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Hydrogeomorphic controls on spatial pattern of fish habitat in a mountain stream Cienciala, Piotr 2014

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Hydrogeomorphic Controls on Spatial Pattern of FishHabitat in a Mountain StreambyPiotr CiencialaB.Sc. (Hons), University of Southampton, 2008A 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)October 2014c© Piotr Cienciala, 2014AbstractSpatial heterogeneity and arrangement of physical habitat strongly influence stream-dwelling organisms. A primary objective of this dissertation was to examine howhydrogeomorphic controls – channel morphology, bed sediment, and flow hy-draulics – shape spatial patterns of habitat for small-bodied trout. Two comple-mentary habitat types, spawning and foraging habitat, were investigated to gainmore comprehensive understanding of these linkages. A secondary objective ofthe dissertation was to evaluate the effects of sample size on errors in estimates ofhydraulic parameters critical for understanding channel dynamics and quantifyingfish habitat.This research was conducted in four reaches of a small mountain stream withdifferent channel morphologies and sediment textures. High resolution field sur-veys and a hydrodynamic model were used to map channel morphology, sedi-ment, and flow properties. Habitat models, which included a bioenergetic foragingmodel, were then applied to evaluate fish habitat availability, quality, and distur-bance at within and between-reach scales.Results indicated existence of two distinct spawning habitat domains. In coarserreaches with simple morphologies potential spawning substrate occurred only insmall, hydraulically sheltered areas, which were also at high risk of disturbancedue to excess fine sediment accumulation. In finer, pool-riffle reaches potentialspawning substrate covered large proportion of the bed and was largely unaffectedby fine sediment disturbance. Bed scour generally did not seem to be an importantdisturbance agent.During low flow, the most energetically profitable foraging habitat was locatedin deep, slow-flowing pools and zones of strong lateral gradients of velocity. Cross-iichannel patterns of net energy intake appeared to vary with fish body size. Duringhigh flow, however, energetically profitable habitat occurred mainly near the banks.The mean net energy intake and the proportion of channel area where fish energybudget was positive were somewhat higher in the reaches with better developedpool-riffle morphology, but the former trend partially reversed during high flow.Error analysis indicated that sample sizes commonly used in river science torepresent hydraulic variables may generate large sampling errors. Errors of thismagnitude in the estimated bed roughness parameter caused substantial differencesin the flow field predicted by a hydrodynamic model.iiiPrefaceThis dissertation presents research conducted by Piotr Cienciala under the super-vision of Dr. Marwan Hassan. Piotr Cienciala was responsible for design of theresearch, collected much of the field data, parameterized and executed the hydrody-namic model, and analyzed and interpreted the data. Dr. Marwan Hassan providedconceptual and analytical support throughout the process.A version of chapter 2 has been published: Cienciala, P., and Hassan, M.A.,2013. Linking spatial patterns of bed surface texture, bed mobility, and channelhydraulics in a mountain stream to potential spawning substrate for small residenttrout. Geomorphology, 197, pages 96-107. Piotr Cienciala wrote the manuscript,which was then reviewed by Dr. Marwan Hassan.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3.1 Small-bodied salmonids and small streams . . . . . . . . 31.3.2 Spatial pattern and scale issues . . . . . . . . . . . . . . . 61.3.3 Fish habitat models: modelling approaches and prior work 81.3.4 Hydrodynamic models, sampling errors, and parameter un-certainty . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 171.4 Thesis objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 18v2 Influence of Bed Surface Texture, Bed Mobility, and Channel Hy-draulics on Availability and Disturbance of Potential Spawning Sub-strate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2.1 Field site . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2.2 Field surveys . . . . . . . . . . . . . . . . . . . . . . . . 242.2.3 GIS analyses . . . . . . . . . . . . . . . . . . . . . . . . 252.2.4 Hydrodynamic model . . . . . . . . . . . . . . . . . . . . 272.2.5 Spawning substrate . . . . . . . . . . . . . . . . . . . . . 292.3 Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.3.1 Hydrodynamic model evaluation . . . . . . . . . . . . . . 322.3.2 Potential spawning substrate availability and disturbance . 322.3.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 422.4 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.4.1 Ecological implications . . . . . . . . . . . . . . . . . . . 442.4.2 Methodological implications . . . . . . . . . . . . . . . . 462.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 Influence of Channel Morphology and Hydraulics on Energetic Prop-erties of Foraging Habitat for Small-Bodied Trout . . . . . . . . . . 483.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.2.1 Field site . . . . . . . . . . . . . . . . . . . . . . . . . . 523.2.2 Field surveys . . . . . . . . . . . . . . . . . . . . . . . . 543.2.3 Hydrodynamic model . . . . . . . . . . . . . . . . . . . . 553.2.4 Bioenergetic model . . . . . . . . . . . . . . . . . . . . . 573.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.4.1 Within-reach patterns . . . . . . . . . . . . . . . . . . . . 723.4.2 Between-reach patterns . . . . . . . . . . . . . . . . . . . 843.5 Conclusions and implications . . . . . . . . . . . . . . . . . . . . 86vi4 Sampling Error in Estimates of Flow Properties in Natural Coarse-Bedded Streams: Effects of Sample Size and Application to Hydro-dynamic Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924.2.1 Field site . . . . . . . . . . . . . . . . . . . . . . . . . . 924.2.2 Field data collection and statistical analyses . . . . . . . . 924.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.4.1 Sampling errors . . . . . . . . . . . . . . . . . . . . . . . 1074.4.2 Consequences of sampling errors for predictions of hydro-dynamic model . . . . . . . . . . . . . . . . . . . . . . . 1114.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1145 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 1165.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1165.2 Summary and synthesis . . . . . . . . . . . . . . . . . . . . . . . 1175.3 Broader implications . . . . . . . . . . . . . . . . . . . . . . . . 121Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124viiList of TablesTable 2.1 Characteristics of the study reaches in East Creek . . . . . . . 22Table 2.2 Flow evaluation measures . . . . . . . . . . . . . . . . . . . . 33Table 4.1 Measures of model performance calculated for all bed rough-ness parameter scenarios . . . . . . . . . . . . . . . . . . . . . 106viiiList of FiguresFigure 2.1 Map of the study area . . . . . . . . . . . . . . . . . . . . . . 23Figure 2.2 Hydrodynamic model evaluation . . . . . . . . . . . . . . . . 33Figure 2.3 Bed topography and textural patches in subsections of the studyreaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Figure 2.4 Modelled grain shear stress distribution in selected sub-sectionsof four study reaches . . . . . . . . . . . . . . . . . . . . . . 36Figure 2.5 Summary of textural characteristics of the study reaches . . . 37Figure 2.6 Spatial pattern of net scour and fill . . . . . . . . . . . . . . . 38Figure 2.7 Summary of net scour in the study reaches . . . . . . . . . . . 39Figure 3.1 Map of the study area . . . . . . . . . . . . . . . . . . . . . . 53Figure 3.2 Maps of predicted net energy intakein Pool-Riffle-3 for fish ofdifferent body lengths . . . . . . . . . . . . . . . . . . . . . 63Figure 3.3 Longitudinal patterns of net energy intake during low flow con-ditions for fish of different body lengths . . . . . . . . . . . . 65Figure 3.4 Maps of net energy intake, flow depth, and velocity in two sub-sections of Pool-Riffle-2 reach . . . . . . . . . . . . . . . . . 66Figure 3.5 Relationship between depth (normalized by the reach-meanvalue) and net energy intake (NEI) during low flow conditions 67Figure 3.6 Transverse structure of NEI in the study reaches during lowflow conditions . . . . . . . . . . . . . . . . . . . . . . . . . 68Figure 3.7 Cumulative distribution plots of net energy intake in three dis-tance bands from the banks modelled for low-flow conditions 69ixFigure 3.8 Longitudinal patterns of net energy intake during high flowconditions for fish of different body sizes (FL) . . . . . . . . 71Figure 3.9 Relationship between depth (normalized by the reach-meanvalue) and net energy intake (NEI) during high flow conditions 72Figure 3.10 Transverse structure of NEI in the study reaches during-highflow conditions . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 3.11 Cumulative distribution plots of net energy intake in three dis-tance bands from the banks modelled for high-flow conditions 74Figure 3.12 Proportion of channel area at low-flow conditions where ve-locities are below the maximum sustainable velocity for troutof a given body size . . . . . . . . . . . . . . . . . . . . . . . 75Figure 3.13 Availability of profitable foraging habitat (NEI > 0 Js-1) dur-ing low-flow conditions . . . . . . . . . . . . . . . . . . . . . 76Figure 3.14 Cumulative distribution plots of net energy intake (NEI) in thestudy reaches during low-flow conditions . . . . . . . . . . . 77Figure 3.15 Reach-average net energy intake (NEI) in the study reaches,under low-flow conditions . . . . . . . . . . . . . . . . . . . 78Figure 3.16 Proportion of channel area at high-flow conditions where ve-locities are below the maximum sustainable velocity for drift-feeding trout of given body size (FL) . . . . . . . . . . . . . 79Figure 3.17 Availability of profitable foraging habitat (NEI > 0 Js-1) dur-ing high-flow conditions . . . . . . . . . . . . . . . . . . . . 80Figure 3.18 Cumulative distribution plots of net energy intake (NEI) forthe study reaches during high-flow conditions . . . . . . . . . 81Figure 3.19 Reach-average net energy intake (NEI) in the study reaches,under high-flow conditions . . . . . . . . . . . . . . . . . . . 82Figure 4.1 The study reaches. Rapid (left) and Pool-Riffle-3 (right). . . . 93Figure 4.2 Examples of local velocity profiles measured in East Creek . . 99Figure 4.3 Spatially averaged velocity profiles . . . . . . . . . . . . . . 100Figure 4.4 Percentage errors in shear stress, < τB > (top row) and hy-draulic roughness expressed as a a multiplier < a > (bottomrow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101xFigure 4.5 Histograms of normalized hydraulic variables with the fittedgamma distribution . . . . . . . . . . . . . . . . . . . . . . . 102Figure 4.6 Percentage errors in gamma distribution shape parameter k forshear stress, velocity, and depth . . . . . . . . . . . . . . . . 103Figure 4.7 Percentage errors in gamma distribution shape parameter θ forshear stress, velocity, and depth . . . . . . . . . . . . . . . . 104Figure 4.8 Results of hydrodynamic modelling (FaSTMECH) under dif-ferent bed roughness parameter scenarios . . . . . . . . . . . 105Figure 4.9 Relative differences in the simulated shear stress with respectto the reference roughness scenario < a >= 0.11 . . . . . . . 107Figure 4.10 Scatter plots of model evaluation data under different rough-ness scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . 108xiAcknowledgementsThis dissertation could not be completed without help of a number of people.First and foremost, I thank my supervisor, Marwan Hassan, for encouragement,support, and excellent guidance he provided throughout the process. I am gratefulfor the freedom he gave me to explore topics of my interest.I also benefited from insightful comments and advice from members of myPh.D. committee, Dan Moore and John Richardson, as well as from conversationswith Michael Church, Brett Eaton, and Hal Voepel.Invaluable field and laboratory assistance was provided by a group of great re-search assistants, David Reid, Tim Reid, Sam Robinson, Laurent Roberge, DanielSchweizer, Chantelle Chan, and Robert Taylor, and my graduate colleague, IlanaKlinghoffer. I also thank Joshua Caulkins and Andre Zimmermann for their con-tribution to field data collection program in East Creek.Burak Yoldemir and Basak Oztas-Yoldemir played a pivotal role by introducingme to my loyal friend MatLab.Useful tips from Rich McDonald were instrumental for completing my firststeps with FaSTMECH model, which over time has become one of the centraltools applied in this research.Simon Donner kindly provided me with access to his high performance com-putational cluster and Vincent Kujala’s patience and tremendous support allowedme to take full advantage of this fantastic resource. Their help greatly reduced thetime needed to complete data analyses.Last, but certainly not the least, I am immensely indebted to my family - myparents, sister, and wife Joey - for their love and endless support in pursuing mydream. Thank you for always being there for me.xiiFunding for this project was provided by NSERC Discovery Grant awardedto Marwan Hassan. During my graduate program I was supported through UBCGraduate Entry Scholarship, UBC Faculty of Arts Graduate Scholarship, UBCUniversity Graduate Fellowship, UBC Four Year Fellowship, and Reginald andAnnie Van FellowshipxiiiChapter 1Introduction1.1 PreamblePhysical environment exerts strong influence on performance and fitness of livingorganisms. For example, abiotic conditions may affect physiological processes,resources availability and costs of their acquisition (e.g. locomotion), as well asan individual reproductive success (e.g. Huey, 1991; Porter et al., 2002, 2010;Cooke and Suski, 2008; Kearney and Porter, 2009). As a result, physical habitatconstitutes an important element of environmental template that shapes life his-tory strategies (Southwood, 1977, 1988). In particular, spatial variability in habitatcharacteristics has long been thought to be of fundamental ecological importance(e.g. MacArthur and Pianka, 1966; Schoener, 1974; Rosenzweig, 1981; Pulliam,1988; Pulliam and Danielson, 1991; Wiens et al., 1993). Physical environmentspecifically has been an integral consideration in a quest to understand how thisheterogeneity controls population dynamics, biotic interactions, and assembly ofcommunities (e.g. Wiens, 1976; Menge and Sutherland, 1987; Turner, 1989; Dun-son and Travis, 1991; Hunter and Price, 1992; Poff, 1997). These topics continue toconstitute a major focus of current ecological research (Jackson et al., 2001; With,2002; Belisle, 2005; Fahrig and Nuttle, 2005; Hastings et al., 2005; Bergman et al.,2006; Kauffman et al., 2007; Melbourne et al., 2007; McPhee et al., 2012). Furtherinquiry into the mechanisms that shape spatial patterns of physical habitat is piv-otal in the light of unprecedented landscape disturbance due to ongoing climate and1land use changes (Solomon et al., 2007; Tetzlaff et al., 2013; Harden et al., 2014).These two aspects of global environmental change involve multifaceted modifica-tions in physical properties of habitat template, including hydrological and geo-morphic conditions and processes (e.g. Solomon et al., 2007; Rosenzweig et al.,2008; Knight and Harrison, 2009, 2012, 2013; Macklin and Lewin, 2008; Hookeet al., 2012; Lane, 2013; Wohl, 2013; Chin et al., 2014).The relationship between living organisms and heterogeneous physical land-scape is particularly strong in fluvial systems (e.g. Hart and Finelli, 1999; Power,2001, 2006). Channel morphology, that is the shape of its bed and banks, controlsthe distribution of in-stream habitat and, along with the textural properties of thesediment that makes up its boundary, defines hydrodynamic forces that act uponthe stream-dwelling biota (e.g. Carling, 1992; Vogel, 1994). The composition ofthis sediment is also an important characteristic of streambed (benthic) habitat,which many lotic organisms utilize at least occasionally. Moreover, erosion, trans-port, and deposition of sediment, driven by fluctuating flow forces, may reshapechannel geometry and create or disturb favourable patches of benthic substrate(e.g. Power, 2001). Thus, a comprehensive framework to study physical habitatin rivers and streams requires that consideration be given to this dynamic inter-actions between channel morphology, hydraulics, and sediment properties, whichcan collectively be termed ‘hydrogeomorphic conditions’. This thesis will focuson exploring this subject, specifically, with regards to small-bodied salmonid fishand mountain streams they inhabit.1.2 Thesis organizationThis thesis is comprised of five chapters. The present chapter provides an intro-duction to the thesis and a brief review of the relevant literature. In particular, Idiscuss key issues central to research presented in this thesis, which include back-ground information on small salmonid fish and their habitat, spatial pattern andscale, approaches to habitat modelling, and uncertainty due to sampling error.The three following chapters constitute the main part of the thesis. They canbe viewed as standalone research documents and contain chapter-specific intro-ductions, description of methods and results, as well as discussion and conclusion2sections. In the second chapter, I present research that examined how channelmorphology, bed texture, and bed mobility influence spatial patterns of spawninghabitat availability and risk of disturbance. The third chapter describes a closelyrelated line of work, in which I focused on effects of channel morphology andhydraulics on the energetic profitability of foraging habitat within the same studysites. This research is complemented by the fourth chapter, in which I evaluate theeffect of sample size on errors in estimates of key hydraulic parameters as well asthe consequences of such errors for predictions of a hydrodynamic model that wasapplied in the two preceding chapters.In the concluding chapter, I integrate findings that emerge from research de-scribed in this thesis to present a more comprehensive view of spatial patterns offish habitat in mountain streams that takes into account complementary habitattypes.1.3 Literature review1.3.1 Small-bodied salmonids and small streamsSalmonids (family Salmonidae, e.g. salmon, trout, charr) play a central role incoupled river-terrestrial ecosystems. As top aquatic predators they can exert strongtop-down control on stream community structure and ecosystem function (e.g.Power et al., 2008; Alvarez and Peckarsky, 2014), including a marked effect oncarbon cycling (Atwood et al., 2013). Because of their trophic position, these fishalso constitute an important food web link that facilitates bi-directional flow of sub-sidies between stream and terrestrial ecosystems (Cederholm et al., 2001; Gendeand Quinn, 2004; Baxter et al., 2005). In addition, a mounting body of evidencesuggests that carcasses of anadromous (sea-run) salmonids provide an importantsource of marine-derived nutrients for aquatic and riparian biota (e.g. Gende et al.,2002; Schindler et al., 2003; Gende and Quinn, 2004).This thesis focuses specifically on physical habitat of small-bodied salmonids(body size <35 cm; after Schuett-Hames et al., 1996) in mountain streams. Thiscategory primarily includes salmonids with stream-resident life history (hereafter‘resident’) but also juvenile life stages of anadromous forms. These fish typically3inhabit small tributary channels (Behnke, 1992; Quinn, 2005; Trotter, 2008) andin mountain drainage basins they utilize primarily reaches with low-to-moderateslopes (typically below 4-5% Hartman and Gill, 1968; De Leeuw and Stuart, 1981;Magee et al., 1996; Rosenfeld et al., 2000, 2002). Resident salmonids spend theirentire lives in these streams while anadromous forms use them for spawning andrearing (e.g. Trotter, 1989, 2008). Importantly, because of their complex life cycle,salmonids may require diverse combinations of physical stream habitat character-istics at different life stages (Bjornn and Reiser, 1991). Thus, habitat types thatprovide non-substitutable resources (‘complementary habitat’ e.g. spawning, for-aging, overwintering) should be considered if a more comprehensive understand-ing of hydrogeomorphic controls on salmonid fish is to be achieved (e.g. Dunninget al., 1992; Schlosser, 1995; Kocik and Ferreri, 1998; Rosenfeld and Hatfield,2006; Lapointe, 2012).Because of the branching structure of the drainage networks, small tributarystreams are a ubiquitous feature of the landscape and constitute a large proportionof the total channel length. In mountain basins these channels constitute a diversecategory. For practical reasons, this thesis focuses exclusively on mountain streamsthat meet the following three criteria:(1) Are ‘small’ channels, that is one in which the ratio of sediment diameter toflow depth (relative roughness) is less than 10. This definition, adopted previouslyby Hassan et al. (2005), encompasses channels that may be described as ‘small’ or‘intermediate’ channels following Church (1992).(2) Have moderate channel slope, ranging between 1% and 4%. This sloperange corresponds to streams often reported to be heavily utilized by small salmonids(e.g. De Leeuw and Stuart, 1981; Magee et al., 1996; Rosenfeld et al., 2000, 2002)and usually display plane-bed or pool-riffle morphology (Montgomery and Buffin-gton, 1997; Buffington et al., 2003).(3) Have single-thread channel, in which the boundary (bed and lower banks)is made up of granular sediment. Thus, we ignore bedrock and braided channels.The composition and texture of channel sediment forms the finest scale of het-erogeneity in such streams and the calibre of particles that comprise the surfaceexposed to flow may range from sand (<2 mm) to boulders (>256 mm). Thebed material particles may be organized into distinct textural patches (Buffington4and Montgomery, 1999b) and contribute to larger-scale topographic variability byforming a hierarchy of coherent three-dimensional aggregations (bedforms). Thesebedforms may range is size from microtopographic sedimentary features, for ex-ample, pebble clusters, to mesoscale transverse ribs and macroscale pool-riffle-bar sequences (Church, 1992; Hassan et al., 2007). In addition, irregular upperbanks reinforced by roots of riparian vegetation, occasional bedrock outcrops, andin-stream wood may act as important elements of the channel architecture. Thisintricate nature of mountain channel morphology in turn results in complex flowpatterns characterized by local accelerations and decelerations and rapid changesin flow directions (e.g. Lisle, 1986; Furbish, 1993). Over larger scales, mountainstream reaches vary in terms of their morphological styles, each with distinct setof characteristic bedforms that reflect the governing geomorphic conditions (e.g.Montgomery and Buffington, 1997; Buffington et al., 2003).Unless affected by some form of landscape disturbance, small mountain streamchannels tend to be geomorphically stable (Hassan et al., 2005, 2007). Flow force iseffectively dissipated by large roughness elements of the channel boundary (Wibergand Smith, 1991) and interlocked sedimentary structures prevent entrainment ofsediment particles (Laronne and Carson, 1976; Church et al., 1998). As a result,redistribution of coarse sediment that makes up the channel is limited, except whenfresh material is supplied from external sources.Importantly, many small channels are commonly thought to have low valuefor fisheries and, despite increasing land use pressures, they receive weak regu-latory protection (e.g. Rosenfeld et al., 2002; Moore and Richardson, 2003, 2012;Richardson et al., 2010, 2012). In addition, research suggests that mountain streamsand fish populations that occupy them may be strongly affected by climate change.Effects of altered thermal environment (Isaak et al., 2010, 2012; Wenger et al.,2011; Isaak and Rieman, 2013) may be accompanied by more severe regime ofhydrogeomorphic disturbance, for example, declines in summer flows and poten-tial increases in the winter floods magnitude (e.g. Loukas et al., 2002; Hamlet andLettenmaier, 2007; Luce and Holden, 2009; Luce et al., 2012).51.3.2 Spatial pattern and scale issuesSpatial patterns of physical habitat are of central ecological importance in heteroge-neous landscapes because they can lead to local differences in performance and fit-ness, drive animal movement, and influence biotic interactions (e.g. Turner, 1989,2005; Wiens et al., 1993). For the purpose of this work, I use the terms patternand structure interchangeably and define them as having two main facets, namely,composition and configuration (modified from Turner, 1989; Dunning et al., 1995).Composition refers to the relative amount of different habitat types within a domainof interest while configuration is related to spatial arrangement of habitat, whichcan be described through spatial relations between spatial units such as proximity,overlap, etc.Given the multi-scale nature of stream channel heterogeneity (Frissell et al.,1986) the key question is that of the adequate scale at which spatial patterns ofhabitat should be investigated. Two aspects of spatial scale need to be considered:resolution (grain) and extent (coverage) (e.g. Addicott et al., 1987; Wiens, 1989,2002). Resolution can be thought of as the spatial density of measurements orcomputational nodes (or size of model grid cells) that is necessary to capture andrepresent the pattern of interest. One way to establish the right resolution is byestimating and matching so-called process scale, which can be defined as a lengthscale over which the variable at question is autocorrelated (Bloschl and Sivapalan,1995). However, I argue that both physical process and ecological process scalesneed to considered jointly. In particular, the dimensions of relevant habitat patchesthat the organism of interest perceives and requires may be helpful in determiningwhich of the hierarchical scales of variation in abiotic variables should be explic-itly resolved (Wiens, 1989; Mac Nally, 2005). A patch of high quality habitatembedded within a matrix of poor quality environment may be sufficient to meetall demands of an organism yet the consideration of habitat properties averagedover a larger area may lead to the opposite conclusion. In the context of salmonidsspecifically, prior research indicates that small-bodied fish, such as resident Cut-throat Trout, may require bed areas of around 0.1 m2 in order to excavate a nest(‘redd’) and bury their eggs (Bjornn and Reiser, 1991). In the same vein, it can beargued that, from a perspective of foraging fish, a relevant ‘hydraulic patch’ will be6roughly equivalent to their capture area or feeding territory. The fish will samplethis hydraulic habitat during feeding forays. For a typical range of body size insmall salmonids territory area can be assumed to range approximately between 0.1m2 and 1 m2 (e.g. Grant and Kramer, 1990). Thus, it appears that a linear lengthscale of around 0.1-0.3 m may be required to resolve relevant fine-scale spatialheterogeneity of physical habitat for small salmonids.The relevant extent of a study domain, on the other hand, can be best deducedusing a Lagrangian frame of reference, which entails the consideration of move-ments of a focal organism across the landscape. Specifically, this approach requiresthat spatial coverage be sufficiently large to represent the amount of heterogeneityencountered and experienced by the organism given its mobility and the objectiveability to disperse (Addicott et al., 1987; Wiens, 2002). Spatial dimensions of this‘ecological neighbourhood’ will of course depend on the ecological process of in-terest (Addicott et al., 1987). Since the locations of complementary habitats that arerequired by the organism of interest may not overlap in space, I hypothesize that,as the time frame of interest increases, so will the adequate spatial extent becausemore life stages and habitat types need to be considered. Importantly, salmonidfish can move over long distances and even those with resident life history aremore mobile than previously thought (Gowan et al., 1994). For example, move-ments between spawning and rearing habitats may extend far beyond their localsurrounding (Gresswell and Hendricks, 2007; Young and Tonn, 2011). However,research using passive tagging and radiotelemetry indicates that in stream-residentfish populations the distribution of movement distances is leptokurtic, that is themajority of the movements are short, for example, between morphological chan-nel units (e.g. pools, riffles) and adjacent reaches (Hilderbrand and Kershner, 2000;Gresswell and Hendricks, 2007). Therefore, it appears that the spatial extent equiv-alent to several neighbouring reaches may be generally well-suited to study how agiven population of resident salmonids may be influenced by physical template ofthe riverscape.Process-based classifications of channel morphology, in which distinct channeltypes reflect different water and sediment supply regimes (e.g. Montgomery andBuffington, 1997), provide a convenient framework for understanding between-reach variation in the characteristics of stream habitat as well as its potential re-7sponses to land use and climate change. There are two basic ways this frameworkcan be applied. First, the governing conditions – hence the concomitant morpho-logical channel types – change in a systematic manner within the drainage basin(e.g. Montgomery and Buffington, 1997; Buffington et al., 2003; Brardinoni andHassan, 2007; Addy et al., 2011, 2014; Buffington and Montgomery, 2013) andthese spatial transitions can be partially predicted using limited topographic infor-mation (e.g. Wohl and Merritt, 2005). Hence, if the morphological channel typescan be linked to distinct sets of ecologically relevant habitat properties, this predic-tive ability may open an interesting avenue for drainage network-wide forecast andassessment of stream habitat, at least to a first order approximation. Such an ap-proach has been already successfully adopted to study basin-scale salmonid spawn-ing habitat (Buffington et al., 2004). Second, flow and sediment regimes, as wellas the associated channel morphology, also evolve in response to temporal fluc-tuations in hydrological cycle and sediment production rates caused by landscapedisturbance. Therefore, careful application of space-for-time substitution may pro-vide useful insights into potential consequences of climate and land use change. Insum, it appears that potential of process-based classifications of channel morphol-ogy to serve as an organizing framework for broad-scale physical habitat studies iscertainly worth exploring.1.3.3 Fish habitat models: modelling approaches and prior workA spatially explicit approach is a useful way to study spatial patterns of habitatacross the landscapes of interest (e.g. Wiens, 1989, 2002; Turner, 1989; Turneret al., 1995; Turner, 2005). Hereafter, by ‘spatially explicit’ I understand thoserepresentations of landscape phenomena that meet the following two criteria: (i)constitute a complete spatial coverage of a geographical domain of interest; and(ii) provide the ability to define locations of and spatial relations (e.g. proximity oroverlap) between all spatial units using a coordinate system (adapted from Dunninget al., 1995). Integral to high resolution research over an extensive spatial domain,which was advocated above for small-bodied salmonids, is the practical challengeof acquiring a large volume of environmental data. It is simply not feasible to meetsuch demands by data derived from direct observations and experiments. To cir-8cumvent this limitation in habitat research, it is necessary to resort to mathematicalmodels (e.g. Amano, 2012). Below I present a brief outline of spatially explicitapproaches to modelling the hydrogeomorphic controls on fish habitat. Because anexhaustive treatment of this topic is beyond the scope of this chapter, the reviewshould be viewed as an inevitably selective attempt to illustrate key directions inthis research domain. In particular, I omit models that focus on relating physicalhabitat to fish communities.Habitat models of interest in this thesis have two principal characteristics. First,they are based on a quantitative relationship