{"@context":{"@language":"en","Affiliation":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","AggregatedSourceRepository":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","Campus":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","Creator":"http:\/\/purl.org\/dc\/terms\/creator","DateAvailable":"http:\/\/purl.org\/dc\/terms\/issued","DateIssued":"http:\/\/purl.org\/dc\/terms\/issued","Degree":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","DegreeGrantor":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","Description":"http:\/\/purl.org\/dc\/terms\/description","DigitalResourceOriginalRecord":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","FullText":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","Genre":"http:\/\/www.europeana.eu\/schemas\/edm\/hasType","GraduationDate":"http:\/\/vivoweb.org\/ontology\/core#dateIssued","IsShownAt":"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt","Language":"http:\/\/purl.org\/dc\/terms\/language","Program":"https:\/\/open.library.ubc.ca\/terms#degreeDiscipline","Provider":"http:\/\/www.europeana.eu\/schemas\/edm\/provider","Publisher":"http:\/\/purl.org\/dc\/terms\/publisher","Rights":"http:\/\/purl.org\/dc\/terms\/rights","RightsURI":"https:\/\/open.library.ubc.ca\/terms#rightsURI","ScholarlyLevel":"https:\/\/open.library.ubc.ca\/terms#scholarLevel","Title":"http:\/\/purl.org\/dc\/terms\/title","Type":"http:\/\/purl.org\/dc\/terms\/type","URI":"https:\/\/open.library.ubc.ca\/terms#identifierURI","SortDate":"http:\/\/purl.org\/dc\/terms\/date"},"Affiliation":[{"@value":"Applied Science, Faculty of","@language":"en"},{"@value":"Civil Engineering, Department of","@language":"en"}],"AggregatedSourceRepository":[{"@value":"DSpace","@language":"en"}],"Campus":[{"@value":"UBCV","@language":"en"}],"Creator":[{"@value":"Glawdel, Joanna","@language":"en"}],"DateAvailable":[{"@value":"2011-11-30T23:42:25Z","@language":"en"}],"DateIssued":[{"@value":"2011","@language":"en"}],"Degree":[{"@value":"Master of Applied Science - MASc","@language":"en"}],"DegreeGrantor":[{"@value":"University of British Columbia","@language":"en"}],"Description":[{"@value":"Sediment transportation occurs during high flow events in gravel bed rivers resulting in a change in bed elevations. Some areas of the river experience a net degradation (scour) and others net aggradation (fill). During these events, incubating salmon eggs can be scoured from their pockets or sediment may be deposited above them, preventing intergravel flow and the emergence of fry. The purpose of this thesis is to develop a framework for estimating the probability of egg loss due to scour and fill for a range of possible high flow events in a river.\nThe developed framework consists of four steps. Steps one and two are the application of 2-dimensional hydrodynamic and morphodynamic models. The hydrodynamic model provides outputs of velocity, depth and shear stress at specified locations within the river. In the second step, these results are input into a morphodynamic model that simulates bed elevation changes during a transient simulation of the event. In the third step for a range of events, pre and post-event bed elevations are compared and the values of scour and fill depth are described by probabilistic distributions. For a specific high flow event, given a specific egg burial depth, a relationship between the proportion of egg loss due to scour and fill may be determined based on these distributions. In the final step, uncertainty in the depth of egg burial is accounted for by developing an egg loss model using reliability analysis that determines the probability of not meeting a target egg survival rate. \nThe developed methodology can be applied to any gravel river and is applicable to any salmon species. A case study of the Campbell River, British Columbia using the 2D hydrodynamic and morphodynamic models, River 2D and R2DM, is developed to demonstrate the methodology. For the case study, the Generalized Pareto Distribution is recommended to describe scour and fill in high flow events in spawning areas.","@language":"en"}],"DigitalResourceOriginalRecord":[{"@value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/39414?expand=metadata","@language":"en"}],"FullText":[{"@value":"ESTIMATING THE PROBABILITY OF EGG LOSS DUE TO SCOUR AND FILL UNDER HIGH FLOWS by JOANNA GLAWDEL B.A.Sc, The University of Ottawa, 2007 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCES in THE FACULTY OF GRADUATE STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) November 2011 \u00a9 Joanna Glawdel, 2011 \fAbstract Sediment transportation occurs during high flow events in gravel bed rivers resulting in a change in bed elevations. Some areas of the river experience a net degradation (scour) and others net aggradation (fill). During these events, incubating salmon eggs can be scoured from their pockets or sediment may be deposited above them, preventing intergravel flow and the emergence of fry. The purpose of this thesis is to develop a framework for estimating the probability of egg loss due to scour and fill for a range of possible high flow events in a river. The developed framework consists of four steps. Steps one and two are the application of 2-dimensional hydrodynamic and morphodynamic models. The hydrodynamic model provides outputs of velocity, depth and shear stress at specified locations within the river. In the second step, these results are input into a morphodynamic model that simulates bed elevation changes during a transient simulation of the event. In the third step for a range of events, pre and post-event bed elevations are compared and the values of scour and fill depth are described by probabilistic distributions. For a specific high flow event, given a specific egg burial depth, a relationship between the proportion of egg loss due to scour and fill may be determined based on these distributions. In the final step, uncertainty in the depth of egg burial is accounted for by developing an egg loss model using reliability analysis that determines the probability of not meeting a target egg survival rate. The developed methodology can be applied to any gravel river and is applicable to any salmon species. A case study of the Campbell River, British Columbia using the 2D hydrodynamic and morphodynamic models, River 2D and R2DM, is developed to demonstrate the methodology. For the case study, the Generalized Pareto Distribution is recommended to describe scour and fill in high flow events in spawning areas. ii \fTable of contents Abstract ......................................................................................................................................................... ii Table of contents .......................................................................................................................................... iii List of tables................................................................................................................................................. vi List of figures .............................................................................................................................................. vii List of symbols .............................................................................................................................................. x Acknowledgements .................................................................................................................................... xiv Chapter 1 - Introduction ................................................................................................................................ 1 1.1 Purpose of work .................................................................................................................................. 1 1.2 Thesis outline ...................................................................................................................................... 3 Chapter 2 - Estimating egg loss under high flow events due to scour and fill .............................................. 5 2.1 Background ......................................................................................................................................... 5 2.1.1 Life cycle of a salmon .................................................................................................................. 5 2.2 Salmon redd burial .............................................................................................................................. 5 2.2.1 Location of redd burial ................................................................................................................. 7 2.2.2 Depth of redd burial ..................................................................................................................... 8 2.3 Proposed framework for estimating egg loss under high flow events due to scour and fill ............... 8 2.4 Hydrodynamic model.......................................................................................................................... 9 2.4.1 River2D ...................................................................................................................................... 10 2.5 Morphodynamic model ..................................................................................................................... 12 2.5.1 Bed mobility in gravel rivers ..................................................................................................... 13 2.5.2 Sediment transport equations ..................................................................................................... 13 2.5.2.1 Meyer-Peter and M\u00fcller Equation (1948) ........................................................................... 14 2.5.3 2-Dimensional (2D) morphodynamic modeling ........................................................................ 15 2.5.4 3-Dimensional (3D) morphodynamic modeling ........................................................................ 17 2.5.5 River2D Morphology (R2DM) .................................................................................................. 17 2.6 Scour and fill model .......................................................................................................................... 18 2.6.1 Previous work ............................................................................................................................ 18 2.6.1.1 Exponential (EX) Distribution ............................................................................................ 19 iii \f2.6.1.2 Mobility ratio model ........................................................................................................... 20 2.6.1.3 Hydrodynamic model predicted Shields stress and bed mobility ....................................... 21 2.6.1.4 Other scour and fill models ................................................................................................. 22 2.6.2 Distribution functions applicable to scour and fill in gravel bed rivers ..................................... 22 2.6.2.1 Three-parameter Generalized Pareto (GP) Distribution...................................................... 23 2.6.3 Proposed scour and fill model .................................................................................................... 24 2.6.4 Choosing the appropriate Probability Density Function (PDF) ................................................. 26 2.7 Probabilistic egg loss model ............................................................................................................. 27 2.7.1 Fitting distribution parameters ................................................................................................... 27 2.7.2 Reliability analysis of scour and fill predictions ........................................................................ 29 Chapter 3 - Case study ................................................................................................................................ 31 3.1 Campbell River watershed ................................................................................................................ 31 3.2 Hydrology ......................................................................................................................................... 33 3.3 Design flows ..................................................................................................................................... 36 3.4 Campbell River fisheries................................................................................................................... 36 3.4.1 Depth of Chinook salmon redd burial ........................................................................................ 37 3.5 Study reach selection ........................................................................................................................ 38 3.5.1 Salmon spawning zone selection ............................................................................................... 39 3.6 Hydrodynamic model........................................................................................................................ 39 3.6.1 Topographic data ....................................................................................................................... 39 3.6.2 Bathymetry ................................................................................................................................. 40 3.6.3 Boundaries ................................................................................................................................. 40 3.6.4 Mesh size ................................................................................................................................... 41 3.7 Morphodynamic model ..................................................................................................................... 41 3.7.1 Field data collection of grain size distribution ........................................................................... 41 3.7.2 Boundaries ................................................................................................................................. 43 3.7.3 Sediment transport function inputs ............................................................................................ 43 3.8 Hydrodynamic and morphodynamic model simulation procedure (R2DM) .................................... 45 Chapter 4 - Results and discussions ............................................................................................................ 47 4.1 Hydrodynamic model verification .................................................................................................... 47 4.2 Morphodynamic model verification.................................................................................................. 49 4.2.1 Post-event bed elevations ........................................................................................................... 52 iv \f4.3 Scour and fill model of the Lower Campbell River .......................................................................... 60 4.3.1 Probabilistic equation of scour and fill in the Lower Campbell River (outcome 1) .................. 64 4.3.1.1 Applications of Generalized Pareto (GP) Distribution ....................................................... 66 4.3.1.1.1 Kanaka Creek, British Columbia ................................................................................. 66 4.3.1.1.2 Trinity Creek, California .............................................................................................. 67 4.3.2 The proportion of egg loss due to scour and fill in a high flow event for a given Dredd (outcome 2) ......................................................................................................................................................... 69 4.4 Probabilistic egg loss model of the Lower Campbell River.............................................................. 70 4.4.1 Generalized Pareto (GP) Distribution parameters for the Lower Campbell River regressed against discharge ................................................................................................................................. 70 4.4.2 Probability of not meeting a target survival rate (F) in the Lower Campbell River (outcome 3) ............................................................................................................................................................ 71 Chapter 5 - Conclusions and future work ................................................................................................... 73 5.1 Thesis conclusions ............................................................................................................................ 73 5.2 Future work ....................................................................................................................................... 74 References ................................................................................................................................................... 76 Appendix A\u2013 Wolman pebble count........................................................................................................... 83 Appendix B\u2013 Anderson-Darling statistic (A2) and significance levels ....................................................... 84 v \fList of tables Table 2-1: Characteristics of sediment transport equations for gravel bed rivers ....................................... 14 Table 2-2: Two-dimensional morphodynamic models ............................................................................... 16 Table 2-3: Properties of reaches discussed in this study ............................................................................. 19 Table 3-1: Return period events and peak discharges at the John Hart Dam.............................................. 35 Table 3-2: Design flows for the Lower Campbell River study ................................................................... 36 Table 3-3: Species of fish in the Lower Campbell River ............................................................................ 37 Table 3-4: Statistical properties of Chinook redd burial depth (Dredd), in the Trinity River ....................... 38 Table 3-5: Roughness coefficients, \u03bas (from BC Hydro, 2004b) ................................................................ 40 Table 3-6: Statistical properties of grain size distributions for the Lower Campbell River ....................... 43 Table 4-1: Hydrodynamic rating curve verification for the Lower Campbell River .................................. 47 Table 4-2: Anderson-Darling test p-values of the Generalized Pareto (GP) and Exponential (EX) Distributions describing depth of scour (Dscour) or depth of fill (Dfill) for spawning areas in the Lower Campbell River ........................................................................................................................................... 64 Table 4-3: Generalized Pareto (GP) Distribution parameters for the Lower Campbell River .................... 64 Table 4-4: Exponential (EX) Distribution parameters for the Lower Campbell River ............................... 65 Table 4-5: Generalized Pareto (GP) and Exponential (EX) Distribution parameters and Anderson-Darling test p-value for Kanaka Creek at a peak discharge of 46.8 m3\/s ................................................................. 66 Table 4-6: Generalized Pareto (GP) and Exponential (EX) Distribution parameters and Anderson-Darling test p-value for Trinity River at peak discharges of 180, 242 and 422 m3\/s ............................................... 68 Table 4-7: Percentage of egg loss due to scour and fill for peak discharges of 220, 450, 1073 and 1127 m3\/s in the Lower Campbell River, given a depth of egg burial (Dredd) of 30 cm....................................... 69 Table 4-8: Parameters of the equation describing the proportion of egg loss due to scour and fill (PT) for the Lower Campbell River .......................................................................................................................... 70 Table 4-9: Probabilistic egg loss model for the Campbell River, pf ........................................................... 