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Estimating the probability of egg loss due to scour and fill under high flows Glawdel, Joanna 2011

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  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 © Joanna Glawdel, 2011  ii  Abstract 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. iii   Table 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 Müller 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  iv  2.6.1.2 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  v  4.3 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– Wolman pebble count ........................................................................................................... 83  Appendix B– Anderson-Darling statistic (A2) and significance levels ....................................................... 84   vi  List 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, κs (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    vii  List 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 (post- installation 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  viii  Figure 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 τ* based on the Meyer-Peter and Müller Equation for D50 of 120 mm ....................................................................................................................... 59  ix  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  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) κT, b) σT, and c) μT 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   x  List of symbols Symbol  Description Unit aκ(t) = Slope of the line of best fit for parameter κt aμ(t) = Slope of the line of best fit for parameter μt aσ(t) = Slope of the line of best fit for parameter σt aθ(t) = Slope of the line of best fit for parameter θt A2 = Anderson-Darlington statistic b = Exponent describing relationship of τi* and τCRi* bκ(t) = Intercept of the line of best fit for parameter κt bμ(t) = Intercept of the line of best fit for parameter μt bσ(t) = Intercept of the line of best fit for parameter σt bθ(t) = Intercept of the line of best fit for parameter σt Cs = Chezy coefficient C90 = Constant estimated by Bray (1980) d = Depth of scour and fill in Haschenburger model cm dതതതത = Reach mean scour and fill depth in Haschenburger model cm D50 = Mean diameter of sediment (the size of 50th percentile grain) m D84 = Diameter of sediment of the 84th 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 Dfillതതതതത = Mean fill depth m Dfill,final = Depth of fill at the end of a R2DM simulation relative to original bed surface m 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 ܦ௦௖௢௨௥തതതതതതതത = Mean scour depth m Dscour,max = Maximum scour depth in a R2DM simulation relative to original bed surface m F = Target egg survival rate fi = Fraction of bed material in class size i g = Gravitational acceleration m/s2 xi  G = Dimensionless bedload transport rate ratio h = Water depth m n = Number of simulations where r ≤ 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 class size i m3/m/s qsx = Volumetric sediment transport rate in the longitudinal direction per unit width m3/m/s qsy = Volumetric sediment transport rate in the lateral direction per unit width m3/m/s 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 kg/m3 S2 = Variance SurvivalT = Probability of egg survival in a flow event accounting for scour and 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  OC xii  u* = 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 Wi* = 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  xiii  Greek Symbols  Description Unit βi = Site specific hiding relationship εt = Eddy viscosity coefficient kg/ms ε1, ε2, ε3, = Constants selected to stabilize turbulent flow in the eddy viscosity equation  γj = Observation point j in the data set  κs	 = Boundary roughness height m χ = Random variable μ = Location parameter of the Generalized Pareto Distribution Ω = Stream power kg m/s3 ψ = Porosity of bed material ρ = Density of water kg/m3 ρs = Density of sediment in the channel bed kg/m3 σ = Scale parameter of the Generalized Pareto Distribution Σ = Substrate τ = Shear stress N/m2 τ* = Dimensionless Shields stress τi* = Dimensionless Shields stress for a particle of class size i τavg = Reach average boundary shear stress N/m2 τCR = Critical shear stress N/m2 ߬஼ோ௜∗  = Dimensionless critical Shields stress for a particle of class size i τo = Bed shear stress N/m2 τxx, τxy, τyx, τyy = Components of turbulent stressors N/m2 ϴ = Model parameter of the Exponential Distribution ω = Shape parameter of the Generalized Pareto Distribution  xiv  Acknowledgements 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 – thank you all for being a part of my life and helping me through this work.  1  Chapter 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 2  limited 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 1-1.  Peak flow (m3/s) Pr op or tio n of  e gg  lo ss  d ue  to  sc ou r an d fil l    0         1 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) 3   3. 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 this outcome is shown in Figure 1-2.  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’s 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 Pr ob ab ili ty  o f n ot  m ee tin g an  ac ce pt ab le  ta rg et  e gg  su rv iv al  ra te  (p f)     0         1 50%F = 10% F = 25% F = 50%  4  case 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.  Figure 1-3: Flow diagram of proposed framework and outline of Chapter 2  Hydrodynamic Model – River2D (bed elevations, boundary conditions) Morphodynamic Model – River2D – Morphology (properties of stream sediment) Scour and Fill Model (location of spawning areas) velocity (v), depth (h), shear stress (τ) in all cells bed elevation proportion of spawning area that scours or fills to a specified depth Knowledge                             Thesis           Thesis Required          Section                Outcome  Hydrodynamic modeling   2.4       Bed mobility   2.5.1 Sediment transport equations 2.5.2 Morphodynamic modeling 2.5     Location of redds  2.2.1 Distribution functions  2.6.2   1, 2      Depth of redd burial  2.2.2 Reliability analysis  2.7.2    3  High flow event (Q) Re pe at ed  fo r a  n um be r o f f lo w  e ve nt s STEP 1 STEP 2 STEP 3 STEP 4 Probabilistic Egg Loss Model (variability in depth of redd burial) 5  Chapter 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. 6   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 ≥ Dredd Dfill ≥ 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 Dredd Eggs Original surface Dfill  Dredd Eggs Dscour a) b) Redd survival threatened: Dscour or Dfill ≥ Dredd 7  the 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 Cascapédia 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. 