between some environmental pre-dictors and an ecological response variable, such as habitat suitability or abun-dance of focal organisms (adapted from: Guisan and Zimmermann, 2000; Dun-bar et al., 2012). As discussed by Guisan and Thuiller (2005), the environmentalpredictors used in the relationship may represent physical factors relevant for eco-physiological limits (e.g., temperature, water velocity, or depth), resources (e.g.food abundance), or disturbances. Second, spatial distribution of the response vari-able within the domain under study is predicted by applying the previously es-tablished relationship to maps of the environmental predictors. In other words, aset of mapped properties of a landscape is translated into a map of the ecologicalresponse variable.Multiple classifications of habitat models and ecological models in generalhave been proposed (for more detailed discussions see Guisan and Zimmermann,2000; Turner, 2001). However, because of the discipline-specific conventions andblurred boundaries between model categories the associated terminology is fraughtwith subjectivity and often debated. Below I will follow definitions that are closeto those proposed by Turner (2001). ‘Process-based’ will refer to models that, atleast potentially, enable establishment of a direct link between the modelled habitatproperties and ecological processes (e.g. translating environmental variables intoindividual performance and fitness, or population dynamics). By contrast, term‘non-process-based’ will denote models that do not allow such a functional rela-tionship to be developed. Rather, models in this category will produce a descriptive(even if quantitative) output, such as organism density or habitat suitability. An in-dependent distinction between ‘mechanistic’ and ‘empirical’ models will not beused dichotomously, as commonly done. Instead, I will view models as forming9a continuum from those that aim to represent in detail the dynamics of the realworld processes (‘mechanistic’, an extreme case would be a model based on thefirst principles) to those that rely on a purely correlative association without a firmtheoretical basis (‘empirical’). In reality a vast majority of mechanistic modelscontain empirical parameters while, on the other hand, in some heavily parame-terized empirical models the processes are grossly simplified but the relation isgrounded in some theory. I suggest that the models falling into the latter categorycan perhaps be called ‘phenomenological’ (although in the literature this term issometimes used interchangeably with empirical).Thus far, most of spatially explicit models of physical fish habitat can be clas-sified as ‘non-process-based’ empirical models. They primarily represent the cate-gory of AER (abundance-environment-relations) or occurrence (presence-absence)models and have been applied across all spatial scales. By far the most com-monly employed paradigm is that of habitat suitability or habitat preference in-dex (HSI/HPI) approach (Bovee, 1982, 1986; Bovee et al., 1998). The premiseof this method is to create empirical curves of suitability, value of which rangesfrom 0 to 1 (in the case of HPIs, the frequency is expressed relative to availabil-ity). The curves are based on correlations between some environmental variablesusually velocity, depth, and substrate and the frequency of fish that were observedto utilize specific values of these variables. Rapid popularization of hydrodynamicmodels (often termed Computational Fluid Dynamics; CFD) and increases in theavailable computational power have led to high interest in integrating these indiceswith simulated flow fields (e.g. Leclerc et al., 1995; Ghanem et al., 1996; Hardy,1998; Waddle et al., 2000). The primary focus of these studies has been in explor-ing effects of channel morphology and flow fluctuation on spawning and rearingfish habitat indices (e.g. Clark et al., 2008; Pasternack et al., 2008; Kozarek et al.,2010; Harrison et al., 2011). For instance, Pasternack et al. (2008) adopted this ap-proach to illustrate the importance of backwaters that are imposed by riffles for lowflow habitat. In another study, focused on bar growth process driven by sedimentsupply, Harrison et al. (2011) used HSI indices to evaluate whether this geomor-phic adjustment led to increased quality of spawning habitat. In addition to thiswork, some research effort has been directed towards cross-referencing HSIs or itsaggregate measures (weighed usable area or WUA) with other habitat indices (e.g.10Clark et al., 2008). HSIs have also been applied in the spatially explicit frame-work for the purpose of predicting positions most likely to be utilized by fish so asto relate this forecast to maps of disturbance such as that due to bed scour or fill(Pasternack et al., 2004; May et al., 2009; Wheaton et al., 2010).In the same vein, correlative AERs have been employed at a coarser resolution.For example, applications of mescoscale models (e.g. Parasiewicz, 2001, 2007)enabled assessment of habitat in multiple reference streams across a large geo-graphical region (e.g. Vezza et al., 2012, 2014). On the other hand, Gosselin et al.(2010) highlighted limitations of such an approach in small channels, where finer-scale heterogeneity appeared to be more relevant. Suitability indices developed formacroscale (reach-level) resolution focused on the association between fish abun-dance and channel slope (Steel and Sheer, 2003) or a combination of slope, chan-nel width, and annual streamflow (Burnett et al., 2007). The latter formulation waslater applied to predict how abundance and distribution of fish habitat may be influ-enced by river valley steepness and concavity may affect (May and Lisle, 2012) andthe rate of downstream increase in valley width (May et al., 2013). Furthermore,a multivariate statistical model was used in another study to predict occurrence ofthree salmonid species across a spatially extensive mountainous region, based ondrainage area, elevation, and topographic slope (McCleary and Hassan, 2008).While the non-process-based, empirical habitat models provide a wealth ofinformation on fish space use and may be successful in predicting their spatial dis-tributions (Knapp and Preisler, 1999; McCleary and Hassan, 2008), they are alsosubject to important limitations. First, as noted in the preceding discussion, it isimpossible to link them to ecological processes (Beyer et al., 2010; Lancaster andDownes, 2010). Second, as correlative relationships, they conflate the influence ofmultiple variables (e.g. Anderson et al., 2006). Although this implicit considera-tion of multiple factors often is what underlies the predictive power of such models,at the same time it precludes understanding of the cause-effect relationship and theoperating mechanisms. Furthermore, in the light of ecological theory the assump-tion that abundance is indicative of high quality habitat, often made in HSI/HPIsmodels, is not always justified and may lead to utterly wrong interpretations (e.g.Lancaster and Downes, 2010). Finally, the transferability of the AER relationshipsbetween sites with different conditions has been questioned (e.g. Moir et al., 2005;11Wenger and Olden, 2012).Spatially explicit fish habitat models that could be classified as ‘process-based’have been adopted substantially less often. Nevertheless, this category includesdiverse models, which differ significantly in terms of their complexity and span abroad spectrum of the mechanistic-empirical continuum. One of the major researchfoci related to hydrogeomorphic habitat controls has been that concerned with pre-diction of salmonid egg mortality risk due to bed scour. Habitat models in thiscategory have been based on a relation between fish body size and the depth of eggburial (for reviews see: DeVries, 1997; Steen and Quinn, 1999), which is then com-pared with the depth of scour (e.g. Pasternack et al., 2004; Wheaton et al., 2010).Microhabitat-resolution studies of this phenomenon have typically modelled scourdepth by differencing digital elevation models (DEM) based on subsequent sur-veys. In contrast, models employed at the macrohabitat resolution, predicted scourdepth using an empirical relation of Haschenburger (1999) (e.g. Tonina et al., 2008;Goode et al., 2013). Building upon the work on vertical mixing by (Hassan andChurch, 1994), Haschenburger (1999) proposed that a negative exponential func-tion can describe the proportion of bed that is disturbed to a progressively largedepth. In contrast to bed scour, much less attention has been directed towards spa-tially explicit examination of another important source of mortality: accumulationof fine sediment in spawning gravels. For example, a threshold value for excessfine sediment, based on an empirical relation between fine material content andmortality, was applied at microhabitat-scale resolution by Maturana et al. (2014).An important challenge in tackling the latter research question is the inability tomake a spatially continuous prediction of subsurface sediment composition.Considerably more mechanistic and complex models have been developed andapplied to study fish foraging. In particular, a model proposed by Hughes andDill (1990) for drift-feeding salmonids has received substantial interest among fishecologists (Hayes et al., 2000, 2007; Guensch et al., 2001; Booker et al., 2004).Although their results clearly suggest that the distribution of energetically prof-itable foraging habitat may be organized by channel morphology at the mesohabi-tat scale, none of these studies has specifically focused on systematic and detailedanalysis of the links between hydrogeomorphic conditions and fish habitat quality.In particular, in contrast to research concerned with scour disturbance, all of these12studies were carried out in a single and usually short reach. Consequently, therehas been no attempt to make comparisons across channels representing differentmorphological styles.One of the limitations of the mechanistic, process-based approach to studyingfish habitat is the fact that, in contrast to AERs, it accounts for only partial infor-mation on the environmental factors that are relevant for fish. Therefore, the abilityto isolate processes of interest comes at the price of reducing the variance in eco-logical processes that can be explained. Moreover, the highly mechanistic process-based models are frequently complex (Piccolo et al., 2014), data-demanding, andmay contain several assumptions (e.g. Hughes et al., 2003). Nevertheless, process-based models offer some advantages of paramount significance. As noted in thepreceding discussion, one of the most important of them is their ability to linkenvironmental conditions to ecological process and establish a cause-effect link.Moreover, predictions of mechanistic process-based models advance our under-standing of the pathways through which specific, isolated environmental factorsinfluence fish and their habitat. Importantly, these models are independent of spe-cific empirical conditions. Therefore, they can, in principle, be extrapolated (Levin,1992) and thus provide a powerful tool to explore various environmental scenariosrelated to the effects of land use or climate change (Gustafson, 2013). The under-standing of biophysical linkages offered by process-based models may form a basisfor new hypotheses, which can be subsequently tested through empirical studies.These models can be also coupled with behavioural (e.g. individual-based models,IBM) or population models to predict the actual response of ecological processes(e.g. Harvey and Railsback, 2009; Railsback et al., 2009, 2013). Overall, therefore,it appears that river science and management would greatly benefit from further re-search carried out by adopting process-based, mechanistic models. Such inquirycould yield valuable new insights and complement the body of knowledge derivedfrom abundance-environment relationships.1.3.4 Hydrodynamic models, sampling errors, and parameteruncertaintyThe properties and dynamics of stream channels and fish habitat are controlledby interactions between channel morphology, hydraulics (e.g. flow velocity, hy-13drodynamic forces), and sediment redistribution, as discussed in Section 1.1. Thetopographic characteristics of a channel and its changes over time due to sedimenttransport are arguably easiest to represent in a spatially explicit model, as modernremote sensing capacities enable rapid collection of high resolution data over ex-tensive areas (e.g. Fonstad and Marcus, 2010; Marcus, 2012; Carbonneau et al.,2012; Fonstad et al., 2013). Similar technologies can be applied to survey sedi-ment properties (Graham et al., 2005; Heritage and Milan, 2009; Warrick et al.,2009), although this endeavour is significantly more challenging and the methodsemployed for large spatial domains provide only simple indices of compositionsuch as median grain size (Carbonneau et al., 2004, 2005). Even when the remotesensing capabilities are limited, as in channels under forest canopy, ground surveysusing total station and low-level photography (e.g. Bird et al., 2010) can provide analternative means of efficient data collection. In contrast, obtaining spatially exten-sive and detailed information on channel hydraulics is far more difficult. Althoughmost recent remote sensing methods offer a promise of rapid hydraulic surveys(e.g. Lee and Julien, 2006; Hauet et al., 2008), these approaches are still beingdeveloped and currently their application is still limited in scope. Consequently,hydrodynamic modelling offers an extremely useful tool to predict spatial charac-teristics of flow fields and, unsurprisingly, has been gaining popularity across var-ious branches of river science during the last few decades (for reviews see: Lane,1998; Bates et al., 2005; Pasternack, 2011; Tonina and Jorde, 2013). These mecha-nistic, mathematical representations of fluid dynamics enable reproduction of flowdepths, velocities, hydrodynamic forces (bed shear stress), and other derived vari-ables with resolution impossible to achieve through field surveys (Lane, 1998).Hydrodynamic models, also referred to as Computational Fluid Dynamics (CFD)models simulate fluid motions using primarily a combination of mass conserva-tion and momentum equations (‘governing equations’), although some empiricalor statistical treatments are necessary, for example, to represent the effects of tur-bulence (‘turbulence closure’). The simplest type of hydrodynamic models is a1D model, in which three-dimensional momentum equations are averaged to sim-plify the solution (e.g. Lane and Ferguson, 2005). The biggest advantage of thisreduced dimensionality is that they can be efficiently applied over extensive spatialdomains, for example, a large portion of channel network. However, these models14have also several limitations. Perhaps the most important of them from the ecolog-ical point of view is their inability to represent channel-transverse variation in theflow field, which is critical for fish habitat (Crowder and Diplas, 2000a,b, 2006).In contrast, the most complete representation of flow fields in natural channels canbe obtained using 3D models. One of the main advantages of these models is thatthey can fully capture complex flow patterns in all dimensions and may yield betterpredictions of bed shear stress (e.g. Lane et al., 1999). However, at the same timethese codes are computationally demanding and research suggests that measuresof their performance frequently fall within the same range of values as those citedfor models with reduced dimensionality (e.g. Clifford et al., 2009). In addition,the ability of 3D hydrodynamic models to accurately reproduce the vertical struc-ture of flow field in coarse bed channels is limited by the quality of bathymetricdata unless additional, empirically-based formulations are incorporated (Olsen andStokseth, 1995; Carney et al., 2006). Overall, by comparison, these models areapplied relatively infrequently in hydrogeomorphic and ecological research (butsee: Booker et al., 2004; MacWilliams et al., 2006) . A balanced compromise be-tween the two end members is provided by 2D models which, consequently, havegarnered popularity across all branches of river science. Importantly, these mod-els can be applied as quasi-3D models if an assumption is made that vertical flowstructure can be approximated by a theoretical semi-logarithmic velocity profilethat resembles a simple boundary layer (Lane and Ferguson, 2005).The importance of flow field properties predicted through hydrodynamic mod-elling for elucidating hydrogeomorphic dynamics and fish habitat warrants a care-ful scrutiny of uncertainties embedded within this method. Such uncertainties mayarise from errors due to inadequate process representation or poor parameteriza-tion. In 2D models, the former types of errors, for example, may be related toturbulence closure or the assumption of hydrostatic pressure distribution (e.g. Laneand Ferguson, 2005). In practice, given the complex nature of coarse-bed channels,local errors due to violation of assumptions that underlie process representation areinevitable. Several comprehensive reviews detail these assumptions, the range ofconditions under which they hold, as well as the consequences of their violationfor predicted flow field (e.g. Lane, 1998; Bates et al., 2005; Pasternack, 2011; Ton-ina and Jorde, 2013). Perhaps even more complex is the problem of parameter15uncertainty. Bed roughness, in particular, is a parameter of great importance be-cause it strongly influences predicted values of the key variables of interest, thatis, shear stress and velocity (Lane and Ferguson, 2005). The roughness parameteris an integral part of formula used to calculate bed stresses, a term introduced togoverning equations due to depth averaging (e.g. Lane, 1998). In terms of its phys-ical meaning, it represents flow momentum loss due to effects of grains, bedforms,and the turbulence they generate (e.g. Tonina and Jorde, 2013). More specifically,it represents ‘residual’ roughness of the surface that is not explicitly captured inthe bathymetry, as mapped onto the computational grid (e.g. Lane, 2005; Lane andFerguson, 2005). As a result, the parameter value for the same surface will vary de-pending on the resolution of topographic survey and computational grid (Nicholas,2001, 2005; Lane, 2005).In practice, the most widespread method for specifying the roughness param-eter is to calibrate the model by minimizing differences between the simulatedand modelled values of a selected hydraulic variable, usually water surface eleva-tion or flow depth (Tonina and Jorde, 2013). This optimization procedure, how-ever, carries a risk of equifinality. Given several model parameters that can beadjusted, multiple combinations of parameters may provide a similarly acceptablesolution (Beven, 2006). Another common approach is to specify bed roughness asa multiple of sediment grain size diameter, based on one of the empirically-derivedrelations (e.g. Hey, 1979; Whiting and Dietrich, 1990; Wiberg and Smith, 1991;Clifford et al., 1992). However, the range of proposed coefficients ranges widely,in most cases between 3 to 4 times D84 (D84 denotes 84th percentile of bed sedi-ment size distribution; Whiting and Dietrich, 1990; Clifford et al., 1992; Ferguson,2007). In addition, the aforementioned scale-dependence poses a challenge fortransferring these equations to hydrodynamic models. An interesting alternativeapproach to this problem involves specyfication of roughness parameter based onfield measurements, for example, by using vertical velocity profiles (Hodskinson,1996). Importantly, vertical flow structure varies within the channel whereas thebed roughness parameter should be representative of the entire modelling domain.Therefore, it appears that the parameter should be based on a spatially averagedvelocity profile. However, as with any statistical estimate, a parameter estimatedusing this method is of course subject to sampling error. Thus, if such method is to16be applied questions regarding the magnitude of sampling error, it dependence onsample size, and effects on hydrodynamic model performance certainly deserve tobe addressed.1.3.5 SummaryThere is a considerable research interest in the effects of heterogeneous physicalenvironments on spatial patterns of habitat for living organisms. Understandingsuch linkages is particularly important in the context of changing climate and in-creased land use pressures. Because of the strong influences that hydrogeomorphicconditions have on lotic organisms, small salmonids and the mountain streams theyinhabit constitute an interesting model system to study this important issue. Theforegoing review of the relevant literature points to four major conclusions:(1) Complementary habitat types should be studied in order to achieve morecomplete understanding of the relationship between hydrogeomorphic processesand fish habitat(2) Spatially explicit investigations into spatial patterns of habitat for small-bodied salmonids should ideally be carried out at a sub-meter resolution and overspatial extents equivalent to several reaches. Thus, for practical reasons, habitatmodelling is an optimal tool to pursue such study.(3) To date, most of the research into this topic has been conducted using nonprocess-based, empirical models. Therefore, process-based studies, which enabledrawing conclusions about fish performance, fitness, or population dynamics areneeded. In addition, more mechanistic models provide a better functional under-standing of the nature of the fish-habitat relationship.(4) Hydraulic models play an important role in such approaches to studyinghydrogeomorphic controls on habitat but more research is needed to evaluate un-certainty in model parameters such as bed roughness. For example, the issue ofsampling error in spatially averaged estimates of this parameter is an interestingsubject for study.171.4 Thesis objectivesThe primary objective of this thesis is to examine how hydrogeomorphic conditionsacross different scales govern spatial patterns of habitat for small-bodied salmonidsin mountain streams. To achieve this goal, I adopted an approach identified in Sec-tion 1.3.5. Specifically, I linked data collected through extensive field surveys witha spatially explicit habitat modelling framework, conducted at a high resolutionand extending over several reaches. I focused on two complementary types of fishhabitat, used for spawning and foraging. I strove to employ process-based habitatmodels in order to generate hypotheses regarding potential implications of our find-ings for ecological processes. Moreover, I chose models which have at least sometheoretical basis and, consequently, potential to advance current understanding ofthe mechanisms involved in the biophysical interactions between hydrogeomorphichabitat and fish.It is worth underscoring that my primary intention was to generate a represen-tation of the ‘riverscape’ (Fausch et al., 2002) as it is likely perceived and expe-rienced by fish and to examine its spatial organization. Although I use the resultsin conjunction with abundant published research on salmonid ecology to specu-late regarding the influences that the modelled patterns might potentially have onanimal behaviour and performance or on population dynamics I do not model orclaim to predict the actual biotic response. However, the process-based nature ofour models enables future work in that direction.The secondary objective of this research was to assess the relationship betweensample size and error in the estimate of spatially averaged bed roughness parameteras well as their implications for the hydraulic variables relevant for fish habitat andderived from a hydrodynamic model. In addition, I took advantage of the availabledata and extended the error analysis to fitted frequency distributions. The latterapproach has the potential to be employed in the future as a way of representingsub-grid heterogeneity within spatially explicit habitat models applied at a broadgeographical scale.18Chapter 2Influence of Bed Surface Texture,Bed Mobility, and ChannelHydraulics on Availability andDisturbance of PotentialSpawning Substrate2.1 IntroductionTexture and mobility of the sediment which makes up alluvial channel bound-ary play a critical role in successful reproduction of salmonid fish (salmon, trout,charr), by defining spawning substrate availability and disturbance. Spawning sub-strate availability may be limited if bed surface material is too coarse to be dis-placed by fish, which prevents them from excavating nests (Kondolf and Wolman,1993). However, even if spawning substrate is available, enabling constructionof a nest (‘redd’), the incubating embryos and freshly hatched juveniles (called‘alevins’) may be at risk of disturbance associated with deposition of fine sedimentand reworking of the bed during floods (e.g. Tripp and Poulin, 1986). Accumula-tion of excess fine sediment within gravel interstices and on the bed surface may19reduce oxygen supply, inhibit removal of their metabolic waste, and entomb alevins(e.g. Sear et al., 2008). Mobilization of bed material, on the other hand, can exposeand destroy eggs and alevins if the bed is scoured below the depth at which theyare buried (e.g. DeVries, 2008).Availability of spawning substrate and risk of scour disturbance also depend onfish body size, which imposes some important biomechanical limitations. Specif-ically, large fish are stronger than small ones and, therefore, can excavate nests incoarser sediment (Kondolf and Wolman, 1993) and bury their eggs deeper underthe bed surface (Steen and Quinn, 1999). These size-dependent limitations may beparticularly important for small-bodied salmonids (body length <35 cm, follow-ing: Schuett-Hames et al., 1996), such as resident Cutthroat Trout, because theyfrequently spawn in small mountain streams (Trotter, 1989), in which bed materialtends to be coarse (e.g. Hassan et al., 2005). Consequently, it appears that small-bodied salmonids inhabiting coarse mountain streams may be facing a particularlydifficult challenge in finding suitable substrate and burying their eggs below thedepth of bed scour (e.g. Goode et al., 2013). Moreover, a large portion of smallstream spawning habitat preferred by these fish, has been lost or degraded due tovarious types of land use that alter flows and sediment supply to channel network(e.g. Costello, 2008; Scheurer et al., 2009). Recent research suggests that theseenvironmental pressures may be further exacerbated by ongoing climate change(Scheurer et al., 2009; Wenger et al., 2011; Goode et al., 2013). Therefore, soundunderstanding of the effects that geomorphic controls, such as bed texture and mo-bility, may have on spawning habitat in mountain streams is vital for sustainablemanagement, conservation, and restoration of associated salmonid populations.Despite a significant progress in the understanding of channel processes inmountain streams (e.g. Hassan et al., 2005, 2007) and impacts of sediment dy-namics on spawning habitat (recent reviews in DeVries, 2008; Sear et al., 2008;Kemp et al., 2011), further research into this topic is certainly needed (e.g. New-son et al., 2012). One aspect of salmonid spawning habitat in mountain streamsthat requires more attention is the consequence of spatial heterogeneity in bed tex-ture and mobility. Which areas within the channel provide potential spawninggravels? Which areas are at risk of disturbance from scour and fine sediment de-position? Do these areas overlap and if so, how much overlap is there? Answers to20these questions are critical, because only undisturbed substrate provides conditionsconducive to successful reproduction. Furthermore, bed scour and fine sedimentaccumulation are only relevant for fish spawning if they affect patches of poten-tially usable substrate. However, investigations focusing on spatial heterogeneityof spawning substrate availability and disturbance are greatly complicated by therange of ecologically relevant scales (e.g. Beechie et al., 2008). On one hand, it isnecessary to represent the broad-scale variation in bed texture and mobility, associ-ated with various channel morphologies (e.g. Montgomery et al., 1999; Buffingtonet al., 2004) that are found within the area defined by fish mobility (Fausch et al.,2002). On the other hand, fish select their spawning locations based on a fine-scalemosaic of habitat patches (‘microhabitat’; e.g. Knapp and Vredenburg, 1996)).In this paper we aimed to advance current understanding of spatial linkages be-tween channel dynamics and the availability and disturbance of spawning substratefor small-bodied salmonids, both at within and between-reach scales. To achievethis we mapped bed texture patches as well as net scour and fill in four reaches, atsub-meter resolution, and linked them with flow fields obtained from a hydrody-namic model. The maps of bed texture and scour were then combined with bodysize-specific criteria for spawning gravel and estimates of egg burial depth. It isworth clarifying at the outset that in this paper we focus exclusively on bed tex-ture and mobility, a small subset of factors that define fish spawning habitat (otherones being water temperature and quality, hyporheic flow, and presence of cover,to name just a few; Bjornn and Reiser, 1991). This scope of interest is reflectedin our terminology, as we chose to use ‘potential spawning substrate’ rather than‘spawning habitat’.2.2 Methods2.2.1 Field siteOur research was conducted in four reaches of East Creek, a small mountain stream(elevation about 150 m.a.s.l.) draining a watershed in the foothills of Coast Moun-tains, 50 km east of Vancouver, British Columbia (Figure 2.1). The study reaches,inhabited by spring-spawning, resident Coastal Cutthroat Trout (Oncorhynchus21Table 2.1: Characteristics of the study reaches in East Creek. <>indicatesreach-average values.Reach Length (m) Width (m) Slope (m m-1) D50 (mm) D84 (mm)Rapid 72 2.3 0.020 55 105Pool-Riffle-1 97 2.5 0.018 49 88Pool-Riffle-2 147 3.0 0.014 40 74Pool-Riffle-3 90 2.7 0.011 30 54clarki clarki), are well-suited for a comparative study because they form a down-stream sequence of changing channel morphologies yet have the same climate,flow regime (there are no tributaries along the entire study domain), underlyinggeology, riparian vegetation, and wood loading.Channel morphologies found within the section under study include one plane-bed and three pool-riffle reaches (Montgomery and Buffington, 1997). The reacheswere named ‘Rapid’ (following Hassan et al., 2005) and ‘Pool-Riffle-1’ to ‘Pool-Riffle-3’, respectively. The transition between the reaches is accompanied by pro-gressively finer bed texture and better developed bed topography, as channel gradi-ent declines from 0.02 in Rapid to 0.01 in Pool-Riffle-3 (Table 2.1). Drainage areais approximately 1 km2 and increases only by about 6% between Rapid and Pool-Riffle-3 due to proximity of all the reaches and elongated shape of the watershed.The study area experiences a maritime climate with warm, dry summers andmild, wet winters. More than 70% of the annual precipitation, which amounts toabout 2200 mm, occurs between October and April. Precipitation falls almost en-tirely as rain, primarily during long-duration frontal storms. Shallow and highlypermeable soils, underlain by compacted glacial till and bedrock (Hutchinson andMoore, 2000), result in a responsive storm hydrograph observed in the creek. Thearea was clear-cut to the stream bank in the 1970’s and large wood (hereafter re-ferred to as LW) was removed from the channel (Young et al., 1999). Most of thelarge wood currently found in East Creek was placed in the 1980’s, as a part ofrestoration effort (Young et al., 1999) and recruitment from stream banks seems tobe limited. The majority of this in-stream wood represents isolated root wads andrelatively small logs projecting from the banks, and there are no major LW dams22British ColumbiaMKRFFraser RiverVancouver, BCKm(study area)RAPPR-3 PR-2PR-1East CreekPool-Riffle-2Pool-Riffle-3RapidPool-Riffle-1180160170150165155145155130215180140150Figure 2.1: Map of the study area: stars on the main map mark the bound-aries of the study reaches (RAP, PR1, PR2 and PR3). Inset map showsthe location of Malcolm Knapp Research Forest (MKRF) in the South-western British Columbia. Numbers on the main map represent eleva-tion values of contour lines (m.a.s.l.)23blocking the channel. Overall, because of the combination of sparse spacing andsmall calibre, wood in our study site occupies a fraction