaches, mostlyin locations such as the Peace River and South Saskatchewan River, which haveincised into easily erodible glaciolacustrine deposits. The measured erosion ratesfor all of the incised reaches ranged from 0.05 to 0.89 m/yr, with a median rateof only 0.32 m/yr (0.3% of the bankfull width each year). Figure C.3b shows a186comparison of the modeled and predicted rates for non-incised gravel-bed reaches.While the model over-predicts erosion rates in most streams, it appears to pro-vide a reasonable upper limit to erosion. The model also performs relatively wellin a number of cases, including several of the wandering reaches considered. Thesix best model predictions are for the Sakwatamau River, Clear River, CoquihallaRiver, Elbow River, James River, and Willow Creek. These streams have relativelyhigh channel gradients (0.003 to 0.013 m/m), and coarse gravel to cobble beds.These results suggest that the model provides a useful tool for estimating long-term erosion rates in the rivers which are most likely to adjust to flood dischargethrough changes in channel width (e.g. highly dynamic wandering streams), butperforms poorly in streams with fine bed material or cohesive banks. These streamsare likely to adjust – at least in part – through bed scour, limiting the extent of bankerosion. The presence of bank protection in pipeline right-of-ways at a numberof the sites also limits the measured average erosion in a number of the reachesrelative to the model predictions.187llllllllll llllllllllllllll l ll0.05 0.20 1.00 5.00 erosion rate (m/yr)Measured erosion rate (m/yr) lllllAnastamosedMeandering − High SinuosityMeandering − Low SinuosityMeandering − Moderate SinuosityWanderingallllllllllllllll l l0.05 0.20 1.00 5.00 erosion rate (m/yr)Measured erosion rate (m/yr) lllllAnastamosedMeandering − High SinuosityMeandering − Low SinuosityMeandering − Moderate SinuosityWanderingbFigure C.3: a) Modeled and predicted bank erosion rates are shown for allgravel-bed reaches considered in the analysis. All predicted and erosionrates were increased 0.05 m/yr to enable plotting of zero values on thelogarithmic axes. The dashed grey line indicates the 1:1 line. b) Thesame data is plotted with 13 incised reaches removed.188Appendix DAdditional TablesD.1 STOCHASIM OutputTable D.1: Erosion and channel mobility are summarized for the five flowvariability scenarios considered.FMI Stability interval Erosion rate Widthyrs m/yr m0.2 37.5 0.15 11.60.4 13.0 0.47 14.60.6 9.1 0.83 17.30.8 7.7 1.3 20.31.0 7.1 1.9 24.3D.2 Flume DataD.3 Fishtrap Creek Field Data189Table D.2: Erosion and channel mobility are summarized for the five rootingdepth values considered.H Stability interval Erosion rate Widthm yrs m/yr m0 33.3 0.44 18.10.2 20.0 0.49 16.30.4 13.0 0.47 14.60.6 9.7 0.44 13.20.8 7.3 0.42 11.8Table D.3: Erosion and channel mobility are summarized for the five Shieldsnumber values considered.