71 vi \fList of figures Figure 1-1: Proportion of egg loss due to scour and fill in a high flow event given a specified depth of redd burial (Dredd) .......................................................................................................................................... 2 Figure 1-2: Probability of not meeting a target egg survival rate (F) due to scour and fill in a high flow event .............................................................................................................................................................. 3 Figure 1-3: Flow diagram of proposed framework and outline of Chapter 2 ............................................... 4 Figure 2-1: Profile of relevant depths of redd (Dredd), scour (Dscour) and fill (Dfill) ....................................... 6 Figure 2-2: Hypothetical depiction of the proportion of a channel that scours and fills depths (Dscour or Dfill) under a) low flows and b) high flows ................................................................................................. 22 Figure 2-3: Resultant depth of scour and depth of fill (Dscour and Dfill) during a morphodynamic simulation .................................................................................................................................................................... 24 Figure 2-4: Determining the proportion of cells in a spawning area which scour or fill using R2DM ...... 25 Figure 2-5: Frequency and cumulative proportion of a spawning area that scours and fills to a given depth .................................................................................................................................................................... 25 Figure 2-6: Proportion of egg loss due to scour and fill (Pt) for a given stream discharge (Q) and depth of redd burial (Dredd) ........................................................................................................................................ 26 Figure 2-7: Probability Density Function (PDF) parameter regressed against discharge (Q) .................... 27 Figure 2-8: Frequency distribution for depth of redd (Dredd) ...................................................................... 29 Figure 2-9: Frequency distribution for the limit state function (r) with a target survival rate (F) from random values of depth of redd (Dredd) ....................................................................................................... 30 Figure 2-10: Probability of not meeting a target egg survival rate (F) due to scour and fill in a high flow event (pf) ..................................................................................................................................................... 30 Figure 3-1: Study site location .................................................................................................................... 31 Figure 3-2: Campbell River system map .................................................................................................... 32 Figure 3-3: Lower Campbell River key map .............................................................................................. 33 Figure 3-4: Mean-monthly discharge at WSC gauge: 08HD003 data from 1940 to present (postinstallation of Campbell River system) and WSC gauge: 08HD001 (pre-installation of Campbell River system) ........................................................................................................................................................ 34 Figure 3-5: Outflow hydrograph for the John Hart Dam under various return period storms .................... 35 vii \fFigure 3-6: Histogram and fitted Normal and Lognormal Distributions for redd egg burial depths (Dredd) of Chinook salmon in the Trinity River ...................................................................................................... 38 Figure 3-7: Location of spawning areas in the Lower Campbell River (Orthophotography from BC Hydro, 2008) ........................................................................................................................................................... 39 Figure 3-8: Downstream boundary rating curve (WSC Gauge 08HD003) ................................................. 41 Figure 3-9: Field survey bed grain size distribution and reported distribution for the First Island spawning area by Anderson (2007) ............................................................................................................................. 42 Figure 3-10: Values of D50 in the Lower Campbell River study reach ....................................................... 44 Figure 3-11: Erodible areas in the Lower Campbell River study reach ...................................................... 45 Figure 3-12: Procedure for hydrodynamic (River2D) and morphodynamic (R2DM) simulations for segments of the operational hydrograph of the Lower Campbell River ..................................................... 46 Figure 4-1: Observed and modeled (a) water depths (h), and (b) velocities (v), along transect T4.3 at a stream discharge of 79 m3\/s ........................................................................................................................ 48 Figure 4-2: Observed versus modeled (a) water depths (h) and (b) velocities (v), at a stream discharge of 79 m3\/s ........................................................................................................................................................ 48 Figure 4-3: Observed versus modeled water surface elevation at a stream discharge of 31.1 m3\/s ............ 49 Figure 4-4: Operational hydrograph at the John Hart Dam from November 20, 2009 at 17:00 through December 4, 2009 at 10:00 ......................................................................................................................... 50 Figure 4-5: Morphodynamic model, R2DM, verification event (343 m3\/s) results .................................... 51 Figure 4-6: Comparison of pre and post event bed elevation for a peak discharge of 220 m3\/s (Orthophotography from BC Hydro, 2008) ................................................................................................ 53 Figure 4-7: Comparison of pre and post event bed elevation for a peak discharge of 450 m3\/s (Orthophotography from BC Hydro, 2008) ................................................................................................ 54 Figure 4-8: Comparison of pre and post event bed elevation for a peak discharge of 1073 m3\/s (Orthophotography from BC Hydro, 2008) ................................................................................................ 55 Figure 4-9: Comparison of pre and post event bed elevation for a peak discharge of 1127 m3\/s (Orthophotography from BC Hydro, 2008) ............................................................................................... 56 Figure 4-10: Comparison of pre and post event bed elevation for a peak discharge of 1240 m3\/s (Orthophotography from BC Hydro, 2008) ................................................................................................ 57 Figure 4-11: Sediment transport rate (qs) as a function of \u03c4* based on the Meyer-Peter and M\u00fcller Equation for D50 of 120 mm ....................................................................................................................... 59 viii \fFigure 4-12: Generalized Pareto (GP) and Exponential (EX) Distributions fit to modeled scour or fill depths (Dscour and Dfill) for simulations with peak discharges of a) 220 m3\/s , b) 450 m3\/s, c) 1073 m3\/s, d) 1127 m3\/s and e) 1240 m3\/s......................................................................................................................... 61 Figure 4-13: Generalized Pareto (GP) and Exponential (EX) Distributions fit to modeled scour depths (Dscour) for simulations with peak discharges of a) 220 m3\/s , b) 450 m3\/s, c) 1073 m3\/s, d) 1127 m3\/s and e) 1240 m3\/s ................................................................................................................................................ 62 Figure 4-14: Generalized Pareto (GP) and Exponential (EX) Distributions fit to modeled fill depths (Dfill) for simulations with peak discharges of a) 220 m3\/s , b) 450 m3\/s, c) 1073 m3\/s, d) 1127 m3\/s and e) 1240 m3\/s ............................................................................................................................................................. 63 Figure 4-15: Generalized Pareto (GP) and Exponential (EX) Distributions fit to observed scour and fill depths (Dscour and Dfill) for Kanaka Creek at a peak discharge of 46.8 m3\/s ................................................ 67 Figure 4-16: Generalized Pareto (GP) and Exponential (EX) Distributions fit to modeled scour and fill depths (Dscour and Dfill) for the Trinity River at areas of Chinook spawning under a peak discharge of a) 180 m3\/s, b) 242 m3\/s and c) 422 m3\/s ........................................................................................................ 68 Figure 4-17: Generalized Pareto (GP) Distribution parameters a) \u03baT, b) \u03c3T, and c) \u03bcT regressed against peak discharge (Q) ...................................................................................................................................... 70 Figure 4-18: Probability of not meeting a target survival rate (F) in the Lower Campbell River, based on 5000 samples............................................................................................................................................... 72 ix \fList of symbols Symbol Description a\u03ba(t) = Slope of the line of best fit for parameter \u03bat a\u03bc(t) = Slope of the line of best fit for parameter \u03bct a\u03c3(t) = Slope of the line of best fit for parameter \u03c3t a\u03b8(t) = Slope of the line of best fit for parameter \u03b8t 2 = Anderson-Darlington statistic b = Exponent describing relationship of \u03c4*i and \u03c4*CRi b\u03ba(t) = Intercept of the line of best fit for parameter \u03bat b\u03bc(t) = Intercept of the line of best fit for parameter \u03bct b\u03c3(t) = Intercept of the line of best fit for parameter \u03c3t b\u03b8(t) = Intercept of the line of best fit for parameter \u03c3t Cs = Chezy coefficient C90 = Constant estimated by Bray (1980) d = Depth of scour and fill in Haschenburger model cm d = Reach mean scour and fill depth in Haschenburger model cm A D50 = Unit th Mean diameter of sediment (the size of 50 percentile grain) th m D84 = Diameter of sediment of the 84 percentile grain m D90 = Diameter of sediment of the 90th percentile grain m Dfill = Depth of fill in a flow event measured from original bed surface m Dfill = Mean fill depth m Dfill,final = Depth of fill at the end of a R2DM simulation relative to original bed m surface Di = Mean diameter of particle of class size i m Dredd = Depth of redd relative to original bed elevation m Dscour = Depth of scour in a flow event measured from original bed surface m = Mean scour depth m = Maximum scour depth in a R2DM simulation relative to original bed m Dscour,max surface F = Target egg survival rate fi = Fraction of bed material in class size i g = Gravitational acceleration m\/s2 x \fG = Dimensionless bedload transport rate ratio h = Water depth n = Number of simulations where r \u2264 0 N = Number of simulations generated for the random variable Dredd pf = Probability of failure pt = Proportion of spawning area that scours or fills to a depth of Dredd PT = Proportion of egg loss in scour and fill in spawning areas for a given Q Q = Discharge m3\/s q = Depth-unit discharge m3\/m\/s qDS = Downstream sediment flux m3\/m\/s qs = Volumetric sediment transport rate m3\/m\/s qsi = Volumetric sediment transport rate per unit width for a particle of m3\/m\/s m class size i qsx = Volumetric sediment transport rate in the longitudinal direction per m3\/m\/s unit width qsy = Volumetric sediment transport rate in the lateral direction per unit m3\/m\/s width qUS = Upstream sediment flux m3\/m\/s qy = discharge per unit width in the lateral direction m3\/m\/s qx = discharge per unit width in the longitudinal direction m3\/m\/s r = Limit state function s = Specific gravity of sediment S2 = Variance SurvivalT = Probability of egg survival in a flow event accounting for scour and kg\/m3 fill Sf = Friction slope m\/m Sfx = Friction slope in the longitudinal direction m\/m Sfy = Friction slope in the lateral direction m\/m So = Bed slope m\/m Sox = Bed slope in the longitudinal direction m\/m Soy = Bed slope in the lateral direction m\/m t = Time s T = Temperature O C xi \fu* = Shear velocity m\/s UW = Upwinding factor v = Velocity m\/s vx = Velocity in the longitudinal direction m\/s vy = Velocity in the lateral direction m\/s W*i = Dimensionless bedload transport rate for particle of class size i zb = Bed elevation m zbnew = Updated time step bed elevation m zbold = Previous time step bed elevation m xii \fGreek Symbols Description \u03b2i = Site specific hiding relationship \u03b5t = Eddy viscosity coefficient \u03b51, \u03b52, \u03b53, = Constants selected to stabilize turbulent flow in the eddy viscosity Unit kg\/ms equation \u03b3j = Observation point j in the data set \u03bas = Boundary roughness height \u03c7 = Random variable \u03bc = Location parameter of the Generalized Pareto Distribution \u2126 = Stream power \u03c8 = Porosity of bed material \u03c1 = Density of water kg\/m3 \u03c1s = Density of sediment in the channel bed kg\/m3 \u03c3 = Scale parameter of the Generalized Pareto Distribution \u03a3 = Substrate \u03c4 = Shear stress \u03c4* = Dimensionless Shields stress \u03c4*i = Dimensionless Shields stress for a particle of class size i \u03c4avg = Reach average boundary shear stress N\/m2 \u03c4CR = Critical shear stress N\/m2 \u2217 = Dimensionless critical Shields stress for a particle of class size i \u03c4o = Bed shear stress N\/m2 \u03c4xx, \u03c4xy, \u03c4yx, \u03c4yy = Components of turbulent stressors N\/m2 \u03f4 = Model parameter of the Exponential Distribution \u03c9 = Shape parameter of the Generalized Pareto Distribution m kg m\/s3 N\/m2 xiii \fAcknowledgements I give my gratitude to my former instructors at the University of Ottawa, Dr. Colin Rennie, Dr. Ioan Nistor and Dr. Ronald Droste who sparked my interest in water resources engineering. This work would not have been completed without the guidance and support from my two supervisors at the University of British Columbia, Dr. Barbara Lence and Dr. Robert Millar as well as Bill Johnstone and Dr. Marwan Hassan who have provided insight into the work. I am particularly grateful to Ali Naghibi who contributed many ideas to this thesis and acted as a mentor and friend throughout my graduate studies. Financial support, data and guidance for this work was provided by BC Hydro. In particular, I thank Mr. Faizal Yusif, Dr. Des Hartford, Mr. Derek Sacramoto and Ms. Kathy Groves for their advice and support in this project. Additional data for analysis were kindly provided by Christine May on studies of the Trinity River. Additional hydrologic data was provided by the Water Survey of Canada. Knowledge of the Campbell River and its fish species as well as many additional questions about the system were answered by Ms. Shannon Anderson at the Department of Ocean and Fisheries. Ms. Sarah Portelance and Mr. Gaven Tang assisted in gathering field data at the Campbell River. I am very grateful to Dr. Steven Kwan who provided technical support and modifications to the River2D Morphology code to complete this thesis. I dedicate this work to my parents, Witold and Ewa Glawdel, who throughout my life have only supported me and my personal pursuits by providing me with unconditional love, showing outstanding amounts of patience and giving me the space to study and pursue my interests. I also give gratitude to my brother, Tomasz, who cast a shadow that challenged me to work hard. To my dearest friends all over the world who have shown that the boundaries of family extend beyond blood \u2013 thank you all for being a part of my life and helping me through this work. xiv \fChapter 1 - Introduction Salmon are of both social and economic importance in British Columbia. Over the past 50 years there has been a declining trend in Pacific salmon populations partially attributed to overexploitation and degradation of habitat (Hyatt et al., 2003). In British Columbia, many salmon spawning reaches are located within streams controlled by flood prevention, water supply and hydropower reservoirs which, through altering flow regimes, preventing upstream migration, and stemming sediment supply, have a significant impact on salmon populations. To assess and reduce the negative effects of hydropower facilities on fish populations, low operational flow regimes are commonly studied. However, fewer studies have focused on the environmental impacts and potential mitigations of the effects of high discharges (i.e., controlled and uncontrolled spills, and dam break and failure). In assessing such consequences, five attributes are often considered: fish abundance and diversity, fish habitat, population of aquatic plants and invertebrates, geomorphology and sedimentation, water quality and temperature, and terrestrial vegetation and wildlife. Of the identified environmental attributes, all except for terrestrial vegetation can be described by the overall fish population dynamics (Naghibi, 2011). Salmonidae spawning habitats are particularly sensitive to increased high flows. Incubating eggs in pockets, called redds, can be scoured from their pockets during a high flow event. Sediment deposition on redds may also prevent the flow of oxygen and nutrients, suffocating the eggs and causing death. This thesis develops a framework to assess the impacts of scour and fill during a high flow event on salmon eggs. The framework is demonstrated for a case study of the Lower Campbell River, British Columbia which provides spawning habitat for Chinook (Oncorphynchus tshawytscha) salmon as well as a variety of other salmonidae species. This watershed is managed by BC Hydro who operates a series of hydropower facilities upstream of the spawning reach of the river. 1.1 Purpose of work Quantifying the loss of eggs under high flow events can be used to inform the development of long term fish population models and to assess the cultural, economic and environmental implications of such events. This knowledge can be included in dam operational procedures to estimate the impacts of controlled high flow events on fish populations and to explore the possibility of altering operations to decrease negative impacts when other conditions, such as loss of life, are not threatened. To estimate egg loss under high flow events, information regarding the stream hydraulics, sediment transport rates, location of redds, depth of redd burial and characteristics of river sediment are required. Often, there is 1 \flimited information related to these factors. Considering the natural variability in egg burial depths in particular can provide a valuable means of accounting for the uncertainty (DeVries, 1997). The objective of this thesis is to develop a framework for estimating the probability of egg loss due to scour and fill for a range of possible high flow events in the system. The approach developed should: a. Make use of two-dimensional (2D) hydrodynamic and morphodynamic modeling; b. Be applicable for use in any gravel river; c. Require limited field data; d. Be applicable for any salmon species; and e. Account for uncertainty in the input parameters. The approach developed to address the thesis objective is demonstrated for the Lower Campbell River case study. The outcomes of the objectives provide key tools for resource managers including: 1. Probabilistic distributions describing scour and fill in spawning areas under high flows. For the Lower Campbell River case study, a three parameter distribution function is recommended. 