8  The 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 (τ) 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, 9  the 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 τ, 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 . 10  2.4.1 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:  11  2-1 ∂h ∂t + ∂qx ∂x + ∂qy ∂y ൌ	0 Where:   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 ∂qx ∂t + ∂ ∂x ൫vxqx൯+ ∂ ∂y ൫vyqx൯+ g∂h2 2∂x =gh൫Sox-Sfx൯+ 1 ρ ൥൭ ∂ ∂x ሺhτxxሻ൱+൭ ∂ ∂y ൫hτxy൯൱൩ and 2-4 ∂qxy ∂t + ∂ ∂x ቀvyqyቁ+ ∂ ∂y ቀvxqyቁ+ g∂h2 2∂y =gh൫Soy-Sfy൯+ 1 ρ ൥൭ ∂ ∂x ൫hτyx൯൱+൭ ∂ ∂y ൫hτyy൯൱൩ Where:   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) τxy, τxx, τyy, τyc = components of the horizontal turbulent stress tensor An example of Sfx in the longitudinal-direction is given as: 2-5 Sfx= τyx ρgh = ටvx2+ vy2 ghCs2 vx 12  Where:  Cs = non-dimensional Chezy coefficient ρ =  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, κs, and h by: 2-6 Cs=5.75log(12	 hκs ) Where:  κs =  boundary roughness height The value for κs 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 κs. The turbulent transverse shear stresses are determined using the Boussinesq-type eddy viscosity formulation.  For example, τxy, is defined as: 2-7 τxy=ቆ∂ݒ௫∂y + ∂ݒ௬ ∂x ቇ ߝ௧ Where:  εt =  eddy viscosity coefficient determined by: 2-8 ߝt=ε1+ε2h ටݒ௫ଶ+ݒ௬ଶ Cs +ε3h2ඨ2 ∂ݒ௫∂x +ቆ ∂ݒ௫ ∂y + ∂ݒ௬ ∂x ቇ 2 +2 ∂ݒ௫ ∂y Where:  ε1, ε2 , ε3  = constants selected to stabilize turbulent flow Through adjusting the constants ε1, ε2 and ε3, turbulent flows may be stabilized.  Here, ε2, is the coefficient describing the portion of turbulence provided by bed shear stressors (τyx and τxx), ε1 may be adjusted to stabilize the flow under shallow conditions, particularly in cases where adjustments to ε2 are insufficient. Adjustments to ε3 are considered when τxy and τyy 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 13  morphodynamic 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 (τ) compared with that of the resistance to motion of the particle.  At a certain value of τ, widespread bed movement occurs.  This value of τ is referred to as the critical shear stress, τCR.  The general dimensionless relationship for the critical Shields stress value for a particle of class size i (߬஼ோ௜∗ ) is expressed as: 2-9 τCRi* = τCR ൫ρs-ρ൯gDi  Where:  Di =  mean diameter of the particle of class size i   ρs =  density of particle In gravel bed rivers, τCR*  values of 0.03 are considered stable, partial mobility is assumed to occur for τCR* < τ < 2τCR*  and full bed mobility occurs at τ > 2߬஼ோ∗   (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, τ, Q, and stream power, Ω) 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 14  the 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 (τ*) 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 Parameter used to Represent Sediment Mixture Developed from Experimental/Field Particle Size Range (mm) Uniform (U) or Mixed (M) Sediment τ* = ߬൫ρs-ρ൯gD50 Meyer-Peter and Müller (1948) Median size (D50) 0.40-28.65 U & M - Parker and Klingeman (1982) Median size (D50) 0.60-102.0 M 0.01-0.042 1 Wilcock and Crowe (2003) Variable grain size 0.5-64 M 0.015-0.0501 1. Diplas and Shaheen, 2007 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‐Peter	and	Müller	Equation	(1948) One of the most commonly applied sediment transport equations is the Meyer-Peter and Müller 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 Müller and is given as: 2-10 qsi=4ටሺs-1ሻgDi3(τi*-0.047) 1.5  Where:  qsi =  volumetric sediment transport rate per unit width for particle of class size i   s =  specific gravity of the sediment   τi*= the general form for a particle of class size, i, expressed as: 15  2-11 τi*= τ൫ρs-ρ൯gDi  Where τ can be simplified in a wide channel as: 2-12 τ=ρghSo 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’s bed-load transport continuity equation given as: 2-13 ሺ1-ψሻ ∂zb∂t + ∂qsx ∂x + ∂qsy ∂y =0 Where:  ψ = 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 “stream tubes” 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. 16  Such 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 Model Developer Numerical Method   Finite Element (FE) or Finite Difference (FD) Mesh Type    Triangular (T) Rectangular (R)  Sediment Transport Equations Sand  Gravel V an  R ijn  (1 98 4)  Y an g (1 97 3)  M ol in as  a nd  W u (1 99 6)  A ck er s a nd  W hi te  (1 97 3)  En ge lu nd  a nd  H an se n (1 96 7)  M ey er -P et er -M ül le r ( 19 48 ) Y an g (1 98 4)  Pa rk er   a nd  K lin ge m an  (1 98 2)  W ilc oc k an d C ro w e (2 00 3)  TELEMAC- SISYPHE LNH FE T •    • • CCHE2D NCCHE (2005) FE R • SED2D-WES USAERDC (2006) FE T&R    • R2DM Vasquez et al. (2008) FE T •    • •   • BRI-STARS USDT (1998) FD Stream Tube  • • • • • • NCCHE – National Centre for Computational Hydroscience Engineering LNH - Laboratoire National d'Hydraulique et Environment Electricité De France, Research & Development USAERDC - U.S Army Engineering Research and Development Centre USDT - U.S Department of Transportation 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 17  degradation 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, Δzb.  The value of bed elevation is updated as: 2-14 zbnew= zbold+Δzb Where:  zbnew =   updated bed elevation at end of time step zbold  =   bed elevation beginning of time step Δzb =  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 Müller (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 18  well 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=ሺ1-UWሻqDS+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¸ i¸according to the volume of that size elementi that enters or leaves the cell.  The corresponding κs value for the updated grain size distributions are determined from the equation: 2-16 κs = 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 19  model to predict τ* 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 length (m) So (m/m) Average bankfull width (m) D50 (mm) Study peak discharge (m3/s) Study peak discharge return period (yr) This study (Campbell River)  1700 0.001-0.003 80 120 1240 +200 Trinity River (May et al. 2009)  1250 0.0020 48 47 422 Not known, bankfull discharge is 218 m3/s Sainte-Marguerite River (Lapointe et al. 2000) Reach A 385 0.0033 44 42.5 90 Reach B 335 0.0028 38 29 250 168 - 398 Reach C 392 0.0026 58 45.5 Carnation Creek (Haschenburger, 1999) Reach 1 900 0.009 15 47 36 8 Reach 2 70 0.004 16 29 48.8 Kanaka Creek (Rennie, 1998)  40 0.002 20 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 fሺχሻ= θe-θχ,          χ ≥ 0 Where:  χ =  random variable f(χ) =  proportion of the distribution greater than the value χ θ =  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). 