of the total bed area (about1%) and, therefore, has only localized influence on channel processes. In this re-spect, the stream is certainly different in character from many wood-rich channelsthat drain old growth forest in the Pacific Northwest.2.2.2 Field surveysBetween spring 2009 and summer 2011 we carried out detailed field surveys ofchannel topography and bed texture. In addition, to support development of thehydrodynamic model, we conducted several hydraulic measurements during twoflow events in 2011. Below we outline details of the employed field methodology.Channel topography in the study reaches was surveyed annually (spring 2009,2010, 2011) using a total station. Because the mean point spacing was about 0.3-0.4 m (point density 10 m-2) we were not able to capture microtopographic featuresobserved in East Creek, such as individual boulders or pebble clusters.Bed texture throughout all study reaches was mapped in spring 2011 in a two-step procedure. In the first step, we identified relatively homogenous texturalpatches and classified them according to dominant sediment size classes (Buffing-ton and Montgomery, 1999b). To enable delineation of patch boundaries we con-ducted a ground-based survey and collected low-level vertical photographs (pole-mounted camera suspended about 9 m above ground), covering the entire studyarea. We made every effort to identify and map any discernible patch equal to orlarger than the typical area of resident Cutthroat Trout redds (0.1 m2; Bjornn andReiser, 1991). In the second step, we estimated bed texture for each type of tex-tural patches using a combination of two methods. First, grain size distribution inpatches containing mostly material <8 mm was sampled using the Wolman gridmethod (Wolman, 1954), with sample size n >100 and lower-tail truncation ap-plied at 8 mm. This enabled us to calculate D50, and D84, (respectively 50th and84th percentiles of bed material grain size distribution; hereafter, Di indicates ithpercentile of grain size distribution). Second, patches where most sediment was<8 mm were assigned D50 based exclusively on the textural classification (Buffin-gton and Montgomery, 1999b). Estimating the percentage of material within each24of the size classes enabled us to identify the size class for which more than 50% oftotal bed surface material within the patch was finer. The central value of the rangeof grain diameters corresponding to that size class was adopted as D50.Hydraulic measurements in the study reaches were collected during two flowevents in 2011 using an electromagnetic current meter. The measurements includeddischarge (velocity-area method), mean velocities and flow depths at a number ofpoints within the channel, water surface elevation at the downstream end of thereaches, and a sample of velocity profiles. One of the flow events was approxi-mately bankfull (Qb f = 0.7 m3s-1) while the other one represented a nearly twicelower discharge (Q = 0.37 m3s-1). We were primarily interested in the bankfullevent for two reasons. First, based on available hydrological data, such dischargeseems to be a reasonable approximation of the maximum floods that may occurin East Creek during the spring spawning and incubation season. Second, bank-full flow is typically associated with mobilization of coarse bed material (e.g. An-drews, 1983); therefore, we deemed it to be well-suited for analysis of hydraulicforces that control bed mobility and textural sorting. However, because we wereable to collect only a limited number of velocity and depth measurements thatwere intended for evaluation of hydrodynamic model evaluation, we decided toadditionally test it using a larger data set, collected at a lower discharge.2.2.3 GIS analysesThe topographic and textural data collected in the field were subsequently pro-cessed in ArcGIS to delineate textural patches and map net scour-fill patterns, re-spectively.In each of the study reaches we delineated the boundaries of textural patchesusing a combination of ground survey maps and georeferenced composites of ver-tical photographs. Values of D50 and D84 were allocated to each patch based on thefield data and the resulting texture map was converted to raster format.To map the spatial pattern and magnitude of net changes in bed topography(net scour and fill) that occurred in response to the bankfull flow, we subtractedpairs of digital elevation models (DEM) based on successive topographic surveys.Development of such map of residuals, termed DEM of difference (DoD), involved25three steps. First, bed elevation values in between the topographic survey pointswere interpolated using Triangulated Irregular Network (TIN) algorithm. Second,the TIN models were converted to raster-format DEMs and occasional artefactsof conversion (single-cell pits and spikes) were removed by setting the value ofthe affected cells to the mean of the neighbouring cells. Third, the DEMs weredifferenced and the minimum value of the actual elevation change, which can bedetected given DEM uncertainty, was estimated by calculating Level of Detection(LoD):LoD = t√σ2s1 +σ2i1 +σ2s2 +σ2i2 (2.1)where t is a critical t-value for selected confidence level, here t = 1; (Laneet al., 2003)), and σs and σi are – respectively – standard deviations of survey andinterpolation error samples associated with both layers being subtracted (denotedby subscripts 1,2). The interpolation errors were obtained by subtracting elevationsat a subset of locations in DEM surfaces that were developed with these data pointsand without them. Survey errors were estimated by repeated measurements of thesame points.We assumed that spatial variation in uncertainty within each DEM layer canbe ignored (similar approach to Brasington et al., 2003). Steep and locally over-hanging banks, typically associated with substantially higher DEM errors, wereexcluded from this analysis as they have no direct significance as potential spawn-ing grounds. Moreover, bed topography was generally well-represented throughoutthe study reaches owing to the high density survey (about 10 points m-2). No de-tectable year-to-year differences in the magnitude of uncertainty were identified inour preliminary analyses; therefore, measurement error was also assumed constantover time. As a result, Equation 2.1 simplified to:LoD = t√2σ2s +2σ2i (2.2)Although the main focus of this study was on the morphological changes be-tween the 2010 and 2011 surveys (because of temporal correspondence to our tex-tural and hydraulic data), we also analyzed net changes that occurred between 2009and 2010. First, prior changes in storage provide a useful indication of local sedi-26ment supply that can help us understand morphodynamic processes. Second, thesedata enabled us to evaluate year-to-year variability in the observed spatial patternsof net scour.As a final stage of our analyses, in order to enable between-reach comparison,local values of D50, D84, and other variables were spatially averaged using theformula:< x >= ∑xiN(2.3)where <>indicates spatial average, xi is local value of the variable of interestin the raster cell, and N is the total number of cells in the raster.2.2.4 Hydrodynamic modelWe complemented our study with hydraulic modelling, hoping to obtain a morecomplete understanding of the mechanisms that control the spatial patterns of bedtexture and mobility and, ultimately, define spawning substrate availability and dis-turbance risk. To this end, we applied FaSTMECH, a 2-dimensional hydrodynamicmodel integrated with MD WSMS interface (Nelson et al., 2003; McDonald et al.,2005). FaSTMECH solves vertically and Reynolds-averaged Navier-Stokes equa-tions cast in a channel-fitted curvilinear coordinate system (e.g. Nelson and Smith,1989) and its inputs include bed topography (represented in a computational mesh),bed roughness parameter, discharge and downstream water surface elevation, andlateral eddy viscosity (LEV). Model outputs include velocity, depth, water surfaceelevation, and shear stress values at each cell of the computational mesh. Belowwe discuss in more depth these inputs, as well as the outputs relevant for this study.Bed topography was interpolated onto the computational grid by applying theTIN algorithm to the total station survey data, including the points representingbed, banks, and large wood. Survey points corresponding to overhanging bankswere modified to represent the banks as near-vertical. In addition, points along thebank and LW perimeters were densified to ensure preservation of their complexshapes. To minimize numerical diffusion at a reasonable computational cost, theadequate cell size for the computational mesh was estimated using Peclet number(e.g. Papanicolaou et al., 2010) as 0.1 m by 0.1 m.27The bed roughness parameter in FaSTMECH (drag coefficient, Cd) is a func-tion of flow depth (d) and roughness height (z0), and was estimated for the studyreaches in a three-step procedure. In the first step, the mean z0 value was calculatedfrom the slope and intercept of a linear regression fitted to a spatially averaged ver-tical velocity profile (Bergeron and Abrahams, 1992). Due to the relatively shallowflows and the size of ECM sensor, the regression included measurements through-out the depth, with few observations close to the bed. We then estimated a mul-tiplier, a = z0/D84 (e.g. Whiting and Dietrich, 1990), which enabled us to relatez0 in any location within the study reaches to the corresponding D84 as z0 = aD84.Because the measurements were carried out in straight channel sections withoutany major bedforms, we believe that the calculated z0 and multiplier a values re-flected primarily hydraulic roughness associated with bed microtopography e.g.small-scale sedimentary structures and large roughness elements (e.g. Lawless andRobert, 2001). Such microtopographic features constitute the primary source offlow resistance in coarse-bedded (e.g. Buffin-Belanger and Roy, 1998). There-fore, we deemed this approach to be well-suited for estimating the bed roughnessparameter because its value should approximate the part of hydraulic roughnesswhich was exerted by features not represented explicitly in our topographic modelinput. In the second step, a spatially uniform Cd value was calculated using thereach-average values of depth, < d >, and roughness height (< z0 >= a < D84 >).This uniform parameter was then used in preliminary model runs to obtain initialvalues of local depth (e.g. Harrison et al., 2011). In the third and final step, a spa-tially variable drag coefficient was calculated as a function of these simulated localdepths and local roughness height values, which were estimated from local bed ma-terial grain size, as: z0 = aD84. In contrast to the bed, roughness values for banksand large wood were calculated simply by converting an estimated Manning’s ninto the z0 value.For each of the study reaches we conducted two simulations correspondingto the flow events for which input data was available (Qb f = 0.7 m3s-1 and Q= 0.37 m3s-1). Model performance was evaluated by comparing modelled andobserved velocities and depths at various locations throughout the study reaches(0.4 d above the bed). In all cases we used the field measured water surfaceelevations at the downstream boundary and lateral eddy viscosity calculated as:28LEV = 0.01 < u >< d >, where < u > is reach-mean velocity (Nelson and Mc-Donald, 1996). In all reaches the obtained LEV values for Qb f event were equal toapproximately 0.003 m2s-1.The modelled flow output was used to analyze flow routing and hydraulicforces in the study reaches. Hydraulic forces were represented by the ‘grain’ com-ponent of bed shear stress, τ ′0, which corresponds to the force exerted on sedi-ment particles and is responsible for sediment entrainment. This measure shouldexclude the effects of microtopographic features, which extract fluid momentumand substantially reduces forces available to mobilize sediment particles (Hassanand Reid, 1990; Wiberg and Smith, 1991). Combining Millar’s (1999) estimateof grain roughness length, k′s = D50, and Smart’s (1999) relation z0 = ks/33, wefirst obtained grain roughness height as: z′0 = D50/33. Grain roughness height wasthen used to calculate grain shear velocity (u′∗), by rearranging Smart’s (1999) flowresistance equation, and, ultimately, to obtain grain shear stress:τ ′0 = ρu′2∗ = ρu1κ[(d+z′0d)ln(d+z′0z′0)−1]2(2.4)where κ is von Karman constant (κ = 0.4), u is modelled velocity, d is modelleddepth, and z′0 is the grain roughness height (z′0 = D50/33).Using this value of τ ′0, we also calculated Shield stress, a measure of flow forcerelative to the submerged weight of bed surface material:θD50 =τ ′0(ρs−ρ)gD50(2.5)where ρs is density of sediment, ρ is density of water, and g is gravitationalacceleration.2.2.5 Spawning substrateTo identify all patches potentially available for spawning (redd construction) weapplied a two-step procedure. In the first step, the maximum median grain size ofbed material that fish of a given size can displace to excavate a nest was establishedusing an envelope curve in the relation suggested by Kondolf and Wolman (1993).29Based on prior research on Cutthroat Trout population in East Creek (Young et al.,1999; De Groot et al., 2007) we adopted 20 cm as an upper-bound body size es-timate for a 3-year-old spawning female. Using this approach, we estimated thatthe maximum D50 of sediment that fish of this size can move in order to buildtheir nest is equal to about 30 mm. We denote this critical grain size value asDmax. In the second step, we identified the patches containing potential spawningsubstrate by applying the criterion D50 ≤ Dmax to the textural maps (Section 2.2.2-Section 2.2.3).In this procedure we did not adopt any lower threshold for spawning gravelavailability. Although evidence exists that fish may display behavioural avoidanceof fine substrate (e.g. Kemp et al., 2011), redds of small-bodied trout have beenobserved in sediment significantly finer than that usually perceived as suitable (e.g.as much as 70% of material <6.3 mm; Knapp and Vredenburg, 1996). Giventhis difficulty in establishing any specific threshold of bed texture that would deterfish from excavating a nest, we chose to treat presence of a large quantity of finesediment in potential spawning gravel only as a factor influencing disturbance risk(see below).We believe that the adopted approach (also applied by Buffington et al., 2004)is well-suited to achieve our objective, which was to identify all bed areas thatcan be potentially used by fish to excavate nests. Other common methods usedin spawning habitat studies include mapping actual spawning sites (May et al.,2009) or using habitat suitability curves (Harrison et al., 2011). However, these ap-proaches provide different types of information (respectively: where fish spawnedand where fish tend to spawn, given available conditions) and do not necessarilyreflect the true limits for where redds can potentially be excavated.To examine disturbance risk associated with fine sediment accumulation inspawning gravels we applied a simple, two-step procedure, analogous to that de-scribed above. In the first step, we established a threshold value for fine sedimentcontent, above which survival of incubating embryos and emergence of alevinsare likely to be significantly reduced. The adopted threshold value for ‘excess’ finesediment was based on species-specific data (Bjornn and Reiser, 1991), which sug-gested that at about 45-50% of material <6.3 mm present in the bed Cutthroat Troutembryo survival approaches 0%. For simplicity, we adopted the closest half-phi in-30terval of the Wentworth scale and assumed that fine sediment disturbance risk forCutthroat embryos was substantial if 50% of sediment was smaller than 5.7 mm.Consequently, patches in which D50 < 5.7 mm were classified as being at highrisk of disturbance due to fine sediment accumulation. Hereafter, this thresholdD50 value is referred to as Dcrit . The second step involved using the textural maps(Section 2.2.2) to identify patches where the above criterion was met. Although therisk of alevin entombment appears to depend not only on texture but also, to somedegree, thickness of the sediment layer accumulated on the bed surface (e.g. Crisp,1993), we are not aware of any data that would allow us to establish any specific,ecologically relevant threshold of burial depth. Consequently, because alevins areknown to move readily within coarse sediment (Dill and Northcote, 1970), we donot consider net fill alone to pose disturbance risk. Instead, we focus exclusivelyon the presence of fine sediment.Finally, the risk of disturbance due to bed scour was evaluated by comparingthe estimated depth at which 20 cm-long Cutthroat Trout would typically burytheir eggs with the measured net changes in bed elevation. A similar approachwas previously applied in other studies (e.g. Lapointe et al., 2000). First, using therelation of Steen and Quinn (1999), we estimated the mean depth of egg burial tobe about 0.08 m for 20 cm-long trout. However, there is some uncertainty involvedin using the mean value, especially given that past research showed that bed scourdepths often display an exponential distribution (DeVries, 2008). Specifically, theestimate of scour disturbance risk may be sensitive to the adopted critical value ofdepth, which we denote as dcrit . In order to constrain this uncertainty, we conductedthe analysis using two alternative values of mean egg burial depths: dcrit = 0.05m and dcrit = 0.08 m. The value of 0.05 m was adopted because, based on arange of data sets collated by Steen and Quinn (1999), it appears to be a goodlower bound estimate of egg burial depths for salmonids of a similar body size totrout in East Creek. In the second step of the procedure, the locations where netscour (Section 2.2.3) exceeded egg burial depths were assumed to be at risk ofdisturbance.312.3 AnalysesWe begin this section by evaluating the performance of the hydrodynamic model.Then, we proceed to address the main goal of this paper, and discuss the effectsof bed texture and mobility on availability and disturbance of potential spawningsubstrate for small Cutthroat Trout. In doing this, we first describe the spatialpatterns observed within each reach and then summarize their consequences forbetween-reach differences. Finally, we close the section by highlighting the mostimportant limitations of the methods employed in this study.2.3.1 Hydrodynamic model evaluationComparison of simulated velocities and depths to those observed at the same lo-cations in the field showed relatively good agreement over the unobstructed bed(Figure 2.2 and Table 2.2; two outliers were removed because our observations in-dicated that they were affected by a measurement error). The plot of the low flowdata set in Figure 2.2 seems to imply that the largest discrepancies between themeasured and modelled values typically occurred in the immediate vicinity of LWbut it is necessary to keep in mind that these features cover only a small fraction ofthe total channel area (Section 2.2.1) and were heavily overrepresented in our sam-ple. Locally weaker agreement of 2D model predictions with the values measuredaround LW parallels findings from other studies (e.g. Pasternack et al., 2004) andis likely due to complex flow structure near such obstructions. Our qualitative as-sessment suggested that the model reproduced reasonably well the spatial patternsand essential features of the flow field, including those near the flow obstructionssuch as LW and bank projections (e.g. flow separation zones). Overall, given thecomplex nature of the study channels and the spatially restricted areas of uncer-tainty, we deemed the accuracy of model results to be acceptable for the purposeof this study.2.3.2 Potential spawning substrate availability and disturbanceTextural sorting observed in the study reaches resulted in two contrasting patternsof potential substrate for resident Cutthroat Trout spawners. In Rapid and Pool-Riffle-1 reaches, bed material that enabled nest excavation by a 20 cm fish (D50 <32Table 2.2: Flow evaluation measures. R2 is the coefficient of determination,b is the regression slope, and RMSE is root mean square error. The re-sults are shown for two flow events. The regression for Q = 0.37 m3s-1 did not include data points representing wood. One outlier point wasremoved from each of the two data sets because they were identified asmeasurement errors.Measures Q = 0.7 m3s-1 Q = 0.37m3s-1Regression velocity depth velocity depthR2 0.77 0.6 0.52 0.81b 0.9 1.08 0.71 0.99Errors velocity (ms−1) depth (m) velocity (ms−1) depth (m)RMSE 0.046 0.035 0.046 0.033Modelled velocity (ms−1 )Observed velocity (ms−1)  0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.600.20.40.60.811.21.41.6Modelled depth (m)Observed depth (m)0 0.1 0.2 0.3 0.4 0.500.10.20.30.40.5Q = 0.7 m3s−1Q = 0.37 m3s−1OLS Q = 0.7m3s−1OLS Q = 0.37 m3s−1LW1:1 lineFigure 2.2: Hydrodynamic model evaluation: (a) velocity; (b) depth. Theregression for Q = 0.37 m3s-1 did not include data points representingwood. One outlier points was removed from each of the two data setsbecause they were identified as measurement errors.3330 mm) was limited to small patches located near flow obstructions, such as LWand bank projections (Figure 2.3 a and b). These distinct deposits of potentialsubstrate were appreciably finer than the rest of the bed surface and comprised finegravel, sand, and silt mixtures. Comparison with the modelled flow field suggestedthat locations of these patches corresponded to conspicuous zones of extremelylow shear stress within the wakes and lateral separation eddies associated with theflow obstructions (Figure 2.4 a and b). Consequently, hereafter we refer to suchlow shear stress areas as ‘hydraulically sheltered’ (e.g. Montgomery et al., 1999;Shellberg et al., 2010) and to the associated distinct patches as ‘wake deposits’or ‘eddy deposits.’ Although we cannot directly demonstrate it, prior researchindicates that, in addition to low hydraulic forces, accumulation of such depositsis promoted by highly efficient entrapment of sediment (Schmidt, 1990), advectedtowards the separation eddy by near-bed flow structure (Nelson and McDonald,1996). In general, a pattern similar to that described above was mapped in theproximal part of Pool-Riffle-2, except in this reach we also found small patches ofpotential spawning substrate on two point bars.In contrast to the coarser portion of the study area, in Pool-Riffle-3 and the dis-tal part of Pool-Riffle-2 even the unobstructed portion of the bed contained abun-dant spawning-calibre gravel (Figure 2.3 c and d). In fact, in the former reach,patches identified as potential substrate covered most of the bed area, with the ex-ception of coarse pools. Hydrodynamic model results indicated that, in this case,the widespread presence of extensive gravelly patches that fulfilled the criterionD50 < 30 mm was a consequence of generally lower shear stress in comparisonwith Rapid and Pool-Riffle-1 (see Figure 2.4). The relatively coarser patches foundin pools were usually associated with flow convergence forced by channel curva-ture, gradual channel width reductions, and abrupt width constrictions due to flowobstructions. As expected, our results implied that the progressive downstreamfining (Table 2.1, Figure 2.5a) resulted in an increasing between-reach trend inpotential substrate availability from Rapid to Pool-Riffle-3 (Figure 2.5b). Closerinspection suggests, however, that this increase occurred in a rather abrupt man-ner. Despite bed fining, there was no substantial change in substrate availabilityfrom Rapid to Pool-Riffle-1 (3.8% and 2.2% of total bed area, respectively). Onthe other hand, in response to moderate changes in < D50 > (Table 2.1), poten-34Potential substrate-coarse 5.7 mm < D50 < 30 mm Potential substrate-excess fine sediment, D50 < 5.7 mm Too coarse to spawn D50 > 30 mm Large Wood Figure 2.3: Bed topography and textural patches in subsections of the studyreaches: (a) Rapid; (b) Pool-Riffle-1; (c) Pool-Riffle-2; (d) Pool-Riffle-3. Boundaries of potential spawning substrate patches (D50 < 30 mm)are shown as bold outlines (red and blue). Blue-colour outlines repre-sent substrate patches where 30 mm > D50 > 5.7 mm while red-colouroutlines indicate those where D50 < 5.7 mm (substrate at high risk offine sediment disturbance).tial substrate increased to 20.5% and over 60% of total bed area in Pool-Riffle-2and Pool-Riffle-3, respectively (Figure 2.5b). This step-like and disproportionatechange was a simple consequence of the almost monotextural nature of the bedwithin each of the study reaches. Although we identified 11-20 patches and 4-8patch types per reach, as much as 80% of the bed area was covered by patches rep-resenting only two types, with a very narrow range of D50 values (Figure 2.5a). Asa result of general bed fining, most of the bed area in the study reaches was eitherbelow or above the threshold sediment calibre defined by fish body size (Dmax =30 mm). Until this threshold was crossed by the dominant textural patches, theavailability of potential spawning substrate in Pool-Riffle-1 and Pool-Riffle-2 was35Potential substrate D50 < 30 mm Large Wood Figure 2.4: Modelled grain shear stress distribution in selected sub-sectionsof four study reaches: (a) Rapid; (b) Pool-Riffle-1; (c) Pool-Riffle-2;(d) Pool-Riffle-3. The locations of potential spawning substrate are alsoshown for reference (bold outlines). Modelled Shields stress showedvery similar spatial pattern, except higher values within the fine-grainedpatches.defined largely by the total extent of hydraulically sheltered areas.Such contrasting patterns of sorting and potential substrate availability in dif-ferent study reaches had significant consequences for the estimated risk of finesediment disturbance. The within-reach analyses presented above (Figure 2.3) im-ply that in all the study reaches sediment patches much finer than most of the bedaccumulated only in the hydraulically sheltered areas and some bars. Importantly,substantial portions of the wake and eddy deposits assessed to be sufficiently fineto enable redd excavation (D50 < 30 mm) were also below the threshold assumedto cause high disturbance risk to incubating Cutthroat Trout (D50 < 5.7 mm; seeFigure 2.3 and Figure 2.5b). These results indicated that the extremely low shearstress within the hydraulically sheltered zones not only promoted deposition of360 20 40 60 80 1000102030405060708090100% Total bed area finerMedian grain size, D 50  (mm)  RAP RP1 RP2 RP3100101102% Total bed / % Potential substrateReach  Preferential disturbance risk indexReachRAP RP1 RP2 RP305101520253035404550RAPRP1RP2RP3SubstrateFine sedimentDisturbance riskFigure 2.5: Summary of textural characteristics of the study reaches: (a) cu-mulative distribution of the total bed area (expressed in percent) oc-cupied by patches with D50 finer than a specific value; (b) bar chartshowing: the percent of total bed area classified as potential substrate,D50 < 30 mm (blue); percent of total bed area classified as fine sed-iment, D50 < 5.7 mm (yellow); and the percent of potential substrateidentified as being at risk of fine sediment accumulation (red); (c) Pref-erential disturbance risk index (percent potential substrate where D50 <5.7 mm standardized by the percent of total bed area where D50 < 5.7mm); values indicate how much more likely substrate disturbance is rel-ative to the reach-average conditions.spawning-calibre gravel (e.g. Buffington and Montgomery, 1999a) but also enabledsettling of large quantities of fine sand and silt fractions. Even though we observedsome evidence for spatial sorting into coarser reattachment and finer separationdeposits, as described by Schmidt (1990) for lateral separation eddies, that rarelyled to formation of potential substrate patches coarser than 5.7 mm. As a result,in Rapid, Pool-Riffle-1, and much of Pool-Riffle-2 reaches, where these locationsconstituted the only areas available for nest construction, there was a substantialspatial overlap between the patches classified as potential spawning substrate andthose estimated to experience high rates fine sediment accumulation (79% in Rapidand 100% in Riffle-Pool-1; Figure 2.5b). Spatial correlation between the patchesclassified as potential substrate and the areas at high disturbance risk implies that,in comparison to the reach average, a disproportionately high percentage of po-tential spawning substrate areas in this portion of study area tends to be at risk ofdisturbance (Figure 2.5c).On the other hand, in Pool-Riffle-3 and the distal part of Pool-Riffle-2, high risk37Potential substrate D50 < 30 mm Large Wood Figure 2.6: Spatial pattern of net scour (red) and fill (blue); values belowLoD are shown in white: (a) Rapid; (b) Pool-Riffle-1; (c) Pool- Riffle-2,2010-2011; (c’) Pool- Riffle-2 2009-2010; (d) Pool- Riffle-3. Locationsof potential spawning substrate patches are shown for reference as boldoutlines.of fine sediment accumulation in the hydraulically sheltered sites affected only asmall proportion (4.8%-7.8%) of the area of patches identified as potential spawn-ing gravels (Figure 2.5b). This was a simple consequence of the fact that in thissection most of the potential substrate for small Cutthroat that was located in un-obstructed flow, where hydraulic forces were higher and effectively prevented de-velopment of distinct patches of fine material on bed surface (Figure 2.4 c andd).The above results and discussion illustrate that the proportion of potential spawn-ing substrate patches affected by fine sediment accumulation can be strongly de-fined not only by spatial extent of the fine deposits but also by their configurationin space relative to potential substrate. Even though the absolute spatial extent offine sediment was around or below 3% in all study reaches, clear between-reach380 0.1 0.2 0.3051015Net scour (m)Exceeded (%total bed) 2009−2010  0 0.1 0.2 0.3051015Net scour (m)Exceeded (%substrate) 2009−2010Preferential disturbance risk indexReach  RAP RP1 RP2 RP30123450 0.1 0.2 0.3051015Net scour (m)Exceeded (total bed) 2010−20110 0.1 0.2 0.3051015Net scour (m)Exceeded (%substrate) 2010−2011Preferential disturbance risk indexReachRAP RP1 RP2 RP30123450.05m0.08mRAPRP1RP2RP30.05m0.08mFigure 2.7: Summary of net scour in the study reaches: top row (a-c) are val-ues based on 2009-2010 differences; bottom row (d-f) represents 2010-2011 data; first column (a, d) shows the cumulative percent of total bedwhere net scour exceeded a given depth; second column (b, e) showsthe cumulative percent of potential substrate where net scour exceededgiven depth; third column preferential disturbance index (percent po-tential substrate where scour > dcrit standardized by the percent of totalbed where scour > dcrit); values > 1 (note the horizontal line) indicatethat substrate is disturbed preferentially relative to the reach-averageconditions.differences existed in the proportion of potential substrate that may be at risk fromthis disturbance agent (Figure 2.5b). Importantly, this finding implies that the studyarea could be divided into two distinct spatial domains, representing two different‘regimes’ of availability and disturbance of spawning substrate for 20 cm-long Cut-throat Trout. The low availability and high disturbance risk in the coarser reachessharply contrast with the high availability and low disturbance risk in the finer ones.Our results of DEM differencing suggested that in each of the two domainsdifferent morphodynamic processes may be important for defining scour distur-bance risk, depending on spatial patterns of potential spawning substrate. In Rapid39and Pool-Riffle-1, the overlap between the potential spawning areas and scour ex-ceeding egg burial depth was defined primarily by bed mobility forced by flowobstructions (Figure 2.6). In these coarse-bedded reaches, much of detectable netscour was concentrated around and downstream of the apices of flow obstacles,while the rest of the bed was relatively stable. In several cases the locations of netscour seemed to closely approximate the position of high modelled velocity in theconstriction as well as shear layer between this zone and the low-velocity area inthe associated recirculating eddy (Figure 2.4). Although the hydrodynamic modelapplied in this study could not represent it, prior research showed that both theseregions of the flow field also experience intense turbulence (e.g. Thompson andWohl, 2009). We hypothesize that, in addition to mean bed shear stress, eddiesshed off the shear layer