2. A relationship between the proportion of egg loss due to scour and fill, given a specific redd burial depth, and peak flows in the system. An example of this relationship is shown in Figure Proportion of egg loss due to scour and fill 0 1 1-1. Peak flow (m3\/s) Figure 1-1: Proportion of egg loss due to scour and fill in a high flow event given a specified depth of redd burial (Dredd) 2 \f3. The probability of not meeting a target egg survival rate (F) due to scour and fill, produced using reliability analysis considering the depth of redd burial to be a random variable. An example of Probability of not meeting an acceptable target egg survival rate (pf) 0 1 this outcome is shown in Figure 1-2. 50%F = 10% F = 25% F = 50% Figure 1-2: Probability of not meeting a target egg survival rate (F) due to scour and fill in a high flow event To produce Outcome 1 of this work, previous principles developed by Haschenburger (1999) are expanded to describe scour and fill in localized spawning areas of a stream under high flow events. For the Lower Campbell River case study, a three-parameter distribution, the Generalized Pareto (GP) Distribution, is recommended for use in high flow events. To achieve Outcome 2, previous work by Lapointe et. al (2000), Evenson (2001) and May et. al. (2009) are adapted to develop a structured method for determining the proportion of egg loss in a high flow event. To the writer\u2019s knowledge, no published studies have provided Outcome 3 of this thesis; however, the need for this work is suggested by DeVries (1997). All three outcomes are demonstrated for the case study and have provided input to a long-term fish population dynamics model developed in parallel with this project (see Naghibi, 2011). 1.2 Thesis outline Figure 1-3 summarizes the proposed framework and indicates the framework steps in bold, required information in parenthesis and inputs and outputs of each step in italics. It also describes the inputs, knowledge required, approaches taken and thesis outcomes achieved at each step of the framework, details of which can be found in the sections of Chapter 2 listed in Figure 1-3. Chapter 3 describes the 3 \fcase study of the Lower Campbell River, British Columbia. The results of the case study are presented and discussed in Chapter 4, and conclusions are presented in Chapter 5. High flow event (Q) Knowledge Required STEP 1 STEP 2 velocity (v), depth (h), shear stress (\u03c4) in all cells Morphodynamic Model \u2013 River2D \u2013 Morphology (properties of stream sediment) bed elevation STEP 3 Repeated for a number of flow events Hydrodynamic Model \u2013 River2D (bed elevations, boundary conditions) Scour and Fill Model (location of spawning areas) STEP 4 Thesis Section Thesis Outcome Hydrodynamic modeling 2.4 Bed mobility Sediment transport equations Morphodynamic modeling 2.5.1 2.5.2 2.5 Location of redds Distribution functions 2.2.1 2.6.2 1, 2 Depth of redd burial Reliability analysis 2.2.2 2.7.2 3 proportion of spawning area that scours or fills to a specified depth Probabilistic Egg Loss Model (variability in depth of redd burial) Figure 1-3: Flow diagram of proposed framework and outline of Chapter 2 4 \fChapter 2 - Estimating egg loss under high flow events due to scour and fill 2.1 Background 2.1.1 Life cycle of a salmon A Pacific salmon begins its life as an egg incubating in a freshwater stream. After a period of approximately two to eight months, the egg hatches and enters the state of an alevin, where, for several weeks it feeds on the yolk sac buried beneath the gravel. The salmon then emerges as a fry and feed in the freshwater stream. Once the salmon reaches the age of a smolt, it spends one to three years at the mouth of the river, preparing for one to seven years at sea as an adult. Once fully matured, the salmon returns to the stream of its birth, to lay or fertilize new eggs and within two weeks of spawning dies (Groot and Margolis, 2003). 2.2 Salmon redd burial Salmon create nests, referred to as redds, in which to lay and incubate their eggs, by digging holes into gravel bed streams. The redd consists of the incubating pocket, pit, cover and bridge layers, and tailspill. By moving the gravel, the salmon creates the egg pocket and covers it with substrate for protection. The act of digging creates the pit in front of the egg pocket. A covering layer is above the eggs which is made of finer material in the bridge layer and coarser material in the cover layer. A loose mound of cover creates the tailspill downstream of the egg pocket (Rennie and Millar, 2000). During the incubation period, alterations in stream flow can affect the survival of eggs by influencing the deposition and infiltration of fine sediments through the redd, altering water quality, creating river bed disturbances and causing stream bed scour and fill (DeVries, 1997). This work focuses on the survival of redds under high flows, i.e., controlled spill releases and catastrophic floods, which is dependent on both the depth of scour (Dscour) and the depth of fill (Dfill) and no other destruction mechanisms. Dscour and Dfill are the resultant elevation of the bed throughout and after a flow event relative to the pre-event bed elevation (i.e., original bed surface elevation) under cases of scour and fill, respectively. In studies estimating the depth of redd (Dredd), one of three values is typically reported. These are the distances to: the top of the egg pocket, the middle (mean depth) of the egg pocket, and the bottom of the egg pocket; each of which is measured from the original bed surface (DeVries, 1997). In this thesis, the Dredd is measured to the bottom of egg pocket. Relevant depths of Dscour, Dfill and Dredd are depicted in Figure 2-1. 5 \fa) b) Dfill Original surface Dscour Dredd Dredd Eggs Eggs Redd survival threatened: Dscour or Dfill \u2265 Dredd Figure 2-1: Profile of relevant depths of redd (Dredd), scour (Dscour) and fill (Dfill) With respect to the scouring mechanism, eggs in the redd are threatened when the Dscour is greater than Dredd, meaning the eggs are being dug out from their nests by moving water. Dscour to the top of redd threatens the survival of the eggs (i.e., there is partial destruction of redds), however, total loss of eggs may not occur. A Dscour value that is equal to the difference between the original bed surface and the bottom of the redd is assumed to lead to total egg loss (Lapointe et al., 2000). Regulated rivers typically have a deficit of coarse material downstream of the regulating reservoir and thus, egg mortality due to scour of redds as opposed to from sediment deposition has been the main focus of past research. However, new evidence suggests that salmon have biologically adapted to burying eggs in areas of low scour and that destruction due to fill may be more threatening to their survival (May et al., 2009). With respect to the fill mechanism of destruction, if the Dfill is greater than or equal to the Dredd, the eggs are thought to suffocate from the prevention of inter-gravel flow, or the frys are thought to be unable to emerge. In this study, loss of eggs is said to occur when: Dscour \u2265 Dredd Dfill \u2265 Dredd This simplistic approach for assessing redd destruction due to scour and fill has deficiencies when considering the natural state of egg burial (DeVries, 1997). For example, the shape and orientation of the egg pocket can affect the number of eggs destroyed. If the egg pocket is oriented horizontally, more eggs are placed nearer to the surface than if the pocket is oriented vertically and thus a smaller portion is in contact with the top of bed. If the egg pocket is conical as opposed to rectangular, initially there will be a large loss of eggs and then fewer will be lost (Evenson, 2001). It is also not understood what happens to 6 \fthe eggs once they are released from the redds after being scoured. It is assumed that the eggs need to be within the redd to incubate; however, this may not be true. Also, the level of sediment above the eggs required for incubation is unknown and death of eggs due to shallow burial may occur. 2.2.1 Location of redd burial The choice of spawning location by salmon varies based on the species of salmon and river conditions. Typically, published studies report the spawning site selection by salmon is based on preferences for water velocity (v), water depth (h) and substrate size composition (i.e., the mean diameter of sediment, D50). However, there is evidence that salmon choose spawning sites based on other factors such as gravel inflow rates, vertical hydraulic gradient, geomorphic channel units, hyporheic water physochemistry, substrate cover, and proximity to other redds (Mull and Wilzbach, 2007). It has been hypothesized that salmon have adapted to protecting their eggs under regular (bankfull) flows by either burying them to a depth where they are protected from scour, or choosing redd locations in areas with low bed mobility (Montgomery et al., 1999; May et al., 2009). For instance, Bull Char eggs are found to be buried to depths below scouring levels of the bankfull flow in Washington State mountain drainage reaches (Shelberg et al., 2010). Studies have also focused on macrohabitat preferences for physical features to understand the choice of location for spawning. Columbe-Pontbriand and Lapointe (2004) survey locations of Atlantic salmon (Salmo salar) redd burial in two Quebec rivers, the Petite Cascap\u00e9dia and Bonaventure Rivers, over three spawning seasons. Spawning site selection preference is demonstrated for riffle locations in which there is a low percentage of sand particles. Also noted is a preference for sites with complex geomorphic forms such as alluvial islands and anabranches, possibly due to the changes in hydraulic gradients and hyporheic zones. Studies of Pacific salmon include investigations of Chinook spawning sites of the Hanford Reach on the Columbia River. Here redds are found to be located in clusters close to complex channel features such as gravel bars and islands (Geist and Dauble, 1998). Schuett-Hames et al. (2000) analyze the Dscour and Dfill during the incubation period of Chum salmon (Oncorhynchus keta) in Kennedy Creek, Washington for two storms with return periods of 1.4 and less than 1-year, in two reaches. They show that the average Dscour is nearly twice as high in a complex, sinuous and wide reach as that in a simple, straight, narrow reach. The average Dscour is also greater in pool-associated habitats, favoured by the salmon, than it is in riffle-associated habitats, suggesting the importance of understanding the specific geomorphologic selection of species. 7 \fThe substrate size and composition is of importance since salmon have limited ability to move coarse gravel, using both the power of the currents and the strength available from flexing their body (MacIssac, 2009). The maximum size of coarse material which can be moved by salmon has been related to a function of fish length which can be used in the design of spawning gravel platforms (Steen et al., 1999; Kondolf, 2000). 2.2.2 Depth of redd burial DeVries (1997) compiles published data regarding Dredd for various salmon species. In each of the included studies a range of Dredd for individual species are reported. He suggests that these are species specific Dredd based on the complied data. The variability in Dredd for Chum, Coho (Oncorhynchus kisutch), and Chinook salmon in three studies are described by frequency distributions. Montgomery et al. (1996) find that the depths to the top of the pocket are lognormally distributed for Chum salmon at Kennedy Creek, Washington based on 40 measurements. In measuring the depths to the middle of the pockets for 34 Chum redds and 30 Coho redds in the Queen Charlotte Islands, Tripp and Poulin (1996) find a skewed-left lognormal distribution. A skewed-left lognormal distribution is also found for Chinook salmon in the Trinity River, California (Evenson, 2001). 2.3 Proposed framework for estimating egg loss under high flow events due to scour and fill Advances in computing allows for the hydrodynamics of complex river systems to be modeled in detail and for the computationally demanding sediment movement equations to be solved in transient simulations. Using readily available hydrodynamic and morphodynamic models, changes in the bed elevations at the spawning sites can be determined for various flow events. In Step 1 of the framework outlined in Figure 1-3, a hydrodynamic simulation is performed using River2D. The model requires information regarding the river bathymetry (i.e., bed elevations and roughness coefficients) and boundary conditions (i.e., inflow, outflow and location of noflow zones). After simulating a given stream discharge in steady state, the model produces values of velocity (v), water depth (h) and shear stress (\u03c4) at each of the computational nodes. The outputs of River2D are input into Step 2 of the framework which applies the morphodynamic model, R2DM. Information regarding the stream sediment properties is input to this model. Simulations applying a chosen sediment transport equation produce updated bed elevations at each node throughout and after the high flow event. Given the transient nature of morphodynamic modeling, for consistency, 8 \fthe duration of the various peak flow events should be the same, or in the case of a non-regulated system, the morphodynamic simulations should be run until equilibrium in the system is achieved. A number of hydrodynamic and morphodynamic simulations should be conducted to have a comprehensive understanding of how scour and fill effects the egg loss and spawning habitat changes in high flow events. In Step 3, a scour and fill model for the spawning locations in the reach is developed. Information regarding bed elevations (i.e., Dscour and Dfill) at nodes located in defined spawning areas are extracted from the morphodynamic model. A Probability Density Function (PDF) (e.g., based on an Exponential, Gamma, or Pareto Distribution) that describes Dscour and Dfill in these areas can be estimated, producing Outcome 1. Further, an equation that describes the proportion of egg loss based on a given Dredd is found, providing in Outcome 2. Step 4 of the framework involves building a probabilistic egg loss model over a range of flows. Considering the value of Dredd to be a random variable, the probability of not meeting a target egg survival value can be determined with reliability analysis using Monte Carlo Simulation, producing in Outcome 3. 2.4 Hydrodynamic model Step 1 of the proposed framework is to conduct hydrodynamic simulations under steady-state conditions to predict the hydrodynamic properties of the stream including the v, h, and \u03c4, given an input of stream discharge (Q). Hydrodynamic numerical modeling in open channel flow problems may be conducted with one-dimensional (1D), two-dimension (2D), or three-dimensional (3D) models. 1D models typically simulate flow in the longitudinal direction, averaging velocity and depth over a cross-section (e.g., HEC-RAS, LISFLOOD-FP, MIKE-11). 1D models are generally inadequate for estimating the localized values of v and h required for fish habitat studies. Thus, 2D models (e.g., River2D, MIKE-21, and TELEMAC-2D) are typically applied in these cases (Smiraowski, 2010). The 2D models calculate depth-averaged properties in both the longitudinal and lateral direction. 3D models provide additional localized details by determining properties in the longitudinal, lateral and vertical directions. 3D model usage in large-scale analysis of streams is limited due to their significant computational requirements. 2D modeling is required to model localized sediment movement. River2D, which is used in this thesis, is discussed in Section 2.4.1 . This model is applied herein because it has the advantage of coupling with the morphodynamic model River2D-Morphology (R2DM), discussed in Section 2.5.3 . 9 \f2.4.1 River2D River2D, developed at the University of Alberta, is a depth-averaged finite element model for natural streams and rivers and is capable of accommodating supercritical\/subcritical flow transitions, ice cover and variable wetted area. Typical applications of River2D are studies of river reaches with lengths of less than or equal to ten times the channel width (Steffler and Blackburn, 2002). The model requires the input of channel bed topography, roughness and transverse eddy viscosity distributions, boundary conditions (i.e., inflow and outflow, noflow), initial flow conditions (i.e., beginning water surface elevations) and a discrete mesh or grid that can capture flow variations. The user defines the mesh size, where typically a higher density mesh (i.e., a mesh with more nodes) results in more detailed and accurate results; however, the choice of mesh size is limited by computational constraints. The model outputs at each node in the computational mesh are two (horizontal) velocity components, vx and vy in the longitudinal and lateral direction, respectively, and h. The model assumes uniform velocity and hydrostatic pressure distributions in the vertical direction which limits the accuracy in streams with steep slopes (slopes greater than 10%) and in areas with rapid bed slope changes. The horizontal velocity distribution is constant, which does not allow for information regarding secondary flows or circulation. Coriolis and wind effects are assumed negligible; however, these may be important for large water bodies such as lakes and reservoirs. The River2D model has been successfully applied in river design and assessment projects. Vasquez (2005) compares results from two lab experiments of open channel flow diversions with the River2D model simulations. The first experiment consists of a 30o lateral channel diverting 50% of the incoming flow with a width:depth ratio of 2:8. The second consists of a narrow 90o lateral channel diverting 81% of the incoming flow with a width:depth ratio of 1:2. The River2D model accurately portrays the flow in both experiments. Waddle (2010) collects field data of the bathymetry, h and v of water under three discharges in the vicinity of two boulders on the South Plate River, Colorado. Field results at 204 locations are compared with simulated River2D results. Deviations between modeled and measured results are found to fall within the likelihood of measurement error, indicating that River2D may be acceptable for modeling in the areas of boulders. River2D is based on the 2D shallow water Saint-Venant Equation and solves the Conservation of Mass Equation given as: 10 \f\u2202h \u2202qx \u2202qy + + \u2202t \u2202x \u2202y Where: 2-1 0 t= time qx = discharge per unit width (or discharge intensity) in the longitudinal direction qy = discharge per unit width (or discharge intensity) in the lateral direction The terms qx and qy are related to the depth-average velocities, vx and vy, in the longitudinal and lateral directions by: 2-2 qx=hvx qy=hvy The two horizontal components of the Conservation of Momentum Equations are given as: 2-3 \u2202qx \u2202 \u2202 g\u2202h2 1 + vx qx + vy qx + =gh Sox -Sfx + \u2202y \u03c1 \u2202t \u2202x 2\u2202x \u2202 h\u03c4 \u2202x xx \u2202 + h\u03c4 \u2202y xy and 2-4 \u2202qxy \u2202t Where: 2 + \u2202 1 \u2202 g\u2202h =gh Soy -Sfy + vy qy + vx qy + \u2202x \u03c1 2\u2202y \u2202y \u2202 h\u03c4 \u2202x yx Sox = bed slope in the longitudinal direction (m\/m) Soy = bed slope in the lateral direction (m\/m) Sfx = friction slope in the longitudinal direction (m\/m) Sfy = friction slope in the lateral direction (m\/m) + \u2202 h\u03c4 \u2202y yy \u03c4xy, \u03c4xx, \u03c4yy, \u03c4yc = components of the horizontal turbulent stress tensor An example of Sfx in the longitudinal-direction is given as: 2-5 \u03c4yx Sfx = = \u03c1gh vx 2 + vy 2 ghC2s vx 11 \fWhere: Cs = non-dimensional Chezy coefficient \u03c1= density of water (kg\/m3) g= gravitational acceleration (m\/s2) Here, Cs describes the roughness of the system and relates to the boundary roughness height, \u03bas, and h by: Cs =5.75log(12 Where: \u03bas = h \u03bas 2-6 ) boundary roughness height The value for \u03bas is estimated as one to three times the largest grain diameter (in units of metres). Subsequently, the model can be calibrated to measured water surface elevations and velocities by adjusting the value of \u03bas. The turbulent transverse shear stresses are determined using the Boussinesq-type eddy viscosity formulation. For example, \u03c4xy, is defined as: 2-7 \u03c4xy = Where: \u03b5t = \u2202 \u2202 + \u2202y \u2202x eddy viscosity coefficient determined by: 2-8 + t =\u03b51 +\u03b52 h Where: \u03b51, \u03b52 , \u03b53 = Cs +\u03b53 h2 2 \u2202 \u2202 \u2202 + + \u2202x \u2202y \u2202x 2 +2 \u2202 \u2202y constants selected to stabilize turbulent flow Through adjusting the constants \u03b51, \u03b52 and \u03b53, turbulent flows may be stabilized. Here, \u03b52, is the coefficient describing the portion of turbulence provided by bed shear stressors (\u03c4yx and \u03c4xx), \u03b51 may be adjusted to stabilize the flow under shallow conditions, particularly in cases where adjustments to \u03b52 are insufficient. Adjustments to \u03b53 are considered when \u03c4xy and \u03c4yy are the dominate sources of turbulence (i.e., deep lake flows or outlets gradients). 