20  The value of θ is estimated by plotting the inverse of the reach mean scour or fill depth, dത, under various flows, against the corresponding value of the ߬௜∗ using functional analysis to generate coefficients for the EX Distribution which, for gravel bed rivers, is given as (Haschenburger, 1999; Bigelow, 2003;): 2-18 ϴ=3.33e-1.52 τi* τCRi* The proportion of the reach that scours or fills to a certain value of d is given as: 2-19 fሺdሻ=ϴe-θd or through substitution of Equation 2-18:  2-20 fሺdሻ=3.33e-1.52 τi* τCRi* e3.33e -1.52 τi* τCRi* d  The model shows potential for use in predicting (dത) 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’s (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 τ0 and net scour and fill in a reach under three flood events on the Ste. Marguerite River, Quebec.  To develop the model, spawning 21  areas are divided into subzones that include the low point (bar), thalweg, and high (cut bank side) areas. Information regarding particle size and τ0 are taken at riffle sites in each of these three subzones and are used to develop a Mobility Ratio under various flows: 2-21 Mobility Ratio= τ0 τCR 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 τ* 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 τ* determined from the hydrodynamic model.  The relative and cumulative frequencies of scouring events for the established τ* 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 τ* and probability of Dscour being greater than or equal to Dredd can be transferred to other unchained sections of the river using the τ* values of these sites determined with the hydrodynamic model. 22  This 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.                  b)      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 Dscour or Dfill (cm) Dscour or Dfill (cm) Pr op or tio n of  ch an ne l Pr op or tio n of  ch an ne l 23  Alternative 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‐parameter	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 ω, scale parameter σ (m) and location parameter μ (m).  Employed throughout this section are the subscripts “s” (ωs, μs and σs), “f” (ωf, μf and σf), and “t” (ωt, μt and σt), 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 ܨሺ߯ሻ ൌ ൞ 1 െ ሺ1 െ ߱ ሺ߯ െ ߤሻߪ ሻ ଵ ఠ	, ߱ ് 0 1 െ ݁ݔ݌ ቀെ߯ െ ߤߪ ቁ , ߱ ൌ 0  Where:  χ =  random variable with range: μ ≤ χ  <൅∞ for κ ≤ 0 and μ ≤ χ ≤ μ-σ/ω	for ω	> 0 The PDF form of the GP Distributions given as: 2-23 24  ݂ሺ߯ሻ ൌ ۖە ۔ ۖۓ1 ߪ ቆ1 െ ߱ሺ߯ െ ߤሻ ߪ ቇ ଵ ఠିଵ , ߱ ് 0 1 ߪ ݁ݔ݌ሺെ ߯ െ ߤ ߪ ሻ ,				߱ ൌ 0  the mean ߯̅ of the distribution is given as: 2-24 	χത	ൌ	μ൅ σ1‐ω ,	ω	൏	1 the variance S2 is given by: 2-25 S2ൌ	 σ 2 ሺ1‐ωሻ2ሺ1‐2ωሻ ,	ω	൏	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 Δt.  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.  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 ≥ 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. Dscour,max Dredd Dscour   Time Step = any time Dfill,final Dredd Dfill  Time Step = final time Original bed elevation 25   Figure 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 shown graphically in Figure 2-5.  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= ൤1-߱௧( Dredd-μt σt ሻ൨ 1 ఠ೟  Where:  Dredd  >  0 m Dscour or Dfill Pr op or tio n of  sp aw ni ng  a re a 0   1  Dscour or Dfill C um ul at iv e pr op or tio n of  sp aw ni ng  a re a 0   1  Dredd Eggs Destroyed Eggs Survival 26  and based on the EX Distribution as: 2-27 Pt=ൣe(-Dreddϴt൧ 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 graphically in Figure 2-6:  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 ܣ௡ଶ ൌ െ݊ െ 1݊෍ሺ2݅ െ 1ሻ൛log ܼ௜ ൅ log൫1 െ ܼሺ௡ାଵି௜ሻ൯ൟ ௡ ௜ୀଵ  Where:  n =  number of observations   Zi =  F(ߓi) i =  1, 2, 3…n ߓj =  the jth observation point in the data set Q (m3/s) P t  0          1  27  The 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 τ* (Haschenburger, 1999; May et al., 2009) or mobility ratio (τavg/τCR) (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., ωt, μt, σt and t) are regressed against Q and a line of best fit is determined (an example using the GP Distribution parameter ωt is shown in Figure 2-7).  Figure 2-7: Probability Density Function (PDF) parameter regressed against discharge (Q) ω t Q Parameter value from scour and fill model Line of best fit 28  The scour and fill model parameters are then described as a function of Q, for example, in the case of the GP Distribution parameter κt: 2-29 ωt=aωሺtሻQ + bωሺtሻ Where:  aωሺtሻ =   slope of the line of best fit for parameter ωt   bωሺtሻ =   intercept of the line of best fit for parameter ωt, Similar functions are evaluated for μt, σt and θt. 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= ቈ1-(aωሺtሻ	Q+bωሺtሻ)( Dredd-(aμሺtሻ	Q+bμሺtሻ	) aσሺtሻ	Q+bσሺtሻ ቉ 1 ௔ഘሺ೟ሻ	Q+௕ഘሺ೟ሻ  Where:  aμ =   slope of the line of best fit for parameter μt aσ =   slope of the line of best fit for parameter σt  bμ =   intercept of the line of best fit for parameter μt bσ =   intercept of the line of best fit for parameter σt Or in the case of the EX Distribution, estimates of θ	as a function of Q may be substituted: 2-31 PT=ൣ1-e(-Dredd(aθQ+bθ)൧ Where:  aθ(t) =   slope of the line of best fit for parameter θt bθ (t) =   intercept of the line of best fit for parameter θt 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- ቈ1-(ܽఠQ+ܾఠ)( Dredd-(aμQ+bμ) aσQ+bσ ቉ 1 aωQ+௕ഘ  And for the EX Distribution: 29  2-33 SurvivalT=1‐ൣ1-e(-Dredd(aθQ+bθ)൧ 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 ≤ 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 shown in Figure 2-8.  Figure 2-8: Frequency distribution for depth of redd (Dredd) Dredd Fr eq ue nc y 30  For each of the randomly generated values of Dredd, the value of r is evaluated for a target survival rate, F. This produces a PDF such as that shown in Figure 2-9:  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: 2-35 pf= nf N  Where:  nf  =  number of simulations where r ≤ 0   N  =  number of simulations generated for the random variable, Dredd 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 meeting a target egg survival rate (F) due to scour and fill, an example of which is shown in Figure 2-10.  Figure 2-10: Probability of not meeting a target egg survival rate (F) due to scour and fill in a high flow event (pf) r Fr eq ue nc y  P ro ba bi lit y of  n ot  m ee tin g an  ac ce pt ab le  ta rg et  e gg  su rv iv al  ra te  (p f) Peak flow (m3/s) F = 10% F = 25% F =  31  Chapter 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’s.  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 32  Rivers 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  Figure 3-3: 3.2 Hydro The Wate System cl 3-3: Lowe maximum entire reco downstrea system wi summer s hydrology power pro JOHN H POWER ELK FA Lower Campbel logy r Survey of C ose to the stu r Campbell R  and minimu rd of data fro m of the hyd th peak disch eason.  