θc Stability interval Erosion rate Widthyrs m/yr m0.02 4.9 0.83 20.60.03 5.0 0.64 17.00.04 13.0 0.47 14.60.05 42.9 0.23 11.00.06 300 0.06 9.0Table D.4: Erosion and channel mobility are summarized for the five mor-phologic index values considered.b Stability interval Erosion rate Widthyrs m/yr m0 15.8 0.36 15.10.2 13.0 0.47 14.60.4 10.3 0.61 14.00.6 8.3 0.80 13.40.8 6.5 1.1 12.6190Table D.5: Erosion and channel mobility are summarized for the five revege-tation coefficients considered.Cv Stability interval Erosion rate Width% yrs m/yr m5 18.8 0.30 16.010 13.0 0.47 14.615 10.3 0.60 13.720 9.1 0.71 13.125 8.1 0.81 12.6191Table D.6: Morphologic characteristics for the 69 surveyed reaches in Fishtrap Creek.Reach ID Latitude Longitude Dist. Length Morph. Conf. Width Gradient GSD D95 No. jamsR01 51.1368 -120.2175 87 87 SP un 8.5 3.3 bgC 493 3R02 51.1362 -120.2176 109 22 fPR un 8.4 3 bcG-m 181 1R03 51.1360 -120.2176 144 35 PB semi 7 2.7 bgC-f 311 0R04 51.1358 -120.2176 179 35 SP semi 8 4.0 bgC-f/bgC-m 426 0R05 51.1355 -120.2176 201 22 fPR semi 11.1 3.4 bgC-f 284 2R06 51.1351 -120.2178 238 37 SP semi 7.1 5 bgC-m 306 2R07 51.1351 -120.2175 278 40 PB un 10.1 2.7 bgC-f 387 2R08 51.1345 -120.2172 315 37 SP un 8 3.9 bgC-m 270 0R09 51.1343 -120.2170 383 68 SP un 8.6 2.4 bcG-m/bcG-c 254 3R10 51.1338 -120.2168 454 71 PB un 8 3.4 bgC-f 311 1R11 51.1332 -120.2168 474 20 SP un 7.5 3.7 bgC-m 241 0R12 51.1330 -120.2166 500 27 fPR un 6.7 3.2 bcG-m 265 1R13 51.1328 -120.2165 602 102 PB un 5.9 2.8 bgC-m 396 0R14 51.1319 -120.2159 649 47 fPR un 6.6 3.4 bgC-m 316 1R15 51.1317 -120.2155 690 41 PB un 7.7 3.1 bgC-f/bgC-m 417 0R16 51.1313 -120.2153 727 37 PB un 12.1 2.2 bgC-m 279 0R17 51.1310 -120.2153 760 33 PB un 14.4 2.8 bcG-m 198 1R18 51.1306 -120.2154 834 74 fPR un 13.5 2.6 160 2192Reach ID Latitude Longitude Dist. Length Morph. Conf. Width Gradient GSD D95 No. jamsR19 51.1302 -120.2153 1100 266 fPR un 9 3.1 scG-m 197 8R20 51.1282 -120.2142 1200 100 PB un 7.6 2.8 bgC-m 249 2R21 51.1272 -120.2146 1272 72 fPR un 8.6 2.5 scG-m/bcG-m 208 3R22 51.1267 -120.2146 1315 43 PB un 9.3 1.6 bgC-f 228 1R23 51.1263 -120.2144 1412 97 fPR un 12.9 4.2 bcG-c/bgC-m 209 11R24 51.1257 -120.2133 1575 164 fPR un 6 1.9 scG-m/scG-c/bcG-m/sgC-m 192 6R26 51.1246 -120.2120 1709 95 PB un 6.1 1.7 bcG-c/bgC-f 251 0R27 51.1240 -120.2112 1888 179 fPR un 8.5 1.8 scG-m/bcG-m/bgC-m 201 7R28 51.1229 -120.2104 1932 44 fPR un 7 1.6 bcG-m 223 2R29 51.1225 -120.2099 1962 30 PB un 4.3 2.9 bC-c/gbC-c 317 0R30 51.1221 -120.2093 2048 86 PB semi 6.1 1.3 bcG-c 307 0R31 51.1218 -120.2082 2062 15 fPR semi 7.3 2.2 bcG-c 208 1R32 51.1218 -120.2082 2088 26 C semi 6.3 5.8 gbC-c 486 0R33 51.1216 -120.2085 2114 26 fPR semi 5.0 3.4 bcG-c 206 1R34 51.1214 -120.2086 2140 