2.5 Morphodynamic model Outputs of the hydrodynamic model are input into a morphodynamic model in Step 2 of the proposed framework (Figure 1-3). Information regarding bed mobility in gravel bed rivers and sediment transport equations provide the background for the morphodynamic modeling. A review of readily available 2-D 12 \fmorphodynamic models is provided in this section, along with a description of River2D-Morphology (R2DM), the program selected for this work. 2.5.1 Bed mobility in gravel rivers Quantitatively describing the movement of sediment in gravel bed rivers is an ongoing research area. In gravel bed rivers, particles can be transported by rolling or sliding along the bed of the river. The degree of mobility depends on the degree of shear force applied by moving water (\u03c4) compared with that of the resistance to motion of the particle. At a certain value of \u03c4, widespread bed movement occurs. This value of \u03c4 is referred to as the critical shear stress, \u03c4CR. The general dimensionless relationship for the critical \u2217 Shields stress value for a particle of class size i ( \u03c4*CRi = Where: ) is expressed as: \u03c4CR 2-9 \u03c1s -\u03c1 gDi Di = mean diameter of the particle of class size i \u03c1s = density of particle In gravel bed rivers, \u03c4*CR values of 0.03 are considered stable, partial mobility is assumed to occur for \u03c4*CR < \u03c4 < 2\u03c4*CR and full bed mobility occurs at \u03c4 > 2 \u2217 (Wilcock and McArdell, 1997; May et al., 2009). From these principles, a wide range of empirical equations have been developed to compute sediment movement rates. 2.5.2 Sediment transport equations In discussing sediment transport in natural rivers, two mechanisms are identified: suspended load and bedload. Suspended (or wash) load considers the finer material (<0.2 mm) carried in suspension. Sources of this material are from banks, catchment area surfaces and soil erosion. Bedload is the material that moves in contact with the bed. Although the complete physics of bedload transport are not fully understood, empirical functions have been developed to quantify bedload movement in rivers by describing the influence of hydraulic parameters (e.g., v, h, So, \u03c4, Q, and stream power, \u2126) on moving particles (Gomez and Church, 1989). Bedload transport formulae are developed for sand (grain sizes less than <0.2 mm) and gravel (grain sizes >0.2 mm). Formulae are developed using either or both field and experimental data with grain mixture sizes that can be uniform or mixed. Typically, bedload transport equations include a parameter that represents the uniform or mixed substrate composition of the channel, the most commonly applied being 13 \fthe D50. However, in many gravel rivers, the sediment distribution is not normally distributed and tends to be negatively skewed (Kondolf and Wolman, 1993; Bunte and Abt, 2001). Thus, the D50 grain size may not be the most appropriate parameter to describe the grain size distribution for many gravel-bed materials. Alternatively, the mode (Almedeij and Diplas, 2003; Barry et al., 2004) or the D84 which is the diameter of the 84th percentile grain in the distribution (Reckling, 2010) have been suggested. Selected gravel bed sediment transport equations and the dimensionless Shields stress (\u03c4*) conditions under which they are developed are given in Table 2-1. Table 2-1: Characteristics of sediment transport equations for gravel bed rivers Sediment Transport Equation Developed from Experimental\/Field Parameter used to Represent Uniform (U) or \u03c4* = Particle Size Range Sediment Mixed (M) \u03c1s -\u03c1 gD50 (mm) Mixture Sediment Meyer-Peter and M\u00fcller Median size (D50) (1948) Parker and Klingeman Median size (D50) (1982) Wilcock and Crowe (2003) Variable grain size 1. Diplas and Shaheen, 2007 0.40-28.65 U&M - 0.60-102.0 M 0.01-0.0421 0.5-64 M 0.015-0.0501 Given the empirical nature of sediment transport equations and the inherent difficulties in describing sediment movement, model predicted transport rates are not always accurate. For example, Gomez and Church (1989) reviewed and tested ten bedload transport equations which have been developed for gravel or sand and gravel channels and none of them perform consistently well when applied to a variety of data sets. 2.5.2.1 Meyer\u2010Peter and M\u00fcller Equation (1948) One of the most commonly applied sediment transport equations is the Meyer-Peter and M\u00fcller Equation (1948). The equation was developed using flume experiments of beds with uniform grain size distribution. The original equation was corrected by Wong and Parker (2006) by analysing the original data of Meyer-Peter and M\u00fcller and is given as: 2-10 qsi =4 Where: 1.5 s-1 gD3i (\u03c4*i -0.047) qsi = volumetric sediment transport rate per unit width for particle of class size i s= specific gravity of the sediment \u03c4*i = the general form for a particle of class size, i, expressed as: 14 \f\u03c4*i = 2-11 \u03c4 \u03c1s -\u03c1 gDi Where \u03c4 can be simplified in a wide channel as: 2-12 \u03c4=\u03c1ghSo Where: So = bed slope 2.5.3 2-Dimensional (2D) morphodynamic modeling 2D morphodynamic models generally average velocity in the horizontal plane (i.e., are depth-averaged), which is suitable for shallow and wide rivers as there is little variation in velocity in the vertical direction. The localized information provided by 2D models compared with that provided by 1D models, offers insight into the location and formulation of bars and pools, aiding in evaluating the impacts on fish spawning habitat (Kwan, 2009). Table 2-2 lists some readily available 2D morphodynamic models. In addition to the 2D hydrodynamic equations (Equations 2-1 to 2-8) 2D morphodynamic models also solve Exner\u2019s bed-load transport continuity equation given as: 1-\u03c8 Where: \u2202qsy 2-13 \u2202zb \u2202qsx + + =0 \u2202t \u2202x \u2202y \u03c8= porosity of the bed material zb = bed elevation qsx = volumetric rate of bedload transport per unit length in longitudinal direction qsy = volumetric rate of bedload transport per unit length in lateral direction 2D morphodynamic models solve Equation 2-13 through either the finite difference or finite element approach. TELEMAC-SISYPHE, CCE2D, SED2D-WES, and R2DM use the finite element approach by specifying either a rectangular or triangular mesh for the system. Triangular meshes allow for better incorporation of bends in rivers than do rectangular meshes. BRI-STARS applies the finite difference approach through the method that models \u201cstream tubes\u201d which divide the channel into pre-selected bands. The solutions allow for the bed elevations to increase or decrease within the stream tube, dependent on the flow characteristics. 15 \fSuch models can simulate the transport of either cohesive (clay) or non-cohesive (sand and gravel) materials. Values of qsx and qsy required for solving Equation 2-13 can be determined from a variety of the transport equations discussed in Section 2.5.2 The sediment transport equations available in 2D morphodynamic models are listed in Table 2-2. Table 2-2: Two-dimensional morphodynamic models Sediment Transport Equations FE T \u2022 CCHE2D NCCHE (2005) FE R \u2022 SED2D-WES USAERDC (2006) FE T&R R2DM FE T Vasquez et al. (2008) \u2022 \u2022 Wilcock and Crowe (2003) \u2022 Parker and Klingeman (1982) \u2022 Yang (1984) Meyer-Peter-M\u00fcller (1948) LNH Engelund and Hansen (1967) TELEMACSISYPHE Gravel Ackers and White (1973) Finite Triangular Element (T) (FE) or Rectangular Finite (R) Difference (FD) Yang (1973) Developer Van Rijn (1984) Model Molinas and Wu (1996) Sand Numerical Mesh Type Method \u2022 \u2022 \u2022 Stream \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 Tube NCCHE \u2013 National Centre for Computational Hydroscience Engineering LNH - Laboratoire National d'Hydraulique et Environment Electricit\u00e9 De France, Research & Development USAERDC - U.S Army Engineering Research and Development Centre USDT - U.S Department of Transportation BRI-STARS USDT (1998) FD 2D models that simulate gravel bed river transport are R2DM and BRI-STARS. Typical applications of BRI-STARS are in the analysis of encroachments due to bridges and culverts in highway design. No published studies were found that use BRI-STARS to assess changes in gravel river bed elevations for fish habitat. The R2DM model is verified with experimental data under four different flume experiments: bed aggradation due to sediment overloading; bed degradation due to sediment feed shut-off (similar to 16 \fdegradation below a dam); knick point migration; and bar formation in a variable-width channel (Vasquez et al., 2007; Kwan, 2009). The model is shown to successfully simulate bed changes along the centreline of the channel for all four flume experiment scenarios. The model is applied by Smiarowski (2010) to the Seymour River, British Columbia, to evaluate the capabilities of simulating overall and local bed changes, and its use as a design tool for bank protection analysis of various riprap orientations. The model shows favourable results in its ability to simulate general changes in the stream bed and proves to be a useful design tool. 2.5.4 3-Dimensional (3D) morphodynamic modeling 3D morphological models solve the complete Navier-Stokes Equations and simulate complex flows and morphological processes such as scour and deposition in beds and meandering rivers. Readily available 3D models in North America include: CH3D-SED (US Army Corps of Engineers) and SSIIM (Olsen, 2011). The application of 3D models in morphological studies is limited due to excessive computational demand. 2.5.5 River2D Morphology (R2DM) River2D is a fixed-based model in that the hydrodynamics (h, qx, qy) are solved at each computational node for a fixed, immobile boundary. R2DM is a mobile-bed module that takes the computed hydrodynamic values and calculates sediment transport in and out of each element, and solves the Exner Equation (Equation 2-20) to determine the change in bed elevation during the timestep, \u0394zb. The value of bed elevation is updated as: 2-14 zbnew= zbold+\u0394zb Where: zbnew = updated bed elevation at end of time step zbold = bed elevation beginning of time step \u0394zb = change in bed elevation during time step Because the hydrodynamic and morphological changes are solved in a step-wise fashion, R2DM is considered to be an uncoupled model (Vasquez et al., 2008). There are five bedload transport equations available, Van Rijn (1984), Engelund and Hansen (1967), Meyer-Peter and M\u00fcller (1948), Wilcock and Crowe (2003) and an empirical relationship. When applying the Wilcock and Crowe Equation (2003) in R2DM, the user is able to identify areas of different grain size distributions (i.e., areas with coarser and finer sediment distributions) in the reach as 17 \fwell as the properties of the subsurface layer. The active layer is defined to have a constant thickness, Ls. Applying the Wilcock and Crowe Equation (2003), R2DM recalculates the surface and subsurface grain distribution at each time step by determining the flow of each grain size fraction in and out of a triangular element using an up-winding (UW) factor. The volumetric sediment transport rate, qs, may then be determined as: 2-15 qs = 1-UW qDS +UWqUS Where: UW = up-winding factor qDS = sediment flux from the downstream direction qUS = sediment flux from the upstream direction. The new surface and subsurface grain distributions are then recalculated for each size element\u00b8 i\u00b8according to the volume of that size elementi that enters or leaves the cell. The corresponding \u03bas value for the updated grain size distributions are determined from the equation: 2-16 \u03bas = C90D90 Where: C90 = Constant estimated by Bray (1980) D90 = diameter of the 90th percentile grain Full details regarding the methodologies employed by R2DM can be found in Kwan (2009). 2.6 Scour and fill model In Step 3 of the framework, a scour and fill model of the spawning areas of the reach is developed based on the results of the morphodynamic simulations. Probability Density Functions (PDFs) are fit to the bed scour and fill depths determined from the morphodynamic model to describe the amount of egg loss in a high flow event. In this section, previous studies that develop scour and fill models for gravel bed streams, proposed adaptations of previous work, and a means of choosing an appropriate PDF to describe system scour and fill, are discussed. 2.6.1 Previous work Published methodologies developed to predict scour and fill in gravel bed channels which can be expanded to quantify egg loss include the: Negative Exponential Distribution (EX) function (Haschenburger, 1999), Mobility Ratio model (Lapointe et al., 2000), and the use of a hydrodynamic 18 \fmodel to predict \u03c4* and bed mobility (May et al., 2009). Properties of reaches in these studies are in Table 2-3. Table 2-3: Properties of reaches discussed in this study Reach So (m\/m) length (m) This study (Campbell River) 1700 0.001-0.003 Trinity River (May et al. 2009) 1250 Average bankfull width (m) D50 (mm) Study peak discharge (m3\/s) Study peak discharge return period (yr) 80 120 1240 +200 48 47 422 Not known, bankfull discharge is 218 m3\/s 42.5 29 45.5 90 0.0020 Sainte-Marguerite River (Lapointe et al. 2000) Reach A 385 0.0033 44 Reach B 335 0.0028 38 Reach C 392 0.0026 58 Carnation Creek (Haschenburger, 1999) Reach 1 900 0.009 15 Reach 2 70 0.004 16 Kanaka Creek (Rennie, 1998) 40 0.002 20 250 168 - 398 47 29 36 48.8 8 58 46.8 3 2.6.1.1 Exponential (EX) Distribution Haschenburger (1999) develops a model for general use in gravel bed rivers for scour and fill depths using the EX Distribution given as: 2-17 -\u03b8\u03c7 f \u03c7 = \u03b8e , Where: \u03c7\u22650 \u03c7= random variable f(\u03c7) = proportion of the distribution greater than the value \u03c7 \u03b8= model parameter The specific model which relates the proportion of the channel that changes to a scour and fill depth (d) is developed using data collected in Carnation Creek, Vancouver Island, British Columbia and other published information on gravel bed coastal streams on Vancouver Island and in England (Haschenburger, 1999; Bigelow, 2003). 19 \fThe value of \u03b8 is estimated by plotting the inverse of the reach mean scour or fill depth, d, under various flows, against the corresponding value of the \u2217 using functional analysis to generate coefficients for the EX Distribution which, for gravel bed rivers, is given as (Haschenburger, 1999; Bigelow, 2003;): 2-18 \u03c4*i -1.52 * \u03c4CRi \u03f4=3.33e The proportion of the reach that scours or fills to a certain value of d is given as: -\u03b8d 2-19 f d =\u03f4e or through substitution of Equation 2-18: 2-20 \u03c4*i \u03c4* -1.52 i d \u03c4* CRi 3.33e -1.52 * \u03c4CRi e f d =3.33e The model shows potential for use in predicting (d) in stable channels under lower flows, which are in the range of flows for which the model was developed. Previous work by Montgomery et al. (1996) with scour chains in the Kennedy Creek, Washington showed that scour depths in a bankfull event followed the EX Distribution. Bigelow (2005) measured scour and fill percentages in two reaches of Freshwater Creek in Northern California. Results show a skewed distribution that follows the EX Distribution as predicted by Haschenburger with errors of 8 and 4%, relative to measured mean depths of scour and fill, respectively. Rennie (1998) finds that the EX Distribution only generally represents the pattern of scour and fill from data collected at Kanaka Creek, British Columbia. The stochastic nature of scour and fill in fully mobile beds makes prediction difficult, and Haschenburger\u2019s (1999) model does not perform well in these cases (Bigelow, 2005). In testing the model on the Trinity River, California, the EX Distribution is found to suit lower flows when beds are partially mobile, however, when beds approach full mobility, the equation is no longer a good fit. At higher flows the scour and fill distribution is skewed to the right and approaches a normal or lognormal distribution (May et al., 2009). 2.6.1.2 Mobility ratio model Lapointe et al. (2000) develop an empirical model from measurement of \u03c40 and net scour and fill in a reach under three flood events on the Ste. Marguerite River, Quebec. To develop the model, spawning 20 \fareas are divided into subzones that include the low point (bar), thalweg, and high (cut bank side) areas. Information regarding particle size and \u03c40 are taken at riffle sites in each of these three subzones and are used to develop a Mobility Ratio under various flows: \u03c40 Mobility Ratio= \u03c4CR 2-21 Net scour and fill is evaluated by comparing pre and post-flood event topographic survey bed elevations in each of the subzones. The proportion of each subzone undergoing scour and fill to 20 cm and 30 cm (i.e., published Dredd for Atlantic salmon) are plotted against the Mobility Ratio and fitted using linear regression. This model is promising for use in predicting egg loss on the Ste. Marguerite River for high flow events as there is a wide range of storm events in the study, including a 1996 flooding event with a return period measured in centuries. It also allows for predicting egg mortality in localized portions of the reach. However, the model is river specific (Bigelow, 2003), and requires post-event topographic surveying which is costly and must take place soon after a large event. Also, this method does not capture what happens through the course of the event and only evaluates the final bed topography of scour and fill. 2.6.1.3 Hydrodynamic model predicted Shields stress and bed mobility Using a combination of hydrodynamic modeling and empirical data collected from the Trinity River in Northern California downstream of the Lewiston Dam, May et al. (2009) propose a probabilistic approach for predicting areas of scour which can impact salmon redds. The method requires a calibrated hydrodynamic model which generates hydraulic parameters used to predict \u03c4* and a statistical model of site selection preferences of salmon. Dscour and Dfill are estimated with a hydrodynamic model and are verified using tracer rocks and scour chains for five different flow events. Categories of bed mobility are identified (i.e., stable, partially mobile, fully mobile) based on values of \u03c4* determined from the hydrodynamic model. The relative and cumulative frequencies of scouring events for the established \u03c4* categories based on field data are used to determine the probability of Dscour to a depth greater than or equal to Dredd. The correlation between \u03c4* and probability of Dscour being greater than or equal to Dredd can be transferred to other unchained sections of the river using the \u03c4* values of these sites determined with the hydrodynamic model. 21 \fThis method is advantageous in that it allows for localized investigation of scour and fill in potential spawning habitat zones and for evaluation of habitat enhancement activities. However, this framework has only been tested on one river and requires a significant amount of data collection. 2.6.1.4 Other scour and fill models Montgomery et al. (1996), observe the pattern of scour for a winter season in a reach of the Kennedy Creek, Washington using 104 scour chains. They measured Chum egg burial depths of 40 redds to the top of the pocket and compared these measurements with the recorded scouring depths of the scour chains measured at the end of season. A relationship between potential egg loss and mean depth of scour in the reach is developed based on the mean egg burial depth. This approach is also applied by Tripp and Poulin (1986) for Chum, Coho and Pink (Oncorhynchus gorbusch) salmon for streams in the Queen Charlotte Islands. Likewise, based on historical studies of scour depths in the Trinity River, Evenson (2001) presents a conceptual approach for evaluating Chinook salmon egg loss. These models could be more widely applicable if they only included the scour chains that were located in the areas of spawning and not a reach average scour value. 