may have an important influence on the net scour observedat the outer edges of potential substrate patches in the adjacent hydraulically shel-tered zones. Moreover, observations on the ground provided us with additionalinsight, suggesting that some areas of net scour within the wake and eddy de-posits were due to rearrangement of the associated LW pieces. This rearrangementexposed some previously sheltered patches in Rapid and Pool-Riffle-1 to high hy-draulic forces (e.g. LW in the distal part of Rapid; Figure 2.6). Therefore, the riskof scour disturbance within hydraulically sheltered patches in the study reachesvaried depending on the stability of the obstructions (similar to Shellberg et al.,2010).In Pool-Riffle-3 and the distal part of Pool-Riffle-2, where a substantial por-tion of potential substrate was in the unobstructed portion of the channels, generalbed scour became as relevant as that forced by flow obstructions. Comparison ofDEMs of difference from both years suggested that the spatial pattern of net scourwas strongly defined by local sediment supply (compare c and c’ in Figure 2.6). Upto 35% of net scour occurred in the areas that experienced net fill in the previousyear, which indicated preferential mobilization of recent deposits. This preferen-tial scour appeared to result from local increases in shear stress in areas wheredeposition raised the bed level. In fact, such a negative feedback mechanism wasobserved to drive morphological channel adjustments in response to both positiveand negative changes in local sediment storage in all the study reaches. The areasof scour in the previous year displayed a tendency for preferential fill. As a re-40sult of this shifting mosaic of net and fill, the risk of disturbance occurring withinpotential spawning substrate patches varied from year to year. However, bed eleva-tion changes resulting from these morphological adjustments were relatively subtleand, in most cases, net scour did not exceed 0.08 m. Consequently, the estimate ofdisturbance risk due to this mechanism was sensitive to the adopted value of burialdepth.Overall, examination of hydrodynamic model results in connection with DEMsof difference suggested that several areas of detectable scour coincided with ele-vated shear stress (compare Figure 2.4 and Figure 2.6) and Shields stress. However,this relationship was highly variable and inconsistent, which is unsurprising, giventhe confounding influence that sediment supply had on sediment redistribution, aswell as the inability of the applied model to represent fluid forces associated withhigh turbulence intensity near flow obstructions. In addition, inevitable errors inthe modelled flow field likely also contributed to such an outcome. The model was,nevertheless, useful for qualitative understanding of hydraulic forcing of morpho-dynamic processes by providing indication of flow routing and first-order approxi-mation of the relative magnitude of hydraulic forces in various locations within thechannel.Figure 2.7 provides a useful summary of the observed patterns of net scour aswell as their consequences for disturbance risk and, therefore, enables between-reach comparisons. Although the net scour exceeding LoD was identified on 5%to 15% of the total bed area, changes equal to or larger than the estimated meanegg burial depth occurred only over 1-6% and 2-10% of total bed area for thresholdvalues of dcrit equal to 0.08 m and 0.05 m, respectively. However, in some cases,as a result of spatial correlation, the proportion of potential spawning substrate af-fected by net scour in excess of dcrit differed from the values calculated for the totalbed area (Figure 2.7 b and d, as well as Figure 2.7 c and f). Interestingly, in thiscase, we observed both positive and negative correlations (Figure 2.7 c and f). InRapid and Pool-Riffle-1 (2009-2010) higher net scour within spawning substraterelative to the total bed was related to rearrangement of unstable LW (up to about12% of potential substrate at risk for dcrit = 0.05 m). In Pool-Riffle-3 and part ofPool-Riffle-2, where potential substrate occurs in unobstructed bed, the variablespatial relationship was primarily an effect of the shifting pattern of sediment sup-41ply, associated with preferential remobilization of recent deposits. In addition, ourfield observations revealed that the large area of bed mobility in Pool-Riffle-2 waspartly related to undercutting of a channel-spanning log. This released a consid-erable pulse of sediment previously stored upstream of the obstruction. Similarmobilization of in-channel sediment sources took place in Rapid due to recent for-mation of LW that deflected flow towards a bar. Overall, because of the complexnature of bed evolution processes in East Creek, there was no consistent between-reach trend in bed mobility (Figure 2.7 a and d). Even though Pool-Riffle-2 andRapid tended to be the most morphologically active reaches during the period ofthis study, this clearly varied with time and local sediment supply.2.3.3 LimitationsSince the objective of this research was to analyze availability and disturbance ofpotential spawning substrate at high resolution and over a substantial spatial do-main, it was necessary to employ a relatively simple methodology and trade-offsome accuracy for sampling efficiency. Although we recognize the uncertaintythat arises from some of the assumptions embedded in our approach, we also be-lieve that the methods were capable of providing at least a first-order approxi-mation of the relevant textural conditions and morphodynamic processes. In thelight of our results, probably the most important source of uncertainty is relatedto the assessment of fine sediment disturbance risk. Specifically, our approach isbased solely on evaluation of bed surface texture and provides no direct informa-tion on the amount of fine material in the subsurface where an egg pocket wouldactually be located. However, field observations in East Creek indicate that thepatches with material <8 mm, which we sampled using Buffington and Mont-gomery (1999b) method, comprised well-mixed material with no obvious verticalstratification. Furthermore, our past data suggest that the coarser patches (>8 mm),sampled using Wolmans method, are unlikely to cross the threshold we adopted forexcess fine material. Specifically, D50 of bed surface in the finest of these patcheswas 27 mm, therefore, armouring ratio (D50sur f ace/D50subsur f ace) of almost 5 wouldbe necessary to reach the threshold of D50 = 5.7 mm for subsurface material. In ourexperience such values are not likely to be found in this creek. For example, bulk42subsurface samples, collected on other occasions, imply that material finer than 5.7mm constitutes no more than 35% of total material in the unobstructed portions ofthe channel.Another noteworthy source of uncertainty in this study was related to the as-sumption that net scour, obtained from DEM differencing, was a reasonable mea-sure of scour disturbance risk. It is widely known that in some cases the maximumscour depth, relevant for egg disturbance, may be masked by subsequent compen-satory fill (e.g. DeVries, 2008). However, the calculated net scour depths generallyseemed to fall within a similar range to the estimates of bed disturbance depth, pro-vided by tracers deployed in East Creek (Hassan, unpublished data). This agree-ment increased our confidence in the results. In addition, Lapointe et al. (2000)suggested that relatively low sediment transport rates in stable gravel-bed channelsare likely to limit the magnitude of compensatory fill.In summary, we stress that our goal in this study was to identify areas likelyto be affected by reduced embryo survival, rather than to quantitatively predictmortality levels. Therefore, considering the large study domain, we deemed theadopted methodology to be a reasonable compromise between simplicity and ac-curacy.2.4 ImplicationsMultiple converging lines of evidence suggested low sediment supply conditions inthe study reaches. Sediment-starved channels are typically characterized by coarsebeds with little textural sorting (e.g. Lisle and Hilton, 1999; Church and Hassan,2005). In addition, they tend to display low values of Shields stress and limitedbed mobility (e.g. Lisle et al., 2000a; Church and Hassan, 2005). All the abovecharacteristics were identified in the four study reaches in East Creek. Therefore,we believe our results and their ecological implications may be thought of as repre-sentative of similar salmonid-bearing mountain streams with low sediment supplyand wood loading.432.4.1 Ecological implicationsOur within-reach analyses seem to point to potentially important ecological impli-cations of the spatial patterns of bed texture and mobility for small-bodied salmonidsthat spawn in coarse-bedded mountain streams. First, it appears that, in the absenceof readily accessible finer-grained reaches (e.g. Pool-Riffle-3 in this study), suchfish may be forced to spawn in small, hydraulically sheltered areas, functionallysomewhat similar to ‘pocket gravel’, described by Kondolf et al. (1991) for steeperstep-pool streams. Although such microhabitats differ significantly from moretypical spawning locations (e.g. pool-riffle transition), research in other streamsshowed that salmonids do utilize them (e.g. Zimmer and Power, 2006; MacInniset al., 2008). The texture of these deposits in the study reaches was largely withinthe range of geometric mean diameter of 2-12 mm, reported by Knapp and Vre-denburg (1996) to be used for spawning by resident golden trout of similar bodysize to the Cutthroat inhabiting East Creek. Such clustered nest distribution mayhave negative consequences for fish. For example, increasing risk of redd superim-position as well as competition both between spawning females and juveniles (e.g.Greene and Guilbault, 2008).Importantly, our results suggested that these hydraulically sheltered spawn-ing sites may also be particularly prone to fine sediment accumulation, which isknown to have deleterious effects on embryo survival (e.g. Sear et al., 2008). Highrisk of fine sediment disturbance in our study sites may appear to be somewhatcounter-intuitive because, generally, such disturbance tends to be associated withhigh sediment supply channels, typical in drainage basins that experience someform of landscape disturbance such as logging, landslides, or wildfires (e.g. Trippand Poulin, 1986), rather than sediment-starved streams like East Creek. It is alsonoteworthy that past research has shown that infiltration of fine sediment into eggpockets is generally enhanced in low-velocity areas (Sear et al., 2008) such as thehydraulically sheltered sites in East Creek, and that deposits of fine material maybe only partially ‘flushed’ from such zones (Rathburn and Wohl, 2003). Althoughthe actual severity of fine sediment impacts on embryo mortality within the hy-draulically sheltered zones will depend on a complex suite of physical processesthat had to, inevitably, be ignored in our simple approach, it seems reasonable to44assume that such locations provide low quality intergravel conditions for salmonidegg incubation. The fine areas are, on the other hand, least likely to be utilized ifbetter quality substrate is available. This in turn depends on both potential sub-strate area and spawner density. Further, detailed work into this subject appears tobe warranted to verify the ecological relevance of our finding.The evidence for the existence of two diametrically different availability-disturbanceregimes in the study reaches is another ecologically relevant finding that emergesfrom this work. First, we hypothesise that habitat fragmentation, which preventsfish movement between reaches that provide abundant spawning substrate andthose that constitute complementary habitat types (e.g. rearing), may have a signif-icant impact on the resident fish in streams similar to East Creek. Second, spatialsensitivity of substrate availability and disturbance to moderate changes in bedtexture may also suggest that the system could shift between these two contrastingstates in response to temporal changes in sediment supply and flow regimes. As aresult, we hypothesize that resident salmonids in sediment-starved and wood-poormountain channels may also be vulnerable to land use and climate changes thatalter flow and sediment supply regimes.Our results from East Creek seem to be consistent with a hypothesis proposedby Montgomery et al. (1999), that small resident salmonids can spawn throughoutlarge portions of a channel network because typical floods during the spawning-incubation period pose rather low risk of substantial bed mobility and, conse-quently, egg scour. This study suggests that such an outcome in stable channelslike East Creek may also be a consequence of restricted lateral and vertical extentof bed mobility even during a bankfull event, an upper-bound estimate for floodsduring spawning-incubation season in our study site. However, the significance ofbed scour for disturbance risk appears to be sensitive to the assumed depth of eggburial and the estimated proportion of affected substrate may reach values of above10%. Moreover, scour is also variable in time, being a function of the shiftingspatial distribution of mobile sediment sources relative to the locations of poten-tial spawning sites. Finally, the actual effect of scour may also depend on habitatchoice by spawning fish, for example, whether they are attracted to spawning inloose, freshly deposited gravel (particularly prone to entrainment).452.4.2 Methodological implicationsIt is evident from the preceding discussion that recognition of some of the eco-logically important effects of bed texture and mobility on spawning substrate re-quired our investigations to be conducted over a spatial domain much larger thana single reach. Such a broad spatial scale may also be relevant from the point ofview of watershed management and fish habitat conservation (e.g. Montgomeryet al., 1999; Buffington et al., 2004; Goode et al., 2013). At the same time, theresults of our within-reach analyses implied that the pattern of spawning substrateavailability may force small fish to spawn in locations in which textural character-istics and morphodynamic processes may be very different from the dominant orreach-average conditions. Such fine-scale heterogeneity has been acknowledgedin earlier work conducted at a coarser resolution (e.g. Montgomery et al., 1999;Buffington et al., 2004; Goode et al., 2013), and our results strongly indicate thatin some cases it may impose a characteristic length scale that may need to be re-solved in investigations of spawning habitat for small-bodied salmonids in coarse-bedded streams. For example, even small spawning sites in hydraulically shelteredsites may be sufficient to support fish populations if relative spawner densities arelow. On the other hand, low textural heterogeneity in East Creek and other, sim-ilar channels with low sediment supply (Church and Hassan, 2005), suggests thatcoarse-resolution approaches may be well-suited for some applications, at leastin relation to species that spawn in such streams in large numbers and, therefore,require extensive bed areas.The within-reach observations carried out in this study also underscore the needto consider various geomorphic processes that affect availability and disturbanceof spawning habitat as well as their spatial configuration relative to one another.Our results imply that adopting an assumption that the proportion of bed affectedby disturbance agent reflects the risk of disturbance to incubating eggs (e.g. Ton-ina et al., 2008; Goode et al., 2013) requires caution because of the possibility ofpositive or negative spatial correlations between the location of disturbance andpotential spawning substrate. We certainly recognize that, given technical difficul-ties in obtaining high resolution data covering a large spatial domain, this implicitassumption is typically necessary when studying broad-scale patterns. Therefore,46we believe that basin-scale assessment of spawning substrate for small-bodied fishin coarse mountain channels remains to be a significant challenge. Current models,adopting the broad-scale and coarse-resolution approach, may need to be furtherrefined for such particular application, so as to consider local heterogeneity andspatial relations between relevant geomorphic processes.2.5 ConclusionsBed texture and mobility constitute important controls on spawning and incubationhabitat for salmonid fish. In this study, we aimed to advance current understand-ing of how spatial patterns in bed texture and mobility define potential spawn-ing substrate availability and disturbance risk in a trout-bearing mountain stream.This research was conducted in four reaches of East Creek, a sediment-starvedand wood-poor mountain stream with moderate gradient (<0.02), and yielded twokey findings. First, based on differences in textural and morphodynamic proper-ties between the study reaches, we identified two contrasting domains of potentialspawning substrate for resident Cutthroat Trout: low availability-high disturbancerisk and high availability-low disturbance risk. Disturbance risk appeared to beprimarily associated with fine sediment deposition while bed scour appeared to begenerally less important. A rapid transition between these two domains in responseto moderate differences in bed texture seems to imply a high sensitivity of spawn-ing substrate conditions. This led us to hypothesise that small-bodied salmonidsthat spawn in mountain streams, may be particularly vulnerable to habitat frag-mentation, which restricts their between-reach movements, and to alteration offlow and sediment regimes, associated with land use and climate changes. Second,this study highlighted the critical importance of investigating spawning habitat forsmall salmonids at high spatial resolution and accounting for spatial configurationof habitat-forming processes relative to those responsible for its disturbance.47Chapter 3Influence of Channel Morphologyand Hydraulics on EnergeticProperties of Foraging Habitatfor Small-Bodied Trout3.1 IntroductionThe spatial arrangement of various attributes and features of stream channel mor-phology strongly influences the quality of foraging habitat for salmonid fish (salmon,trout, charr). Importantly, by regulating the ability of animals to obtain food re-sources, this physical habitat template can have strong impact on individual fitnessand ultimately by affecting survival and fecundity on population dynamics (e.g.Chapman, 1966; Pyke, 1984; Hill and Grossman, 1993; Kennedy et al., 2008).Small-bodied salmonids inhabiting streams are primarily drift-feeding fish, that is,they consume aquatic and terrestrial invertebrates suspended within the water col-umn (Keeley and Grant, 2001). They typically adopt a sit-and-wait strategy, hold-ing their feeding position and making occasional forays to intercept prey itemscarried by the current (Bachman, 1984; Hughes et al., 2003). There are two ba-sic mechanisms through which channel morphology shapes physical conditions48relevant for salmonid foraging. First, it affects the supply of food resources and,second, it defines the concomitant costs of resource acquisition.Both of these mechanisms are mediated by hydraulic properties imposed bythe template of channel morphology. At any given discharge, the shape of thealluvial boundary (bed and banks) controls the spatial variability in flow depth,hence, the volume of available habitat space, which can be used to obtain food (e.g.Rosenfeld and Taylor, 2009). Other factors being constant, the deeper the flow, themore food items foraging fish can catch, at least up to the limit defined by themaximum distance at which prey items can be detected and intercepted. Moreover,the shape and textural properties of the channel boundary, along with non-alluvialfeatures such as large in-stream wood, control flow resistance and routing, and,consequently, spatial pattern of velocity field (Dietrich and Smith, 1983; Lisle,1986; Nelson et al., 1991; Whiting and Dietrich, 1991; Thorne and Furbish, 1995;Lawless and Robert, 2001). Under the assumption of constant prey concentration,the higher the velocity the higher is the flux of food that the fish can potentiallyfeed upon. Overall, therefore, by controlling the distribution of depth and velocity,channel morphology influences the supply of food resources and thus energy thefish are able to gain. However, at the same time, stream fish are constantly exposedto the drag of the moving fluid and need to actively swim in order to maintain itsposition in the flow. As a result, the higher current velocity the more energy fishneed to expend to hold their feeding stations and make forays (e.g. Brett and Glass,1973). For any potential foraging position the balance between energy gain andcost, termed net energy intake (hereafter NEI), defines local habitat profitability,that is, how much energy is available to sustain essential activities, maintenance,and growth (Brett, 1995).Given the heterogeneous nature of lotic habitat, the hydrogeomorphic chan-nel attributes may vary over a wide range of spatial scales, from the focal pointoccupied by fish at any given time (microhabitat), to morphological units (meso-habitat), to reaches (macrohabitat) or even entire basins (e.g. Frissell et al., 1986).All of these spatial scales are ecologically relevant, both from the perspective ofindividual organisms moving across landscape and from the perspective of spa-tial variation in habitat characteristics across a bounded domain such as a drainagebasin. For example, fish select their microhabitat based on fine-scale variation in49habitat and resources as well as biotic interactions (e.g. Fausch, 1984; Hughes andDill, 1990; Hughes, 1992; Gowan, 2007). In addition, they occasionally sampletheir habitat and track resources at the reach scale (e.g. Gowan and Fausch, 2002)and, over the duration of their lives, may disperse over longer distances within thechannel network, for example, in association with ontogenetic habitat changes (e.g.Gresswell and Hendricks, 2007).The associations between fish and various geomorphic and hydrological chan-nel characteristics have been the subject of intense research interest at a range ofspatial scales. In particular, a plethora of studies have tried to link fish abundanceto specific microhabitat variables usually utilized depth, velocity, substrate type- and this accumulating evidence has led to rapid popularization of Habitat Suit-ability Indices (HSI, e.g. Bovee, 1982; Hickman and Raleigh, 1982). Likewise, aconsiderable attention has been directed towards the mesohabitat unit scale. Forinstance, conspicuous spatial partitioning of habitat among the age cohorts wasobserved in stream salmonids; most adult fish are usually found in pools, juvenilestend to occupy riffles (e.g. Chapman, 1966; Glova, 1986), while fry typically occurin channel margins (‘lateral habitat’ e.g. Moore and Gregory, 1988). A number offactors were proposed as possible explanations for such distributions of individu-als, variable predation risk being probably most frequently invoked interpretationin case of of juvenile and adult fish (Power, 1987). Finally, at the macrohabi-tat scale, salmonids have commonly been found to prefer stream reaches with anabundance of pools (e.g. Watson and Hillman, 1997; Rosenfeld et al., 2000; Lat-terell et al., 2003). In other cases, researchers reported that peak densities of fishoccurred in reaches with low-to-moderate channel slopes (e.g. Watson and Hill-man, 1997; Latterell et al., 2003; Bryant et al., 2004; Quist and Hubert, 2005) orbroad alluvial valleys (e.g. Reeves et al., 1998; Baxter et al., 1999; Muhlfeld et al.,2001b; Deschłnes and Rodrguez, 2007).Although these studies provide important information on space use by salmonidfish, the correlative approach prevents inferences regarding the quality of this habi-tat and, in particular, the role of foraging or other specific mechanisms that may un-derlie the observed pattern. Importantly, the observed relationship between fish andhabitat conflates the effects of multiple abiotic and biotic factors and their ecologi-cal functions (foraging, refuge, etc). For example, the microhabitat associations of50a fish may vary depending on available cover (e.g. Shirvell, 1990; Fausch, 1993; In-oue and Nakano, 1998), or position in the social dominance hierarchy (e.g. Hughes,1992). Controlled exclusion experiments of mesohabitat choice have demonstratedthat, in the absence of adult fish, juveniles may shift their feeding positions fromriffles to pools (e.g. Rosenfeld and Boss, 2001). The patterns of mesohabitat unituse have also been found to differ depending on whether the species of interestexisted in sympatry or allopatry (e.g. Bisson et al., 1988). Occurrence at the reachscale can also be affected by the neighbourhood effects (e.g. Dunning et al., 1992),with complementary habitat type being located in proximity (e.g. Schlosser, 1991,1995; Kim and Lapointe, 2011; Falke et al., 2013).Mechanistic approaches to studying fish-habitat relationships present an excel-lent way to circumvent these problems and provide a powerful tool to isolate therole of specific ecological processes such as foraging. By linking the propertiesof the physical environment directly to fish physiology and explicitly consideringcritical scaling variables, such as body size (e.g. Brett and Glass, 1973; Webb,1995), they provide a process-based insight into these interactions. Physiolog-ical and biomechanical aspects of fish foraging have been well-studied throughlaboratory experiments (e.g. Elliott, 1976; Brett, 1995) and bioenergetic modelsfor drift-feeding fish based on this knowledge have been extensively tested (e.g.Hughes et al., 2003; Rosenfeld and Taylor, 2009; Urabe et al., 2010). These mod-els, most of which represent some refinement of the original formulation proposedby Hughes and Dill (1990), have been primarily applied to answer two researchquestions. First, such models have been extensively applied to predict habitat selec-tion based on the Optimal Foraging Theory (Pyke, 1984; Piccolo et al., 2014). Thetheory posits that, given the fundamental importance of the energetic trade-off, ani-mals should choose their habitat so as to maximize NEI. Indeed, such behaviour hasbeen observed also in salmonids and other fish (Fausch and White, 1981; Fausch,1984) and the model predictions are often remarkably accurate (Hughes and Dill,1990; Hughes, 1992; Guensch et al., 2001; Grossman et al., 2002; Booker et al.,2004; Hayes et al., 2007). Second, these models have been coupled with otherformulations describing fish metabolism in order to predict fish growth (e.g. Hayeset al., 2000; Rosenfeld and Taylor, 2009). Although the latter application is muchmore challenging (Hughes et al., 2003), the aforementioned studies demonstrated51that good results can be achieved. Surprisingly, despite the growing body of re-search in which this approach is used, to date, the role of channel morphology andthe associated hydraulic habitat has garnered little attention.The results of few studies that employed a bioenergetic approach and have ex-plicitly focused on this subject have indicated that mesoscale morphological varia-tion may be of fundamental importance for salmonid fish. Specifically, Rosenfeldand Boss (2001) found that adult fish required pool habitat to maintain growth,while juveniles were able to achieve this in both pools and riffles. Confirmingand building upon these findings, Rosenfeld and Taylor (2009) showed that withincreasing body size, fish are forced to occupy deeper habitat in order to sustaingrowth. The importance of pools was further corroborated by Jenkins and Kee-ley (2010), who also investigated the potential impact of climate change on streamsalmonids. In addition to the above findings, recent bioenergetic simulations con-ducted by Hafs et al. (2014) suggested that increased in-stream wood loading maygreatly increase the area of channel where fish growth is positive. This effect wasachieved by reduction of mean velocities and creating velocity gradients due topresence of flow obstructions. In another recent study, Rosenfeld (2014) used abioenergtic model to estimate the percentage of pool habitat that is likely to maxi-mize energetic profitability for salmonids.In this chapter, we focus on the linkages between channel morphology and thespatial pattern of foraging habitat for small-bodied salmonids in mountain streams.To this end, we integrate a bioenergetic model and a 2-dimensional hydrodynamicmodel, and applied them to four reaches of a trout-bearing mountain stream. Weexamine microscale and mescoscale patterns and then aggregate the results to in-vestigate the differences between study reaches with different morphology and tex-ture.3.2 Methods3.2.1 Field siteThe field sites for this study were established in four reaches of East Creek, a smallmountain stream located 60 km east of Vancouver, British Columbia Figure 3.1.52Figure 3.1: Map of the study area.The reaches have moderate channel slope, which declines downstream from 0.02 to0.01, low wood loading, and bankfull discharge a little in excess of 0.7 m3s-1. Thegradual change in slope is associated with transition in channel morphology fromplane-bed to progressively better developed pool-riffle morphology Montgomeryand Buffington (1997). Accompanying this morphological change is a pronouncedreduction in dominant bed material calibre, from cobble-boulder (D50 = 55 mm) inplane-bed to coarse gravel in pool-riffle reaches (D50 = 30 mm). This sequence ofmorphologically and sedimentologically distinct reaches provides a great oppor-tunity for a comparative study. Conveniently, there are no significant tributariesalong the study section therefore discharge and channel dimensions remain ap-proximately constant throughout the study section. As a result, despite changesin morphology, channel scale remain the same. Consistent with previously estab-lished terminology, hereafter we refer to the study reaches as ‘Rapid’ (plane-bed)and ‘Pool-Riffle-1’, ‘Pool-Riffle-2’ and ‘Pool-Riffle-3’.East Creek is inhabited by an allopatric population of Coastal Cutthroat Trout(Oncorhynhus clarki clarki), which has been a subject of intensive research over53the last three decades (e.g. Young et al., 1999; Boss and Richardson, 2002; De Grootet al., 2007; Zhang and Richardson, 2007, 2011; Sheldon, 2010). This research wasconducted specifically within the study section or in the adjacent reaches and pro-vides a wealth of information regarding the population characteristics such as fishdensity, size-frequency relationship, demographic structure, etc. In addition, someof the above studies have reported concentration of invertebrate drift (e.g. Boss andRichardson, 2002; Zhang and Richardson, 2007). We have taken advantage of thisextensive data set in order to parameterize our model.3.2.2 Field surveysTo parameterize the hydrodynamic model we conducted several field surveys andcollected extensive topographic, sedimentological, and hydraulic data. The topo-graphic survey was carried out in the summers of 2011 and 2012 using total sta-tion and with the mean point density of about 10 m-2. For the purpose of spatialinterpolation (TIN algorithm) points representing top of overhanging banks weredisplaced landward so that to form near-vertical bank line. In addition, to help pre-serve the complex geometry of large in-stream wood and some bank projectionssurvey points that represented outline of these features were densified. Prior evalu-ation of multiple data sets collected in these field sites with the same equipment andfollowing the same protocol yielded interpolation errors approximately equal to themedian grain size of bed material and suggested that the topographic errors did notshow substantial inter-annual differences (Cienciala and Hassan, 2013). Sedimen-tology of the study reaches was represented by 84th percentile of bed material grainsize distribution (hereafter D84), which is the most commonly used reference mea-sure of sediment calibre for hydraulic applications (e.g. Millar, 1999). To calculateD84 we used a detailed bed survey collected in 2011 and described in Ciencialaand Hassan (2013). Although our observations (M.A. Hassan, unpublished data)suggest that the reach-average sediment calibre in East Creek does not change sub-stantially over time, the extent and characteristics of individual textural patchescould have been modified by local scour or