26 C conf 4.5 3.1 bgC-f 286 1R35 51.1212 -120.2088 2180 40 fPR conf 4 4.0 scG-c/bcG-c 272 2R36 51.1208 -120.2091 2209 29 SP conf 4.0 2.9 bgC-c 352 0R37 51.1208 -120.2094 2247 38 fPR conf 3.7 1.2 scG-c/bcG-m 240 1R38 51.1205 -120.2097 2342 95 SP conf 4.7 2.8 bcG-c/bgC-m/gbC-c 280 1R39 51.1200 -120.2089 2452 111 fPR conf 4.9 3.7 bcG-m 147 4193Reach ID Latitude Longitude Dist. Length Morph. Conf. Width Gradient GSD D95 No. jamsR40 51.1193 -120.2094 2670 218 fPR semi 6.5 1.9 bcG-m 176 8R41 51.1178 -120.2105 2742 72 fPR un 10.5 2.6 bcG-m 145 3R42 51.1175 -120.2112 2870 128 fPR semi 8.6 2.2 bcG-m 155 3R43 51.1165 -120.2116 2946 76 fPR semi 6 2.4 bgC-m 167 2R44 51.1159 -120.2119 3047 101 fPR semi 6.6 2.2 bcG-m 139 2R45 51.1152 -120.2116 3116 69 fPR semi 10.1 2.2 bcG-m 103 2R46 51.1148 -120.2121 3280 164 C conf 7.8 4.9 bgC-c 84 5R47 51.1139 -120.2133 3390 110 SP conf 7.7 3.8 bgC-c/bC-c 129 1R48 51.1130 -120.2135 3430 40 SP semi 9.1 5.8 bgC-m 226 1R49 51.1128 -120.2139 3492 62 C semi 5.5 4 gbC-c 240 0R50 51.1122 -120.2139 3542 50 SP semi 5.4 3.2 gbC-c 197 0R51 51.1116 -120.2138 3593 51 PB un 5.5 2.2 bcG-c 209 2R52 51.1113 -120.2141 3631 38 fPR un 5.7 5.0 bcG-c/bgC-f 198 2R53 51.1109 -120.2139 3700 69 SP semi 5.8 4.3 bcG-c/gbC-c 249 0R54 51.1103 -120.2132 3810 110 fPR semi 7 4.3 bcG-c 205 5R55 51.1094 -120.2133 3844 34 C semi 9 6.7 bC-c 274 1R56 51.1092 -120.2133 3922 78 fPR semi 11.4 1.9 cG-f/bcG-m 188 2R57 51.1086 -120.2133 4040 118 C conf 6.6 7.2 bC-c 277 3R58 51.1075 -120.2140 4242 202 C semi 6.1 5.2 gbC-c 229 4R59 51.1060 -120.2133 4303 61 fPR un 9.8 3.8 scG-m/bgC-f 296 2194Reach ID Latitude Longitude Dist. Length Morph. Conf. Width Gradient GSD D95 No. jamsR60 51.1056 -120.2133 4392 89 C un 6.4 6.2 gbC-c 1R61 51.1049 -120.2140 4452 60 C semi 12.8 7.8 gbC-c 5R62 51.1043 -120.2139 4517 65 SP semi 4.3 5.5 gbC-c/bC-c 0R63 51.1038 -120.2141 4557 40 C un 7.5 7 bcG-c/gbC-c 0R64 51.1034 -120.2139 4592 35 fPR un 5 4.5 gbC-c 2R65 51.1032 -120.2139 4748 156 C un 5.7 6.9 gbC-c/gcB/B 4R66 51.1019 -120.2137 4763 15 fPR un 4.8 7.1 bC-c 1R67 51.1019 -120.2137 4822 59 C un 7.4 7.3 gbC-c 0R68 51.1013 -120.2133 4882 60 C un 5.7 4.3 gbC-c 0R69 51.1009 -120.2133 4925 43 fPR un 9.6 5.9 gbC-c 2R70 51.1004 -120.2133 5000 75 C un 10.1 5.5 gbC-c 2195Table D.7: A summary of jam size and location for 135 jams surveyed alonga 5 km segment of Fishtrap Creek.Jam ID Latitude Longitude Reach ID SizeJ001 51.1368 -120.2175 R1 smallJ002 51.1366 -120.2175 R1 smallJ003 51.1366 -120.2174 R1 smallJ004 51.1362 -120.2176 R2 mediumJ005 51.1355 -120.2176 R5 smallJ006 51.1353 -120.2176 R5 smallJ007 51.1351 -120.2178 R6 largeJ008 51.1349 -120.2176 R6 smallJ009 51.1349 -120.2174 R7 smallJ010 51.1347 -120.2172 R7 smallJ011 51.1345 -120.2170 R9 smallJ012 51.1342 -120.2168 R9 smallJ013 51.1340 -120.2168 R9 smallJ014 51.1336 -120.2170 