The c  of the Lowe duction caus ART    STATION QUINSA RIVER LLS 0 FIRST  ISLAND  LEGEN WSC G Study R Reach l River key map anada (WSC dy reach, the iver key map m flow data f m the WSC roelectric fac arge during t onstruction o r Campbell R ing an altered SECOND & SIDE C M   8HDOO3 D auge each Break  ) maintains tw se are the 08H ).  Gauge 08 rom 1949 to gauge are sho ility and disp he winter rai f the hydroel iver by incre  seasonal pat  ISLAND  HANNEL  o active stre D003 and 0 HD003 – Ca the present. wn in Figure lays a flow p ny season and ectric system asing the ann tern of flows H am gauges o 8HD022 gau mpbell River The monthly  3-4.  This st attern that is  minimal dis  on the Camp ual flows; re ; and regulati E ighway 19 n the Lower ges (location  near Quinsa  mean discha ream gauge i typical of a r charges durin bell River ha gulating flow ng flows to m BERT ROAD 08H Campbell Riv s shown on F m River, has rges based on s located egulated flow g the drier s altered the s for storage eet daily DO22 33  er igure daily  the   and 34  variations 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 – 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 “coastal reservoir”, 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 mean annual discharge is 98 m3/s.  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 0 20 40 60 80 100 120 140 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec M on th ly  D is ch ar ge  D at a (m 3 /s ) WSC Gauge 08HD003 WSC Gauge 08HD001 35  regulated 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 Flow Rate (m3/s) Condition < 2-years <180 Event is passed with power releases only 2-8-Years 180-450 Event is passed with power releases and controlled spilling > 8-years  20-Year event = 1073 m3/s 50-Year event = 1127 m3/s 200-Year event = 1240 m3/s >450 Events requires all facilities to be fully open for a period of 12 hours or more   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.  Figure 3-5: Outflow hydrograph for the John Hart Dam under various return period storms 0 200 400 600 800 1000 1200 1400 0 20 40 60 80 100 120 D is ch ar ge  (m 3 /s ) Time (h) 220 m3/s 450 m3/s 1073 m3/s 1127 m3/s 1240 m3/s Peak Flow 220 3/s 450 3/s 1073 3/s  3/s  3/s 36  It 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 John Hart Dam Operating Condition Peak Discharge (m3/s) Hydrodynamic calibration event – Water surface elevations Power release 31 Hydrodynamic calibration event Depths and velocities Power release 79 Hydrodynamic verification event - Outflow rating curve WSC Gauge 08DH003 – Oct 20, 2003 Controlled spill 323 Hydrodynamic verification event - Outflow rating curve WSC Gauge 08DH003 –Nov 18, 1995 Controlled spill 561 Morphodynamic verification event Nov 26, 2009 Controlled spill 343 Egg loss estimation event Power release 220 Egg loss estimation event Controlled spill 450 Egg loss estimation event Uncontrolled spill 1,073 Egg loss estimation event Uncontrolled spill 1,127 Egg loss estimation event Uncontrolled spill 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) 37  Trout.  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 Incubation Period Common name Binomial nomenclature Chinook Oncorhynchus tshawytscha October 8 – April 21 Chum Oncorhynchus keta October 15 – April 15 Coho Oncorhynchus kisutch October 15 – April 15 Cutthroat (anadromous) Oncorhynchus clarkii February 1 – June 21 Cutthroat (resident) Oncorhynchus clarkii February 1 – June 30 Pink Oncorhynchus gorbusch September 8 – March 31 Sockeye Oncorhynchus nerka October 1 – April 7 Steelhead (summer) Oncorhynchus mykiss February 15 – May 31 Steelhead (winter) Oncorhynchus mykiss March 1 – June 15 All species  September 8 – 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’s 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 (ܦ௥௘ௗௗതതതതതതത), standard deviation (ܵ௥௘ௗௗଶ ) and coefficient of variance (Covredd) for the sample set are provided in Table 3-6. 38   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) Dreddതതതതതതത 30 Sredd2  8.4 Covredd 28.0  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. 0 0.1 0.2 0.3 0.4 0.5 0.6 10 20 30 40 50 60 C um ul at iv e Fr eq ue nc y Dredd (cm) Trinity Creek Redd Burial Depth Normal Lognormal  3.5.1 Salm Two key C Figure 3-7 Figure 3-7: 3.6 Hydro 3.6.1 Top Digital El open area  O L  L After this by BC Hy available John Gene W on spawnin hinook salm  and are refe Location of spaw dynamic m ographic dat evation Mode s.  DEM data rthophotogra ake/Mc Ivor iDAR DEM study was co dro, however after a substa Elk F  Hart Power rating Statio olman pebble g zone select on spawning rred to in this ning areas in th odel a l (DEM) dat  were derived phy taken on Bay to Disco of BC Hydro mpleted, mor , these data w ntial amount alls Canyon  n  count ion  areas in the  document as e Lower Campb a were provid  from:  October 30, very Passage  transmission e current LiD ere not inco of hydrodyna Sec Th study reach id  the First and ell River (Orth ed by BC Hy  2006 that ex  and  corridors AR informa rporated into mic and mor First Island Chinook S ond Island alweg entified by B  Second Isla ophotography fr dro with ver tends from th tion (Februar the modeling phodynamic  pawning Are Seco Chin  urt (2004) a nd spawning om BC Hydro, tical accuracy e eastern end y 2, 2011) w  analysis as t modeling wa a nd Island ook Spawni re shown in  areas. 2008)  of +/- 0.25  of John Har as made avai hey were ma s complete. ng Area 39  m in t lable de 40  3.6.2 Bathymetry Lower Campbell River bathymetry data were provided by BC Hydro with associated κs 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 κs values used in the hydrodynamic and morphodynamic model are provided in Table 3-5. Table 3-5: Roughness coefficients, κs (from BC Hydro, 2004b) Particle Size (mm) κs (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 “as constructed drawings” from Anderson (2007) with an elevation of 12.5 m and a κs 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: 3-1 q =αhm Where:   α =  constant describing the relation of q and h   m =  exponent describing the relation of q and h The downstream boundary rating curve was established from the WSC Gauge 08DH003 shown in Figure 3-8 . 41   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 “smoothed” 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 q = h1.4952 R² = 0.9987 0 100 200 300 400 500 600 700 0 0.5 1 1.5 2 2.5 3 3.5 q (m 3 /s /m ) h (m) 42  and 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.  