deposition. Therefore, in this studywe used only the reach-average values of D84. We complemented the topographicand sedimentological surveys with hydrological and hydraulic data sampled during54the 2011-2013 period. First, we gauged flow discharge on several occasions usingvelocity-area method and an electromagnetic current meter (ECM). In conjunctionwith discharge, we measured flow depths at cross-sections located at the down-stream end of the study reaches (discharge range: 0.03 m3s-1 - 0.71 m3s-1). Thesedata were then used to develop a discharge-stage power law relation of the form:S = aQb (3.1)where S is stage, Q is stream discharge, while a and b are fitted parameters. Therelation enabled us to estimate water surface elevation for any flow within the sam-pled range, which was achieved by adding the predicted stage to the correspondinglocal bed elevation. Finally, to characterize flow field in our study reaches, werecorded over two hundred velocity profiles using an ECM (Cienciala and Hassan,manuscript in preparation).3.2.3 Hydrodynamic modelTo represent the flow fields within our study sites we used FaSTMECH, a 2-dimensional hydrodynamic model embedded within the MS WSMS interface (Nel-son et al., 2003; McDonald et al., 2005). The model solves vertically and depth-averaged Navier-Stokes equations posed in a channel-fitted coordinate system (Nel-son and Smith, 1989). The model has been successfully applied and extensivelytested in a variety of natural river channels that ranged from large rivers to smallmountain streams (e.g. Lisle et al., 2000b; May et al., 2009; McDonald et al., 2010;Harrison et al., 2011; Cienciala and Hassan, 2013). Model inputs include channelbathymetry, bed roughness parameter, lateral eddy viscosity, as well as water dis-charge and water surface elevation at the downstream end of the modelling domain.We used the topographic survey data as the bathymetric input while bed roughnesswas parameterized using the procedure described in Cienciala and Hassan (2013),with a small modification that involved using the reach-average rather than spa-tially variable bed material size to calculate hydraulic roughness. We took advan-tage of spatially averaged velocity profiles to estimate roughness height, z0, andthen expressed these values as a multiply of the reference sediment calibre D84:55z0 =< a > D84 (3.2)The obtained multiplier < a > = 0.11 and reach-average < D84 > were enteredinto the model’s built-in roughness calculator. To estimate LEV , we used a relationproposed by Rodi (1984):LEV = 0.135u∗d (3.3)where d is the mean depth and u∗ is shear velocity. The multiplier 0.135 fallsbetween the value 0.11 proposed for rivers (Keefer, 1971; Olsen, 1999) and 0.15,the lower bound of the range suggested by Jenkins (1993) for channels with roughboundaries (also, close to 0.14 recommended by Ghanem et al., 1996). The meandepth values were based on our field survey while shear velocity values were cal-culated from the mean boundary shear stress (τ0 = ρgRS):u∗ =(τ0ρ)0.5= (gRS)0.5 (3.4)where R is hydraulic radius, g is gravitational acceleration, and S is the channelslope. We simulated flow fields at two different flows, Q = 0.37 m3s-1 and Q =0.08 m3s-1, for which water surfaces elevations were either directly measured orpredicted from the Equation 3.1. The former discharge is well above the baseflowconditions even during winter months but can be thought of as representing a mod-est storm event, which may occasionally occur until late spring or, exceptionally,in response to large summer storms.We have previously tested and evaluated the hydrodynamic model at the dis-charges of 0.71 m3s-1 and 0.37 m3s-1 (Cienciala and Hassan, 2013). In both casesestimated errors in velocity and depth were within the range typical for hydrody-namic models applied in coarse-bedded channels (Clifford et al., 2009; Kozareket al., 2010; Grantham, 2013) and, therefore, its performance was considered satis-factory. Because in this study we used the same parameterization scheme, we didnot conduct a separate error analysis.The two-dimensional depth-averaged velocity field simulated by the hydrody-namic model was transformed into a quasi-3D form. To this end, in each compu-56tational node we distributed velocities along the vertical according to the law ofthe wall using the modelled shear velocity, u∗. The law of the wall posits that thevelocity in steady, uniform flow increases with the logarithm of distance above thebed. Several studies, as well as our own results presented in Chapter 4, have shownthat, even though physical assumptions behind this formulation are not strictly metin coarse-bedded channels, this formulation provided reasonable approximation ofthe mean flow structure above the crests of roughness elements (Wiberg and Smith,1991; Byrd et al., 2000; Franca et al., 2008; Franca and Lemmin, 2009). In this pa-per we take advantage of this quasi-3D representation to account for flow fieldanisotropy within fish capture area (see Section 3.2.4). At the same time, for sim-plicity, we assume that trout holds station at a vertical position that coincides withthe mean velocity of the water column (approximately 0.4 depth above the bed).Although some salmonids are known to take advantage of flow shelters behind bedroughness elements, Cutthroat Trout has been observed to do so primarily duringhigh flows, especially in winter (Cunjak, 1988). Under regular flow conditions,Cutthroat has been typically reported to forage in the mid-water column (Nakanoet al., 1992; Bonneau and Scarnecchia, 1998).3.2.4 Bioenergetic modelTo estimate the energetic profitability of habitat in the study reaches we modified amodelling framework first proposed by Hughes and Dill (1990) and subsequentlyextended by other authors (e.g. Hughes et al., 2003). A computational domain forthe bioenergetic model was defined by the extent of the wetted channel (di > 0,where di is local flow depth) within the output of the hydrodynamic model. Theprocedure that was applied to each node within that domain, as a potential foragingposition (microhabitat), involved two major steps. First, we estimated the capturearea for fish of three body size (FL) classes: 5 cm, 10 cm and 15 cm. In thetrout population inhabiting East Creek, these classes roughly correspond to young-of-the-year (hereafter age-0), yearling (age-1), and adult (age-2+) age classes (e.g.Young et al., 1999; De Groot et al., 2007). Second, we calculated the energy budget(NEI, Js-1) for each of these potential foraging locations by balancing gross energy(GEI) intake against energetic costs of swimming (SC):57NEI = GEI−SC (3.5)The capture area sub-model assumes that fish hold stations oriented into theflow and detect prey as it enters a reaction volume, the surface of which is definedby an estimated reaction distance (Hughes and Dill, 1990, following). The reactiondistance (RD, cm) depends on fish body size (FL, cm) and prey length (PL, mm)(Hughes and Dill, 1990):RD = 12PL(1− exp−0.2FL) (3.6)To delineate the capture area we subdivided a cross-sectional plane withinwhich the node of interest (i.e. fish focal point) is located into a fine grid withcell size 0.01 m by 0.01 m. The capture area included all the cells within the cross-section for which the Euclidean distance between the cell centre and the focal pointwas smaller or equal to the maximum lateral capture distance (MCD, cm):MCD =√RD2−(RDu¯ui)2(3.7)where u¯ is the distance-weighed mean velocity along the straight line connect-ing the focal point with the cell of interest and ui is interception velocity. This formof this equation was based on a formulation proposed by Hughes and Dill (1990).However, we followed the findings of rigorous experiments by Hughes et al. (2003)and instead of using maximum sustainable velocity - as most of authors to date -we assumed that fish intercepts the prey by swimming at the velocity equal to thatof the drifting prey. Flow velocity in the cell of interest was assumed to representthe velocity of drifting prey. Because our approach could result in unrealisticallyhigh estimates of interception times at very low flow (prey) velocity, we assumeda lower threshold of interception velocity equivalent to 1.5FLs-1 (one fish bodylength per second). The latter assumption was based on work of Ware (1978) onoptimal foraging swimming speed of pelagic fish and on data from experiments ofMurray et al. (2013). Overall, our method for estimating MCD is a modified ver-sion of that applied by Hughes et al. (2003), who first considered spatial variabilityin the maximum capture distance. These authors, however, defined the shape of the58capture area by projecting 35 numerically approximated radials (subsequently alsoemployed by Hayes et al., 2007). Our approach, although computationally moredemanding, enables complex capture area shapes that reflect flow field anisotropyand avoids potential problems in the numerical approximation procedure.The gross energy intake (GEI) for each of the potential foraging positions wascalculated as the sum of GEI at all the cross-sectional cells that fell within thecapture area. GEI (Js-1) for an individual cell was obtained from the followingformulation:GEIi =(ERiCSiECEA1+∑ERi(IT +HT ))(3.8)where ER is encounter rate (s-1), CS is capture success (proportion, 0-1), ECis prey energy content per prey item (J), EA is the proportion of energy that canbe assimilated, IT is interception time (s), and HT is handling time (s). The Equa-tion 3.8 is a modified version of Holling’s Disc Equation (Holling, 1959), whichmodels the rate of prey capture by predator as a function of prey density and thetime required to intercept and handle it. As a result of the time spent to handle theprey, the rate of capture increases with increasing prey density, however, it does soat a declining rate. This theoretical ‘functional response type II’ has been testedand validated for trout (Gustafsson et al., 2010) and other fish (e.g. Murray et al.,2013). The prey encounter rate (ER; m-2) in Equation 3.8 was calculated as theproduct of prey concentration (m-3), modelled flow velocity in the cell (m-1), andthe surface area of the cell (m2). The concentration of prey (3 m-3) was estimatedusing the values reported for our study site by Boss and Richardson (2002) andZhang and Richardson (2007). To estimate the probability of prey capture suc-cess in Equation 3.8, we employed the formulation of Rosenfeld and Taylor (2009)based on the data and approach of Hill and Grossman (1993) and Grossman et al.(2002):CS =expp1+ expp(3.9)where exp is the mathematical exponential constant while p is a parametercalculated according to:591.28−0.0588uFL−0.0918(√(xFP− xc)2 +(yFP− yc)2RD)−0.21u(√(xFP− xc)2 +(yFP− yc)2RD)(3.10)where xFP, yFP, xc, and yc denote Cartesian coordinates of, respectively, thefocal point and the centre of a cross-sectional cell of interest. In other words, thenumerators in the fractional terms represent the Euclidean distance (in the cross-sectional plane) between the fish focal point and the centres of the capture areacells. By including Equation 3.9 into the Holling’s Disc Equation we were able toaccount for unsuccessful forays by trout Hughes et al. (2003) due to high veloc-ities at which prey is drifting (Hill and Grossman, 1993; Piccolo et al., 2008) aswell as for large capture distances (Hill and Grossman, 1993; Piccolo et al., 2007).A similar approach was previously adopted by Rosenfeld and Taylor (2009). Theenergy content per prey item (EC, J) in Equation 3.8 was approximated as 28.3PMfollowing the formulation of Hughes et al. (2003) based on work by Cummins andWuycheck (1971). Prey mass (PM, mg), in turn, was estimated using the relationthat links body mass of aquatic invertebrates to their body length (Benke et al.,1999). Instead of the more commonly used relation of (Smock, 1980) we choseto apply that proposed by Benke et al. (1999) because data in the latter includedinvertebrates from across North America, rather than only from one geographicalregion. The similarity of its predictions with another study of size-mass relation-ship in Canadian aquatic invertebrates (Johnston and Cunjak, 1999) supports ourchoice. The mean length of the drifting invertebrates (2.8 mm) in East Creek wasback calculated from the data of Zhang and Richardson (2007). For the purposeof Equation 3.8, the proportion of energy content that can be assimilated (EA) wasassumed to be 0.58 (Elliott, 1976). The latter constant reflects energy losses due todigestion (14%) and excretion (28%) (Elliott, 1976).An important modifications that we introduced into the model is that the de-nominator in Equation 3.8 explicitly distinguishes the interception time (IT ) andhandling time (HT ). Thus far, bioenergetic models for drift-feeding fish have eitherignored the time fish need to handle the prey and calculated only the interceptiontime based on the capture area dimensions (e.g. Hughes and Dill, 1990; Hughes60et al., 2003; Hayes et al., 2007) or assumed a constant handling time (e.g. Guen-sch et al., 2001; Rosenfeld et al., 2005; Rosenfeld and Taylor, 2009; Jenkins andKeeley, 2010). In the latter case, the handling time was assumed to be equal to5 s, based on observations of Bachman (1984). An obvious disadvantage of theformer approach is that it can result in a gross overestimation of the capture rateas the denominator in Equation 3.8 is very small. The latter approach, on the otherhand, ignores existing ecological evidence that handling time depends on both preyand predator size (e.g. Werner, 1974). In this paper, we account for both intercep-tion time and the handling time for the number of prey that have been successfullyintercepted (thus, it is multiplied by the capture success parameter, CS). We esti-mated the interception time (per foray) as the mean time needed to reach each cellof the capture area and return to its focal point. For example, in case of a circular-shaped capture area, the mean distance to all the points within it will equal 0.667 ofits radius (MCD). Several other models applied a roughly similar approach.Hayeset al. (2000), Hughes et al. (2003), and Booker et al. (2004) assumed half of thereaction distance as the capture location, while Guensch et al. (2001) and Rosen-feld and Taylor (2009) adopted the distances equivalent to half of the maximumcapture distance. Handling time in our study was estimated using a relation basedon experimental data of Bannon and Ringler (1986):HT = 1+0.84exp2.35( PLMW ) (3.11)where MW is fish mouth width (mm), estimated as a function of body length(expressed in cm): MW = FL using data presented by (Bannon and Ringler, 1986).The energy budget in Equation 3.5 was completed by calculating swimmingcost (J-1). To this end, we applied a relation for ‘routine swimming’ based onexperiments of Boisclair and Tang (1993). We chose this formulation because ittakes into account the high energetic cost of spontaneous manoeuvres, such asaccelerations and changes in direction (e.g. Hughes and Kelly, 1996). In contrast,to date, most bioenergetic models for drift-feeding fish have applied relations basedon ‘forced swimming’ experiments, in which the fish are prompted to swim againsta unidirectional flow of constant velocity (Boisclair and Tang, 1993). This is knownto underestimate the true energetic expenditure, in extreme cases by as much as an61order of magnitude or more (Boisclair and Tang, 1993; Hughes and Kelly, 1996). The equation developed by Boisclair and Tang (1993) calculates swimming cost(SC) as a function of fish body weight (FW ) and flow velocity (u):log10 SC = 0.54log10 FM +1.09log10 u−0.93 (3.12)To convert fish body size (FL) into body weight (FW ) we used a relation de-veloped specifically for Cutthroat Trout in East Creek (De Groot et al., 2007):log10 FM = 3.03log10 FL−2.05 (3.13)The swimming cost was calculated separately for interception and holding sta-tion, by partitioning the time spent by fish for both of these activities. As a finalstep, we have estimated the maximum sustainable fish swimming velocity, Vmax(cms-1) (Hughes et al., 2003):Vmax = 32.23FL0.19 (3.14)Only the areas of the channel where velocity is below Vmax, which means thatfish can hold position for prolonged time, should be considered as potential forag-ing habitat.3.3 ResultsModelled patterns of trout foraging microhabitat in the study reaches were highlyheterogeneous (Figure 3.2), with clear longitudinal (downstream) and transverse(cross-stream) structure. Variation in fish body size resulted in somewhat differentspatial arrangements of habitat (compare panels a, b and c in Figure 3.2). In addi-tion, markedly dissimilar patterns emerged at low and high flows, which indicatedtemporal variability in the spatial organization of foraging habitat (compare topand bottom panels in Figure 3.2). Below we examine these results in detail.During low flow conditions, the longitudinal component of spatial habitat struc-ture was clearly defined by morphological units such as riffles and pools (Figure 3.2and Figure 3.3). Because pools are defined by high depth relative to the adjacentchannel areas, this habitat pattern is reflected in Figure 3.3 through an evident co-62v (a) FL=5  Q = 0.08m3s-1 (b)  FL=10  Q = 0.08m3s-1 (c)  FL=15  Q = 0.08m3s-1 (f)  FL=15  Q = 0.37m3s-1 (e)  FL=10  Q = 0.37m3s-1 (d)  FL=5  Q = 0.37m3s-1 Pool-Riffle-3 0 – 0.02 0 .02– 0.04 0 .04– 0.06 > 0.06 -0.02 - 0 -0.04 – -0.02 < -0.04 Flow direction Figure 3.2: Maps of predicted net energy intake (NEI) in Pool-Riffle-3 forfish of different body lengths: FL = 5 cm, FL = 10cm and FL = 15cm.variation of cross-section averaged values of depth and net energy intake. In gen-eral, the most profitable feeding positions were typically found in pools, especiallythe deep ones, while riffles were associated with low NEI values. Even in shallowpools in the Rapid reach net energy gain was often noticeably higher relative tothe adjacent rapids and runs. These ‘incipient’ pools corresponded to scour holesaround flow obstructions or were formed by transverse ribs, a type of sedimentarybedform made of cross-stream lines of coarse sediment particles, which acted asweirs. Although the general trend for higher NEI in pools and lower NEI in riffles,rapids, and runs was rather consistent across all three body size classes, the rela-tive differences between these morphological units were amplified for larger fish.63In particular, NEI predicted by the model for larger fish in riffles and the shallowchannel units were typically well below zero, indicating highly negative energybudget. On the other hand, the rate of energy intake for smaller fish remainedhigher in these morphological units and the cross-sectional mean NEI values werearound zero for the smallest size class. In contrast to the channel areas where flowis shallow, large fish in pools were predicted to have NEI in excess of the valuesmodelled for the smaller fish.A closer inspection of the modelled spatial patterns revealed two important nu-ances in this general trend. First, the energetic profitability of pools displayed con-siderable variability and some of them did not differ substantially from riffles andother shallow habitat units or were even lower ( Figure 3.4). Examples of two poolsin Figure 3.4 illustrate that, despite increase in depth (Figure 3.4 b and e) net energyintake was lower than or similar to the adjacent morphological units (Figure 3.4 aand d). This appeared to be true of pools in which velocity was relatively high de-spite deeper flow (Figure 3.4 c and f). Second, many pools were internally highlyheterogeneous, which resulted in a substantial scatter in the relation between localvalues of flow depth and NEI (Figure 3.5). Note that negative NEI values weremodelled for flow as deep as three times the reach-average flow depth (Figure 3.5).A good example of such internal variability was provided by pools formed in thelateral separation eddies. The shear layers, where steep lateral gradients of flowvelocity existed, enabled fish to take advantage of high specific flux of prey in theunobstructed current within the channel constrictions while holding position in theadjacent hydraulically sheltered zones (e.g. Figure 3.2 and Figure 3.4 c-f). Chan-nel expansion downstream of constriction also provided good feeding conditionsin such units while the jet flow zone and the parts of separation eddy distant fromthe shear layer were often characterized by low NEI. Moreover, within-unit gra-dients in net energy intake reflected convective decelerations between pool headsand mid-pools as well as accelerations between mid-pools and pool tails.The transverse component of the spatial structure in NEI at the low flow condi-tions was as important as the longitudinal one Figure 3.6. This lateral arrangementof foraging habitat varied among the study reaches and fish body size classes. Onaverage, the most energetically profitable feeding locations were typically locatednear the banks although in the Rapid reach a secondary peak was identified in the640 10 20 30 40 50 60 70 80−0.1−0.0500.05NEI (Js−1 )RAP reach  00.150.30.45Flow Depth (m)FL=5FL=10FL=15Depth0 10 20 30 40 50 60 70 80 90 100−0.1−0.0500.05NEI (Js−1 )PR1 reach9 00.150.30.45Flow Depth (m)0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150−0.1−0.0500.05NEI (Js−1 )PR2 reach9 00.150.30.45Flow Depth (m)0 10 20 30 40 50 60 70 80 90−0.1−0.0500.05NEI (Js−1 )Distance downstream (m)PR3 reach9 00.150.30.45Flow Depth (m)Figure 3.3: Longitudinal patterns of net energy intake (NEI) during low flow conditions for fish of different bodylengths (FL).65(d)  (d)  NEI (J/s), FL=10  (e)  Depth (m)  (f)  Velocity (m/s)  (d)  (d)  Pool-Riffle-2  (a)  NEI (J/s), FL=10  (d)  (b)  Depth (m)  (d)  (c)  Velocity (m/s)  Flow direction 0 - 0.02 0 .02 - 0.04 0 .04 - 0.06 > 0.06 -0.02 - 0 -0.04 - -0.02 < -0.04 Figure 3.4: Maps of net energy intake (a and d), flow depth (b and e), and ve-locity (c and f) in two sub-sections of Pool-Riffle-2 reach. Black circlesand red arrows highlight pools where high velocities resulted in NEIvalues lower than in the adjacent riffles.channel centre. Such a pattern of mean NEI within the distance bands ( Figure 3.6)reflects consistently positive values in the near-bank zone. In addition to the meanpatterns, it is also informative to investigate the upper percentiles of the distributionof NEI values, which reflect the location of best microhabitat patches. For exam-ple, 95th percentiles of NEI indicated that the most profitable feeding locationsfor small trout (FL = 5 cm) were typically located within 0.5 m from the bank.The exception to this pattern was Pool-Riffle-2, in which equally good foraginglocations appeared to be located away from the channel margins (1-1.5 m lateraldistance). In case of larger fish (FL = 10 cm and 15 cm) 95th percentiles either didnot differ much within the distance range of 0.5 m and 1.5 m from the banks (Rapidreach) or increased towards the channel centre, peaking around 1-1.5 m from thechannel margins (the Pool-Riffle reaches). Although the relatively high values ofNEI near the channel margins can partly reflect locations of lateral scour pools, the66Figure 3.5: Relationship between depth (normalized by the reach-meanvalue) and net energy intake (NEI) during low flow conditionsnear-bank areas within riffles and other shallow units certainly contributed to suchoutcome (Figure 3.2 and Figure 3.4).To further explore the transverse habitat patterns, we examined cumulative dis-tributions of NEI within three wider distance bands: near-bank, transitional zone,and the channel centre (respectively: 0-0.5 m, 0.5-1 m, and 1-1.5 m away fromthe bank) (Figure 3.7). When the values of NEI between 0 and 0.01 Js-1 wereconsidered, the plots revealed that the near bank zone offered higher proportion ofprofitable foraging habitat compared to the other bands and this effect appeared tobe slightly stronger in the reaches with less developed morphology. The cumulativedistributions within this range nearly converged for Pool-Riffle-2, indicating littledifference between the distance bands. Above NEI = 0.01 Js-1 the pattern con-verged and in some cases even reversed, thus suggesting that the areas with NEIfalling within the highest 10% value were often located away from the channelmargins.A comparison of the baseflow NEI patterns described above with those mod-670 0.5 1 1.5 2−0.02−0.0100.010.02RAPNEIFL = 5cm (Js−1)  0 0.5 1 1.5 2−0.02−0.0100.010.02PR10 0.5 1 1.5 2−0.02−0.0100.010.02PR20 0.5 1 1.5 2−0.02−0.0100.010.02PR30 0.5 1 1.5 2−0.04−0.0200.020.04NEIFL = 10cm (Js−1 )0 0.5 1 1.5 2−0.04−0.0200.020.040 0.5 1 1.5 2−0.04−0.0200.020.040 0.5 1 1.5 2−0.04−0.0200.020.040 0.5 1 1.5 2−0.06−0.04−0.0200.020.04NEI FL = 15cm (Js−1 )Distance from bank (m) 0 0.5 1 1.5 2−0.06−0.04−0.0200.020.04Distance from bank (m) 0 0.5 1 1.5 2−0.06−0.04−0.0200.020.04Distance from bank (m) 0 0.5 1 1.5 2−0.06−0.04−0.0200.020.04Distance from bank (m)P95P75meanFigure 3.6: Transverse (cross-stream) structure of NEI in the study reachesduring low flow conditions. The values represent percentiles/means ofall values within a given reach that fall within narrow (0.1 m width)distance bands from the bank (either).elled for the higher discharge enabled a limited assessment of temporal changesin foraging habitat arrangement. Although in some sections of the study reachesthe overall longitudinal pattern of variation in NEI with flow depth was preservedunder the high flow conditions (Figure 3.8), in others a reversed pattern was ob-served. In several pools (for example, the upstream-most pool in Pool-Riffle-3)NEI values during the high-flow dropped below those modelled for the adjacentriffle areas (Figure 3.8). As a result, in the high flow scenario there was no well-defined relation between the depth and NEI (Figure 3.9). In all high flow cases,the values within the channel centre were well below zero (Figure 3.2). More-over, velocities in this central portion of the study reaches were in excess of themaximum velocity that fish could maintain for prolonged time, which suggestedthat they would be prevented from foraging in these zones by biomechanical con-straints. The areas of excessive velocity roughly coincided with the red patches inFigure 3.2 (bottom panels). The low values of modelled net energy intake within68−0.05 0 0.0500.20.40.60.81F(NEI)RAP, FL=5−0.05 0 0.0500.20.40.60.81 RP1, FL=5−0.05 0 0.0500.20.40.60.81 RP2, FL=5−0.05 0 0.0500.20.40.60.81 PR3, FL=5−0.1 −0.05 0 0.05 0.100.20.40.60.81F(NEI)RAP, FL=10−0.1 −0.05 0 0.05 0.100.20.40.60.81 RP1, FL=10−0.1 −0.05 0 0.05 0.100.20.40.60.81 RP2, FL=10−0.1 −0.05 0 0.05 0.100.20.40.60.81 PR3, FL=10−0.2 −0.15 −0.1 −0.05 0 0.0500.20.40.60.81NEI (Js −1)F(NEI)RAP, FL=15  −0.2 −0.15 −0.1 −0.05 0 0.0500.20.40.60.81NEI (Js −1)RP1, FL=15−0.2 −0.15 −0.1 −0.05 0 0.0500.20.40.60.81NEI (Js −1)RP2, FL=15−0.2 −0.15 −0.1 −0.05 0 0.0500.20.40.60.81NEI (Js −1)PR3, FL=15near−bankintermediatecentreFigure 3.7: Cumulative distribution plots of net energy intake in three dis-tance bands from the banks (near bank: 0.5-1m; intermediate: 0.5-1m;centre: 1-1.5m) modelled for low-flow conditions.the channel centre sharply contrasted with high, positive values along the channelmargins (Figure 3.2). A comparison between the top and bottom panels of Fig-ure 3.2 indicated that in some cases these marginal areas (e.g. separation eddies)expanded relative to the low-flow conditions. The transverse habitat structure illus-trated in Figure 3.10 considers only the areas where velocities are within the rangesuitable for pronlonged feeding. The patterns displayed by the 95th percentile linessuggested that, despite the clear decrease in meanNEI towards the channel centre,highly profitable habitat patches can exist away from the banks even during high-flow conditions. In fact, within the limited areas of channel accessible to fish giventheir swimming abilities, the most profitable habitat was, in many cases, associatedwith that central portion of the channel (Figure 3.11). Taken together, however, theabove evidence clearly indicated that during high flow foraging habitat quality gen-erally declined away from the bank for all fish size classes and in all study reaches.When results were aggregated for the reach scale analyses, it was necessaryto exclude the areas where fish were unable to maintain position for prolonged69time because of excessive velocities. During low flow conditions the proportion ofareas that were available for fish given these biomechanical limitations was lowerin Rapid and Pool-Riffle-1 (about 80% and 85-90%, respectively) than in Pool-Riffle-2 and Pool-Riffle-3 (95-97%) (see Figure 3.12). The proportion of the areaswithin the study reaches that were available for foraging trout increased weaklyfrom Rapid to PoolRiffle-2 but no further increase was detectable in Pool-Riffle-3(Figure 3.13). In addition, there was a consistent trend indicating that the smallerthe fish the larger the area of positive NEI (Figure 3.13). However, cumulativedistributions of NEI aggregated over a reach suggested that above NEI of around0.01 J s-1 higher proportion of habitat was available for larger fish (Figure 3.14).The reach-scale results also indicated a relatively complex pattern in the reach-mean NEI (Figure 3.15). For the smallest fish mean NEI increased consistentlyfrom Rapid to Pool-Riffle-3. For the intermediate body size class, the two coarserreaches (RAP and PR-1) had lower mean NEI in comparison to the finer, pool-riffle reaches. When the largest fish were considered, no systematic trend could bedetected.The model generated a considerably different set of reach-scale predictionsunder high flow conditions. The proportion of area to which fish foraging wasrestricted because of excess velocities once again increased from Rapid to Pool-Riffle-3 (Figure 3.16). However, the absolute values were significantly lower andsuggested that fish could utilize between 30% and 55% of the channel area. TheRapid and Pool-Riffle-1 reaches appeared to provide somewhat smaller proportionof the channel area where fish could maintain feeding positions. The larger fishwere consistently able to utilize a larger proportion of the channel areas in com-parison to smaller individuals. The proportion of available habitat where NEI waspositive showed attenuated differences between the reaches in comparison with thelow flow scenario, and no differences were noted when only the areas accessibleto fish were considered (Figure 3.17). Similar to the low flow case, the cumulativedistribution plots showed that the tendency for smaller fish to have larger areas ofpositive habitat than larger individuals reversed for NEI in excess of about 0.01Js-1 (Figure 3.18).The mean NEI within the area hydraulically suitable for foraging partially re-versed its pattern relative to the low-flow conditions (Figure 3.19). For example, th700 10 20 30 40 50 60 70 80−0.1−0.0500.05NEI (Js−1 )RAP reach  00.150.30.45Flow Depth (m)FL=5FL=10FL=15Depth0 10 20 30 40 50 60 70 80 90 100−0.1−0.0500.05NEI (Js−1 )PR1 reach9 00.150.30.45Flow Depth (m)0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150−0.1−0.0500.05NEI (Js−1 )PR2 reach9 00.150.30.45Flow Depth (m)0 10 20 30 40 50 60 70 80 90−0.1−0.0500.05NEI (Js−1 )Distance downstream (m)PR3 reach9 00.150.30.45Flow Depth (m)Figure 3.8: Longitudinal pattern of net energy intake (NEI) during high flow conditions for fish of different body sizes(FL).71Figure 3.9: Relationship between depth (normalized by the reach-meanvalue) and net energy intake (NEI) during high flow conditions.mean NEI for the largest fish body size class showed a clear decrease from Rapidto Pool-Riffle-3. In the case of the intermediate body size class, the Rapid reachalso seemed to provide, on average, superior conditions for foraging trout relativeto the pool-riffle reaches. No evident trend was observed for the smallest fish bodysize class. These results indicated that in the morphologically simpler reaches thechannel areas where fish could maintain feeding stations were often of better ener-getic quality compared to the reaches with better developed bed topography.3.4 Discussion3.4.1 Within-reach patternsOur mesoscale results suggested that, on average, pools in East Creek constitutedbioenergetic hot spots for fish of all sizes. This relative superiority of pool overother morphological units is in line with the findings of bioenergetic models appliedby Guensch et al. (2001), Rosenfeld and Boss (2001), Rosenfeld and Taylor (2009),720 0.5 1 1.5 2−0.02−0.0100.010.02RAPNEIFL = 5cm (Js−1)0 0.5 1 1.5 2−0.02−0.0100.010.02PR10 0.5 1 1.5 2−0.02−0.0100.010.02PR20 0.5 1 1.5 2−0.02−0.0100.010.02PR30 0.5 1 1.5 