2.6.2 Distribution functions applicable to scour and fill in gravel bed rivers Studies have shown that the EX Distribution suggested by Haschenburger (1999) applies under low flow scenarios (Bigelow, 2003), however, as the magnitude, duration or frequency of the flood increases, the EX Distribution no longer applies (Haschenburger, 1999; Rennie, 1998; DeVries, 2000; Bigelow, 2003, May et al., 2010) because it does not represent the tail ends of scour depths for high flows. At higher flows, the range of Dscour in the channel increases (i.e., there is an increase in the magnitude of Dscour), causing an elongation of the right tail and a lowering of the left tail (Haschenburger, 1999). This relationship is depicted in Figure 2-2b. Important information at the tail ends of the data is required to predict survival of salmon eggs as the left tail of the data will most influence predictions of egg loss. Proportion of channel Proportion of channel b) Dscour or Dfill (cm) Dscour or Dfill (cm) Figure 2-2: Hypothetical depiction of the proportion of a channel that scours and fills depths (Dscour or Dfill) under a) low flows and b) high flows 22 \fAlternative distributions to the one-parameter EX Distribution have been explored to describe channel scour and fill. For example, Rennie (1998) fits a two-parameter exponential distribution to scour and fill data collected on Kanaka Creek, British Columbia and shows this model to be more accurate than the EX Distribution. A three-parameter distribution may provide a better fit in the tail region compared with a two parameter distribution (Chernobai, et al., 2007; Arshad et al., 2002). However, the computational effort required for a three-parameter model needs to be weighed against the accuracy of prediction obtained. 2.6.2.1 Three\u2010parameter Generalized Pareto (GP) Distribution In cases where the EX Distribution can be used but does not provide a proper fit of the tail ends of the distribution, the Generalized Pareto (GP) Distribution may be applied (Hosking et al., 1987). The GP Distribution was introduced by Pickands (1975) to describe excesses over an upper limit value. The GP Distribution is applied in water resources by Hosking and Wallis (1987) who use the distribution to model the annual maximum flood on the River Nidd, England. Rainfall intensity is estimated using the GP Distribution to model maximum rainfall data in Pakistan (Arshad et al., 2002). Other applications include the analysis of extreme events (i.e., flood frequency analysis, maximum wind loads, breaking strengths of materials, earthquakes), and the modeling of large insurance claims (Arshad et al., 2002; Ahsanullah, 2004). The GP Distribution is a three-parameter right-skewed distribution with shape parameter \u03c9, scale parameter \u03c3 (m) and location parameter \u03bc (m). Employed throughout this section are the subscripts \u201cs\u201d (\u03c9s, \u03bcs and \u03c3s), \u201cf\u201d (\u03c9f, \u03bcf and \u03c3f), and \u201ct\u201d (\u03c9t, \u03bct and \u03c3t), which are estimates of these parameters for data related to scour, fill, and the total combined scour and fill, respectively. The GP Distribution Cumulative Density Function (CDF) is given as: 2-22 1 1 Where: \u03c7= 1 , , 0 0 random variable with range: \u03bc \u2264 \u03c7 < \u221e for \u03ba \u2264 0 and \u03bc \u2264 \u03c7 \u2264 \u03bc-\u03c3\/\u03c9 for \u03c9 > 0 The PDF form of the GP Distributions given as: 2-23 23 \f1 1 , 1 , 0 0 the mean \u0305 of the distribution is given as: \u03c7 \u03c3 \u03bc ,\u03c9 1\u2010\u03c9 2-24 1 the variance S2 is given by: S2 \u03c32 1\u2010\u03c9 2 1\u20102\u03c9 2-25 ,\u03c9 0.5 2.6.3 Proposed scour and fill model As opposed to steady state, in a transient R2DM a net scour or net fill are reported for a given \u0394t. Two mechanisms can cause death of redds: 1) in one time step there is a Dscour beyond Dredd and 2) the Dfill in the final time step leads to egg suffocation or prevents fry emergence. Figure 2-3 shows an example of each of these cases. Dscour Time Step = any time Dredd Dscour,max Dfill Time Step = final time Dfill,final Original bed elevation Dredd Figure 2-3: Resultant depth of scour and depth of fill (Dscour and Dfill) during a morphodynamic simulation In post-R2DM simulation analysis the maximum scour value (Dscour,max) and final deposition (Dfill, final) at each node is extracted. Dscour,maxis only evaluated for those nodes which have a resulting net scour. Dfinal,fill values are \u2265 0 m. If the difference between the original and final bed elevation is < 0 (i.e., there is net scour), then the Dfinal,fill value is set to 0. Figure 2-4 shows a schematic of a hypothetical result of R2DM at the end of the simulation. Assuming redds have the same likelihood of being buried anywhere in the spawning area, the values of Dscour, max and Dfill, final at all nodes within the spawning areas are evaluated. Where the cell experiences a net scour, net fill, or no scour or fill, is assessed based on the average value of bed elevation change at the cell nodes. 24 \fFigure 2-4: Determining the proportion of cells in a spawning area which scour or fill using R2DM A frequency analysis of the absolute values of Dscour,max and Dfill,final is then conducted and the cumulative proportion of the spawning area that scours or fills to a given depth is determined. For a given Dredd, the proportion of egg loss in an event can be determined from the cumulative function, where, the amount of egg loss is the proportion of the channel that has a Dscour or Dfill greater than Dredd. These relationships are 1 Eggs Survival Eggs Destroyed Dredd 0 0 Proportion of spawning area Cumulative proportion of spawning area 1 shown graphically in Figure 2-5. Dscour or Dfill Dscour or Dfill Figure 2-5: Frequency and cumulative proportion of a spawning area that scours and fills to a given depth A CDF (i.e, the EX or GP Distributions) that best describes the proportion of scour and fill in the spawning areas can then be fit. For example, the proportion of the spawning area that scours or fills to Dredd, Pt, is determined based on the GP Distribution as: 2-26 Pt = 1Where: ( Dredd -\u03bct 1 \u03c3t Dredd > 0 m 25 \fand based on the EX Distribution as: 2-27 Pt = e(-Dredd \u03f4t Where: Dredd > 0 m The values of Pt are evaluated for all flow rates of interest and a specific Dredd in a repeated process. The value of Pt as a function of Q for a given Dredd is Outcome 2 of this thesis, an example of which is shown 0 Pt 1 graphically in Figure 2-6: Q (m3\/s) Figure 2-6: Proportion of egg loss due to scour and fill (Pt) for a given stream discharge (Q) and depth of redd burial (Dredd) 2.6.4 Choosing the appropriate Probability Density Function (PDF) The Anderson-Darling statistic (A2) is used to determine estimates of the distribution parameters for the scour and fill models. The statistic is defined as: 2-28 1 Where: 2 n= number of observations Zi = F( i) i= 1, 2, 3\u2026n j = 1 log log 1 the jth observation point in the data set 26 \fThe A2 test gives more weight to the tails of the data compared with other available distribution fitting tests (i.e., the Kolmogorov-Smirnov or Chi Square tests). It is found to be a robust tool in fitting both the EX and GP Distribution functions (Choulakian and Stephens, 2001; Ashard et al., 2002; Lai and Wu, 2008). Statistical hypothesis testing is used to determine if the data is appropriately represents by the distribution. In this test, the null hypothesis is that the distribution does represent the data (i.e., the alternative hypothesis is that the distribution does not represent the data). The value A2 is related to a upper tail percentage value (p-value) and a chosen significance level in which the distribution is rejected Tables relating A2 values and p-values for the GP Distribution are found in Appendix B. 2.7 Probabilistic egg loss model In Step 4 of the framework, a probabilistic egg loss model is developed based on the results of the scour and fill models. Using linear regression, the parameters of the fitted cumulative distributions are regressed against Q to develop an equation that describes the general proportion of egg loss due to scour and fill (PT). A probabilistic equation can be used to estimate the probability of a given survival rate of eggs for a given peak Q. Alternatively, methods discussed in Section 2.6.1 , such as the \u03c4* (Haschenburger, 1999; May et al., 2009) or mobility ratio (\u03c4avg\/\u03c4CR) (Lapointe et al., 2000) method may be applied. 2.7.1 Fitting distribution parameters For each of the proposed scour and fill models developed for different discharges, Q, parameters of the PDFs (i.e., \u03c9t, \u03bct, \u03c3t and t) are regressed against Q and a line of best fit is determined (an example using the GP Distribution parameter \u03c9t is shown in Figure 2-7). \u03c9t Line of best fit Parameter value from scour and fill model Q Figure 2-7: Probability Density Function (PDF) parameter regressed against discharge (Q) 27 \fThe scour and fill model parameters are then described as a function of Q, for example, in the case of the GP Distribution parameter \u03bat: 2-29 \u03c9t =a\u03c9 t Q + b\u03c9 t Where: a\u03c9 t = slope of the line of best fit for parameter \u03c9t b\u03c9 t = intercept of the line of best fit for parameter \u03c9t, Similar functions are evaluated for \u03bct, \u03c3t and \u03b8t. By substituting these parameters in Equation 2-26 the proportion of egg loss due to scour and fill (PT) for a peak flow event is determined by: 2-30 PT = 1-(a\u03c9 Where: t Q+b\u03c9 t )( Dredd -(a\u03bc a\u03c3 t t Q+b\u03bc Q+b\u03c3 t 1 Q+ ) t a\u03bc = slope of the line of best fit for parameter \u03bct a\u03c3 = slope of the line of best fit for parameter \u03c3t b\u03bc = intercept of the line of best fit for parameter \u03bct b\u03c3 = intercept of the line of best fit for parameter \u03c3t Or in the case of the EX Distribution, estimates of \u03b8 as a function of Q may be substituted: 2-31 (-Dredd (a\u03b8 Q+b\u03b8 ) PT = 1-e Where: a\u03b8(t) = slope of the line of best fit for parameter \u03b8t b\u03b8 (t) = intercept of the line of best fit for parameter \u03b8t A reliability function is developed to describe the general egg survival (SurvivalT), based on the GP Distribution, this is given as: 2-32 SurvivalT =1- 1-( Q+ )( Dredd -(a\u03bc Q+b\u03bc ) 1 a\u03c9 Q+ a\u03c3 Q+b\u03c3 And for the EX Distribution: 28 \f2-33 SurvivalT =1\u2010 1-e(-Dredd (a\u03b8 Q+b\u03b8 ) The SurvivalT can be used in reliability analysis to determine the probability of redd survival in a flow event given random realizations of Dredd. The Survival function can also be written for the mechanisms of scour and fill separately. 2.7.2 Reliability analysis of scour and fill predictions The existing and proposed scour and fill equations are deterministic in nature and do not account for the variability of Dredd, resulting in an unknown risk of scour and fill. A reliability analysis can be performed using the developed SurvivalT functions to estimate the probability of a specific survival threshold being exceeded. Typically, Q also differs within a stream due to runoff and tributary flows. However, as River2D and R2DM are limited to lengths of ten times the channel width, a constant peak flow may be applied through the entire reach. Thus there is only one random variable, Dredd, in the proposed scour and fill model. Using a limit state function (r) the probability of not meeting a target egg survival rate (F), can be determined, where: 2-34 r=SurvivalT -F Where: F= target egg survival rate Failure is said to occur when r \u2264 0, meaning SurvivalT < F. To estimate r, a Monte-Carlo Simulation can be conducted by developing a series of randomly generated values of Dredd based on a prescribed published frequency distributions (see Montgomery et. al.,1996, Tripp and Poulin, 1996, and Evenson, 2001) or on site collected information, an example of which is Frequency shown in Figure 2-8. Dredd Figure 2-8: Frequency distribution for depth of redd (Dredd) 29 \fFor each of the randomly generated values of Dredd, the value of r is evaluated for a target survival rate, F. Frequency This produces a PDF such as that shown in Figure 2-9: r Figure 2-9: Frequency distribution for the limit state function (r) with a target survival rate (F) from random values of depth of redd (Dredd) The probability of failure (pf) may be estimated based on the results of a Monte Carlo Simulation and is given as: nf pf = N Where: nf = number of simulations where r \u2264 0 N = number of simulations generated for the random variable, Dredd 2-35 To provide an accurate pf, a large number of samples is recommended. The results of the Monte Carlo Simulation produce the probabilistic egg loss model (Outcome 3) where the pf is the probability of not Probability of not meeting an acceptable target egg survival rate (pf) meeting a target egg survival rate (F) due to scour and fill, an example of which is shown in Figure 2-10. F = 10% F = 25% F= Peak flow (m3\/s) Figure 2-10: Probability of not meeting a target egg survival rate (F) due to scour and fill in a high flow event (pf) 30 \fChapter 3 - Case study A study reach on the Lower Campbell River on Central Vancouver Island, British Columbia was selected to demonstrate the framework for describing the scour and fill of salmon eggs during high flow events. This river was selected due to the availability of data, the presence of various salmonidae species, the presence of a hydroelectric facility which may control high flows, and the economic significance of the salmon to the community. 3.1 Campbell River watershed The Lower Campbell River is located within the Regional District of Comox-Strathcona on Vancouver Island (see Figure 3-1) and originates in a rugged mountain terrain in Strathcona Provincial Park draining an area of 1460 km2. The river discharges into Discovery Passage between the mainland of British Columbia and Vancouver Island. Elevations in the basin range from greater than 2200 m in the headwaters of Strathcona dam to sea level at the outlet. Figure 3-1: Study site location Alterations to the natural system for hydroelectric operations began in the 1940\u2019s. The Campbell River Hydroelectric system is shown in Figure 3-2. Three facilities are located on the lower portion of the river: the Strathcona, Ladore and John Hart Dams, creating Upper Campbell Lake Reservoir, Lower Campbell Lake Reservoir, and John Hart Reservoir, respectively. The river system above the John Hart Dam is referred to as the Upper Campbell River and that below is the Lower Campbell River. The Herber River and Crest Creek are diverted into the Upper Campbell Lake Reservoir, and the Salmon and Quinsam 31 \fRivers are diverted into the Lower Campbell Lake to provide additional flows to those systems. The total average annual inflow to the system is 101 m3\/s. The Strathcona Dam provides a storage of 300 x 106 m3 (Klohn Leonoff, 1989), the Ladore Dam 34 x 106 m3 and the John Hart Dam of 3.3 x 106 m3 (Klohn Leonoff, 1989). The John Hart Dam diverts its outflow to a powerhouse located downstream of Elk Falls. The spillway, which serves in flood management and as a means of providing minimal environmental flow requirements for fisheries, has a three-bay sluice gate with discharge capacity of 1557 m3\/s at full pool reservoir (BCRP, 2000). The majority of flow to the Lower Campbell River enters the John Hart generating station with a small continuous flow of 3.5 m3\/s that is released from the reservoir through the Elk Falls Canyon to meet minimal fish habitat flow requirements (BC Hydro, 2004a). Figure 3-2: Campbell River system map 32 \fELK FA ALLS FIRST ISLAND SECOND D ISLAND & SIDE CHANNEL C JOHN HART H POWER R STATION EEBERT ROAD 08HDOO3 0 QUINSA AM RIVER 08H HDO22 LEGEN ND WSC Gauge G H Highway 19 Study Reach R Reach Break Figure 3-3: Lower Campbelll River key map p 3.2 Hydro ology The Wateer Survey of Canada C (WSC C) maintains tw wo active streeam gauges oon the Lower Campbell Rivver System cllose to the stu udy reach, theese are the 08H HD003 and 008HD022 gauuges (locations shown on F Figure 3-3: Loweer Campbell River R key map p). Gauge 08 8HD003 \u2013 Caampbell Riverr near Quinsaam River, has daily maximum m and minimu um flow data from f 1949 to the present. The monthlyy mean dischaarges based onn the entire reco ord of data fro om the WSC gauge are sho own in Figuree 3-4. This sttream gauge iis located downstreaam of the hyd droelectric faccility and disp plays a flow ppattern that is typical of a rregulated flow w system wiith peak disch harge during the t winter rainy season andd minimal disscharges durinng the drier summer season. The construction c of o the hydroellectric system m on the Camppbell River haas altered the y of the Loweer Campbell River R by increeasing the annnual flows; reegulating flow ws for storage and hydrology power pro oduction caussing an altered d seasonal patttern of flowss; and regulatiing flows to m meet daily 33 \fvariations in electrical requirements for consumer consumption resulting in short term (daily and hourly) fluctuations in flows (Burt, 2004). Gauge 08HD022 is located near the mouth of the river and includes the influence of the additional flow provided by the Quinsam River. This gauge is located downstream of the study reach and was not used in analysis. A non-active WSC gauge, 08HD001 \u2013 Campbell River at Campbell Outlet, provides 40 years of data from 1920-1949. These data are prior to the construction of the hydroelectric facilities on the Campbell River and may be considered to be representative of the natural, unregulated flow regime of the system as shown in Figure 3-4. The flow regime is classified as a \u201ccoastal reservoir\u201d, meaning the highest peak flow event in the Campbell River catchment occurs during high rainfall seasons between October and March (i.e., seasonal rainstorms), and during snowmelt in May to June (BC Hydro, 2004a). The historical mean annual discharge prior to construction of the hydroelectric system is 86 m3\/s. Post-construction, the Monthly Discharge Data (m3\/s) mean annual discharge is 98 m3\/s. 140 WSC Gauge 08HD003 120 WSC Gauge 08HD001 100 80 60 40 20 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Figure 3-4: Mean-monthly discharge at WSC gauge: 08HD003 data from 1940 to present (post-installation of Campbell River system) and WSC gauge: 08HD001 (pre-installation of Campbell River system) Klohn Leonoff Ltd. (1989) developed floodplain mapping of the Campbell and Quinsam Rivers and discharge frequency relationships for the John Hart Dam,. These are return periods developed from WSC Gauge 08HD001 which considers the flow rates in the river under natural conditions and not in a 34 \fregulated regime. Operational conditions and return periods identified by Klohn Leonoff Ltd. (1989) are listed in Table 3-1. Table 3-1: Return period events and peak discharges at the John Hart Dam Return Period < 2-years 2-8-Years Flow Rate (m3\/s) <180 180-450 > 8-years >450 Condition Event is passed with power releases only Event is passed with power releases and controlled spilling Events requires all facilities to be fully open for a period of 12 hours or more 20-Year event = 1073 m3\/s 50-Year event = 1127 m3\/s 200-Year event = 1240 m3\/s Presently, a review of the past 20-years of flow data from the dam is being conducted to update the return-period and output hydrograph data. It should be noted that in the past 50-years of data collection, post-facility installation, the maximum peak flow event was 561 m3\/s suggesting that the return-period events identified by Klohn Leonoff (1989) may be over-estimated. A review and updating of flow scenarios is outside of the scope of this thesis. From the operational peak discharges for various return periods, operational hydrographs were produced from the operating procedures manual of the John Hart Dam as indicated in Klohn Leonoff Ltd. (1989). The operating hydrographs for various storms with peak flows of 220, 450, 1073, 1127 and 1240 m3\/s are in 6-hour time step increments, shown in Figure 3-5. 