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 0 10 20 30 40 50 60 70 80 90 100 >2562561801289064453222.61611.385.64 C um ul at iv e Fi ne r T ha n  (% ) Grain Size (mm) Field collected reach average Anderson (2007) Field collected first island spawning platform Field collected bar 43  communication 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) Field Collected Reach Average (mm) Field Collected First Island Spawning Platform (mm) Field Collected Bar (mm) Anderson (2007) (mm) D50 (Median) 120 53 95 120 Mode 180 64 100 180 D84 205 118 128 206 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 Müller 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 Müller Equation (1948).  Figure 3-10 shows the ranges of D50 grain size distribution throughout the reach.  Figure 3-10 R2DM all the materi unrealistic inflow bo model sta The Meye the transp particles a study, a m which are features. the mean The latter grain size Erodible a of Anders study is to : Values of D50 i ows for areas al of the Firs  as the mode undary of the bility.  This a r-Peter and M ort of particle re much grea ethod of non  considered n Here, areas w annual discha  of which is i s in these are reas in the st on, 2007 (i.e  assess bed e 16-64 64-128 128-256 256-762 >762 Grain Size (mm) n the Lower Ca  in the reach t Island was a l does not acc  reach to the rea also cont üller (1948) s classified a ter than the d -erodible are on-erodible i ith D50 value rge event (i.e ncluded as it as through a f udy reach are ., D50 of 120 m levation chan mpbell River stu  to be modele llowed to ero ount for stre upstream sid ains the bedro  and Wilcock s cobbles and iameter of pa as, allowed fo n a river are s greater than , 100 m3/s) a is thought tha ield survey i  identified in m).  This gr ges in the sp dy reach d as non-ero de, the morp ngthening fac e of the First ck canyon an  and Crowe (  boulders (i. rticles the eq r as a feature large boulder  256 mm and re greater tha t these areas s difficult.  Figure 3-11 ain size distr awning areas ding surfaces hodynamic c tors such as Island is mad d areas of la 2003) Equat e., particle di uations were  in R2DM is s, rip rap, con  areas of the n 1.5 m are a  will have a c and have an ibution is cho . .  In prelimin hanges at the root cohesion e non-erodin rge boulders ions may not ameters >256  developed u  applied.  Ty crete aprons  thalweg whe lso specified oarse surface assumed grai sen as the pu  ary simulatio  island were .  Thus area g to allow fo . adequately m  mm) as thes nder.  In this pically, areas  and other re depths dur  as non-erodi  and that def n size distrib rpose of this 44 ns at the r odel e  ing ble. ining ution   Although events, it effects of suspensio Figure 3-11 A ψ value The UW f simulation 3.8 Hydro River2D s for each o hydrograp model and morphody the First and is possible th material prov n. : Erodible areas  of 0.30 was actor was set s. dynamic an imulations ar f the scenario hs shown in  steady-state namic mode  Second Islan at erosion wo ided by these in the Lower Ca determined u  to zero and a d morphody e conducted s identified i Figure 3-5.  T  simulation is l. Erodible are d, as well as uld occur and  areas are ign mpbell River st sing Komura ψ=1  transport rat namic mode to solve hydr n Table 3-2, he inflow di  executed.  T a the banks, are  material wo ored in this udy reach ’s (1963) em - 2 So + 0.229 SoD500.21 e factor of on l simulation odynamic pro with 6-hour s scharge of th he results are  considered uld be transp study.  R2DM pirical relatio  e is applied  procedure ( perties of v, egments of th e hydrograph  saved to ser non-erodible orted in the s  does not m nship: for all morph R2DM)  h, and τ at no e total 120-h  is input into ve as inputs t , in high flow ystem.  The odel particles odynamic des in the m our operation  the River2D o the 45   in  3-2 esh al 46  Assessing 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 100- second 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.             Figure 3-12: Procedure for hydrodynamic (River2D) and morphodynamic (R2DM) simulations for segments of the operational hydrograph of the Lower Campbell River 0 500 1000 1500 0 100 Q  (m 3 /s ) Time (h) River 2D Run: steady state simulation River 2D - Morphology Run: transient simulation at goal time step 100 seconds Q for increment of hydrograph Updated bed elevations (zb) and roughness height (ks) in all cells Ite ra tiv e pr oc ed ur e fr om  t= 0 to  t= 12 0 ho ur s  Provide inflow and outflow boundary  Load non-eroding layer  Provide sediment properties  Choose sediment transport equation  Report bed elevations at goal time step Velocity (v), depth (h), shear stress (λ) in all cells 47  Chapter 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) WSC Water Surface Elevation (m) River2D Water Surface Elevation (m) Error +/- (m) Oct 20, 2003 323 8.73 8.63 -0.10 Nov 18, 1995 561 9.67 9.58 -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= 100 n ෍ฬ			hmod-hobs hobs 	ฬ  Where:   hmod =   modeled depth hobs =  observed depth 48  n =  number of samples The MAE calculated for h and v are 28.6% and 58.9%, respectively. (a)  (b)  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 (a)  (b)  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%. 0 0.5 1 1.5 2 2.5 0 20 40 60 80 100 h (m ) Distance along transect (m) Modeled Observed ‐0.5 0 0.5 1 1.5 2 0 50 100 v (m /s) Distance along transect (m) Modeled Observed 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 h m od (m ) hobs (m) 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 v m od (m /s ) vobs (m/s) 49   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 6 8 10 12 14 16 6 8 10 12 14 16 M od el le d W at er  S ur fa ce  El ev at io n (m ) Observed Water Surface Elevation (m) 50  26, 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.  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 Müller 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. 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 D is ch ar ge  (m 3 /s ) Time (hr) 100 hours Peak flow (343 m3/s)  Figure 4-5: After the deposition communic August 17 Platform, Island. In the R2D area was f area of de greater tha informatio  First spaw platf Morphodynamic 343 m3/s even  area on the ation Anders , 2011.  The however, this M model, a ound, and co position show n 343 m3/s h n).  Island ning orm  model, R2DM t, as noted b right bank at on, 2011), sh deposited gra  material ma new elevated nfirmed by fi  that the sed ave a diamet Locatio noted a sedimen , verification eve y staff at the the upstream own in Figur vel is though y originate fr  area approx eld visit Aug iment which er greater tha Depos mater ns of field ccumulated t nt (343 m3/s) re Department o  end of the Se e 4-5.  