2−0.06−0.0300.030.06NEIFL = 10cm (Js−1 )0 0.5 1 1.5 2−0.06−0.0300.030.060 0.5 1 1.5 2−0.06−0.0300.030.060 0.5 1 1.5 2−0.06−0.0300.030.060 0.5 1 1.5 2−0.12−0.0600.06Distance from bank (m)NEI FL = 15cm (Js−1 )  0 0.5 1 1.5 2−0.12−0.0600.06Distance from bank (m) 0 0.5 1 1.5 2−0.12−0.0600.06Distance from bank (m) 0 0.5 1 1.5 2−0.12−0.0600.06Distance from bank (m)P95P75meanFigure 3.10: Transverse (cross-stream) structure of NEI in the study reachesduring high-flow conditions. The values represent percentiles/meansof all values within a given reach that fall within narrow (0.1 m width)distance bands from the bank (either).and Jenkins and Keeley (2010) in similar or somewhat larger channels. Therefore,our work adds to the mounting body of evidence that energetic profitability may bean important mechanism that underlies both the higher rates of growth in pools thatwere observed in small scale experiments (Rosenfeld and Boss, 2001; Rosenfeldet al., 2005; Jenkins and Keeley, 2010) and the correlation between pool habitatavailability, growth, and apparent survival reported in large-scale field surveys (e.g.Pess et al., 2011). Further, this structure of foraging habitat quality may also be animportant factor underlying the observed patterns of fish occurrence and abundance(e.g. Rosenfeld et al., 2000; Kawai et al., 2014).However, our simulations in East Creek also suggest that the mesoscale patternof energetic habitat profitability may be somewhat more complex than a dichoto-mous conceptual pool-riffle model proposed by Rosenfeld and Boss (2001). First,the results of our bioenergetic model indicated that morphological and hydraulicdiversity of pools may result in a considerable variability of their quality as forag-73−0.05 0 0.0500.20.40.60.81F(NEI)RAP, FL=5−0.05 0 0.0500.20.40.60.81 RP1, FL=5−0.05 0 0.0500.20.40.60.81 RP2, FL=5−0.05 0 0.0500.20.40.60.81 PR3, FL=5−0.1 −0.05 0 0.05 0.100.20.40.60.81F(NEI)RAP, FL=10−0.1 −0.05 0 0.05 0.100.20.40.60.81 RP1, FL=10−0.1 −0.05 0 0.05 0.100.20.40.60.81 RP2, FL=10−0.1 −0.05 0 0.05 0.100.20.40.60.81 PR3, FL=10−0.2 −0.15 −0.1 −0.05 0 0.0500.20.40.60.81NEI (Js −1)F(NEI)RAP, FL=15  near−bankintermediatecentre−0.2 −0.15 −0.1 −0.05 0 0.0500.20.40.60.81NEI (Js −1)RP1, FL=15−0.2 −0.15 −0.1 −0.05 0 0.0500.20.40.60.81NEI (Js −1)RP2, FL=15−0.2 −0.15 −0.1 −0.05 0 0.0500.20.40.60.81NEI (Js −1)PR3, FL=15Figure 3.11: Cumulative distribution plots of net energy intake in three dis-tance bands from the banks (near bank: 0.5-1m; intermediate: 0.5-1m;centre: 1-1.5m) modelled for high-flow conditions.ing habitat. While during lows most pools in East Creek indeed formed patches ofhigher net energy intake relative to the adjacent channel areas, in a few cases theydid not seem to confer such benefits. In the aforementioned example, illustrated inFigure 3.4, low NEI was related to high velocities that resulted from flow conver-gence into a narrow thalweg. Such channel geometry is by no means exceptional.Although pools are commonly thought to be associated with larger depth and lowvelocity relative to adjacent riffles, the latter does not always have to the case.While flow depth expansion is at the heart of pool definition (e.g. Lisle, 1987),the occurrence and magnitude of convective deceleration also hinges upon differ-ences in channel width between the pool and riffle sections. In mountain streamsflow convergence due to width contractions or local constrictions may be the veryreason for formation of forced pools (e.g. Lisle, 1986; Buffington et al., 2002).Over time, of course, scour acts to expand the cross-section and adjust it to elevatedvelocities and shear stresses. However, before this adjustment is accomplished, ve-locities similar to or even exceeding those in the adjacent morphological units may74RAP PR1 PR2 PR300.20.40.60.81ReachPoportion V < Vmax  FL=5FL=10FL=15Figure 3.12: Proportion of channel area at low-flow conditions where veloci-ties are below the maximum sustainable velocity for drift-feeding troutof a given body size (FL).occur in the actively forming pool. In some cases, full adjustment of cross-sectionalgeometry may never occur because bed armouring or local exhaustion of alluvialsubstrate may limit the vertical extent of scour. As a result, occasionally, in moun-tain streams cross-sectional area in pool may be reduced relative to adjacent riffles,thus maintaining high velocities in the former morphological unit. This findingpoints to the importance of hydraulic and morphological diversity of pool types,which may also result from various pool-forming mechanisms (plunge, dammed,scour, lateral separation etc.). Such diversity is recognized in several channel unitclassifications (e.g. Bisson et al., 1982, 1996; Hawkins et al., 1993; Rabeni andJacobson, 1993; Montgomery and Buffington, 1997; Halwas and Church, 2002)and its implications for fish have been discussed by some stream ecologists (Roniand Quinn, 2001; Bryant et al., 2009). However, to our best knowledge, to date,75RAP PR1 PR2 PR300.10.20.30.40.50.60.7ReachProportion NEI > 0 Js−1  RAP PR1 PR2 PR300.10.20.30.40.50.60.7Poportion NEI > 0 Js−1ReachFL=5FL=10FL=15Figure 3.13: Availability of profitable foraging habitat (NEI > 0 Js-1) duringlow-flow conditions. Left: proportion of the total channel area whereNEI > 0 Js-1. Right: proportion of the area accessible for foraging(u < Vmax) where NEI > 0 Js-1these differences have not been mechanistically and quantitatively linked to for-aging habitat quality. We believe that this study highlights the need to recognizemorphologically and hydraulically distinct sub-categories of morphological unitsas potentially relevant for ecological processes and habitat quality.Another important finding that emerges from this study and complements themodel proposed by Rosenfeld and Boss (2001), is related to the high internal het-erogeneity of morphological units in terms of their hydraulic properties and bioen-ergetic microhabitat value. In particular, transverse heterogeneity was well illus-trated in lateral separation pools, common in our study reaches. For example, themodel identifies elongated lateral shear layer zones as potential locations of highlyprofitable feeding stations. This is in line with the field observations that fish of-ten feed across velocity gradients (Fausch and White, 1981; Fausch, 1984). Thehydraulically sheltered foraging positions adjacent to swift current are commonin East Creek, because projections of rough banks and occasional in-stream woodact as flow obstructions and induce flow separation. We believe that it is thesestrong hydraulic gradients near the channel margins that result in the model pre-dictions which, in contrast to the findings of Rosenfeld and Boss (2001), indicate76−0.1 −0.05 0 0.0500.51F(NEI)NEI (Js −1)RAP  −0.1 −0.05 0 0.0500.51F(NEI)NEI (Js −1)PR1−0.1 −0.05 0 0.0500.51F(NEI)NEI (Js −1)PR2−0.1 −0.05 0 0.0500.51F(NEI)NEI (Js −1)PR3FL=5FL=10FL=15Figure 3.14: Cumulative distribution plots of net energy intake (NEI) in thestudy reaches for different fish body sizes (FL), during low-flow con-ditions. Note that only the areas where velocities are below maximumsustainable swimming velocity are considered.that profitable feeding stations may locally exist in riffles even for larger, adultfish. Although in this study we do not explicitly simulate fish growth, the modelpredicts that locally similar range of NEI values may occur in shear layers andpools; therefore, we assume that these conditions may enable positive fish growth.It appears, then, that the energetic benefit of lateral gradients can at least partlyoffset the effects of depth-limited nature of near-bank habitat.This finding highlights an advantage of our spatially explicit approach, whichallowed us to represent the full range of fine-scale habitat heterogeneity. Researchshowed that such variability in foraging habitat quality can also manifest itself inlongitudinal dimension. For example, results of Hayes et al. (2007) suggested that77RAP PR1 PR2 PR3−0.04−0.035−0.03−0.025−0.02−0.015−0.01−0.00500.005ReachMean NEI (Js−1 )  FL=5FL=10FL=15Figure 3.15: Reach-average net energy intake (NEI) in the study reaches fordifferent fish body sizes (FL), under low-flow conditions. Only theareas of the channels where velocities are below the maximum sus-tainable velocity for fish of given size were considered.the positions at the head pool were energetically advantageous for drift-feedingtrout. Similarly, Rosenfeld et al. (2008) observed that fish in enclosures locatednear an inlet of an experimental pool analogue grew faster than fish in enclosureslocated elsewhere within that habitat unit. In contrast to our study, Rosenfeld andBoss (2001) modelled NEI within each of the morphological unit types using alimited sample of focal points, which they deemed as most likely to be utilized byfish.We wish to reiterate that our results support the conclusion of Rosenfeld andBoss (2001) that, on average, pools provide a superior foraging habitat. The presentdiscussion should be viewed as contributing to a more nuanced perspective ratherthan contradicting the model of Rosenfeld and Boss (2001). We hypothesize that,in addition to the effect of fine-scale heterogeneity, the seeming divergence be-78RAP PR1 PR2 PR300.10.20.30.40.50.60.70.80.91ReachPoportion V < Vmax  FL=5FL=10FL=15Figure 3.16: Proportion of channel area at high-flow conditions where ve-locities are below the maximum sustainable velocity for drift-feedingtrout of given body size.tween this study and that of Rosenfeld and Boss (2001) regarding the ability oflarger, adult fish to maintain growth in riffles is likely to be partly a product of site-specific combination of habitat variables (depths, velocities) and their relation tofish body size. For example, near-bank zones in East Creek can be often relativelydeep even in riffle sections, because of steep banks and approximately trapezoidalshape of the channel cross-sections. This seems to suggest that a more informativeapproach to assessing fish habitat quality would be to account explicitly for fine-scale microhabitat variability and treat hydraulic habitat variables as a continuumrather than employ a simple distinction between pools, riffles, or other channelunits. Further, in order to ensure generality it may be fundamentally important toscale these variables using physiologically-relevant parameters, a readily availableproxy of which can be body size. Such approach is in fact widespread among fish79RAP PR1 PR2 PR300.050.10.150.20.250.30.35ReachProportion NEI > 0 Js−1  FL=5FL=10FL=15RAP PR1 PR2 PR300.10.20.30.40.50.60.7Poportion NEI > 0 Js−1ReachFigure 3.17: Availability of profitable foraging habitat (NEI > 0 Js-1) duringhigh-flow conditions. Left: proportion of the total channel area whereNEI > 0 Js-1. Right: proportion of the area accessible for foraging(u < Vmax) where NEI > 0 Js-1biologists (e.g. Bjornn and Reiser, 1991).Interestingly, the fine-scale results of this study illustrate how transverse habi-tat structure may differ substantially depending on body size. This finding seems tosuggest distinct energy landscapes for different age classes within a population. Inparticular, the pattern of most profitable patches may promote spatial segregationof fish that belong to different cohorts. Some of the energetically most profitablepatches for the smallest fish were predicted to occur near the banks. In contrast, themodel indicated that the best foraging positions for large fish were in the channelcentre. Such spatial distribution of fish with different body sizes has been observedin many field studies (e.g. Cunjak and Power, 1986). In addition to space use,this pattern of energetic habitat could have important consequences for fish perfor-mance and fitness. However, any speculations regarding this matter are hamperedby relatively poor understanding of the trade-offs associated with the risk of pre-dation. For example, the proximity of undercut banks seems to provide cover forfish but the shallow nature of flow in channel margins increases their vulnerabilityto avian predators (e.g. Power, 1987).In addition to the spatial patterns discussed in the preceding paragraphs, ourstudy provides a set of predictions regarding temporal fluctuations in the mosaic of80−0.1 −0.05 0 0.0500.51F(NEI)NEI (Js −1)RAP  −0.1 −0.05 0 0.0500.51F(NEI)NEI (Js −1)PR1−0.1 −0.05 0 0.0500.51F(NEI)NEI (Js −1)PR2−0.1 −0.05 0 0.0500.51F(NEI)NEI (Js −1)PR3FL=5FL=10FL=15Figure 3.18: Cumulative distribution plots of net energy intake (NEI) in thestudy reaches for different fish body sizes (FL), during high-flow con-ditions. Note that only the areas where velocities are below maximumsustainable swimming velocity are considered.foraging habitat patches. The two simulated flows can be viewed as end membersof the range of spring or early summer flows, during which trout in East Creekwould feed on drifting insects. During lower flows in late summer and early fall,flow in most riffles become too shallow for fish while pools turn into bodies ofalmost standing water, except for a jet entering pool head from the upstream riffle.Under these circumstances, fish may switch to surface (Dunbrack and Dill, 1983;Gregory and Northcote, 1993) or benthic feeding (Gregory and Northcote, 1993;Fausch et al., 1997; Nislow et al., 1998; Nakano et al., 1999). These modes offoraging, under most conditions considered to be less profitable (Dunbrack andDill, 1983; Nielsen, 1992), are not considered in our model. On the other end of81RAP PR1 PR2 PR3−0.06−0.05−0.04−0.03−0.02−0.010ReachMean NEI (Js−1 )  FL=5FL=10FL=15Figure 3.19: Reach-average net energy intake (NEI) in the study reaches fordifferent fish body sizes (FL), under high-flow conditions. Only theareas of the channels where velocities are below the maximum sus-tainable velocity for fish of given size were considered.the spectrum, even during extreme flows we expect to see rather minor changesrelative to the 0.37 m3s-1 simulation because feeding would remain restricted tothe same hydraulically sheltered areas. Only limited changes in the spatial patternsmay occur due to expansion of separation eddies at high discharge (e.g. Schmidt,1990). We view our high-flow simulations as a case of a spate, which may occur inEast Creek in response to spring storms. Under such an assumption, application ofthe same temperature and drift concentration as those used in the low-flow scenariois reasonable. Past research showed that increased rates of drift due to elevatedboundary shear stress rapidly fall after only a few minutes due to exhaustion ofbenthic supply (Gibbins et al., 2010).Temporal reorganization of foraging habitat in East Creek simulations adds82to the aforementioned spatial complexity of the ‘energy landscape’. Our findingsindicate that, as discharge increases, the profitable habitat patches are primiarilyclustered near the banks. Thus, in order to optimize their net energy intake, fishshould adjust their positions by moving towards the channel margins perhaps inresponse to velocity cues (Gowan, 2007). Indeed, a tendency for such lateral shiftin fish position has been observed with increasing discharge (e.g. Muhlfeld et al.,2001a; Schwartz and Herricks, 2005). Because of the reduced area of energeti-cally profitable habitat in the central part of the channel, expansion of separationeddies during high flows has a fundamental importance for availability of potentialforaging positions.We speculate that the temporal changes in the bioenergetic habitat value mayoccur at different rates in different morphological units, depending on channel ge-ometry. The logic underlying this conjecture is based on predictions of at-a-stationhydraulic geometry (Leopold and Maddock, 1958; Ferguson, 1986). For example,in a narrow section of the channel with steep banks velocity will increase muchfaster than in wider sections with low-angle banks. Thus, differences betweenmorphological units such as pools and riffles are likely to manifest itself also interms of temporal habitat dynamics.Furthermore, the variations in spatial structure of foraging habitat at the timescaleof hydrological event are superimposed on those expected to occur due to the sea-sonal changes in discharge (e.g. Jenkins and Keeley, 2010) and longer-term geo-morphic adjustments of channel morphology. For example, our previous researchrevealed that formation of an energetically poor pool in Figure 3.4 (a-c) was a resultof flow incision into a wedge of sediment stored upstream of a large wood piece,which recently was rearranged (Cienciala and Hassan, 2013). This adjustment wasstill ongoing at the time of our surveys, which may explain high velocities foundwithin this morphological unit. Thus, we propose that better understanding of dy-namic, four-dimensional fish habitat requires that consideration be given not justto flow variability but also to the morphological channel changes.833.4.2 Between-reach patternsAt the macrohabitat scale our low flow simulations generally indicated that reacheswith better developed morphology tend to provide more profitable foraging habitat.This finding is in concert with field observations of juvenile coho salmon (e.g. Pesset al., 2011) and a recent study that employed bioenergetic modelling approach(Rosenfeld, 2014). Moreover, our results seem to be indirectly supported by sum-mer reach-scale habitat use pattern reported for small-bodied salmonids such asCutthroat Trout (Rosenfeld et al., 2000).Under the low-flow conditions, East Creek reaches with pool-riffle morphol-ogy were predicted to provide higher proportion of channel where fish are able tohold station, higher proportion of the area of positive NEI, and higher reach-meanNEI values (except for the largest fish). Although the increase of reach-scale en-ergetic habitat quality in pool-riffle morphology was unsurprising considering ourmesoscale results, the between-reach differences were smaller than we expected.We attribute this largely to the fact that the differences in gross channel morphologybetween the study reaches were rather modest. For example, a completely planarbed in Rapid reach would almost certainly result in a more pronounced differ-ence in comparison with the pool-riffle reaches. Despite the reach being classifiedas plane-bed morphology, its bed was not entirely devoid of bedforms sufficientlylarge to influence flow field properties relevant for small fish. Our high spatial reso-lution enabled us to capture these features of bathymetry in the topographic survey.As noted in the Results section, the mescoscale bedforms such as transverse ribscan create backwater effect on their upstream side during low flows, consequently,forming small and shallow pools. Scour around flow obstructions, such as woodand bedrock outcrops, is another mechanism, which may contribute to formationof similar, ‘incipient pools’. The extent and depth of these scour holes may be lim-ited by the coarse nature of the bed (e.g. Inoue and Nakano, 1998), which preventsformation of a well-developed forced pool.Our model implies that, in spite of their relatively small magnitude, the subtleincreases in flow depth can be sufficient to markedly improve bioenergetic condi-tions for small-bodied salmonids. This finding highlights, yet again, that body sizeappears to be an important parameter that moderates the way fish interacts with84its physical environment. Equally noteworthy are two effects of bed texture on re-ducing the contrast between morphological channel types. First, the coarse natureof the bed in Rapid reach (represented in bed roughness parameter) offsets highervelocity that could be expected in a reach with limited form resistance and steeperslope. Second, the dimensions of micro- and mescoscale bedforms scales with bedmaterial size (Hassan et al., 2007), therefore, fine-grained plane-bed morphologywould not provide similar hydraulic benefits even to smallest fish. Thus, the ratioof fish body size to sediment calibre appears to play an important role in definingthe spatial scale for identification of physiologically relevant topographic featuresand to moderate the way fish interacts with its physical environment.Similar to the finer-scale findings, the model predictions indicated that the spa-tial organization of foraging habitat in East Creek at the between-reach scale mayalso change substantially during higher flow conditions. As the reach-mean veloc-ity increases, the channel area where fish can hold foraging positions is reducedin all study reaches, although this process seems to be partly offset by expansionof separation eddies in the channel margins. In East Creek, inaccessibility of mostof the channel centre for fish under high flow conditions resulted in a significantmodification of the patterns in the modeled habitat quality at low flow. Specifi-cally, in two coarser reaches with less developed channel morphology, the meanvalues of net energy intake were higher or approximately equal to those found inthe two finer-grained pool-riffle reaches. This finding seems to further support andunderscore the importance of rough banks as a habitat-forming channel feature. Athigher flow, it is that near-bank zone that defines the properties of habitat availableto fish. Our results show that the near-bank habitat is temporally stable, because itpersists regardless of flow magnitude and provides a critical hydraulic refuge forsalmonids. Such refuge is important in particular during the high flow season. Forexample, even though trout metabolic rates are lower at low temperatures, the fishcontinue to actively feed during winter (Cunjak and Power, 1986).We acknowledge that this study involved a highly limited sample of channelreaches, therefore, extrapolation of the macrohabitat-scale patterns beyond EastCreek requires extreme caution. Certainly, our findings are not directly trans-ferrable to reaches in unconstrained valleys with extensive floodplains, where sec-ondary channels are typically fundamentally important for salmonids (e.g. Tschap-85linski and Hartman, 1983; Rosenfeld et al., 2005). Another potential factor thatneeds to be considered is the downstream increase in channel scale typically ob-served in drainage networks (e.g. Leopold and Maddock, 1958). Differences be-tween our study reaches were purely due to distinct channel morphology and hy-draulic characteristics. In contrast, the downstream increase in flow dischargewould result in a change in the absolute area of habitat, roughness of banks rel-ative to channel width, as well as the dimensions of topographic features relativeto fish body size. Moreover, systematic downstream increase in velocity and depthwould influence both the mean net energy intake and its spatial patterns for a fishof given body size (Rosenfeld et al., 2007). The limited number of reaches in thisstudy is simply a function of the data-demanding nature of spatially explicit enquiryconducted at sub-meter resolution. However, we hope that, over time, gradual ac-cumulation of data from morphologically diverse streams and rivers of differentchannel scale will enable extending our findings to provide a more representativeand comprehensive range of ‘energetic landscape’ heterogeneity.3.5 Conclusions and implicationsIn this study we explored links between channel morphology, hydraulics, andspatial pattern of foraging habitat for trout. To achieve this goal we linked a 2-dimensional hydrodynamic model and a bioenergetic model for drift-feeding troutand applied them to four reaches of a mountain stream with distinct morphologies.High resolution, spatially explicit simulations provided predictions of body-sizespecific ‘energy landscapes’ that spanned micro-, meso- and macrohabitat scales.Interpretation of the model output suggested that:1. Downstream variation in flow depth at the morpological unit scale (e.g.along pool-riffle sequences) defined the longitudinal structure of foraging habitat,with pools typically being the energetic hot spots.2. Variability between mesoscale units of any type (e.g. riffle, pools) wereimportant and, occasionally, resulted in higher net energy intake in riffles relativeto pools. This led us to propose that this heterogeneity should be recognized inmesoscale studies.3. Microscale variability within each individual unit was substantial and we86suggested that ignoring or averaging out this heterogeneity may have an importantbearing on the conclusions that are reached.4. Differences in transverse (cross-stream) structure of foraging habitat qualityseem to provide an energetic mechanism which may promote spatial segregationbetween body-size (and age) classes.5. Fish body size is also an important scaling parameter for habitat variablesand sets the reference scale for physiologically-relevant features of channel mor-phology. We suggested that using body size-scaled continuous habitat variables,instead of fixed-scale classifications (e.g. pool, riffles), may help circumvent theproblem of idiosyncratic relations between the organism and channel characteris-tics, thus, enabling comparison and synthesis of various studies.6. During high flow conditions, the area of foraging habitat was reduced asvelocity in the channel centre exceeded the sustainable swimming velocities fortrout of all size classes. The near-bank zone provided most of the energeticallyprofitable habitat patches.7. Comparison of the data aggregated for the entire reaches (macroscale) sug-gested that under low flow conditions both the proportion of profitable habitatpatches and the reach-mean net energy intake increased systematically with pro-gressively better developed pool-riffle morphology.8. However, during high flows the above patterns no longer held or even re-versed. Specifically, the mean net energy intake for small fish decreased in reacheswith better developed variations in bed topography. We attribute the high-flow pat-terns mostly to the differences in bank roughness. The trend reversal observed inEast Creek suggested that broad-scale habitat connectivity may greatly benefit troutinhabiting the stream, by allowing them to maximize their energy intake throughmovement between the reaches as discharge fluctuates.The modelled between-reach patterns point to important implications for sen-sitivity of salmonid foraging habitat to climate- and land use-related landscapedisturbances. For example, moderate sediment supply regime associated withwell-developed pool-riffle morphology (e.g. Montgomery and Buffington, 1997)appears to result in the most energetically profitable foraging habitat. The qual-ity of this habitat may be sensitive to alterations of the balance between sedimentand flow regimes sufficient to result in loss of morphological complexity. Such87loss of bed variability can arise both due to increased and decreased sedimentsupply, which leads to channel aggradation and degradation, respectively. Fur-thermore, given the evidence for sensitivity of net energy intake to limited flowdepth, salmonid foraging habitat in mountain streams may be strongly impactedby changes in sediment and flow regimes that cause reduction in the surface flow(e.g. May and Lee, 2004). Finally, it appears that populations of salmonids may behighly vulnerable to habitat fragmentation that precludes long-distance movement.88Chapter 4Sampling Error in Estimates ofFlow Properties in NaturalCoarse-Bedded Streams: Effectsof Sample Size and Application toHydrodynamic Modelling4.1 IntroductionFlow fields in coarse-bedded streams are characterized by high complexity thatarises from the irregular nature of the channel boundary. Poorly sorted sediment,with the calibre of large particles of the same order of magnitude as flow depth,micro to marcoscale bedforms, rough banks, and occasional non-alluvial flow ob-structions (in-stream wood and bedrock outcrops) deflect the flow and contribute toan intricate pattern of local flow accelerations and decelerations (Lisle, 1986; Fur-bish, 1993; Buffin-Belanger and Roy, 1998; Tritico and Hotchkiss, 2005; Thomp-son and Wohl, 2009). Because of this heterogeneity, representing velocities andhydrodynamic forces that drive geomorphic processes and define hydraulic habitatis particularly challenging in these streams. The hydraulic properties vary appre-89ciably over a hierarchy of length scales, which may range from that of the channelscale down to the turbulent eddies (e.g. Church, 2007) and the unresolved hetero-geneity introduces noise into the recorded data (Cushman, 1986). In addition, indi-vidual hydraulic measurements taken with the apparatus typically deployed in thefield (e.g. Stone and Hotchkiss, 2007b; Muste et al., 2012), such as ElectromagneticCurrent Meter (ECM), Acoustic Doppler Velocimeter (ADV) or Acoustic DopplerCurrent Profiler (ADCP), integrate flow properties over a small sampling volumeand, essentially, can be considered as point measurements. In most cases, even asample that includes multiple measurements may cover only a small fraction of thearea or volume of interest.Because of these two challenges, the choice of adequate sample size is ofparamount importance for reducing sampling variability, bias, and the associatedsampling errors. Sampling error constitutes one of the fundamental considerationsfor measuring and representing heterogeneous environmental phenomena such asflow in natural river channels. Sampling error can be broadly defined as a discrep-ancy between the estimate of a quantity that was based on a sample and the truevalue of that quantity in the target population. The uncertainty in flow properties,which arises due to such errors, may also propagate into predictions of hydraulichabitat quality and geomorphic processes such as sediment transport, which aremade based on the estimated values.To date, two approaches to using point measurements of flow properties to rep-resent internally heterogeneous spatial domains have been commonly employed invarious branches of river science. First, various formulations of spatially averagedflow have been used to derive the mean value of velocity, shear stress, or other hy-draulic variables within the domain of interest (e.g. Smith and McLean, 1977; Nel-son et al., 1991; Wiberg and Smith, 1991; Bennett and Best, 1995; Byrd et al., 2000;Aberle et al., 2008; Franca and Czernuszenko, 2006; Franca et al., 2008; Pokrajacet al., 2008; Czernuszenko, 2011; Robert and Tran, 2012). This approach, for ex-ample, can be used to estimate bed roughness parameters for hydrodynamic mod-els (Hodskinson, 1996; Cienciala and Hassan, 2013). Second, in cases in which aspatially explicit approach is impossible or impractical, properties of a hydraulicdomain have also been represented though probability distributions of locally mea-sured values. For example, in several studies the within-reach variability of shear90stress was represented by fitting a gamma distribution (e.g. Paola, 1996; Nicholas,2000; Hoey et al., 2001; Ferguson, 2003; Segura et al., 2011; Pitlick et al., 2012).Probability distributions of mean velocity and depth have also been widely used infreshwater ecology to describe reach or unit-scale habitat (Lamouroux et al., 1995;Lamouroux, 1998; Lamouroux et al., 1998; Schweizer et al., 2007; Saraeva andHardy, 2009; Rosenfeld et al., 2011; Girard et al., 2012).Importantly, despite the potential for sampling errors in estimates of spatiallyaveraged variables and fitted probability distribution parameters in natural rivers,surprisingly little attention has been directed towards examining this fundamen-tal issue. To the best of our knowledge, only a few relevant investigations havefocused exclusively on relatively simple flows in straight laboratory flumes withsmooth sidewalls and planar beds (Buffin-Belanger et al., 2006; Aberle et al., 2008;Cooper and Tait, 2010). For example, drawing upon the confidence interval for-mula for normally distributed variables, Buffin-Belanger et al. (2006) reasoned thata 10-fold increase in precision in the arithmetic average of local velocity values willrequire a 100-fold increase in sample size. Their data seem to indicate that, with asample size n = 99 and confidence level α = 0.01, the confidence intervals for themean velocity were up to around 10% of the mean value. However, it is uncertainwhether these findings regarding precision may be representative of flow propertiesfor which the assumption of normal distribution is not justified. In a similar labora-tory study, Cooper and Tait (2010) demonstrated that precision of various hydraulicvariables calculated from double-averaged Navier-Stokes equations (Nikora et al.,2007a,b) strongly depended on the measurement density relative to topographiccomplexity. Taken together, this