1400 Peak Flow 220 220 m3\/s m3\/s 450 450 m3\/s m3\/s 1073 1073 m3\/s m3\/s 1127 1127 m3\/s m3\/s 1240 1240 m3\/s m3\/s Discharge (m3\/s) 1200 1000 800 600 400 200 0 0 20 40 60 Time (h) 80 100 120 Figure 3-5: Outflow hydrograph for the John Hart Dam under various return period storms 35 \fIt should be noted that the operational conditions shown in Table 3-1 and Figure 3-5 may not represent the actual operating conditions at the dam and are developed from the publicly available operational procedure information. 3.3 Design flows Table 3-2 provides a list of the various flow scenarios and their conditions that are explored for the Campbell River in this study. Table 3-2: Design flows for the Lower Campbell River study Description of Design Flow Hydrodynamic calibration event \u2013 Water surface elevations Hydrodynamic calibration event Depths and velocities Hydrodynamic verification event Outflow rating curve WSC Gauge 08DH003 \u2013 Oct 20, 2003 Hydrodynamic verification event Outflow rating curve WSC Gauge 08DH003 \u2013Nov 18, 1995 Morphodynamic verification event Nov 26, 2009 Egg loss estimation event Egg loss estimation event Egg loss estimation event Egg loss estimation event Egg loss estimation event John Hart Dam Operating Condition Peak Discharge (m3\/s) Power release 31 Power release 79 Controlled spill 323 Controlled spill 561 Controlled spill 343 Power release Controlled spill Uncontrolled spill Uncontrolled spill Uncontrolled spill 220 450 1,073 1,127 1,240 3.4 Campbell River fisheries There are numerous fish species in the Campbell River system including five adronomous species of salmonids: Chinook, Coho, Chum, Pink and Sockeye (Oncorhynchus nerka) and Steelhead Trout (Oncorhynchus mykiss. Resident fish species include Rainbow and Cutthroat (Oncorhynchus clarkia) 36 \fTrout. The dates of the incubation period for the species occupying the Lower Campbell River are provided in Table 3-3 (BC Hydro, 2004a). Table 3-3: Species of fish in the Lower Campbell River Species Common name Chinook Chum Coho Cutthroat (anadromous) Cutthroat (resident) Pink Sockeye Steelhead (summer) Steelhead (winter) All species Binomial nomenclature Oncorhynchus tshawytscha Oncorhynchus keta Oncorhynchus kisutch Oncorhynchus clarkii Oncorhynchus clarkii Oncorhynchus gorbusch Oncorhynchus nerka Oncorhynchus mykiss Oncorhynchus mykiss Incubation Period October 8 \u2013 April 21 October 15 \u2013 April 15 October 15 \u2013 April 15 February 1 \u2013 June 21 February 1 \u2013 June 30 September 8 \u2013 March 31 October 1 \u2013 April 7 February 15 \u2013 May 31 March 1 \u2013 June 15 September 8 \u2013 June 30 While all of the species listed in Table 3-3 have been found to spawn in the Lower Campbell River, the Chinook and Chum salmon have the greatest population. Campbell River fish stocks are extremely important to the local economy which attracts thousands of anglers in pursuit of the river\u2019s famous Tyee salmon (i.e., Chinook salmon in excess of 30 pounds). Campbell River fish stocks are also important to commercial fisherman in Alaska and northern British Columbia as well as being culturally significant to the First Nation people of Campbell River (Burt, 2004). 3.4.1 Depth of Chinook salmon redd burial There are no studies of Chinook egg burial depths on the Lower Campbell River. Published Dredd values for Chinook salmon range from 19 to 80 cm to the bottom of the redd (DeVries, 1997). Evenson (2001) collected Dredd data from three reaches of the Trinity River, downstream of the Lewiston Dam. Dredd measurements of 28 redds were taken using liquid-nitrogen freeze-core sampling. These measurements range from 10.5 to 51.5 cm. The data follow a skewed right lognormal distribution as shown in Figure 3-6. Statistical properties of the mean ( ), standard deviation ( ) and coefficient of variance (Covredd) for the sample set are provided in Table 3-6. 37 \f0.6 Trinity Creek Redd Burial Depth Normal Cumulative Frequency 0.5 Lognormal 0.4 0.3 0.2 0.1 0 10 20 30 40 Dredd (cm) 50 60 Figure 3-6: Histogram and fitted Normal and Lognormal Distributions for redd egg burial depths (Dredd) of Chinook salmon in the Trinity River Table 3-4: Statistical properties of Chinook redd burial depth (Dredd), in the Trinity River Statistical property Value (cm) 30 Dredd 2 8.4 Sredd 28.0 Covredd It should be noted that Chinook in the Campbell River have been known to bury their eggs more than 1 m deep (personal communication Anderson, 2011). For this study, the Dredd to the bottom of pocket reported for Chinook salmon on the Trinity River, North-Western California by Evenson (2001) are used due to the completeness of the sample set. 3.5 Study reach selection BC Hydro (2004b) develop a 2D-hydrodynamic model of the Lower Campbell River using River2D. The River2D model simulates the Lower Campbell River in two reaches. The upper reach (Reach 2) extends from the John Hart Tailrace to the Quinsam River confluence and the lower reach (Reach 1) includes the length from the Quinsam River confluence to Discovery Passage. These reaches are shown in Figure 3-3. Present Chinook spawning activities take place in the area extending from the John Hart Tailrace to the Quinsam River (Reach 2). This study focuses on the resulting egg loss of salmon due to scour and fill located in Reach 2. 38 \fmon spawnin ng zone selecttion 3.5.1 Salm Two key Chinook C salm mon spawning g areas in the study reach iddentified by B Burt (2004) aare shown in Figure 3-7 7 and are refeerred to in thiss document ass the First andd Second Islaand spawning areas. Elk Falls F Canyon First Island d Chinook S pawning Areea Secoond Island Chin nook Spawniing Area John n Hart Powerr Geneerating Statio on Second Island Wolman W pebblee count Thalweg Figure 3-7: Location of spaw wning areas in th he Lower Campb bell River (Orthhophotography frrom BC Hydro, 2008) 3.6 Hydro odynamic model 3.6.1 Topographic datta ded by BC Hyydro with verrtical accuracyy of +\/- 0.25 m in Digital Ellevation Modeel (DEM) datta were provid open areaas. DEM dataa were derived d from: \uf0b7 Orthophotogra O aphy taken on n October 30, 2006 that exxtends from thhe eastern endd of John Harrt Lake\/Mc L Ivor Bay to Disco overy Passagee and \uf0b7 LiDAR L DEM of BC Hydro o transmission n corridors After this study was co ompleted, morre current LiD DAR informaation (Februarry 2, 2011) w was made available by BC Hy ydro, howeverr, these data were w not incorporated into the modelingg analysis as tthey were maade available after a substaantial amount of hydrodynaamic and morrphodynamic modeling waas complete. 39 \f3.6.2 Bathymetry Lower Campbell River bathymetry data were provided by BC Hydro with associated \u03bas values ranging from 0.02 to 0.51 m. Sources and methodologies applied for collecting spatial data can be found in BC Hydro (2004b). The range of \u03bas values used in the hydrodynamic and morphodynamic model are provided in Table 3-5. Table 3-5: Roughness coefficients, \u03bas (from BC Hydro, 2004b) Particle Size (mm) \u03bas (m) Fines <2 0.02 Small gravel 2-16 0.04 Large gravel 16-64 0.08 Small cobble 64-128 0.20 Large cobble 128-256 0.35 Small boulder 256-762 0.40 Large boulder >762 0.45 Bedrock\/bank N\/A 0.50 Rip rap N\/A 0.54 The First Island channel spawning platform was added to the river bathymetry using \u201cas constructed drawings\u201d from Anderson (2007) with an elevation of 12.5 m and a \u03bas of 0.5. 3.6.3 Boundaries Spatial information from outside the BC Hydro River2D model boundaries was included by integrating information from the DEM data provided in Section 3.6 to allow for higher flow conveyance. The inflow boundary was set at the John Hart Tailrace using the flow vs. tailrace elevation rating curve provided in BC Hydro, 2004b. The downstream boundary was set with a depth-unit discharge (q) rating curve given as: q =\u03b1hm Where: \u03b1= constant describing the relation of q and h m= exponent describing the relation of q and h 3-1 The downstream boundary rating curve was established from the WSC Gauge 08DH003 shown in Figure 3-8 . 40 \f700 600 q = h1.4952 R\u00b2 = 0.9987 q (m3\/s\/m) 500 400 300 200 100 0 0 0.5 1 1.5 h (m) 2 2.5 3 3.5 Figure 3-8: Downstream boundary rating curve (WSC Gauge 08HD003) 3.6.4 Mesh size A mesh size of 25 m2 is applied to the reach as it is a reasonable representation of river habitat when assessing fish habitat i.e., one node for every five m in length (BC Hydro, 2004b), and also minimizes computational time. The mesh is generated by aligning the triangular elements to the breaklines which identify flow patterns of the river. Within the River2D Mesh editor, the mesh was \u201csmoothed\u201d to a quality index of 0.20, which falls within the typical acceptable values that are on the order of 0.15 to 0.5 (Waddle and Steffler, 2002). 3.7 Morphodynamic model 3.7.1 Field data collection of grain size distribution Field data collection was conducted during the seasonal low flow period, September 7-8, 2010, and again on August17, 2011 to obtain information regarding the sediment size and distribution for the study reach. Flow at the time of the field visits were approximately 50 m3\/s, which did not allow for safe access to many areas of the river. Access to the bars and elevated portions of the reach such as the First and Second Island spawning areas was only possible at the time of field visit. Limited field survey information was collected as a result. Surface sampling was used to determine the grain size distribution. Wolman pebble counts were conducted at accessible portions of the river near the First and Second Island spawning areas during 2010 41 \fand along the bar between the First and Second Islands in 2011. The locations of sampling are shown on Figure 3-7. Using all collected surface sampling data (Appendix A); a field reach average grain size distribution is estimated and shown in Figure 3-9. Anderson (2007) 90 Field collected first island spawning platform Field collected bar 80 70 60 50 40 30 Cumulative Finer Than (%) 100 Field collected reach average 20 10 0 4 5.6 8 11.3 16 22.6 32 45 64 Grain Size (mm) 90 128 180 256 >256 Figure 3-9: Field survey bed grain size distribution and reported distribution for the First Island spawning area by Anderson (2007) The grain size distribution from the Wolman pebble count for the First Island spawning area are shown generally in Figure 3-9. This may be compared with the distribution identified by Anderson (2007), also shown in Figure 3-9, which is considered to be optimal for spawning Chinook and was used in the construction of the First Island gravel placement project in 2006. It should be noted that since the installation of the First Island spawning platform based on the Anderson (2007) distribution, two events with peak flows greater than the design shear stress (i.e., events greater than 225 m3\/s) occurred. It is noted that after these two events, the First Island spawning platform degraded and there is an accumulation of new gravels on the bar between the First and Second Island. The source of this new gravel is thought to be from the First Island spawning platform (personal 42 \fcommunication Anderson, 2011). Grain size distributions at the bar were collected to estimate the particle size that were transported in the two large and is shown in Figure 3-9. The D50, D84 and mode of the grain size distributions are given in Table 3-6. Table 3-6: Statistical properties of grain size distributions for the Lower Campbell River Distribution Property (mm) D50 (Median) Mode D84 Field Collected Reach Average (mm) 120 180 205 Field Collected First Island Spawning Platform (mm) Field Collected Bar (mm) Anderson (2007) (mm) 53 64 118 95 100 128 120 180 206 3.7.2 Boundaries The sediment feed was set at 0 m3\/s, representing a sediment supply that is cut-off via the damming of the system. In natural bed rivers, the inflow and outflow boundaries are not fixed. 3.7.3 Sediment transport function inputs Localized information of scour and fill is required in this study. When applying the Meyer-Peter and M\u00fcller Equation (1948) bed material transport is calculating with a D50 applied throughout the whole reach. However, the grain size distribution throughout the study reach varies from that in areas of large boulders (i.e., areas with D50 values greater than 756 mm) to that in areas of larger gravels (i.e., areas with D50 values between 16 to 64 mm), and bed material movement in localized areas may not be accurately accounted for using the Meyer-Peter and M\u00fcller Equation (1948). Figure 3-10 shows the ranges of D50 grain size distribution throughout the reach. 43 \fGrain Size (mm) 16-64 64-128 128-256 256-762 >762 Figure 3-10: Values of D50 in i the Lower Caampbell River stu udy reach R2DM alllows for areass in the reach to be modeleed as non-ero ding surfacess. In preliminnary simulatioons the materiial of the Firsst Island was allowed a to ero ode, the morpphodynamic cchanges at thee island were unrealisticc as the modeel does not acccount for streengthening facctors such as root cohesionn. Thus area at the inflow boundary of thee reach to the upstream side of the First Island is madde non-erodinng to allow foor model staability. This area a also contains the bedro ock canyon annd areas of laarge boulders. The Meyeer-Peter and M\u00fcller M (1948)) and Wilcock k and Crowe ((2003) Equattions may not adequately m model the transp port of particlees classified as a cobbles and d boulders (i. e., particle diiameters >2566 mm) as thesse particles are a much greaater than the diameter d of paarticles the eqquations weree developed uunder. In this study, a method m of non n-erodible areas, allowed fo or as a featuree in R2DM iss applied. Tyypically, areass which aree considered non-erodible n in i a river are large boulderrs, rip rap, conncrete apronss and other features. Here, areas with w D50 valuees greater than n 256 mm andd areas of thee thalweg wheere depths durring the mean annual dischaarge event (i.ee, 100 m3\/s) are a greater thaan 1.5 m are aalso specifiedd as non-erodiible. The latterr of which is included as it is thought thaat these areass will have a ccoarse surfacee and that deffining grain sizes in these areas through a field f survey is difficult. Erodible areas a in the sttudy reach aree identified in n Figure 3-11 and have an assumed graiin size distribution of Andersson, 2007 (i.e., D50 of 120 mm). m This grrain size distrribution is choosen as the puurpose of thiss study is to o assess bed elevation e chan nges in the sp pawning areass. 44 \fnd, as well as the banks, aree considered non-erodible, in high flow w Although the First and Second Islan hat erosion wo ould occur and d material woould be transpported in the ssystem. The events, it is possible th vided by thesee areas are ign nored in this study. R2DM M does not m model particless in effects of material prov suspension. Erodible areea Figure 3-11: Erodible areas in the Lower Caampbell River sttudy reach A \u03c8 valuee of 0.30 was determined using u Komuraa\u2019s (1963) em mpirical relatioonship: 2 0.229 \u03c8=1- + 1 So So D0.21 50 3-2 The UW factor f was sett to zero and a transport ratte factor of onne is applied for all morphhodynamic simulation ns. 3.8 Hydro odynamic an nd morphody ynamic modeel simulation n procedure ((R2DM) River2D simulations s arre conducted to solve hydrrodynamic prooperties of v,, h, and \u03c4 at noodes in the m mesh for each of o the scenario os identified in i Table 3-2, with 6-hour ssegments of thhe total 120-hhour operationnal hydrograp phs shown in Figure 3-5. The T inflow diischarge of thhe hydrographh is input into the River2D model and d steady-statee simulation iss executed. The T results aree saved to serrve as inputs tto the morphody ynamic model. 45 \fAssessing the scour and fill from peak flows in localized areas of the reach is conditional to the duration of exposure of the bed surface to shear stress. A transient, mobile bed simulations is executed with 100second goal time step outputs for the duration of the 6-hour segment in the operational hydrograph for the given event. Once the simulation is complete, the updated bed elevations of the R2DM simulation are saved and opened in the River2D program to input a new inflow rate of the operational hydrograph. This iterative procedure is conducting until the complete 120 hours of simulation have been executed. The procedure is shown in Figure 3-12. Q for increment of hydrograph 1500 Q (m3\/s) 1000 500 0 Iterative procedure from t=0 to t=120 hours 0 Time (h) 100 River 2D Run: steady state simulation Velocity (v), depth (h), shear stress (\u03bb) in all cells River 2D - Morphology Run: transient simulation at goal time step 100 seconds \uf0b7 \uf0b7 \uf0b7 \uf0b7 \uf0b7 Updated bed elevations (zb) and roughness height (ks) in all cells Provide inflow and outflow boundary Load non-eroding layer Provide sediment properties Choose sediment transport equation Report bed elevations at goal time step Figure 3-12: Procedure for hydrodynamic (River2D) and morphodynamic (R2DM) simulations for segments of the operational hydrograph of the Lower Campbell River 46 \fChapter 4 - Results and discussions This Chapter discusses the verification procedure of the hydrodynamic (River2D) and morphodynamic models and the results of the proposed framework applied to the case study of the Lower Campbell River. 4.1 Hydrodynamic model verification The hydrodynamic model is validated for water surface elevations using two events shown in X from WSC gauge 08DH003. Table 4-1: Hydrodynamic rating curve verification for the Lower Campbell River Event Q (m3\/s) Oct 20, 2003 Nov 18, 1995 323 561 WSC Water Surface Elevation (m) 8.73 9.67 River2D Water Surface Elevation (m) 8.63 9.58 Error +\/- (m) -0.10 -0.09 The table lists the error associated with using the rating curve to predict water surface elevations at the higher flows. Data for v and h provided by BC Hydro at a transect midday between the First Island are used to evaluate River2D model performance under a flow rate of 79 m3\/s. The results of the model along the transect are shown in Figure 4-1. The general relationship between modeled and observed h in Figure 4-1a and Figure 4-2a are appropriate, though the model tends to under-predict h. Ideally, a one to one relationship between modeled and observed values is preferred. The relationship between modeled and observed v is much less consistent as shown in Figure 4-1b and Figure 4-2b. It is unknown who or how the v data were collected. The accuracy of the data is questionable as it shows a uniform value across the transect, where the expected values of v would be maximum in the higher h regions as shown by the modeled values. Errors between observed and modeled results are calculated using the mean absolute error (MAE) by the following equation: 4-1 MAE= Where: hmod = modeled depth hobs = observed depth 100 n hmod -hobs hobs 47 \fn= number of samples The MAE calculated for h and v are 28.6% and 58.9%, respectively. (a) (b) 2.5 2 Modeled Observed 2 1.5 v (m\/s) 1.5 h (m) Modeled Observed 1 1 0.5 0.5 0 0 0 0 20 40 60 80 Distance along transect (m) 100 50 \u20100.5 100 Distance along transect (m) Figure 4-1: Observed and modeled (a) water depths (h), and (b) velocities (v), along transect T4.3 at a stream discharge of 79 m3\/s (b) 2.5 2.5 2 2 vmod(m\/s) hmod (m) (a) 1.5 1 0.5 1.5 1 0.5 0 0 0.5 1 hobs (m) 1.5 2 0 0 0.5 1 vobs (m\/s) 1.5 2 Figure 4-2: Observed versus modeled (a) water depths (h) and (b) velocities (v), at a stream discharge of 79 m3\/s A second set of collected field data for water surface elevations in August, 2009 were taken by BC Hydro at locations upstream of the Second Island were provided by BC Hydro under a flow rate of 31.1 m3\/s. Field collected data were provided at point locations and River2D results modeled for a flow rate of 31.1 m3\/s were estimated for these locations. Modeled results compared well for this event (see Figure 4-3) with a MAE of 26.6%. 