This i t to have orig om the bar w imently 50 m ust 17, 2010. is mobilized n 100 mm (se ition of ial Secon spawn sults f Fisheries a cond Island s confirmed b inated from hich extends  downstream   Wolman pe in events with e Section 3.7 d Island ing platform nd Oceans, a was formed ( y a field vis the First Islan  downstream  of the First I bble counts c  peak flows .1 for field c    new gravel personal it conducted d Spawning  of the First sland spawni onducted in t equal to and ollected 51 ng his 52  To 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 Müller 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.    Figure 4-6: 2008) Firs Comparison of p F t Island re and post eve irst Island Sp nt bed elevation awning Area Sec Cha  for a peak disch Second Is ond Island nnel arge of 220 m3/ land Spawni Secon s (Orthophotogr ng Area d Island aphy from BC H 53 ydro,    Figure 4-7: 2008) Fi Comparison of p F rst Island re and post eve irst Island Sp nt bed elevation awning Area Se Ch  for a peak disch  Second I cond Island annel arge of 450 m3/ sland Spawn Seco s (Orthophotogr ing Area nd Island aphy from BC H 54  ydro,   Figure 4-8: Hydro, 2008 F Comparison of p ) Fir irst Island re and post eve st Island Spaw nt bed elevation ning Area Se Ch  for a peak disch Second Isla cond Island annel arge of 1073 m nd Spawnin Seco 3/s (Orthophotog g Area nd Island raphy from BC 55   Figure 4-9: Hydro, 2008 F Comparison of p ) Fi irst Island re and post eve rst Island Spa nt bed elevation wning Area S C  for a peak disch Second Is econd Island hannel arge of 1127 m land Spawnin Sec  3/s (Orthophotog g Area ond Island raphy from BC 56   Figure 4-10 Hydro, 2008 In all simu proportion the reach station to that will a In all simu near the b lower and proportion : Comparison of ) lations, simi  of the chann of interest for the end of the ffect scour an lations, the F ank and edge  sediment sco  of the First Firs First Island  pre and post ev lar sediment el which sco  discussion i  Second Isla d fill in the i irst Island sp  of an existin ured in the s Island spawn t Island Spaw ent bed elevatio movement pa urs or fills in s from immed nd spawning dentified spa awning platf g bar which s pawning plat ing area unde ning Area n for a peak disc tterns are ob creases with iately downs platform.  It wning areas. orm experien how net fill. form is depos rgoing scour Second Isla Second Islan Channel harge of 1240 m served within increasing pe tream of the is the sedime  ces net scour  It is in these ited.  With in ing increases nd Spawning Se d 3/s (Orthophoto  the study re ak discharge John Hart Po nt movement  except for s  areas where creasing pea , as does the  Area cond Island graphy from B ach.  The .  The portion wer Generat  in this sectio ome cells loc shear stresse k flow event average depth 57  C  of ing n ated s are s, the  of 58  scour.  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 (τ*) is above the threshold value of 0.047 in the Meyer-Peter and Müller 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 59  not 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 non- erodible 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 τ*, there is a large variation in the transport rate, qs as shown for the Meyer-Peter and Müller Equation (1948) in Figure 4-11.  As such, the predicted transport rates by the equations may not apply to the natural river being studied.  Figure 4-11: Sediment transport rate (qs) as a function of τ* based on the Meyer-Peter and Müller Equation for D50 of 120 mm 0 0.005 0.01 0.015 0.02 0.025 0.03 0.05 0.07 0.09 0.11 0.13 0.15 0.17 q s (m 3 /m /s) τ* 60  The Meyer-Peter and Müller 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.  61  a)  b) c)  d) e) 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 0.0 0.2 0.4 0.6 0.8 1.0 0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 1. 2 1. 4 1. 6 1. 8 2. 0 Fr eq ue nc y Dscour and Dfill(m) Q=220 m3/s Model Prediction GPD (p-value < 0.01) EXP (p-value < 0.01) 0.0 0.2 0.4 0.6 0.8 0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 1. 2 1. 4 1. 6 1. 8 2. 0 Fr eq ue nc y Dscour and Dfill(m) Q=450 m3/s Model Prediction GPD (p-value < 0.01) EXP (p-value < 0.01) 0.0 0.2 0.4 0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 1. 2 1. 4 1. 6 1. 8 2. 0 Fr eq ue nc y Dscour and Dfill(m) Q=1073 m3/s Model Prediction GPD (p-value = 0.23) EXP (p-value < 0.01) 0.0 0.2 0.4 0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 1. 2 1. 4 1. 6 1. 8 2. 0 Fr eq ue nc y Dscour and Dfill(m) Q=1127 m3/s Model Prediction GPD (p-value > 0.25) EXP (p-value < 0.01) 0.0 0.2 0.4 0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 1. 2 1. 4 1. 6 1. 8 2. 0 Fr eq ue nc y Dscour and Dfill(m) Q=1240 m3/s Model Prediction GPD (p-value > 0.25) EXP (p-value < 0.01) 62   a)  b) c) d) e) 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 0.0 0.2 0.4 0.6 0.8 1.0 0. 0 0. 4 0. 8 1. 2 1. 6 2. 0 2. 4 2. 8 Fr eq ue nc y Dscour (m) Q=220 m3/s Model Prediction GPD (p-value <0.01) EXP (p-value <0.01) 0.0 0.2 0.4 0.6 0.8 0. 0 0. 4 0. 8 1. 2 1. 6 2. 0 2. 4 2. 8 Fr eq ue nc y Dscour (m) Q=450 m3/s Model Prediction GPD (p-value <0.01) EXP (p-value <0.01) 0.0 0.2 0.4 0.6 0. 0 0. 4 0. 8 1. 2 1. 6 2. 0 2. 4 2. 8 Fr eq ue nc y Dscour (m) Q=1073 m3/s Model Prediction GPD (p-value <0.01) EXP (p-value <0.01) 0.0 0.2 0.4 0.6 0. 0 0. 4 0. 8 1. 2 1. 6 2. 0 2. 4 2. 8 Fr eq ue nc y Dscour (m) Q=1127 m3/s Model Prediction GPD (p-value <0.01) EXP (p-value <0.01) 0.0 0.2 0.4 0.6 0. 0 0. 4 0. 8 1. 2 1. 6 2. 0 2. 4 2. 8 Fr eq ue nc y Dscour (m) Q=1240 m3/s Model Prediction GPD (p-value <0.01) EXP (p-value <0.01) 63  a)  b) c) d) e) 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 0.0 0.2 0.4 0.6 0.8 1.0 0. 0 0. 4 0. 8 1. 2 1. 6 2. 0 2. 4 2. 8 Fr eq ue nc y Dfill (m) Q=220m3/s Model Prediction GPD (p-value <0.01) EXP (p-value <0.01) 0.0 0.2 0.4 0.6 0.8 1.0 0. 0 0. 4 0. 8 1. 2 1. 6 2. 0 2. 4 2. 8 Fr eq ue nc y Dfill (m) Q=450m3/s Model Prediction GPD (p-value <0.01) EXP (p-value <0.01) 0.0 0.2 0.4 0.6 0.8 1.0 0. 0 0. 4 0. 8 1. 2 1. 6 2. 0 2. 4 2. 8 Fr eq ue nc y Dfill (m) Q=1073m3/s Model Prediction EXP (p-value<0.01) GPD (p-value <0.01) 0.0 0.2 0.4 0.6 0.8 1.0 0. 0 0. 4 0. 8 1. 2 1. 6 2. 0 2. 4 2. 8 Fr eq ue nc y Dfill (m) Q=1127m3/s Model Prediction EXP (p-value<0.01) GPD (p-value <0.01) 0.0 0.2 0.4 0.6 0.8 1.0 0. 0 0. 4 0. 8 1. 2 1. 6 2. 0 2. 4 2. 