research has provided important insight into therole of sample size and sampling density on flow properties measured at the scaleof a small patch of bed. However, the laboratory findings under simplified condi-tions may not be transferrable to more complex flow fields in natural coarse-beddedchannels.In this chapter, we use an extensive field data set to investigate the effects ofsample size on sampling errors in: (1) the mean boundary shear stress and rough-ness length derived from spatially averaged velocity profiles; and (2) shape andscale parameters of gamma distribution fitted to local values of shear stress, veloc-ity, and depth. We carried out these analyses for the entire channel reaches and,91in order to reduce hydraulic heterogeneity, for data stratified according to mor-phological unit types. We extend the analyses focusing on roughness length todemonstrate the consequences that sampling error in an estimate of bed roughnessparameter may have for flow fields simulated by a hydrodynamic model. Specifi-cally, we used the range of sampling errors in bed roughness length obtained froma spatially averaged velocity profile to conduct a sensitivity analysis for a 2D hy-drodynamic model.4.2 Methods4.2.1 Field siteField data for this study were collected in two reaches of East Creek, a small moun-tain stream (Figure 4.1). The channel drains a forested watershed and is locatedabout 60 km east of Vancouver, British Columbia. One of the study reaches has apool-riffle morphology (Montgomery and Buffington, 1997), mean bed slope S =0.01, and the median and 84th percentile of bed grain size distributions (D50 andD84, respectively) are equal to 30 mm and 56 mm. The second study reach has aplane-bed morphology (Montgomery and Buffington, 1997), slope S = 0.02, andD50 = 55 mm and D84 = 105 mm. Hereafter, the reaches are referred to as ‘Pool-Riffle’ and ‘Rapid’, consistent with previously used terminology (e.g. Ciencialaand Hassan, 2013), and code-named PR and RAP, respectively.4.2.2 Field data collection and statistical analysesAt least 100 vertical profiles of time-averaged velocity were collected in each ofthe study reaches using an electromagnetic current meter. Approximately 60% ofthe profiles in the Pool-Riffle reach were located in pools and the remaining 40%in riffles. We collected the measurements during a period of low flow (Q ≈ 0.08m3s-1) in order to avoid significant changes in discharge, which are typical duringhigher discharge. To obtain the maximum number of data points in each verticalprofile, the measurements were collected throughout the flow depth. As a result,we collected at least 4 and up to 10 measurements at each vertical (in most cases≥ 5), with spacing ranging between 1-2 cm. Because of the limitation imposed by92Figure 4.1: The study reaches. Rapid (left) and Pool-Riffle-3 (right).the size of the sensor, its lowest position was set at approximately 0.02 m abovethe bed. To account for this effect, we followed previous research (e.g. Einsteinand El-Samni, 1949; Jackson, 1981; Wiberg and Smith, 1991; Smart, 1999) andintroduced a correction to the origin of the measured profiles. Specifically, wechose to displace it downwards by the distance of 0.25D84, which in our studysites is equivalent to 0.5D50 used by Wiberg and Smith (1991). In this a way, weaimed to set the origin approximately at the mean bed level, as recommended byNikora et al. (2002) and Smart et al. (2004).In addition to the hydraulic measurements, we surveyed bed material textureusing the methods described in Cienciala and Hassan (2013). Textural patcheswere first delineated using the method of Buffington and Montgomery (1999b) andthen the Wolman grid sampling (Wolman, 1954) was carried out within each of thepatch types. Using these data we calculated both local and area-weighted indicesof grain size distribution (D50 and D84, as well as < D50 > and < D84 >; where<> indicates spatially averaged values).Sampling error analysis involved a three step procedure: (1) calculation ofmean shear stress and roughness height from spatially averaged velocity profiles;(2) calculation of best-fit parameters for the probability distributions of local shearstress, velocity, and depth values; (3) calculation of sampling errors for the hy-draulic variables obtained in steps (1) and (2), and evaluation of sample size ef-fects. We carried out this procedure for both reaches and, within the Pool-Riffle93reach, for stratified pool and riffle observations separately.To calculate spatially averaged velocity profiles, we found the arithmetic meansof velocities measured at constant heights above the boundary. In cases in which noobservation at the exact vertical position was available, we interpolated the velocityvalues from the two neighbouring values located above and below it. Consideringthe close vertical spacing between the measurements, linear interpolation was as-sumed to produce values that closely approximate the true ones. The spatially av-eraged value of shear stress (< τB > and roughness height (< z0 >) was calculatedfrom the coefficients of linear regression, as spatially averaged velocity (<u>)were regressed on the logarithms of the corresponding heights over the boundary(e.g. Bergeron and Abrahams, 1992). First, the law of the wall was rewritten asfollows in order to enable fitting a linear regression:uz =1κ u∗ ln(zz0)= b1 ln(zz0)= b1 ln(z)−b1 ln(z0) = b0 +b1 ln(z) (4.1)where uz is velocity at the height above the bed z, κ is von Karman constant(κ = 0.4), u∗ is shear velocity, z0 is roughness height, and b0 and b1 are, respec-tively, the intercept and slope of a linear regression. In Equation 4.1, b0 and b1are equivalent to b0 = −b1 ln(z0) and b1 = u∗/κ . Second, these expressions wererearranged so as to solve for u∗ and z0 and the former was inserted into the shearstress formula (< τB >, Pa):< τB >= ρ < u∗ >2= ρ(κb1)2 (4.2)where ρ is water density.< z0 >= exp−b0b1 (4.3)We then expressed roughness height as a multiplier < a >, which describes therelations between z0 and a reference grain size of bed material e.g. D84 (Whitingand Dietrich, 1990):< z0 >=< a >< D84 >∴< a >=< z0 >< D84 >(4.4)94Although, in theory, the law of the wall typically applies only in the so-calledlogarithmic region near the bed, many studies found that it holds reasonably wellthroughout the flow depth (e.g. Smart, 1999). Moreover, despite inflections ob-served in the lower part of velocity profiles in flows over rough beds (e.g. Jarrett,1990; Wiberg and Smith, 1991), such effects may be localized (Lamarre and Roy,2005; Franca and Lemmin, 2009). As a result, when spatially averaged approachis adopted, semi-logarithmic profile can provide a reasonable approximation ofvertical velocity structure even in coarse-bedded channels (e.g. Franca and Czer-nuszenko, 2006).In the second step of data analysis, which involved fitting probability distri-butions to local values of hydraulic variables, we chose the gamma distribution,commonly used for this purpose in prior research (e.g. Paola, 1996; Nicholas, 2000;Rosenfeld et al., 2011). The two parameter Gamma distribution probability densityfunction is:y = (x|k,θ) = 1θ 2Γ(k)x(k−1) exp(−xθ ), 0 < x < ∞ (4.5)where x is the variable of interest, k and are two distribution parameters, eis the base of natural logarithms, and Γ is the gamma function.The parameter kdefines the shape of the distribution, which may vary from nearly symmetrical athigh values of k to strongly right-skewed at low values of k. In particular, if k= 1 the x variable has negative exponential distribution with the rate parameterequal to θ−1. On the other hand, at very large values of k, gamma distribution mayapproach a normal distribution (however, it remains more assymetrical). Therefore,the advantage of the gamma distribution is that it is flexible and may provide areasonable fit in a variety of situations.The values of gamma distribution parameters that provided best fit to the localvalues of hydraulic variables were calculated using maximum likelihood estimationimplemented in MatLab (Mathworks, 2010). For the purposes of distribution fittingwe used the measured local values of depth (d) and depth-averaged velocity (u),which were calculated for each vertical profile using the velocity measurementstaken at different heights above the bed (uz) and integrating uz with respect to depth.Following Byrd et al. (2000), we expected that at least a part of the local velocity95profiles will show substantial scatter; therefore, we chose to calculate local shearstress (τB) using local depth-averaged velocity (u) rather than the method based onfitted regression coefficients. To this end, we combined the formulation τB = ρu2∗with the flow resistance relationship of Smart (1999) rearranged to solve for u∗:τB = ρu2∗ = ρu1κ[(d+z0d)ln(d+z0z0)−1]2(4.6)The value of z0 in Equation 4.6 was taken as < a > D84.To estimate sampling variability and error (the third step in data analysis), weemployed a simple Monte Carlo algorithm for bootstrapping. For the spatially av-eraged variables, we first drew a random sample of profiles with replacement (abootstrap sample). The values of spatially averaged shear stress and roughnessheight (expressed as the multiplier < a >) were then calculated from this boot-strap sample and the procedure was repeated 5000 times. To evaluate the effects ofsample size on sampling errors the procedure was extended so as to incrementallyincrease the bootstrap sample from 5 to N, where N is the total number of observa-tions available for given reach or morphological units. For each of the < τB > and< a > estimates, which were calculated based on an individual bootstrap sample,we quantified the sampling error, following:ε(<τB>) =(< τB(n) >−< τB(N) >< τBN >)100% (4.7)and:ε(<z0>) =(< z0(n) >−< z0(N) >< z0N >)100% (4.8)where x is a variable of interest (e.g. shear stress or roughness length), ε(<x>)denotes sampling error in a bootstrap sample based on sample size n; < x(n) > isthe value estimated from that specific bootstrap sample; and < x (N)> is the meanof the sampling distribution of x (5000 bootstrap samples) at n equal to the full dataset, N, assumed to be best estimate of the true value of x.The 5th, 25th, 75th, and 95th percentiles of the distributions of < τB >, and< a > values (denoted by P5, P25, P75, and P95, respectively) served to quantita-96tively illustrate the range of sampling errors. These percentiles can be combinedinto measures of spread that are robust to outliers: the 25% trimmed range, alsoreferred to as interquartile range (IQR = P25−P75), and the 5% trimmed range(P5−95 = P5−P95). An analogous approach was applied to sampling variability anderrors in the fitted parameters of gamma distribution. Overall, this non-parametricapproach has the major advantage that it can be applied to estimate sampling er-rors and confidence intervals even in cases in which a normal distribution cannotbe assumed.As the final, additional step of our analysis we investigated the effect that sam-pling errors in spatially averaged roughness height – employed as the bed rough-ness parameter – may have on flow field characteristics predicted by a hydrody-namic model. For this purpose we used FaSTMECH, an established 2D hydro-dynamic model (Nelson et al., 2003). Specifically, we revisited simulations con-ducted for a bankfull event observed in East Creek (for details see Chapter 2 andCienciala and Hassan, 2013). For the purposes of this paper, we have rerun thesimulation, modifying only the bed roughness parameter (expressed by < a >, thespatially averaged multiplier of D84) so as to reflect the range of sampling errorsyielded by the Monte Carlo procedure described above. First, we employed thebest estimate of < a >, obtained from Rapid reach at n = N, as the reference value.Because the reach lacks a well-developed macroscale bed topography, we assumedthat this value was likely to reflect primarily the roughness of sediment grains andsmall-scale sedimentary structures. Given the spatial resolution of bathymetric data(about 10 points m-2), these features were not explicitly represented in the input bedtopography and, therefore, needed to be reflected in the roughness parameter value(e.g. Lane, 2005). Second, model sensitivity analysis was carried out using therange of sampling errors approximately equivalent to the interquartile range and5% trimmed range obtained at the sample size n = 30. All other input parameterswere kept constant. The effects of sampling errors on results of the simulationswere analysed in terms of probability distributions and spatial patterns of modelledvelocity, depth, and shear stress values calculated using Equation 4.5. To assess theeffect of sampling errors on some common measures of model performance (e.g.coefficient of determination), we also compared the modelled values of velocityand depth with those observed in the field.974.3 ResultsLarge variability was evident in local velocity profiles but in most locations verticalflow structure followed the law of the wall reasonably closely (Figure 4.2) andfitting linear regression yielded high coefficient of determination (in 82% profilesR2 > 0.7, in 75% profiles R2 > 0.8, and in 57% R2 > 0.9). However, as expected,in some locations departures from the law of the wall were substantial and theprofiles took linear, s-shaped, or irregular forms (for examples see Figure 4.2 f-h). In these cases, either no significant linear relationship existed between u andthe logarithm of z or the obtained values would not produce physically meaningfulvalues. Importantly, the spatial averaging procedure seemed to effectively removethe effects of such local departures from the log-normal velocity distribution. Asa result, the linear fit in the spatially averaged velocity profiles was very good forboth reaches and morphological unit types, with R2 values between 0.98 and 0.99(Figure 4.2).Consistent with the high spatial heterogeneity of vertical velocity structure, weobserved a large range of sampling errors in the spatially averaged hydraulic pa-rameters < τB > and < a > (Figure 4.4). Generally, these errors declined asymp-totically with increasing sample size, n. For example, in both study reaches and forboth parameters of interest, the interquartile range of percentage sampling errorsdecreased from approximately 100% of the mean value (±50%) at sample size n= 5, to 45-50% at n = 30, and about 20% (±10%) at n = 100. Similarly, the 5%trimmed range (P5−95) decreased from over 200% at n = 5 to 100-110% (±50-55%) at n = 30, and approximately 25-30% (±12-15%) as n approached 100. Atlow sample sizes P50 and P75 (positive error) corresponded to slightly higher ab-solute values of percentage errors in comparison to P5 and P25 (negative error) butthis effect was small and diminished relatively rapidly with the increasing samplesize. Notably, relatively little reduction in the interquartile range of sampling er-ror was achieved beyond the sample size of about 30. However, the 5% trimmedrange continued to decline with increasing sample size and this decline appearedto be substantial until at least 50 < n < 70. The measures of spread in samplingerrors seemed to show a small reduction when data were stratified according to themorphological unit type, but this reduction was noticeable primarily in pools (Fig-980.5 1 1.500.51uz/uz/d0.5 1 1.500.51uz/uz/d0.5 1 1.500.51uz/uz/d0.5 1 1.500.51uz/uz/d0.5 1 1.500.51uz/uz/d0.5 1 1.500.51uz/uz/d0.5 1 1.500.51uz/uz/d0 1 200.51uz/uz/d0 1 200.51uz/uz/d0.5 1 1.500.51uz/uz/d0.5 1 1.500.51uz/uz/d0.5 1 1.500.51uz/uz/dFigure 4.2: Examples of local velocity profiles measured in East Creek. Ve-locites at different vertical positions, uz are standardized by the depth-averaged values, u¯. The heights above the bed, z, are expressed as theproportion of the flow depth, d.99−3.5 −3 −2.5 −20.20.250.30.350.40.45ln height above the bedVelocity (ms−1 )  −3.5 −3 −2.5 −20.20.250.30.350.40.450.5ln of height above the bedVelocity (ms−1 )  Rapid, R 2  = 0.98Pool−Riffle, R 2  = 0.99 Pool, R2 = 0.98Riffle, R 2  = 0.99Figure 4.3: Spatially averaged velocity profiles: Rapid and Pool-Rifflereaches (left); pools and riffles within the Pool-Riffle reach (right).ure 4.4). In contrast, sampling variability and errors in unit-averaged parametersderived from the riffles data were within the same range as those observed for thereach-average values.Spatial heterogeneity in flow properties was also important for sampling errorsassociated with the best-fit maximum likelihood estimates of gamma distributionparameters. Normalized histograms indicated that the range of local velocities anddepths was equivalent to approximately double their mean values and four-to-sixtimes the mean value in case of shear stress (Figure 4.5). In general, gamma dis-tributions provided reasonable fits for both reaches and morphological unit types,with the exception of velocity in the Pool-Riffle reach. Specifically, the statisticaldistribution of local velocity values in this reach seemed to display some degree ofbimodality (Figure 4.5 e).Ranges of sampling errors for both k and θ parameters of gamma distributiondeclined asymptotically with the increasing sample size, generally similar in termsof the pattern and error magnitudes to those previously described for < τB > and< a > (Figure 4.6 and Figure 4.7). For example, the interquartile range of the per-centage sampling error for the shape parameter k ranged from approximately 70%at n = 10 to 35-40% at n = 30 and 25-30% at n = 100. The 5% trimmed range de-creased from over 200% at n = 10 to 90-100% at n = 30 and approximately 45-50%1000 50 100−100−50050100PR: < τB> errorsample size, npercentage error  0 50 100−100−50050100RAP: < τB> errorsample size, npercentage error0 20 40 60−100−50050100Pools: < τB> errorsample size, npercentage error0 10 20 30 40 50−100−50050100Riffles: < τB> errorsample size, npercentage error0 50 100−100−50050100PR: < a> errorsample size, npercentage error0 50 100−100−50050100RAP: < a> errorsample size, npercentage error0 20 40 60−100−50050100Pools: < a> errorsample size, npercentage error0 10 20 30 40 50−100−50050100Riffles: < a> errorsample size, npercentage errorP5 & P95P25 & P75medianFigure 4.4: Percentage errors in shear stress, < τB > (top row) and hydraulic roughness expressed as a a multiplier< a > (bottom row). Blue lines represent 5th and 95th precentiles, red lines represent 25th and 75th precentiles,and the black line represents the median.1010 2 4 6 801020304050 RapidNormalized shear stress 0 2 4 605101520 PoolsNormalized shear stress 0 2 4 6051015 RifflesNormalized shear stress0 1 2 301020304050FrequencyNormalized velocity 0 0.5 1 1.5 20510152025Normalized velocity 0 0.5 1 1.5 205101520Normalized velocity 0 0.5 1 1.5 2051015Normalized velocity0 1 2 30102030FrequencyNormalized depth 0 1 2 30510152025Normalized depth 0 1 2 305101520Normalized depth 0 1 2 302468Normalized depth0 2 4 60102030FrequencyNormalized shear stressPool−Riffle  histogramgamma fitFigure 4.5: Histograms of normalized hydraulic variables with the fittedgamma distribution (line): shear stress (top row), depth-averaged ve-locity (middle row), and depth (bottom row). The columns represent(from left to right): Rapid reach, Pool-Riffle reach, Pools (PR reach),and Riffles (PR reach).at n = 100. Moreover, in all variables of interest we observed a clear asymmetryin the distributions of sampling errors. For instance, P75 and P95 (positive errors)for the shape parameter (k) error represented much higher percentage errors thanP5 and P25 (negative errors) while the opposite was true for the scale parameter θ .These effects seemed to be more pronounced for smaller sample sizes. Consis-tent with these positively and negatively skewed distributions of errors, the meansof the sampling distributions of estimated gamma parameters showed clear trendswith increasing sample size. Specifically, for the parameter k it declined and for θit increased as they asymptotically converged towards the reference value. Over-all, stratification of data into pools and riffles resulted in a small reduction in thesampling error range relative to that observed in pooled data for the Pool-Rifflereach.In the last step of our analyses, we used the results outlined above to inform the1020 50 100−100−50050100PR: τB, errors in gamma parameter ksample size, npercentage error  0 50 100−100−50050100RAP: τB, errors in gamma parameter ksample size, npercentage error0 20 40 60−100−50050100Pools: τB, errors in gamma parameter ksample size, npercentage error0 10 20 30 40 50−100−50050100Riffles: τB, errors in gamma parameter ksample size, npercentage error0 50 100−100−50050100PR: u , errors in gamma parameter ksample size, npercentage error0 50 100−100−50050100RAP: u , errors in gamma parameter ksample size, npercentage error0 20 40 60−100−50050100Pools: u , errors in gamma parameter ksample size, npercentage error0 10 20 30 40 50−100−50050100Riffles: u , errors in gamma parameter ksample size, npercentage error0 50 100−100−50050100PR: d, errors in gamma parameter ksample size, npercentage error0 50 100−100−50050100RAP: d, errors in gamma parameter ksample size, npercentage error0 20 40 60−100−50050100Pools: d, errors in gamma parameter ksample size, npercentage error0 10 20 30 40 50−100−50050100Riffles: d, errors in gamma parameter ksample size, npercentage errorP5 & P95P25 & P75medianFigure 4.6: Percentage errors in gamma distribution shape parameter k for shear stress (top row), velocity (middle row),and depth (bottom row). Blue lines represent 5th and 95th precentiles, red lines represent 25th and 75th precentiles,and the black line represents the median.1030 50 100−100−50050100PR: τB, errors in gamma parameter θsample size, npercentage error0 50 100−100−50050100RAP: τB, errors in gamma parameter θ sample size, npercentage error0 20 40 60−100−50050100Pools: τB, errors in gamma parameter θsample size, npercentage error0 10 20 30 40 50−100−50050100Riffles: τB, errors in gamma parameter θsample size, npercentage error0 50 100−100−50050100PR: u , errors in gamma parameter θsample size, npercentage error0 50 100−100−50050100RAP: u , errors in gamma parameter θsample size, npercentage error0 20 40 60−100−50050100Pools: u , errors in gamma parameter θsample size, npercentage error0 10 20 30 40 50−100−50050100Riffles: u , errors in gamma parameter θsample size, npercentage error0 50 100−100−50050100PR: d, errors in gamma parameter θsample size, npercentage error0 50 100−100−50050100RAP: d, errors in gamma parameter θsample size, npercentage error0 20 40 60−100−50050100Pools: d, errors in gamma parameter θsample size, npercentage error0 10 20 30 40 50−100−50050100Riffles: d, errors in gamma parameter θsample size, npercentage errorFigure 4.7: Percentage errors in gamma distribution shape parameter θ for shear stress (top row), velocity (middlerow), and depth (bottom row). Blue lines represent 5th and 95th precentiles, red lines represent 25th and 75thprecentiles, and the black line represents the median.1040 0.5 1 1.5 2 2.505001000150020002500 Probability distribution, uFrequencyVelocity (ms −1)  0 0.1 0.2 0.3 0.4 0.5 0.6 0.705001000150020002500 Probability distribution, dFrequencyDepth (m)0 10 20 30 40 50 60 70 80010002000300040005000600070008000 Probability distribution, τBFrequencyShear stress (Pa) 0 0.01 0.02 0.03 0.04 0.05 0.0600.20.40.60.81Shields stressProportion smallerCumulative distribution, τ*< a>=0.055< a>=0.0825< a>=0.11< a>=0.1375< a>=0.165Figure 4.8: Results of hydrodynamic modelling (FaSTMECH) under differ-ent bed roughness parameter scenarios: frequency distributions of mod-elled velocity (top left); frequency distribution of modelled depth (topright); frequency distributions of shear stress calculated using Equa-tion 4.6 (bottom left); cumulative frequency distributions of Shieldsstress (bottom right).choice of bed roughness parameter values for sensitivity analysis of the hydrody-namic model. Specifically, we tested the following values: <a>= 0.11 (the meanof the sampling distribution for Rapid reach at n = N, adopted as the referencevalue), < a > = 0.1375 (the reference value + 25%), < a > = 0.165 (the referencevalue + 50%), < a > = 0.0825 (the reference value 25%), and < a > = 0.055(the reference value 50%). The range ±50% error represented the 5% trimmedrange of errors in < a > observed at n = 30, which implies that there is a 90%probability that the roughness parameter estimate based on such sample will havea smaller or equal sampling error. The range ±25% approximately corresponds tothe interquartile range at n = 30 but is also roughly equivalent to the 5% trimmedrange at n = 100. This implies that, when samples of 30 or 100 profiles were col-lected there would be, respectively, a 50% or 90% probability that the roughnessparameter estimate would fall within the range bounded by these error values.105Table 4.1: Measures of model performance calculated for all bed roughnessparameter scenarios. < a > is the roughness parameter, expressed as amultiplied of D84, R2 is coefficient of determination, b is the slope oflinear regression, and RMSE denotes root mean square error (values inparentheses express it as a percentage of the mean value)Roughness Velocity Depth< a > R2 Slope, b RMSE (%) R2 Slope, b RMSE (%)0.055 0.76 1.25 0.21 (25.3) 0.75 1.07 0.024 (8.4)0.083 0.76 1.10 0.18 (21.7) 0.70 1.06 0.027 (9.4)0.110 0.75 0.89 0.15 (18.1) 0.64 1.04 0.031 (10.6)0.138 0.75 0.83 0.14 (16.9) 0.56 1.03 0.036 (12.3)0.165 0.74 0.80 0.14 (16.9) 0.48 1.02 0.042 (14.5)Mapping of our results showed that local differences in shear stress, expressedas a proportion change relative to the reference value (τB based on < a > = 0.11),varied between -1 and 1. This suggested up to 100% change in local shear stressvalue due to a change in the bed roughness parameter (Figure 4.9). However, themajority of the bed area experienced changes within ±0.4 (40% difference) andonly occasionally exceeded ±0.6 (60%). These relative difference maps yieldedtwo other important insights. First, the magnitude of changes in τB had a clearspatial structure with large and small differences in the modelled shear stress be-ing clustered in space. Second, the direction of changes in shear stress varied inspace under the same bed roughness scenario and different parts of the bed expe-rienced positive and negative changes in τB. The areas where shear stress changeswere positively correlated to changes in roughness value appeared to roughly cor-respond to low velocity zones (backwater, near-bank) while the areas where shearstress changes were negatively correlated to the changes in bed roughness tendedto occupy high velocity zones.Interestingly, the measures of linear regression fit for velocity data differedrelatively little in response to large changes in the bed roughness parameter (Fig-ure 4.10 and Table 4.1).More substantial differences were observed for flow depth,although mostly in response to a large change in the bed roughness parameter.106< a > = 0.055  < a > = 0.0825  < a > = 0.1375  < a > = 0.165  Relative shear  stress difference -0.8 – -0.6  -0.4 – -0.2  -0.2 – 0 0 – 0.2  0.2 – 0.4  0.6 – 0.8  0.8 – 1  > 1  -1 – -0.8  0.4 – 0.6  -0.6 – -0.4  Figure 4.9: Relative differences in the simulated shear stress with respect tothe reference roughness scenario < a >= 0.11. From left to right: <a >= 0.055, < a >= 0.0825, < a >= 0.1375, and < a >= 0.165.4.4 Discussion4.4.1 Sampling errorsOur results from East Creek suggest that, despite the complex nature of the flowfield, distributions of spatially averaged velocity above the bed roughness layerwere reasonably described by the law of the wall. This outcome stemmed fromthe fact that the measured portions of the local velocity profiles were often ap-proximately semi-logarithmic, a finding that is in line with a number of previousstudies conducted in other coarse-bedded channels (e.g. Nikora and Smart, 1997;Lamarre and Roy, 2005; Stone and Hotchkiss, 2007a; Franca and Lemmin, 2009).Within the sampled range of heights above the bed there was no strong evidence1070 0.2 0.4 0.6 0.8 1 1.2 1.4 1.600.20.40.60.811.21.41.6 Evaluation, uModelled velocity (ms−1)Observed velocity (ms−1)  0.2 0.25 0.3 0.35 0.4 0.450.20.250.30.350.40.45 Evaluation: depth, dModelled depth (m)Observed depth (m)< a>=0.055< a>=0.0825< a>=0.11< a>=0.1375< a>=0.165Figure 4.10: Scatter plots of model evaluation data under different roughnessscenarios: velocity (left); and depth (right). Solid lines represent best-fit regression lines.of a persistent wake effect (e.g. Bathurst, 1988; Jarrett, 1990; Wiberg and Smith,1991), which would result in an s-shaped spatially averaged velocity profile thatresembles a mixing layer (e.g. Katul et al., 2002). One possible explanation forthe lack of a clear inflection in the spatially averaged velocity profile in East Creekand the good linear regression fit is our inability to measure flow within the bedroughness layer. We hypothesize that the form drag responsible for such a wakeeffect manifested itself primarily in that near-bed region below our sampling do-main, where the concentration of sediment particles was sufficiently high to extracta substantial amount of momentum from the flow (Wiberg and Smith, 1991). Localaccelerations and decelerations recorded in our local profiles probably reflected thepresence of particularly large roughness elements and appeared to largely cancelout in the spatially averaged flow structure. Overall, we assumed that applicationof the law of the wall to spatially averaged flow above roughness layer was justi-fied and that the derived values of < τB > and < z0 > reflected shear stress andhydraulic roughness at the roughness crests (Franca and Lemmin, 2009).The bootstrapping procedure revealed that the high spatial heterogeneity of theflow field in East Creek resulted in substantial sampling errors in the spatially av-eraged shear stress and roughness height values. The effects of this sampling vari-108ability on accuracy of estimates can be considered from the perspective of samplingbias and precision. For the purpose of this paper, we followed Walther and Moore(2005) and accepted the definition of precision as ‘the statistical variance of the es-timation procedure’ (West, 1999). Bias, on the other hand, was understood as ‘thedifference between a population mean of the measurements or test results and anaccepted reference or true value’ (Bainbridge, 1985). Our results from East Creekindicated that the estimates of spatially averaged hydraulic variables, < τB > and< z0 >, had very low precision unless a large sample size was employed. Impor-tantly, in current practice in river science, sample sizes have been commonly <30and spatially averaged properties of flow are often calculated based on a few mea-surements only (e.g. Robert et al., 1992; Robert, 1997; Lawless and Robert, 2001;Robert and Tran, 2012). The interquartile range and 5% trimmed range of errorsillustrated that, even at sample size n = 30, the probability of sampling errors ex-ceeding 20-25% was as high as 0.5 and the probability of errors exceeding ±50%was 0.1. At lower values of n, the probability of errors in excess of±50% equalledor even exceed 0.5. According to our results, the estimates of < τB > and < a >were unbiased. Our findings regarding the relationship between sample size andprecision are broadly consistent with the pattern expected under the assumption ofnormal distribution (e.g. Buffin-Belanger et al., 2006). Specifically, the errors de-clined at a similar rate as a function of approximately n-0.5, although in our data theexponent appeared to be somewhat lower. Overall, the outcomes of this analysisare qualitatively similar to the laboratory findings of Buffin-Belanger et al. (2006)and Cooper and Tait (2010).Results of the second part of our analysis indicated that, in most cases, a gammadistribution provided a reasonable or even good fit to the data sets of local veloc-ities, depth, and shear stress. However, bimodality observed in the measured ve-locities in the Pool-Riffle reach resulted in a noticeable discrepancy between thepattern observed in field data and that modelled by a gamma distribution based onthe best-fit parameters. We attribute this bimodality to rather pronounced differ-ences between velocities in pools and riffles. Our measurements were conductedat relatively low flow, when differences between these two types of morphologi-cal units tend to be accentuated. A much better fit of gamma distribution that wasachieved when the velocity data were stratified according to morphological unit109type seemed to confirm our interpretation. This finding highlights