48 \fModelled Water Surface Elevation (m) 16 14 12 10 8 6 6 8 10 12 14 16 Observed Water Surface Elevation (m) Figure 4-3: Observed versus modeled water surface elevation at a stream discharge of 31.1 m3\/s The MAE for h and water surface elevations is within a reasonable range. The large grain size in the Lower Campbell River and the presence of boulders creates highly localized sensitivities in the measured h and v readings, particularly at lower flows, which, when averaging over a mesh size of 25 m2 accounts for the variations between model and field data. For example, if a field reading of v is taken near a riffle, the upstream side of the riffle will record deep, slow moving water and that on the downstream side will record shallow, fast moving water. Applying a uniform grid size of 25 m2, the large variation of the riffle feature is averaged in the hydrodynamic model cell and a large error when comparing field data will result. 4.2 Morphodynamic model verification The ideal method for calibrating a morphodynamic model requires the collection of bed elevation and grain size distribution data prior to and after a high flow event. This can be undertaken using scour chains or by determining bed elevations with survey equipment (i.e, a total station) or LiDAR. The transient morphodynamic model would then be run with the pre-event surveyed bed elevation and grain size data under a transient storm event. A comparison of the modelled post-event and surveyed after event elevation data would identify the accuracy of the assumptions in the morphodynamic model and the validity of the sediment transport equations applied. However, project limitations did not allow for the surveying required. The morphodynamic model bed elevations are from BC Hydro Data surveyed in 2004 (see Section 3.6.1 ). During field visits conducted on September 7-9, 2010, and August 17, 2011 a visual verification of general changes in the river bed was conducted. Since the installation of the First Island spawning platform in 2006, an event with a peak discharge of 343 m3\/s occurred (WSC gauge 08DH003, November 49 \f26, 2009). This event, which began on November 20, 2009 and extended through December 4, 2009, exceeded the stable design conditions at the First Island, mobilizing the sediment and causing scouring in the First Island spawning area. The hourly operational hydrograph of this event beginning on November 20, 2009 at 17:00 and ending December 4, 2009 at 10:00 is provided by BC Hydro and shown in Figure 4-4. 400 Peak flow (343 m3\/s) Discharge (m3\/s) 350 300 250 200 100 hours 150 100 0 50 100 150 200 Time (hr) 250 300 350 Figure 4-4: Operational hydrograph at the John Hart Dam from November 20, 2009 at 17:00 through December 4, 2009 at 10:00 To evaluate how the model generally represents morphodynamic changes at the First Island spawning area, a R2DM simulation using the Meter Peter and M\u00fcller Equation (1948) with a D50 of 120mm and peak discharge of 343 m3\/s is conducted. Only six hours of the hydrograph are simulated at the peak discharge as only general changes in bed elevations are of interest. Modelled results are compared with the original bed surface elevations prior to the 343 m3\/s event (i.e., with the bed elevations from BC Hydro, 2004), shown in Figure 4-5. 50 \fDepossition of materrial Firstt Island spaw wning platfform Secon nd Island spawn ning platform m Locatio ons of field noted accumulated a sedimen nt Figure 4-5: Morphodynamicc model, R2DM, verification eveent (343 m3\/s) reesults After the 343 m3\/s even nt, as noted by b staff at the Department oof Fisheries aand Oceans, a new gravel n area on the right bank at the upstream m end of the Seecond Island was formed ((personal deposition communiccation Andersson, 2011), sh hown in Figurre 4-5. This iis confirmed bby a field visit conducted August 17 7, 2011. The deposited graavel is though ht to have origginated from the First Islannd Spawning Platform, however, thiss material maay originate frrom the bar w which extendss downstream m of the First Island. DM model, a new elevated d area approximently 50 m downstream m of the First IIsland spawniing In the R2D area was found, f and co onfirmed by field fi visit Aug gust 17, 2010.. Wolman peebble counts cconducted in tthis area of deeposition show w that the sed diment which is mobilized in events with th peak flows equal to and greater thaan 343 m3\/s have h a diametter greater thaan 100 mm (seee Section 3.77.1 for field ccollected informatio on). 51 \fTo confirm where deposition material originates in this system, tracer rock studies should be conducted. The general changes that R2DM simulates at the First Island platform are reasonable, however, without surveying a large area for new bed elevations, the accuracy of the model results are not known. The accuracy of the morphodynamic model is not essential for testing the methodology developed in this thesis. 4.2.1 Post-event bed elevations R2DM simulations of events with peak discharges of 220 and 450 m3\/s identified in Table 3-2 were conducted as per the procedure inFigure 3-12. In these cases, a modification to the procedure is made for simulations with peak discharges of 1073, 1127 and 1240 m3\/s. The simulation duration is shortened to run the length from the beginning of the hydrograph to the end of 6-hours of peak discharge (i.e, the duration of the simulated hydrograph is 60-hours). This modification is made to reduce the amount of computational time required for these simulations as it is thought that the majority of the morphodynamic changes will occur during the period before and up to the peak flow in the hydrograph. Also processes such as armouring are not simulated with the Meyer-Peter and M\u00fcller Equation (1948) in R2DM. However, sensitivity to the complete hydrograph should be tested. Figure 4-6 through Figure 4-9 compare the pre and post-event bed elevations, indicating areas of net scour and net fill. 52 \fFirst Island Sp pawning Area Firsst Island Second Issland Spawniing Area Seconnd Island Second Island Chaannel Figure 4-6: Comparison of pre p and post eveent bed elevation n for a peak dischharge of 220 m3\/\/s (Orthophotogrraphy from BC H Hydro, 2008) 53 \fFirst F Island Sp pawning Areaa Fiirst Island Second IIsland Spawnning Area Secoond Island Seecond Island Ch hannel p and post eveent bed elevation n for a peak dischharge of 450 m3\/\/s (Orthophotogrraphy from BC H Hydro, Figure 4-7: Comparison of pre 2008) 54 \fFirst Island Spaw wning Area First Island Second Islaand Spawninng Area Secoond Island Seecond Island Ch hannel p and post eveent bed elevation n for a peak dischharge of 1073 m3\/s (Orthophotoggraphy from BC C Figure 4-8: Comparison of pre 8) Hydro, 2008 55 \fFiirst Island Spaawning Area First F Island Second Issland Spawninng Area Seccond Island Second S Islandd Channel C p and post eveent bed elevation n for a peak dischharge of 1127 m3\/s (Orthophotoggraphy from BC C Figure 4-9: Comparison of pre 8) Hydro, 2008 56 \fFirsst Island Spaw wning Area First Island Second Islaand Spawningg Area Seecond Island Second Islannd Channel Figure 4-10: Comparison off pre and post ev vent bed elevatio on for a peak disccharge of 1240 m3\/s (Orthophotoography from BC 8) Hydro, 2008 In all simu ulations, simiilar sediment movement paatterns are obbserved withinn the study reach. The proportion n of the chann nel which sco ours or fills in ncreases with increasing peeak dischargee. The portionn of the reach of interest forr discussion is from immed diately downsstream of the John Hart Poower Generating station to the end of thee Second Islaand spawning platform. It is the sedimeent movementt in this sectioon a scour an nd fill in the identified i spaawning areas. that will affect In all simu ulations, the First F Island sp pawning platfform experiennces net scourr except for some cells loccated near the bank b and edgee of an existin ng bar which show s net fill. It is in thesee areas where shear stressees are lower and d sediment sco oured in the spawning s plattform is depossited. With inncreasing peaak flow eventts, the proportion n of the First Island spawn ning area undeergoing scourring increasess, as does the average depthh of 57 \fscour. Sediment which is scoured from the First Island spawning platform is then deposited immediately downstream of the area. The shear stress in the area of deposition is significantly lower than that in the First Island spawning platform due to the lower depth of water at the bar. These simulations show that under a high flow event, the bar which extends from the First Island will accumulate sediment at the left side and provide sediment to the system from the right side. The Second Island spawning platform is located near the river thalweg and the bar which extends upstream from the Second Island. Under the 220 m3\/s peak discharge event, there are little changes within this spawning area. In the 450 m3\/s peak discharge event, a sequenced scour-fill pattern is observed in the area adjacent to the thalweg which corresponds to a sequence of high shear stress followed by a lower shear stress area. In the simulations with peak flows equal to and greater than 1073 m3\/s, an area of fill occurs at the area located on the existing bar. This material originates from sediment scoured at the bar located downstream of the First Island. In all simulations, the Second Island spawning platform experiences both net scour and net fill which makes it important to know the mechanisms of egg loss in the river. Some areas experience a large amount of scour (i.e, Dscour >1 m), which are associated with areas of high shear stress. These anomalously high shear stress values occur when there is a rapid change in flow depth over a short distance, such as the location next to a bar, a bank or over a boulder. In these locations, transport rates can be over-estimated. In the case of the First Island spawning platform, there is a high magnitude of scour in many of the cells in the middle of the spawning area for flows greater than 450 m3\/s. This is not due to the same anomaly as there is are consistent high flows and high shear stresses due to the large depths of water in this portion of the river. In this area, for simulations over 450 m3\/s, the calculated critical Shields stress (\u03c4*) is above the threshold value of 0.047 in the Meyer-Peter and M\u00fcller Equation (1948). Some areas result in net fill in excess of 2.0 m for peak discharges equal to and greater than 450 m3\/s. The cause of these depositional areas is the transporting of material into a dry cell, or a cell with very little depth of water (i.e., an existing bar or zone of deposition, a bank, or in front of a boulder). These areas occur typically at one specific node in the triangular network of cells. The averaging and interpolation between the nodes of the cell creates the appearance of a larger area of fill. One such area is immediately downstream of the First Island spawning platform. Here, there is an existing gravel bar which extends from the First Island, and has a depth of water of 0.1-0.5m under a peak flow of 450 m3\/s. Material is continuously deposited as the water is too shallow to allow for sediment transport from this area (note: sediment transport is allowed at a minimum water depth of 0.0001 m). This anomaly should 58 \fnot affect the scour and fill values obtained for the First Island Spawning platform. However, if material is indeed transported further downstream, it may be deposited in the Second Island Spawning area. The thalweg which extends on the right side of the First Island (see Figure 3-7) is modeled as a nonerodible area to account for the coarse surface. However, net scour results in this area under simulations with peak discharge greater than 450 m3\/s. This is due to the interpolation by the program from a node that is erodible to one which is non-erodible. The addition of nodes, and adjustments to the mesh and the erodible regions, can be made to lessen the extent of the interpolation, nevertheless, the magnitude of net scour in this area is generally less than 0.2 m and some erosion is expected in the thalweg under these high flows. Also, the material is deposited on the right bank of the river, and impacts in the Second Island spawning areas should be minimal. In the simulations with peak flows of 220 and 450 m3\/s, there are no bed elevation changes within the Second Island channel. There are boulders at the entrance at this location which restrict the flow to the main portion of the river and create a pool within the side channel. A weir has been placed at the exit of the side channel, resulting in scouring immediately below the exit of the weir. The applied sediment transport equation is empirically derived from laboratory studies. For instance, for a small change in the parameter \u03c4*, there is a large variation in the transport rate, qs as shown for the Meyer-Peter and M\u00fcller Equation (1948) in Figure 4-11. As such, the predicted transport rates by the equations may not apply to the natural river being studied. 0.03 qs (m3\/m\/s) 0.025 0.02 0.015 0.01 0.005 0 0.05 0.07 0.09 0.11 \u03c4* 0.13 0.15 0.17 Figure 4-11: Sediment transport rate (qs) as a function of \u03c4* based on the Meyer-Peter and M\u00fcller Equation for D50 of 120 mm 59 \fThe Meyer-Peter and M\u00fcller Equation (1948) is expected to over-predict transport in mixed sediment as processes such as bed armouring are ignored (Wong and Parker, 2006). Typically, a transport reduction factor can be applied to calibrate the transport equations to the river being studied. However, in this case study, there is no information regarding bedload transport rates or localized scour and fill values, and a calibration of the sediment transport equations cannot be undertaken. Further field investigations to determine sediment transport rates, and localized scour and fill values and tracer rock studies to determine paths of sediment transport and deposition are warranted in the study reach to increase confidence in modeled results. Project limitations did not allow for gathering this information at this time. 4.3 Scour and fill model of the Lower Campbell River During the morphodynamic simulation, bed elevation changes are recorded in each of the spawning area nodes at increments of 100 seconds. The Dscour,max and Dfill, final values (refer to Section 4.3 for definition) at all nodes within the spawning area are recorded and are representative of the Dscour and Dfill value for the peak discharge simulation, respectively. A frequency analysis of the absolute values of Dscour and Dfill is conducted with histograms of results presented in Figure 4-12. A frequency analysis is also conducted for the Dscour,max and Dfill,final values separately to assess the individual impacts of each mechanism of egg loss. In the fill frequency analysis, if the final elevation in a node in a spawning area is below the original bed surface (i.e, Dfinal,fill < 0), a Dfinal,fill value of 0 is assigned for that cell. Figure 4-13 and Figure 4-14 show the results of the frequency analysis for Dscour and Dfill, respectively. 60 \fa) Q=220 m3\/s 0.8 Model Prediction 0.8 GPD (p-value < 0.01) Frequency EXP (p-value < 0.01) 0.6 Q=450 m3\/s Model Prediction GPD (p-value < 0.01) 0.6 EXP (p-value < 0.01) Frequency 1.0 b) 0.4 0.4 0.2 0.2 Dscour and Dfill(m) 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.0 Dscour and Dfill(m) c) d) Model Prediction 0.4 Q=1127 m3\/s Model Prediction GPD (p-value = 0.23) GPD (p-value > 0.25) EXP (p-value < 0.01) EXP (p-value < 0.01) 0.2 Frequency Q=1073 m3\/s Frequency 0.2 Dscour and Dfill(m) 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.0 0.0 0.4 Dscour and Dfill(m) e) 0.4 Q=1240 m3\/s Model Prediction GPD (p-value > 0.25) Frequency EXP (p-value < 0.01) 0.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0 Dscour and Dfill(m) Figure 4-12: Generalized Pareto (GP) and Exponential (EX) Distributions fit to modeled scour or fill depths (Dscour and Dfill) for simulations with peak discharges of a) 220 m3\/s , b) 450 m3\/s, c) 1073 m3\/s, d) 1127 m3\/s and e) 1240 m3\/s 61 \fa) Q=220 m3\/s 0.8 Model Prediction 0.8 GPD (p-value <0.01) Frequency EXP (p-value <0.01) 0.6 Q=450 m3\/s Model Prediction GPD (p-value <0.01) 0.6 EXP (p-value <0.01) Frequency 0.4 0.4 0.2 0.2 Dscour (m) 2.8 2.4 2.0 1.6 1.2 0.8 0.0 2.8 2.4 2.0 1.6 1.2 0.8 0.4 0.0 0.0 0.0 0.4 1.0 b) Dscour (m) c) d) Q=1073 m3\/s Model Prediction 0.6 Q=1127 m3\/s Model Prediction GPD (p-value <0.01) Frequency EXP (p-value <0.01) 0.2 GPD (p-value <0.01) 0.4 EXP (p-value <0.01) Frequency 0.4 0.2 Dscour (m) 2.8 2.4 2.0 1.2 0.8 0.4 0.0 2.8 2.4 2.0 1.6 1.2 0.8 0.4 0.0 0.0 0.0 1.6 0.6 Dscour (m) e) 0.6 Q=1240 m3\/s Model Prediction GPD (p-value <0.01) 0.4 Frequency EXP (p-value <0.01) 0.2 2.8 2.4 2.0 1.6 1.2 0.8 0.4 0.0 0.0 Dscour (m) Figure 4-13: Generalized Pareto (GP) and Exponential (EX) Distributions fit to modeled scour depths (Dscour) for simulations with peak discharges of a) 220 m3\/s , b) 450 m3\/s, c) 1073 m3\/s, d) 1127 m3\/s and e) 1240 m3\/s 62 \fb) a) Q=220m3\/s 1.0 Model Prediction 0.8 Frequency EXP (p-value <0.01) GPD (p-value <0.01) EXP (p-value <0.01) 0.6 Dfill (m) 2.8 2.4 2.0 1.6 1.2 0.0 2.8 2.4 2.0 1.6 1.2 0.0 0.8 0.0 0.4 0.2 0.0 0.2 0.8 0.4 0.4 0.4 Model Prediction 0.8 GPD (p-value <0.01) 0.6 Q=450m3\/s Frequency 1.0 Dfill (m) d) Q=1073m3\/s Model Prediction 0.8 EXP (p-value<0.01) Frequency GPD (p-value <0.01) 0.6 Q=1127m3\/s Model Prediction 0.8 EXP (p-value<0.01) GPD (p-value <0.01) 0.6 Dfill (m) 2.8 2.4 2.0 1.6 1.2 2.8 2.4 2.0 1.6 1.2 0.0 0.8 0.0 0.4 0.2 0.0 0.2 0.8 0.4 0.4 0.4 1.0 0.0 1.0 Frequency c) Dfill (m) e) 1.0 Q=1240m3\/s Model Prediction 0.8 GPD (p-value<0.01) Frequency EXP (p-value<0.01) 0.6 0.4 0.2 2.8 2.4 2.0 1.6 1.2 0.8 0.4 0.0 0.0 Dfill (m) Figure 4-14: Generalized Pareto (GP) and Exponential (EX) Distributions fit to modeled fill depths (Dfill) for simulations with peak discharges of a) 220 m3\/s , b) 450 m3\/s, c) 1073 m3\/s, d) 1127 m3\/s and e) 1240 m3\/s 63 \f4.3.1 Probabilistic equation of scour and fill in the Lower Campbell River (outcome 1) The EX and GP Distributions are fit to each of the Dscour and Dfill, data sets for the different peak discharge events as shown in Figure 4-12. The distributions are also fit to the separate Dscour and Dfill data sets shown in Figure 4-13 and Figure 4-14, receptively. The distributions are assessed for their strength in describing the data sets by the Anderson-Darling test. The determined Anderson-Darling statistic is related to a p-value, provided in Appendix B. A significance level of 0.05 is used in the hypothesis testing where the null hypothesis is that the distribution fits the data. Therefore, a p-value of less than 0.05 leads to the rejection of the null hypothesis (i.e., the distribution does not fit the data). Resulting pvalues of the test are listed in Table 4-2. Table 4-2: Anderson-Darling test p-values of the Generalized Pareto (GP) and Exponential (EX) Distributions describing depth of scour (Dscour) or depth of fill (Dfill) for spawning areas in the Lower Campbell River Peak GP Distribution (p-value) EX Distribution (p-value) Discharge Dscour and Dfill Dscour Dfill Dscour and Dfill Dscour Dfill (m3\/s) <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) 220 <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) 450 <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) 1073 0.23 (P) <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) 1127 >0.25 (P) <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) 1240 >0.25 (P) P- above significance level of 0.05 F- below significance level of 0.05 Tabulated parameters of the GP (i.e, \u03c3, \u03bc, and \u03c9) and EX (i.e, \u03b8) Distributions are in Table 4-3 and Table 4-4, respectively. Table 4-3: Generalized Pareto (GP) Distribution parameters for the Lower Campbell River Peak Discharge (m3\/s) 220 450 1073 1127 1240 DFill Dscour \u03c3S \u03c9s \u03bcs (cm) (cm) 0.975 -0.354 0.681 36.883 -3.438 0.369 66.720 -13.871 0.094 70.657 -13.248 0.059 76.541 -16.026 0.113 \u03c3F (cm) 0.040 1.545 6.636 5.928 24.100 \u03bcF (cm) -0.018 -0.570 -2.235 -2.129 -2.850 Dscour and DFill \u03c3T (cm) 0.937 1.439 0.716 20.309 0.605 87.946 0.681 94.447 0.525 105.870 \u03c9F \u03bcT (cm) \u03c9T -0.485 4.121 -7.869 -8.146 -6.470 0.609 0.143 -0.119 -0.152 -0.140 64 \fTable 4-4: Exponential (EX) Distribution parameters for the Lower Campbell River Peak Discharge (Q) (m3\/s) 220 450 1073 1127 1240 Dscour DFill \u03b8s (cm) \u03b8F (cm) 0.370 0.061 0.017 0.016 0.014 1.637 0.205 0.069 0.061 0.049 Dscour and DFill \u03b8T (cm) 0.313 0.051 0.014 0.013 0.012 For the fitted GP and EX Distributions, the decreasing value in parameters \u03bc and \u03b8 with increasing magnitude in discharge causes the distributions to skew to the right. This represents the lowering of the front (left) tail and elongation of the end (right) tail which is expected as the range of Dscour and Dfill increases with increasing discharge. The proportion of the spawning area with an active bed (i.e., Dscour, value > 0) also increases with the magnitude of discharge. This causes the distribution to stretch to the right and also reduces the front (left) tail, shown by the increasing value of the scale parameter (\u03c3). The curve of the distribution also becomes less concave, shaped by the decreasing \u03c9 component. Based the results of the Anderson-Darling test given a p-value threshold of 0.05, for Dscour and Dfill under all peak discharge events, the GP Distribution is a more robust than the EX Distribution. As the peak discharge increases, there is an improvement in the fit of the GP Distribution for these data. The EX Distribution does not fit the data well in any of the simulations. In a previous study, the EX Distribution was found to fit conditions of partially mobile beds (Haschenburger, 2000). In this study, the proposed method of evaluating scour and fill includes areas in spawning zones only, whereas in the other study, mobility of the entire reach is fitted to data. Neither the GP nor the EX Distributions accurately describe the processes of scour and fill individually in the spawning areas. For the Dscour analysis, the data are processed by including \u201czero\u201d values for nodes in the spawning area which do not record a Dscour,max \u2264 0 (i.e., during the simulation the node only experiences net fill). Likewise, in the Dfill analysis, zero values are assigned to nodes which have only a resulting net scour value. In a previous study (May et al., 2010) that fit the EX Distribution to individual scour and fill data, it is uncertain if the zero values were included in the analysis. Others (Rennie, 1998; May et al., 2010) also conclude that in higher flows, the EX Distribution does not represent the processes of scour and fill individually. 