8 Fr eq ue nc y Dfill (m) Q=1240m3/s Model Prediction GPD (p-value<0.01) EXP (p-value<0.01) 64  4.3.1  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 p- values 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 Discharge (m3/s) GP Distribution (p-value) EX Distribution (p-value) Dscour and Dfill Dscour Dfill Dscour and Dfill Dscour Dfill 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) <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) <0.01 (F) P- above significance level of 0.05 F- below significance level of 0.05  Tabulated parameters of the GP (i.e, σ, μ, and ω) and EX (i.e, θ) 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  Dscour DFill Dscour and DFill (m3/s) σS (cm) μs (cm) ωs σF (cm) μF (cm) ωF σT (cm) μT (cm) ωT 220 0.975 -0.354 0.681 0.040 -0.018 0.937 1.439 -0.485 0.609 450 36.883 -3.438 0.369 1.545 -0.570 0.716 20.309 4.121 0.143 1073 66.720 -13.871 0.094 6.636 -2.235 0.605 87.946 -7.869 -0.119 1127 70.657 -13.248 0.059 5.928 -2.129 0.681 94.447 -8.146 -0.152 1240 76.541 -16.026 0.113 24.100 -2.850 0.525 105.870 -6.470 -0.140   65  Table 4-4: Exponential (EX) Distribution parameters for the Lower Campbell River Peak Discharge (Q) Dscour DFill Dscour and DFill (m3/s) θs (cm) θF (cm) θT (cm) 220 0.370 1.637 0.313 450 0.061 0.205 0.051 1073 0.017 0.069 0.014 1127 0.016 0.061 0.013 1240 0.014 0.049 0.012  For the fitted GP and EX Distributions, the decreasing value in parameters μ and θ 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 (σ).  The curve of the distribution also becomes less concave, shaped by the decreasing ω 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 “zero” values for nodes in the spawning area which do not record a Dscour,max ≤ 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. 66  Based 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 Anderson- Darling 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 τo 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 Anderson-Darling Test ω σ (cm) μ (cm) θ (cm) GPD (p-value) EXP (p-value) 11.342 12.471 -0.489 0.071 >0.25 (P) <0.01 (F) P- above significance level of 0.05 F- below significance level of 0.05  67     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. 0.0 0.1 0.2 0.3 0.4 0.5 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 Fr eq ue nc y Dscour; Dfill(m) Q=46.8m3/s Rennie (1999) GPD EXP (p-value = 0.67) (p-value < 0.05) >0.25) 68  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 Flow Rate (m3/s) Number of Scour Chains Number of Scour Chains in Spawning Area GP Distribution Parameters EX Distribution Parameter Anderson-Darling Test ω σ (cm) μ (cm) θ (cm) GP (p-value) EX (p-value) 180 72 39 -0.06 4.60 -0.49 0.26 0.11 (P) <0.01 (F) 242 72 33 0.19 8.88 -0.63 0.10 >0.25 (P) <0.01 (F) 422 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  a) b)  c)    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 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. 04 0. 08 0. 12 0. 16 0. 2 0. 24 0. 28 0. 32 0. 36 0. 4 0. 44 Fr eq ue nc y Dscour and Dfill (m) Q=180 m3/s May et al. (2009) GPD EXP -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. 04 0. 08 0. 12 0. 16 0. 2 0. 24 0. 28 0. 32 0. 36 0. 4 0. 44 0. 48 Fr eq ue nc y Dscour and Dfill (m) Q=242 m3/s May et al. (2009) GPD EXP 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. 04 0. 08 0. 12 0. 16 0. 2 0. 24 0. 28 0. 32 0. 36 0. 4 0. 44 0. 48 Fr eq ue nc y Dscour and Dfill (m) Q=422 m3/s May et al. (2009) GPD EXP (p-value = 0.11) (p-value < 0.05) (p-value >0.25) (p-value < 0.05) (p-value >0.25) (p-value < 0.05) 69  The 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) R2DM Modeled Results GP Distribution EX Distribution 220 0 0 0 450 28 24 22 1073 67 66 65 1127 69 68 67 1240 73 71 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. 70  4.4 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 (ω, σ, and μ) 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)  c)  Figure 4-17: Generalized Pareto (GP) Distribution parameters a) κT, b) σT, and c) μT 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 aω(t) -0.0007 bω(t) 0.6163 aμ(t) 0.0010 bμ(t) 0.2372 aσ(t) -0.0001 bσ(t) 0.0454  y = -0.0007x + 0.6163 R² = 0.8709 -0.5 0.0 0.5 1.0 0 1000 2000 ω T Q (m3/s) y = 0.001x - 0.2372 R² = 0.9985 0.0 0.5 1.0 1.5 0 500 1000 1500 σ T Q (m3/s) y = -0.0001x + 0.0454 R² = 0.7305 -0.10 -0.05 0.00 0.05 0 500 1000 1500μ T Q (m3/s) 71  The 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-(‐0.007Q+0.6163)( Dredd+0.0010 െ 0.0454)0.001Q-0.2372 ൨ ଵ ‐0.007Q+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‐ ൤1-(‐0.007Q+0.6163)( Dredd+0.0010 െ 0.0454)0.001Q-0.2372 ൨ ଵ ‐0.007Q+0.6163  The limit state function (r) for the Lower Campbell River is given as: 4-4 ݎ ൌ 1‐ ൤1-(‐0.007Q+0.6163)( Dredd+0.0010 െ 0.0454)0.001Q-0.2372 ൨ ଵ ‐0.007Q+0.6163 െ ܨ 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 72    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%.  0 10 20 30 40 50 60 70 80 90 100 0 500 1000 Po ba bi lit y of  n ot  m ee tin g an  a cc ep ta bl e ta rg et  e gg  su rv iv al  r at e (p f) (% ) Peak Discharge (m3/s) F=25% F=50% F=75% 73  Chapter 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:  It is time-dependent as the eggs have to be incubating in the redds during the time of the simulated flood event.  It does not account for multiple storm events occurring in sequence.  It does not consider the natural state of egg burial such as the shape and orientation of the egg pocket.  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).  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. 74   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 75  river, 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). A study of how well the program predicts localized scour and fill and relative bed elevation changes is warranted. To improve upon the R2DM modeling software: 6. A feature which allows for the adjustment of critical shear stress values in the different sediment transport equations to reduce or increase transport rates based on field collected measurements is warranted. 7. Improvements in the assignment and mixing of grain size distributions in the Wilcock and Crowe (2003) are recommended.  76  References Ackers, P. and White, W.R. 1973. Sediment transport: New approach and analysis. ASCE Journal of the Hydraulics Division, (99): HY11. Ahsanullah, M. 2004. Record Values – Theory and Applications. University Press of America, Oxford, UK. Almedeij, J.H. and Diplas, P. 2003. Bedload transport in gravel-bed streams with unimodal sediment. Journal of Hydraulic Engineering, 129(11): 896-904. Anderson, S. 2007. Campbell River Mainstem Spawning Gravel Placement - 2006 First Island. Tyee Club of British Columbia. BCRP 06.CBR.08. Anderson, S. 2011. Personal Communication. Campbell river, British Columbia. Arshad, M., Rasool, M.T. and Ahmad, M.I. 2002. Rain fall intensity estimates by Generalized Pareto Distribution. Journal of Applied Science, 2 (7): 774-776. Arshad, M., Rasool, M.T., and Ahmad, M.I. 2002. Rain fall intensity estimates by Generalized Pareto Distribution. Journal of Applied Sciences, 2: 774-776. Arshad, M., Rasool, M.T., and Ahmad, M.I. 2003. Anderson Darling and modified Anderson Darling tests for Generalized Pareto Distribution. Pakistan Journal of Applied Sciences, 3(2): 85-88. Baake, P.D., Basdekas, P.O., Dawdy, D.R., and Klingeman, P.C. 1999. Calibrated Parker-Klingeman model for gravel transport. Journal of Hydraulic Engineering, 25 (6): 657-660. Barry, J.J., Buffington, J.M., and King, J.G. (2004). A general power equation for predicting bed load transport rates in gravel bed rivers. Water Resources Research, 40, W10401. BC Hydro. 