that, despite itsflexibility, application of a gamma distribution at the reach scale may be limited inlow flow conditions.The parameters of the gamma distribution fitted to the data sets of local shearstress, depth, and depth-averaged velocity displayed sampling variability and errorbroadly similar in magnitude to that in spatially averaged variables. This low pre-cision of parameter estimates led to a substantial uncertainty as to true probabilitydistribution of hydraulic variables of interest. Our results also suggested that sam-pling errors for the parameters were assymetrical. Further analyses revealed thatthe non-zero values of the median errors observed at low sample sizes paralelledthose of the mean errors, which we interpreted as indicative of bias. Bias in k,was positive and indicated a systematic overestimation of the parameter value. Incontrast, the scale parameter θ was clearly affected by a negative bias. We believethat this bias is not a function of the sampling procedure but rather of the MLEparameter estimation method. Past research has reported that MLE can producebias at small sample sizes, including specifically the situation when it is applied toestimate gammma distribution parameters (e.g. Bownan and Shenton, 1982; Gilesand Feng, 2009). Taken together, such imprecision and systematic errors may haveprofound implications for characteristics of the resulting distribution. For exam-ple, our results suggested that at low sample sizes, gamma distribution fitted tothe East Creek data was more symmetrical and had smaller spread than the ‘true’distribution (or, strictly speaking, the best estimate thereof). In river research prac-tice, the sample sizes employed to fit statistical distributions of hydraulic variablestend to vary between 30 and a few hundred measurements (e.g. Paola, 1996; Lam-ouroux et al., 1998; Schweizer et al., 2007; Rosenfeld et al., 2011). If our resultsare broadly representative of other streams, that would imply a great deal of un-certainty as to the fitted distribution parameters in cases falling near the lower endof this sample size spectrum. Conversely, samples sizes that are closer to the otherextreme should be unbiased and the potential for errors as well as their magnitudeshould be much lower.There were two evident commonalities in the results of bootstrapping analysisapplied to the spatially averaged variables and probability distribution parameters.First, data stratification according to the morphological unit type achieved rela-110tively little in terms of reducing sampling variability and error. Second, becauseerrors seem to decline with approximately square root of the sample size, in bothanalyses the increase in the estimate precision beyond the sample size of 60-70 wasconsidered small relatively to the required sampling effort. We recognize that greatcaution is needed in extrapolating the results of our study and that the choice ofsample size will obviously vary from case to case, depending on the study objec-tives and the desired (or acceptable) magnitude of errors. Nevertheless, we believethat our results can be used as a first-order approximation to guide sampling designfor surveys that involve similar hydraulic measurements in streams broadly similarto East Creek.Overall, based on the results of both bootstrapping analyses we suggest thatspatial representativeness of hydraulic measurements deserves significantly moreattention than it has received thus far. Spatially representative measurements ofhydraulic properties are crucial for linking flow to geomorphic or ecological phe-nomena. For example, sediment transport rates measured by bedload samplers orpit traps integrate effects of flow forces exerted over some areas of the bed up-stream of the device. Similarly, mobile aquatic organisms such as fish ‘sample’flow, which varies across their territory. In these and many other cases, meaningfulintegration of data sets requires that they are expressed at a consistent spatial scale.Given high spatial heterogeneity of flow in natural coarse-bedded channels, largenumbers of point measurements seem to be required for such application. Impor-tantly, sampling errors in the estimated values of hydraulic variables may propagateinto derived quantities, for example, habitat quality measures or sediment transportrates (especially given the non-linear character of sediment transport relations).4.4.2 Consequences of sampling errors for predictions ofhydrodynamic modelOur case study demonstrated that sampling-related errors in the bed roughness pa-rameter estimate strongly influenced the predictions of the hydrodynamic model.Varying the roughness parameter within the interquartile range and 5% trimmedrange of errors observed at the sample size equal to 30 resulted in pronounceddifferences in both probability distributions and spatial patterns of velocity, depth,and shear stress. Because the proportion of the total bed area predicted to be par-111tially mobile (Shields stress >0.03) was as low as 20-25% in all five simulations,the 3.5% differences between them were equivalent to 15-20% error in the spatialextent of these zones relative to the reference scenario (< a > = 0.11). It appearsthat both the magnitude and non-random spatial structure of the observed errorsin the modelled hydraulic quantities have significant implications for morphody-namic and ecological modelling. For example, in response to a given change inroughness parameter the modelled τB in East Creek increased in some parts of thechannel and decreased in other parts. Enhanced shear stress heterogeneity seemedto occur when the roughness parameter was underestimated and the opposite wastrue when it was overestimated. These findings are important because morphody-namic processes in coarse-bedded rivers have been shown to be sensitive to theirspatial configuration (e.g. Lane and Richards, 1997), which i turn is controlled bythe spatial pattern of bed shear stress. Because velocity, depth, and shear stressare considered to be ecologically relevant for aquatic organisms, the differencesin flow field properties under the range of tested bed roughness parameter valueswould also result in different availability, distribution, and suitability of modelledhabitat. The relative locations of predicted habitat and geomorphic processes may,in turn, be critical for establishing habitat disturbance risk (e.g. May et al., 2009;Wheaton et al., 2010; Cienciala and Hassan, 2013). Taken together, these resultscomplement those reported by Legleiter et al. (2011) for errors in bed topographyand we echo their call for incorporation of input data uncertainty into the hydrody-namic modelling framework. In light of our results, we suggest that the stochasticapproach they proposed for bathymetric data should be expanded and include alsoother model parameters such as bed roughness.Although the range of errors in <a>adopted for sensitivity analysis may seemrather high (especially ±50% equivalent to 5% trimmed range at n =30), we be-lieve that similar errors could also arise from other parameterization methods. Forexample, one of the common ways of expressing hydraulic roughness is througha roughness length parameter, denoted as ks (e.g. Booker et al., 2004; Lacey andMillar, 2004). Empirical data reported in the literature indicates that the value ofks is a function of bed material calibre but there is some uncertainty regarding itsexact value, which usually falls within the range of 3-4 D84 (e.g. Hey, 1979; Whit-ing and Dietrich, 1990; Wiberg and Smith, 1991; Clifford et al., 1992; Ferguson,1122007). Roughness length and roughness height are related to one another in thefollowing way: ks = 33z0 (e.g. Smart, 1999). Thus, the uncertainty in roughnesslength value translates to the following range of possible roughness heights: 0.09< a < 0.12. Moreover, it has been argued in the context of hydrodynamic modelsthat the value of these multipliers may differ depending on spatial resolution (e.g.Nicholas, 2001; Horritt, 2005; Lane and Ferguson, 2005). Specifically, the valuesmay depend on the spatial scale of bed roughness that is not captured in bathymet-ric data and, therefore, needs to be represented by the parameter value (Lane andFerguson, 2005). The uncertainty in the multiplier value is further exacerbated bythat associated with indices of bed material calibre. For example, Rice and Church(1996) showed that sediment surveys using the popular Wolman method may resultin 20-25% sampling errors in grain size indices such as D50 and D84 when sam-ple size is equal to 100. This error in bed material size would propagate into theestimated value of ks or z0.In light of this discussion, it is interesting to note that the best estimate of bedroughness in this study, < z0 >= 0.11D84, was in close agreement with prior re-search in gravel-bed channels, in which the reported values of z0 usually oscillatedaround 0.09 - 0.1D84 (e.g. Whiting and Dietrich, 1990; Wiberg and Smith, 1991).Moreover, this is almost exactly equivalent to ks = 3.5D84, which was proposed asthe measure of hydraulic roughness that includes the effects of small-scale sedi-mentary structures (Clifford et al., 1992). This in turn seems to suggest that such aparameter value was suitable given the spatial scale of bed roughness, which wasnot explicitly represented in our bathymetric data.Importantly, considering the large range of bed roughness parameter errorsused in this sensitivity analysis, its effects on model performance measures weresurprisingly modest. It appears that the regression-based performance indices, atleast those for the range of ±25% error, were similar enough that any of the so-lutions could be considered as acceptable. Moreover, given that some degree ofuncertainty is associated with all data that constitute model input, we hypothe-size that small differences in the remaining model parameters or bed topographycould result in even closer convergence between the outcomes of model evalua-tions. Therefore, our results seem to point to a high potential for model equifinality,that is, a situation in which multiple sets of parameters can yield equally acceptable113solutions (e.g. Beven, 2006). We suspect that such situations can arise not only dueto sampling variability in model parameters derived from field data but also whenthey are calibrated so as to obtain best fit between measured and predicted valuesof a selected variable (in practice usually water surface elevation). For example, insmall-to-intermediate channels, according to the classification proposed by Church(1992), relative roughness falls into the range: 1 < d/D84 < 10. In our experience,mean bed elevation errors in topographic input to a model (DEM) are frequentlyof the same order of magnitude as the median size of bed material: ε ≈ D50 (e.g.Cienciala and Hassan, 2013). Assuming D50 ≈ 0.5D84 (as in East Creek), we ob-tain: 0.05 <ε/d <0.5, which means that DEM errors in such channels may rangebetween 5% and 50% of the flow depth. In such a case, calibration of a model toobtain a good fit between modelled and observed water surface elevations (e.g. Mayet al., 2009; Harrison et al., 2011; Sandbach et al., 2012) may often lead to substan-tial errors in the simulated velocity and depth. If bed elevation is overestimated,forcing the water surface to match the measured one will lead to underpredictionof depth and, consequently, overprediction of velocity. These errors will in turnpropagate into the modelled shear stress. As a result, we conclude that – unlike inlarge rivers (e.g. Sandbach et al., 2012) – use of water surface elevation to calibrateand evaluate hydrodynamic models in coarse-bedded channels with intermediaterelative roughness may not be superior over other approaches. We suggest thatfuture research into this subject should consider whether, in the case of hydrody-namic models applied to coarse-bedded streams, evaluation procedures could beimproved by joint consideration of flow depth and velocity.4.5 ConclusionsIn summary, this study has investigated the effect of sample size on sampling vari-ability and error in hydraulic variables quantified from spatially averaged velocityprofiles and in parameters of probability distributions fitted to samples of local hy-draulic data. We found that, due to substantial sampling variability, the precision ofsuch estimates was low unless a very large sample size was employed. Moreover,in case of fitted parameters of the gamma distribution, the accuracy of estimatesobtained from small samples was affected by bias. We attributed this bias to the114application of MLE method to a small sample rather than to our sampling proce-dure. Considering the sample sizes typically employed in river science, it appearsthat spatially averaged hydraulic variables as well as parameters of probability dis-tributions fitted to local data may often be associated with high uncertainty. Thisstudy also highlighted the practical importance of such uncertainty by demonstrat-ing that errors in hydraulic variables may propagate into various derived quanti-ties. Specifically, the predictions of a hydrodynamic model differed substantiallyin terms of probability distributions and spatial patterns of the modelled variablesas the value of roughness parameter was varied to assess the effects of samplingerrors. Overall, these findings led us to suggest that in the practice of river sciencemore consideration should be given to the problem of sampling variability and er-ror. Given the widespread use of various formulations of spatially averaged flowstructure and fitted probability distributions in hydrological, geomorphic, and eco-logical disciplines or river science, we believe that further research into this subjectis warranted.115Chapter 5Concluding Remarks5.1 IntroductionThere is considerable interest in understanding how hydrogeomophic conditionsdefine habitat for salmonids in running waters. Interdisciplinary research focusedon such linkages contributes to a better insight into the broader issue of interactionsbetween organisms and their physical environment. Appreciation of these linkagesis essential for tackling the pervasive degradation of lotic ecosystems (Ricciardiand Rasmussen, 1999; Arthington et al., 2006; Vorosmarty et al., 2010; Poff et al.,2012; Poff and Matthews, 2013) and developing much-needed scientific underpin-nings for sustainable land and resource management in the face of climate changeand intensifying land use (e.g. Battin et al., 2007; Beechie et al., 2010).The overarching goal of this thesis was to investigate how heterogeneity inhydrogeomorphic channel processes and characteristics controls the spatial pat-tern of fish habitat. Specifically, I focused on habitat for small-bodied salmonids inmountain streams as a model system for such biophysical relationships. To achievethis goal, I linked extensive field data, collected over the period of 2009-2012 infour reaches of a trout-bearing mountain stream (East Creek), with mathematicalmodels. In particular, I used detailed topographic surveys and GIS-based terrainmodelling to represent channel morphology during each year of this period. Dif-ferencing of sequential digital elevation models enabled me to track inter-annualmorphological changes. In addition, photo and ground-based surveys served to116map patches of bed texture while bed surface sampling provided information onsediment composition within the patches. Furthermore, I carried out a range of hy-draulic measurements that included velocity profiles, discharge, and water surfaceelevations at various flows ranging from spring baseflow conditions to a bankfullevent. I used the bathymetric, textural, and hydraulic data to parameterize and eval-uate a 2D hydrodynamic model, which enabled me to simulate velocities, depths,and shear stress at three different discharges. Overall, the above data allowed meto examine the interactions between channel morphology, flow forces, and bed tex-ture within the four study reaches. A range of habitat models were then employedto translate these hydrogemorphic controls into ecologically meaningful descrip-tion of habitat availability, quality, and disturbance. While the spawning habitatmodels were based on pre-existing relations, I modified and expanded a bioener-getic model for foraging habitat of drift-feeding trout. In particular, I explicitlyaccounted for both prey interception and handling time and adjusted the intercep-tion swimming speed to reflect published experimental data. High resolution ofthe field data and their considerable geographic coverage provided a unique op-portunity to gain insight into the spatial pattern of fish habitat across scales, frommicrohabitat to between-reach.5.2 Summary and synthesisIn Chapter 2, I focused on spawning habitat availability and disturbance risk. Fine-resolution analysis showed that availability of potential spawning substrate anddisturbance risk differed substantially between the study reaches. In two reachesdominated by cobble-gravel sediment, most of the bed was generally too coarsefor spawning and potential substrate appeared to be restricted to small areas pro-tected from flow by in-stream wood or channel bank projections. However, thefine texture of sediment associated with these zones was assessed as posing highdisturbance risk. In contrast, generally finer character of the bed in the remainingtwo reaches was associated with high availability of potential spawning substrate.Moreover, much of these sedimentary patches were unaffected by excess fine sed-iment deposition, because they were located in the unobstructed portions of thechannel and exposed to relatively high shear stress. In all study reaches bed mobil-117ity and risk of scour disturbance was relatively limited and showed no correlationwith the modelled shear stress. However, we observed a clear dependence of scouron local sediment supply.Aggregation of these results at the reach (macrohabitat) scale indicated that twohabitat domains exist within the study section of East Creek. The coarser reacheswere associated with low availability of potential substrate and high disturbancerisk. In contrast, the finer reaches had abundant spawning gravel and low distur-bance risk. Because of low sediment supply and limited hydraulic diversity, bedtexture, which controls suitability of bed for spawning, changed roughly uniformlyover most of the bed. The abrupt nature of transition between the two contrast-ing domains led us to hypothesize that small-bodied salmonids in similar mountainstreams may be vulnerable to habitat fragmentation that prevents fish movementbetween reaches. In addition, sensitivity of bed mobility to local sediment supplythat was observed in this research suggested that bed scour may become a more im-portant disturbance agent in similar stream reaches if environmental change leadsto increased sediment supply.Chapter 3 extended this research by considering foraging habitat in the samestudy reaches. Fine-scale analyses suggested that pools constitute the most en-ergetically profitable habitat patches although some pools associated with stronglateral constrictions did not provide habitat superior to other types of morphologi-cal units. Moreover, substantial heterogeneity existed within morphological units.In particular, the lateral pattern of net energy intake revealed that channel mar-gins can provide foraging positions that provide relatively high energy intake. Thisnear-bank zone was especially profitable habitat for small fish, while best feedinglocations for large individuals occurred in the channel centre. A comparison ofthe modelled patterns of habitat at low and high flows suggest that as dischargeincreases profitable habitat patches shift toward the banks. Overall, our findingsled us to propose that irregular banks are an essential feature of salmonid habitatin mountain streams.Upon the aggregation of low flow results to analyze between-reach pattern, wedetected a relatively consistent increases in the area of positive net energy intakeand the mean NEI in reaches with better developed pool-riffle topography. How-ever, under high flow conditions the latter trend no longer held or even reversed,118indicating that coarser reaches with a simple morphology provided more profitableforaging habitat. We attributed this outcome to effects of rough channel banks inthe coarser study reaches. The reach-scale findings also suggested that the mo-saic of foraging patches of different quality may shift substantially in response tohydrograph fluctuations.Taken together, these two studies provide a more comprehensive insight intothe effects of the hydrogeomorphic character of the channel on complementarytypes of fish habitat. There are two ways in which the observed differences betweenthe study reaches can be interpreted. First, each of the reaches can be thought of asrepresentative of a different stream or as a sub-section of a stream that is isolatedfrom other reaches that display different morphological styles by barriers impass-able to fish. Second, each of the study reaches can be viewed in the spatial contextof the reaches adjacent to it, which are potentially available for dispersing fish. Inthe former scenario, for example, productivity of habitat in streams represented byRapid and Pool-Riffle-1 reaches would be negatively affected by the shortage ofspawning habitat. On the other hand, the considerable amount of foraging habitatrelative to potential spawning gravel would act to reduce competition between ju-venile fish, thus promoting better growth and better survival. In contrast, streamsrepresented by Pool-Riffle-2 and Pool-Riffle-3 reaches would probably face the op-posite situation. High availability of spawning habitat would likely lead to higherproduction of age-0 fish but, given higher density, growth and survival of juvenilefish would be more strongly limited by competition for food and space. Using anenclosure experiment, Boss and Richardson (2002) demonstrated that growth ofCutthroat in East Creek is in fact food-limited. This limitation of course would bemore severe under increased fish density. The lack of complementary rearing habi-tat was previously proposed as an explanation for limited production of juvenilefish in other trout-bearing streams (e.g. White and Rahel, 2008).Entirely different population dynamics would be likely to arise in the secondscenario, in which the adjacent study reaches are accessible to moving fish. First,the competition between juvenile fish in the two finer pool-riffle reaches wouldbe likely to promote dispersal of subordinate, outcompeted individuals in searchfor energetically profitable habitat. For example Wilzbach (1985) showed thatemigration of trout from experimental channels was much higher under low food119abundance. In the absence of movement barriers sampling of resources would belikely to take place at between-reach distances, as observed by Gowan and Fausch(2002). The coarser two reaches, themselves most probably having low recruit-ment, would provide highly needed additional rearing habitat for the outmigrantsfrom the pool-riffle reaches. Thus, spatial clustering of individuals generated byspawning would be reduced at later life stages by progressive fish dispersal (Einumet al., 2008). For example, the model of ideal free distribution of unequal competi-tors (Parker and Sutherland, 1986), which posits that distribution of animals atequilibrium should result in a match between resource availability and their rela-tive competitive weights, has gained supported in salmonid fish (Grand, 1997). Areverse direction of movement would be expected for individuals which occupy thetwo coarser reaches and reached sexual maturity (age-2+; De Groot et al., 2007).These fish would likely seek to access spawning sites in Pool-Riffle-2 and Pool-Riffle-3 reaches, where spawning gravel is much more abundant.In summary, in the scenario that assumes habitat connectivity, the between-reach movements of fish would likely be induced by a combination of ontogenetichabitat shift and the spatial configuration of complementary habitat patches. Suchmovements would add to those that occur at the between-unit scale and are asso-ciated with spatial reorganization of habitat due to hydrograph fluctuation. Indeed,field observations suggest that unit to reach-scale movement appears to be the dom-inant mode of mobility in resident Cutthroat Trout populations (e.g. Gresswell andHendricks, 2007). Overall, then, we hypothesise that the synergistic exchanges be-tween reaches with different relative proportions of complementary habitat typeswould be likely to result in higher total habitat productivity in comparison to thesum of habitat productivity of the same reaches in isolation. Results reported byKim and Lapointe (2011) and Falke et al. (2013) lend support to the central role ofcomplementary habitats for salmonid space use.In Chapter 4, we examined the issue of sampling error, with the goal of ad-dressing the question of how it can affect the parameter and output of a modelapplied in this research. In particular, we focused on bed roughness, a key parame-ter of the hydrodynamic model. For comparison, we extended this investigation toparameters of fitted distributions of other hydraulic parameters. Fitting probabilitydistributions is a method commonly used in fish habitat studies to represent habitat120heterogeneity in the absence of spatially explicit data such as those generated by ahydrodynamic model. Our findings illustrated that large errors in the variables ofinterest may arise when their estimates are based on sample sizes commonly usedin river science. Errors of such magnitude in bed roughness parameter resulted inconsiderably different characteristics of the predicted flow field.5.3 Broader implicationsThis thesis contributes to better understanding of mechanisms that link hydrogeo-morphic channel processes in mountain streams to spawning and foraging habitatfor salmonid fish. This insight can inform predictions regarding the consequencesthat alterations in the conditions that govern channel behaviour may have on fishhabitat in running waters (e.g. Jenkins and Keeley, 2010; Wenger et al., 2011, 2013;Leach et al., 2012; Goode et al., 2013). As noted in the preceding sections, the gov-erning conditions of fluvial systems have been strongly influenced by land use andclimate change. Below, we briefly situate our findings in the broader context ofhydrogeomorphic aspects of this environmental change, focusing specifically onPacific Northwest.Changes in flow regime, for example, are likely to substantially alter hydroge-omorphic controls relevant to fish habitat. In particular, peak flow frequency, du-ration, and magnitude (hereafter ‘peak flows’) are important factors shaping chan-nel morphology and texture. In addition, low flow magnitude and duration (‘lowflows’) are critical for defining the volume of available hydraulic habitat. Forestharvest, as the most prominent land use in Pacific Northwest, has been reportedto cause no to modest increases in peak flows while summer streamflow was typi-cally found to increase (Moore and Wondzell, 2005; Grant et al., 2008). However,a reduction in summer baseflows, attributed to changes in vegetation compositionduring regrowth stage, was also reported (Hicks et al., 1991; Jones and Post, 2004).Hydrological effects of climate change in each specific case may vary substantiallydepending on the type of hydrological regime (e.g. Pike et al., 2008). For instance,increases in peak flows are expected to occur due to increased frequency of rain-on-snow events (Hamlet and Lettenmaier, 2007) or, in pluvial regime streams, of highintensity rainstorms (Loukas et al., 2002). In addition, reduction in snow storage121in snowpack may amplify winter flows at the expense of the spring freshet in chan-nels with nival and hybrid flow regimes (e.g. Stewart et al., 2005). On the otherhand, smaller floods may result from reduced frequency of rain-on-snow eventsin low elevation channels (McCabe et al., 2007). Furthermore, smaller overwintersnow storage in streams of nival and hybrid regimes are likely to lead to reducedsnowmelt freshets (Luce et al., 2012). Summer low flows, on the other hand, areexpected to decline regardless of the hydrological regime (Pike et al., 2008; Luceet al., 2012).In the context of our findings, the diminished summer low flows may be amongthe most important hydrological effects on salmonid habitat in mountain streams.A decrease in flow depth is likely to contribute to reductions in net energy intake,especially for larger fish. However, potential peak flow modifications could alsoinfluence both foraging and spawning habitat. For example, other factors beingconstant, increased peak flows could degrade bars and riffles, causing loss of highquality foraging habitat in pools. In contrast, in streams with high sediment supply,higher peak flows could contribute to increasing topographic variability and pooldevelopment. Finally, the elevated peak flows would also lead to bed coarsening.As a result, availability of spawning gravels in mountain streams in which, similarto East Creek, bed material calibre is close to a threshold of suitability for spawningfish, could be substantially reduced.The findings presented in this thesis suggest that such increases in sedimentsupply may have far reaching effects for salmonids in the affected streams. Whileincreased sediment inputs to streams have been well documented result of landuse-related landscape disturbance (e.g. Roberts and Church, 1986), recent researchsuggests that sediment supply regime alteration could also arise due to climatechange. For example, increased occurrence of landslides has been predicted forsouthwest coastal British Columbia due to higher frequency of intense rainfallevents (Jakob and Lambert, 2009). Observational data from the northern part ofthis province suggests such increases in the frequency of large mass movementsin the recent decades (Geertsema et al., 2006). Increased occurrence of wildfiresis another important factor which may contribute to reduced slope instability andelevated sediment supply to streams in semi-arid climate (Goode et al., 2012).Our results suggest that streams similar to East Creek may be sensitive to122changes in sediment supply regime. We believe that the nature of fish habitat re-sponse will depend on the current hydrogeomorphic regime and the magnitude ofthe change. For example, a shift to a high supply state and the concomitant lossof pools filled by sediment (e.g. Madej and Ozaki, 1996) would strongly affectforaging habitat quality, especially for larger fish. This impact could be further ex-acerbated by a decrease in food availability due to a shift to burrower invertebratetaxa (Suttle et al., 2004) and reduced hydraulic connectivity as a higher proportionof summer streamflow in deep alluvium occurs as hyporheic flow (May and Lee,2004). Finer nature of sediment under high sediment supply regime (e.g. Hassanet al., 2007) would also prevent formation of mesoscale bedforms, which createshallow pools predicted by our model to be beneficial for small-bodied fish. Inaddition, increased sedimentation could lead to negative impacts of fine materialon incubation habitat. Past research showed that effects of sediment inputs maypersist especially long in hydraulically sheltered areas (Rathburn and Wohl, 2003),which appeared to provide spawning sites in the coarser East Creek reaches. On theother hand, a moderate increase in sediment supply might actually benefit coarserstream that have plane-bed morphology. According to our findings, growth of barsas sediment storage elements (e.g. Church, 1983) and development of pool-riffletopography in such channels would act to enhance the energetic quality of forag-ing habitat. Is it also possible that increased inputs of sediment in these mountainstreams would, to some extent, offset bed coarsening and exert positive influenceon spawning gravel availability. However, general prediction of textural response isimpossible because it would depend on the relative effect of changes in flow regime(e.g. peak flow magnitude and duration) and sediment supply regime (magnitudeand composition of supplied material). Finally, our findings also illustrate thatincreased sediment supply would most likely result in higher risk of bed scour dis-turbance. Such outcome may be further exacerbated by increased peak flows, forexample, in streams displaying nival hydrological regime (Goode et al., 2013).123BibliographyAberle, J., Koll, K., and Dittrich, A. 2008. 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