65 \fBased on the results of the scour and fill model fit for the case study, the GP Distribution is recommended for the Lower Campbell River as it outperforms the EX Distribution when evaluated with the AndersonDarling test. However, the GP Distribution has not previously been recommended to describe scour and fill in rivers. 4.3.1.1 Applications of Generalized Pareto (GP) Distribution The use of the GP is applied here to published Dscour and Dfill data for two other rivers to tests its applicability in describing the nature of scour and fill in gravel channels. 4.3.1.1.1 Kanaka Creek, British Columbia Rennie (1998) conducted a study using 55 wiffle-ball monitors during 1997-1998 at Kanaka Creek, British Columbia to assess if Dscour in salmon redds differs from that of the surrounding bed. Properties of Kanaka Creek are summarized in Table 2-3. Of the monitored peak flow events during the study period, the one with the largest magnitude is chosen to test the application of the GP and EX. This event has an average peak discharge of 46.8 m3\/s, an approximate return period of 3-years, and a \u03c4o of 28.8N\/m2 in the reach. In the event, wiffle-ball monitors recorded active channel depths (i.e., areas with Dscour or Dfill > 0) of 1-72 cm and 1-45 cm for Dscour and Dfill, respectively. The data is fitted to both the GP and EX Distribution with associated p-values from the Anderson-Darling test values shown in Table 4-5. The frequency analysis of Dscour and Dfill as well as the fitted distribution are shown graphically in Figure 4-15. Table 4-5: Generalized Pareto (GP) and Exponential (EX) Distribution parameters and Anderson-Darling test p-value for Kanaka Creek at a peak discharge of 46.8 m3\/s GP Distribution Parameters EX Distribution Parameter \u03c9 \u03c3 (cm) \u03bc (cm) \u03b8 (cm) 11.342 12.471 -0.489 0.071 Anderson-Darling Test GPD (p-value) EXP (p-value) >0.25 (P) <0.01 (F) P- above significance level of 0.05 F- below significance level of 0.05 66 \f0.5 Rennie (1999) Q=46.8m3\/s = 0.67) GPD (p-value >0.25) Frequency 0.4 EXP (p-value < 0.05) 0.3 0.2 0.1 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4 0.44 0.48 0.52 0.56 0.6 0.64 0.68 0.72 0.76 0.0 Dscour; Dfill(m) Figure 4-15: Generalized Pareto (GP) and Exponential (EX) Distributions fit to observed scour and fill depths (Dscour and Dfill) for Kanaka Creek at a peak discharge of 46.8 m3\/s The GP Distribution proves to be a good fit to the data whereas the EX Distribution does not fit the data well according the significance testing. It is important to note that the proposed methodology focuses on scour and fill in spawning areas only, whereas the distributions fit with data from Kanaka Creek considers various locations within a reach such as pools, riffles and bars. 4.3.1.1.2 Trinity Creek, California May et al. (1999) recorded scour and fill depths using scour chains over a three-year period from 2004 to 2006. During the monitoring period, three high flow events of discharges of 180, 242, and 422 m3\/s, occurred in which the scour chains recorded significant amounts of bed movement. For each of the three events, only scour chains in Chinook spawning areas were considered. These chains were identified by using the scour chain location coordinates and overlaying them with the spawning location map of the Trinity River provided in May et al. 2009. Of these chains, the recorded Dscour,max and Dfinal,fill are examined. Table 4-6 indicates the quantity of scour chains employed in the full reach, those in the spawning areas, the parameters of the fitted GP and EX Distribution parameters and resulting p-values determined from the Anderson-Darling test. Frequency analysis of Dscour and Dfill, as well as the fitted GP and EX distributions are shown graphically in Figure 4-16. 67 \fTable 4-6: Generalized Pareto (GP) and Exponential (EX) Distribution parameters and Anderson-Darling test p-value for Trinity River at peak discharges of 180, 242 and 422 m3\/s Flow Rate (m3\/s) 180 242 422 EX Anderson-Darling Number of Number of GP Distribution Distribution Test Scour Scour Parameters Parameter Chains Chains in Spawning \u03c9 \u03c3 (cm) \u03bc (cm) \u03b8 (cm) GP EX Area (p-value) (p-value) 72 39 -0.06 4.60 -0.49 0.26 0.11 (P) <0.01 (F) 72 33 0.19 8.88 -0.63 0.10 >0.25 (P) <0.01 (F) 66 37 -0.53 10.43 -0.25 0.15 0.21 (P) <0.01 (F) P- above significance level of 0.05 F- below significance level of 0.05 b) May et al. (2009) GPD (p-value = 0.11) 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4 0.44 EXP (p-value < 0.05) Dscour and Dfill (m) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 Q=242 m3\/s May et al. (2009) GPD (p-value >0.25) EXP (p-value < 0.05) 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4 0.44 0.48 Q=180 m3\/s Frequency 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 Frequency a) Dscour and Dfill (m) c) 0.7 0.6 Q=422 m3\/s May et al. (2009) GPD (p-value >0.25) 0.4 EXP (p-value < 0.05) Frequency 0.5 0.3 0.2 0.1 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4 0.44 0.48 0.0 Dscour and Dfill (m) Figure 4-16: Generalized Pareto (GP) and Exponential (EX) Distributions fit to modeled scour and fill depths (Dscour and Dfill) for the Trinity River at areas of Chinook spawning under a peak discharge of a) 180 m3\/s, b) 242 m3\/s and c) 422 m3\/s 68 \fThe GP Distribution proves to be a good fit to the data of Trinity Creek when analysing for scour and fill in spawning areas only whereas the EX Distribution does not fit the data well according the significance testing using the Anderson-Darling test. 4.3.2 The proportion of egg loss due to scour and fill in a high flow event for a given Dredd (outcome 2) To describe the amount of egg loss by scour and fill during a high flow event given a value of Dredd, the cumulative proportion of spawning area with a Dscour and Dfill value greater than a given Dredd is determined from the frequency analysis in Section 4.3. A Dredd of 30 cm is chosen based on the distribution identified in Section 3.4.1. GP and EX Distributions fit to the scour and fill model are also evaluated at this Dredd. Results are tabulated in Table 4-7. Table 4-7: Percentage of egg loss due to scour and fill for peak discharges of 220, 450, 1073 and 1127 m3\/s in the Lower Campbell River, given a depth of egg burial (Dredd) of 30 cm % Egg Loss (the cumulative proportion of spawning area with a Dscour,max and Dfinal,fill value > Dredd of 30 cm) Peak Discharge (m3\/s) 220 450 1073 1127 1240 R2DM Modeled Results GP Distribution EX Distribution 0 28 67 69 73 0 24 66 68 71 0 22 65 67 71 Relative to the R2DM modeled results, the prediction of egg loss by the GP Distribution slightly outperforms the predictions of the EX Distribution. However, although the egg loss estimated by both distributions is similar, it is the distribution that best describes the complete data set (i.e, the distribution with the higher p-value determined from the Anderson-Darling test) that is preferred for developing a probabilistic egg loss model. DeVries (2000) suggests that the magnitude of local scour does not necessarily increase with increasing magnitude of flow and as such, a greater egg loss may not result. However, in these simulations, the proportion of the spawning areas which are active (i.e, with Dscour or Dfill > 0) is constant for flows greater than 1073 m3\/s, though the magnitude of local scour does increase, causing more egg loss. However, the local scale used by DeVries (2000) and the one used in this study (grid size of 25 m2) are not the same. 69 \f4.4 Probabilistic egg loss model of the Lower Campbell River The results of the scour and fill model for the Lower Campbell River and fitted GP Distributions are used to develop a probabilistic egg loss model which incorporates the variability in the parameter Dredd. 4.4.1 Generalized Pareto (GP) Distribution parameters for the Lower Campbell River regressed against discharge The parameters of the GP Distribution (\u03c9, \u03c3, and \u03bc) for the scour and fill models (i.e., the models which include both Dscour and Dfill) are regressed against peak discharge. Line of best fit results using linear regression are shown in Figure 4-17. a) b) y = -0.0007x + 0.6163 R\u00b2 = 0.8709 1.0 \u03c9T 0 1000 Q (m3\/s) 2000 y = -0.0001x + 0.0454 R\u00b2 = 0.7305 0.00 0.5 0.0 -0.5 0.05 y = 0.001x - 0.2372 R\u00b2 = 0.9985 \u03c3T 0.5 1.5 \u03bcT 1.0 c) 0 500 1000 1500 -0.05 0.0 0 500 1000 Q (m3\/s) 1500 -0.10 Q (m3\/s) Figure 4-17: Generalized Pareto (GP) Distribution parameters a) \u03baT, b) \u03c3T, and c) \u03bcT regressed against peak discharge (Q) The GP parameters are described as a function of Q and summarized in Table 4-8. Table 4-8: Parameters of the equation describing the proportion of egg loss due to scour and fill (PT) for the Lower Campbell River Parameter Value a\u03c9(t) -0.0007 b\u03c9(t) 0.6163 a\u03bc(t) 0.0010 b\u03bc(t) 0.2372 a\u03c3(t) -0.0001 b\u03c3(t) 0.0454 70 \fThe proportion of egg loss due to scour and fill (PT) for a given peak discharge event in the Lower Campbell River is determined by: 4-2 PT 1-(\u20100.007Q+0.6163)( Dredd +0.0010 0.0454) 0.001Q-0.2372 \u20100.007Q+0.6163 The general egg survival (SurvivalT) and corresponding limit state function (r) based on the GP Distribution are given as: 4-3 SurvivalT =1\u2010 1-(\u20100.007Q+0.6163)( Dredd +0.0010 0.0454) 0.001Q-0.2372 \u20100.007Q+0.6163 The limit state function (r) for the Lower Campbell River is given as: 4-4 1\u2010 1-(\u20100.007Q+0.6163)( Dredd +0.0010 0.0454) 0.001Q-0.2372 \u20100.007Q+0.6163 4.4.2 Probability of not meeting a target survival rate (F) in the Lower Campbell River (outcome 3) A total of 5000 randomly generated values of Dredd created from the distribution of egg burial identified in Section 3.4.1 are evaluated in the limit state function (Equation 4-4). The probability of failure (pf) for various peak discharges are estimated based on the results of a Monte Carlo Simulation tabulated in Table 4-9 and shown graphically in Figure 4-18. Table 4-9: Probabilistic egg loss model for the Campbell River, pf Peak Discharge (m3\/s) pf (%) 25 50 75 220 0.0 0.0 0.0 450 0.3 3.3 31.5 550 0.7 12.7 82.9 700 1.6 48.7 99.8 800 1.6 77.3 100 1073 2.6 99.9 100 1127 10.4 100 100 1240 13.5 100 100 71 \fPobability of not meeting an acceptable target egg survival rate (pf) (%) 100 F=25% 90 F=50% 80 F=75% 70 60 50 40 30 20 10 0 0 500 Peak Discharge (m3\/s) 1000 Figure 4-18: Probability of not meeting a target survival rate (F) in the Lower Campbell River, based on 5000 samples The determined probability of egg loss in Figure 4-18 is considered an approximation. It can provide insight into operational management procedures as to what peak discharge can cause unacceptable loss in eggs. Adaptions to the operating procedures (i.e., reducing the peak discharge) can be made if other factors such as loss of life are not compromised. For instance, in this case study, given an acceptable egg survival rate (F) of 75% and peak discharge event of 450 m3\/s, there is a 31.5% probability of not meeting this target. If the peak discharge is reduced to 400 m3\/s, this probability reduces to 12.5%. 72 \fChapter 5 - Conclusions and future work 5.1 Thesis conclusions This thesis develops a framework for estimating the probability of egg loss due to scour and fill for a range of possible high flow events in gravel bed rivers. The framework begins with simulating hydraulic properties of the river (velocity, depth and shear stress) using the program River2D. These hydrodynamic results used by the input into a morphodynamic module, R2DM, which simulates bed elevation changes and provides the maximum depth of scour and final fill elevations in the spawning areas during the transient simulation. A scour and fill model for the spawning areas is developed by fitting a probabilistic distribution (i.e., Exponential and Generalized Pareto) to the data. With the determined probabilistic distribution and a known specific egg burial depth, an egg loss model is developed that provides the proportion of egg loss due to scour and fill for a specified peak discharge event. Uncertainties in the depth of egg burial are accounted for by using reliability analysis and the probability of not meeting a target egg survival rate is found. When considering applying this framework, the following should be considered: \uf0b7 It is time-dependent as the eggs have to be incubating in the redds during the time of the simulated flood event. \uf0b7 It does not account for multiple storm events occurring in sequence. \uf0b7 It does not consider the natural state of egg burial such as the shape and orientation of the egg pocket. \uf0b7 It is assumed that the death of an egg occurs when it is scoured to the bottom or filled to a depth equal to its burial; however death can occur earlier or later. The developed framework allows for modification in the assumption of when death of an egg occurs and data can be processed for the mechanisms of scour and fill alone (i.e., distributions that describe scour in the spawning areas can be used). \uf0b7 There is no consideration for the disturbance to the bed surface caused by salmonids during egg burial. The original depth of the bed is considered prior to the construction of a redd. Typically, the cover layers of the redd pocket is above the original bed surface. 73 \f\uf0b7 The framework was developed for a regulated system where the duration of the bed exposure to a peak discharge is consistent among events due to dam operational procedures. However, in real cases, the hydrograph may not be that of the operating procedure. A typical storm duration and intensity should be applied. For the case study of the Campbell River, British Columbia, a R2DM model is created. Results of the simulated bed changes for high flow events in these models showed the complexity in modeling sediment transport in gravel bed rivers. Determining localized values of scour and fill with models is difficult, particularly as processes such as bed armouring, and the creation of bed forms are complicated to simulate. R2DM is verified for modeling overall bed changes in the river and not localized values of scour and fill which may be better accomplished using 3D morphodynamic modeling. Also, applying empirically derived sediment transport equations without a method of calibrating for a specific river is difficult as computed transport rates are sensitive to the selective grain size and properties. The developed framework is adaptable given any improvements in 2D or 3D morphodynamic modeling. 5.2 Future work To extend the applicability of the developed framework: 1. Other mechanisms which affect redd survival in high flows such as altered water quality and the infiltration of fine sediments can be included. 2. The framework relates peak discharge to the proportion of egg loss in a high flow event. However, other measureable variables such as the mobility ratio or Sheilds stress may be appropriate. To test the use of the Generalized Pareto (GP) Distribution to describe scour and fill in gravel bed rivers: 3. For the case study the GP Distribution was found to fit the scour and fill data of the spawning areas in the study reach. The distribution was found to describe scour and fill data on Kanaka Creek, British Columbia and Trinity River, California. The GP Distribution used in describing scour and fill on other systems is warranted. To improve up the case study morphodynamic model: 4. The framework is tested on a case study which does not have adequate field data for calibrating the morphodynamic model. To improve upon the assumptions made, extensive field data are required. This would include sampling of the grain size distribution in the various areas of the 74 \friver, acquiring bed elevations prior to and after a large flow event, and collection of sediment transport rates. Parameters in the morphodynamic model can be adjusted to provide results similar to the field determined bed elevations. 5. R2DM has been tested for its ability to predict overall changes in the bed (see Smiarowski, 2010). 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Journal of Hydraulic Engineering. 110 (12):1783-1797. 82 \fAppendix A\u2013 Wolman pebble count Wolman Pebble Count Campbell River Project site: Survey Date: 08Sep10 > < < < < < < < < < < < < < Size (mm) >256 256 180 128 90 64 45 32 22.6 16 11.3 8 5.6 4 > < < < < < < < < < < < < < 17Aug11 Size (mm) >256 256 180 128 90 64 45 32 22.6 16 11.3 8 5.6 4 Survey Date: Count-1 Count-2 Count-3 Count-4 Count-5 13 1 8 1 3 3 1 3 0 0 15 5 7 6 3 7 3 6 4 7 2 8 8 8 1 6 11 15 1 5 14 7 0 2 6 3 3 2 0 2 0 2 1 0 2 1 0 0 0 2 0 0 0 0 0 0 0 2 1 2 0 0 50 13 50 50 50 Bar 1 1 4 23 28 34 14 1 0 0 0 0 0 0 0 Bar 2 1 2 3 17 15 7 3 2 0 0 0 0 0 0 83 \fAppendix B\u2013 Anderson-Darling statistic (A2) and significance levels Upper tail percentage values (p-value) for the Anderson-Darling statistic (A2) when F(x) is completely known (from Arshad et al. 2003). 2 A 0.25 1.248 0.15 1.610 Upper tail percentage values (p-value) 0.10 0.05 0.025 1.933 2.492 3.020 0.01 3.857 84 ","@language":"en"}],"Genre":[{"@value":"Thesis\/Dissertation","@language":"en"}],"GraduationDate":[{"@value":"2012-05","@language":"en"}],"IsShownAt":[{"@value":"10.14288\/1.0050716","@language":"en"}],"Language":[{"@value":"eng","@language":"en"}],"Program":[{"@value":"Civil Engineering","@language":"en"}],"Provider":[{"@value":"Vancouver : University of British Columbia Library","@language":"en"}],"Publisher":[{"@value":"University of British Columbia","@language":"en"}],"Rights":[{"@value":"Attribution-NoDerivs 3.0 Unported","@language":"en"}],"RightsURI":[{"@value":"http:\/\/creativecommons.org\/licenses\/by-nd\/3.0\/","@language":"en"}],"ScholarlyLevel":[{"@value":"Graduate","@language":"en"}],"Title":[{"@value":"Estimating the probability of egg loss due to scour and fill under high flows","@language":"en"}],"Type":[{"@value":"Text","@language":"en"}],"URI":[{"@value":"http:\/\/hdl.handle.net\/2429\/39414","@language":"en"}],"SortDate":[{"@value":"2011-12-31 AD","@language":"en"}],"@id":"doi:10.14288\/1.0050716"}