R10 smallJ015 51.1330 -120.2167 R12 smallJ016 51.1319 -120.2159 R14 largeJ017 51.1310 -120.2153 R17 smallJ018 51.1308 -120.2154 R18 largeJ019 51.1304 -120.2152 R18 hugeJ020 51.1300 -120.2153 R19 smallJ021 51.1298 -120.2154 R19 smallJ022 51.1296 -120.2153 R19 mediumJ023 51.1293 -120.2151 R19 mediumJ024 51.1291 -120.2150 R19 smallJ025 51.1289 -120.2146 R19 smallJ026 51.1287 -120.2146 R19 mediumJ027 51.1283 -120.2142 R19 largeJ028 51.1276 -120.2146 R20 small196Jam ID Latitude Longitude Reach ID SizeJ029 51.1274 -120.2146 R20 smallJ030 51.1270 -120.2146 R21 mediumJ031 51.1270 -120.2146 R21 smallJ032 51.1268 -120.2146 R21 smallJ033 51.1263 -120.2144 R22 smallJ034 51.1263 -120.2144 R23 smallJ035 51.1263 -120.2145 R23 smallJ036 51.1261 -120.2144 R23 smallJ037 51.1261 -120.2142 R23 smallJ038 51.1261 -120.2142 R23 mediumJ039 51.1261 -120.2138 R23 smallJ040 51.1261 -120.2137 R23 smallJ041 51.1259 -120.2136 R23 smallJ042 51.1259 -120.2139 R23 largeJ043 51.1259 -120.2135 R23 smallJ044 51.1257 -120.2136 R23 mediumJ045 51.1255 -120.2133 R24 smallJ046 51.1255 -120.2132 R24 mediumJ047 51.1253 -120.2135 R24 smallJ048 51.1252 -120.2133 R24 mediumJ049 51.1251 -120.2131 R24 smallJ050 51.1251 -120.2129 R24 smallJ051 51.1238 -120.2111 R27 mediumJ052 51.1238 -120.2110 R27 smallJ053 51.1236 -120.2107 R27 largeJ054 51.1236 -120.2106 R27 smallJ055 51.1235 -120.2102 R27 mediumJ056 51.1233 -120.2102 R27 smallJ057 51.1231 -120.2102 R27 smallJ058 51.1225 -120.2101 R28 smallJ059 51.1225 -120.21 R28 large197Jam ID Latitude Longitude Reach ID SizeJ060 51.1218 -120.2081 R31 smallJ061 51.1216 -120.2086 R33 mediumJ062 51.1214 -120.2086 R34 smallJ063 51.1212 -120.2088 R35 smallJ064 51.1210 -120.2089 R35 smallJ065 51.1208 -120.2094 R37 smallJ066 51.1201 -120.2095 R38 smallJ067 51.1200 -120.2089 R39 smallJ068 51.1197 -120.2086 R39 smallJ069 51.1195 -120.2089 R39 mediumJ070 51.1193 -120.2092 R39 mediumJ071 51.1191 -120.2095 R40 smallJ072 51.1190 -120.2097 R40 mediumJ073 51.1188 -120.2099 R40 mediumJ074 51.1186 -120.2105 R40 smallJ075 51.1186 -120.2106 R40 smallJ076 51.1186 -120.2107 R40 smallJ077 51.1184 -120.2105 R40 mediumJ078 51.1182 -120.2104 R40 smallJ079 51.1178 -120.2105 R41 largeJ080 51.1178 -120.2107 R41 mediumJ081 51.1176 -120.2110 R41 smallJ082 51.1173 -120.2112 R42 smallJ083 51.1171 -120.2116 R42 mediumJ084 51.1167 -120.2115 R42 smallJ085 51.1163 -120.2116 R43 smallJ086 51.1161 -120.2118 R43 mediumJ087 51.1154 -120.2116 R44 largeJ088 51.1152 -120.2116 R44 smallJ089 51.1152 -120.2116 R45 largeJ090 51.1150 -120.2120 R45 large198Jam ID Latitude Longitude Reach ID SizeJ091 51.1148 -120.2122 R46 smallJ092 51.1148 -120.2125 R46 smallJ093 51.1148 -120.2129 R46 smallJ094 51.1146 -120.2131 R46 smallJ095 51.1141 -120.2132 R46 smallJ096 51.1139 -120.2133 R47 mediumJ097 51.1130 -120.2133 R48 smallJ098 51.1116 -120.2138 R51 smallJ099 51.1114 -120.2139 R51 smallJ100 51.1113 -120.2141 R52 mediumJ101 51.1109 -120.2140 R52 mediumJ102 51.1103 -120.2132 R54 mediumJ103 51.1100 -120.2133 R54 smallJ104 51.1098 -120.2133 R54 smallJ105 51.1096 -120.2133 R54 largeJ106 51.1094 -120.2133 R54 smallJ107 51.1092 -120.2133 R55 smallJ108 51.1088 -120.2135 R56 largeJ109 51.1088 -120.2133 R56 largeJ110 51.1084 -120.2133 R57 smallJ111 51.1077 -120.2138 R57 smallJ112 51.1077 -120.2139 R57 smallJ113 51.1075 -120.2139 R58 smallJ114 51.1073 -120.2139 R58 smallJ115 51.1068 -120.2135 R58 smallJ116 51.1066 -120.2135 R58 smallJ117 51.1060 -120.2133 R59 hugeJ118 51.1056 -120.2133 R59 mediumJ119 51.1054 -120.2136 R60 smallJ120 51.1049 -120.2141 R61 mediumJ121 51.1049 -120.2140 R61 small199Jam ID Latitude Longitude Reach ID SizeJ122 51.1047 -120.2139 R61 smallJ123 51.1043 -120.2140 R61 smallJ124 51.1045 -120.2140 R61 smallJ125 51.1034 -120.2139 R64 mediumJ126 51.1032 -120.2138 R64 mediumJ127 51.1028 -120.2140 R65 smallJ128 51.1026 -120.2139 R65 smallJ129 51.1026 -120.2137 R65 smallJ130 51.1021 -120.2137 R65 smallJ131 51.1019 -120.2137 R66 smallJ132 51.1007 -120.2133 R69 largeJ133 51.1004 -120.2133 R69 smallJ134 51.1002 -120.2133 R70 mediumJ135 51.1000 -120.2133 R70 small200Appendix EAdditional FiguresE.1 STOCHASIM OutputE.2 Flume Experiments2010 20 40 60 80 100020406080Time (years)Discharge (m3s)FMI = 0.2FMI = 0.4FMI = 0.6Median flood0 20 40 60 80 1005152535Time (years)Top width (m)FMI = 0.2FMI = 0.4FMI = 0.6Regime widthFigure E.1: Time series plots of flood magnitude and channel width for threeflow variability scenarios. a) The first 100 years of the randomly gen-erated flood sequence is shown for three of the flow variability sim-ulations. Despite differences in flow variability, each simulation has amedian flood of 20 m3/s. b) Variability in channel width over 100 yearsin a stream characterized by a bankfull discharge of 20 m3/s is shownfor 5 runs (each with the same flood sequence) from each of three flowvariability scenarios; dashed lines represent the median width associ-ated with each scenario.2020 10 20 30 4050100150Time since erosion (years)Q critical (m3s)llll lllllll lFMI = 0.2FMI = 0.4FMI = 0.6a0 10 20 30 4050100150200Time since erosion (years)D50 (mm)FMI = 0.2FMI = 0.4FMI = 0.6bFigure E.2: The effect of a large widening event on a) the critical dischargerequired to produce further widening, and b) the grain size that can bemobilized by a 2-year flood (i.e. the flow competence) over time duringthe recovery period (i.e. time since the last erosion event).203Figure E.3: Wood position during Experiment 1.204Figure E.4: Wood position during Experiment 2.205Figure E.5: Wood position during Experiment 3.206Figure E.6: Wood position during Experiment 4.207


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