2004a. Campbell River Water Use Plan: Consultative Committee Report. A Project of BC Hydro. ISBN 0-7726-5182-5. BC Hydro, 2004b. Campbell River Flow-habitat Modeling with River2D; Water Use Plan – Technical Note. Ref: WUP-JHT-TN-F03 BC Hydro. 2007. Campbell River System - Deficiency Investigations: Flood Life Safety Risk Mitigation Report.  Report No. E552 77  Bigelow, P.E. 2003. M.A.Sc. Thesis: Scour, fill and salmon spawning in a California coastal stream. Humboldt State University, Arcata, California. Bigelow, P.E. 2005. Testing and improving predictions of scour and fill depths in a Northern California coastal stream. River Research and Applications, 21: 909-923. Bray, D.I. 1980. Evaluation of effective boundary roughness for gravel bed rivers. Canadian Journal of Civil Engineering, 7: 392-397. Bridge Coastal Restoration Program (BCRP). 2000. Bridge-Coastal Fish and Wildlife Restoration Program. Strategic Plan. Volume 2: Campbell River Watershed. BC Hydro, Burnaby, British Columbia.Bunte, K. and Abt, S.R. 2001. Sampling frame for improving pebble count accuracy in coarse gravel-bed streams. Journal of the American Water Resources Association, 37 (4):1001-1014. Burt, D.W. 2004. Restoration of the Lower Campbell River, a review of projects to 2003 and plan for future works. Prepared For The Department of Fisheries and Oceans, The Ministry of Water, Land and Air Protection and The Campbell River Gravel Committee Chernobai, A.S., Rachev, S.T. and Fabozzi, F.J. 2007. Operational Risk: A Guide to Basel II Capital Requirements, Models and Analysis. John Wiley & Sons, New Jersey. Choulakian, V. and Stephens, M.A. 2001. Goodness-of-Fit test for the Generalized Pareto Distribution. Technometrics, 43(4): 478-484. Coulombe-Pontbriand, M. and Lapointe, M. 2004. Geomorphic controls, riffle substrate quality, and spawning site selection in two semi-alluvial salmon rivers in the Gaspe Peninsula, Canada. River Research and Applications, 20: 577-590. DeVries, P.E. 1997. Riverine salmonid egg burial depths: review of published data and implications for scour studies. Canadian Journal of Fisheries Aquatic Sciences, 54: 1685-1698. DeVries, P.E. 2000. MASC Thesis: Scour in low gradient gravel bed streams: patterns, processes, and implications for the survival of salmonid embryos. University of Washington, Seattle. Diplas, P. and Shaheen, H. 2007. Bedload transport and streambed structure in gravel streams. In: Developments in earth surface processes,. Eds. Habersack, H., Piegay, H., and Rinaldi, M. Volume 11, Gravel-bed rivers VI: From process understanding to river restoration, 291-308. Engelund, F. and Hansen, E. 1967. A monograph on sediment transport in alluvial streams. Technical Forlag, Copenhagen, Denmark. 78  Evenson, D.F. 2001. MSC Thesis: Egg pocket depth and particle size composition within Chinook salmon redds in the Trinity River, California.  Humboldt State University, Arcata, California. Gaeuman, D., Andrews, E.D., Krause, A., and Smith, W. 2009. Predicting fractional bedload transport rates: Application of the Wilcock-Crowe equation to a regulated gravel bed river. Water Resources Research, 45. Geist, D.R. and Dauble, D.D. 1998. Redd site selection and spawning habitat use by fall Chinook salmon: The importance of geomorphic features in large rivers. Environmental Management, 22 (5): 655-669. Gomez, B. and Church, M. 1989. An assessment of bedload sediment transport formulae for gravel bed rivers. Water Resources Research, 25: 1161-1186. Groot, C. and Margolis, L. 2003. Pacific Salmon Life Histories. UBC Press, University of British Columbia. Haschenburger, J.K. 1996. Ph.D Thesis: Scour and fill in gravel-bed channel: observations and stochastic models. University of British Columbia, Vancouver. Haschenburger, J.K. 1999. A probability model of scour and fill depths in gravel-bed channels. Water Resources Research, 35 (9): 2857-2869. Hoey, T.B. and Ferguson, P. 1994. Numerical simulations of downstream fining by selective transport in gravel bed rivers: Model development and illustration. Water Resources Research, 30: 2251-2260. Holly, F.M. and Rahuel, J.L. 1990. New numerical/physical framework for mobile-bed modeling, Part 1. Numberical and physical principals. Journal of Hydraulic Research, 28 (4): 401-446. Hosking, J.R.M. and Wallis, J.R. 1987. Parameter and quantile estimation for the generalized Pareto Distribution. Technometrics, 29 (3): 339-349. Hyatt, K.D., Stockwell, M.M., and Rankin, D.P. 2003. Impact and adaptation responses of Okanagan River sockeye salmon (Oncorhynchus nerka) to climate variation and change effects during freshwater migration: Stock restoration and fisheries management implications. Canadian Water Resources Journal, 28 (4): 689-713.Klohn Leonoff. 1989. Floodplain mapping program – Campbell and Quinsam Rivers. 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University of British Columbia, Vancouver. Lai, L-H. and Wu, P-H. 2008. Estimating the threshould value and loss distribution: rice damaged by typhoons in Taiwan. African Journal of Agricultural Research, 3(12): 818-824. Lapointe, M., Eaton, B., Driscoll, S. and Latulippe, C. 2000. Modeling the probability of salmonid egg pocket scour due to floods. Canadian Journal of Fisheries and Aquatic Sciences, 57: 1120-1130. MacIssac, E.A.2009. Chapter 14 – Salmonids and the Hydrologic and Geomorphic Features of their Spawning Streams in British Columbia.In Compendium of Forest Hydrology and Geomorphology in British Columbia [In Prep.] R.G. Pike et al. (editors). B.C. Ministry of Forests and Range Research Branch, Victoria, B.C. and FORREX Forum for Research and Extension in Natural Resources Society, Kamloops, B.C. Land Management Handbook. May, C.L., Pryor, B., Lisle, T.E, and Lang, M. 2009. Coupling hydrodynamic modeling and empirical measures of bed mobility to predict the risk of scour and fill of salmon redds in a large regulated river. Water Resources Research, 45: 1-22. Meyer-Peter, E. and Müller, R. 1948. Formulas for Bed-Load Transport. In: Sec. Int. IAHR Congress, Stockholm, 39-64. Molinas, A. 2000. User’s Manual for BRI-STARS (BRIdge Stream Tube model for Alluvial River Simulation). U.S Department of Transportation; McLean, Virginia. Publication No. FHWA-RD-99-190. 80  Montgomery, D.R., Buffington, J.M., Peterson, N.P., Schuett-Hames, D., and Quinn, T.P. 1996. Stream- bed scour, egg burial depths and the influence of salmonid spawning on bed surface mobility and embryo survival. Canadian Journal of Fisheries and Aquatic Sciences¸56: 1061-1070. Montgomery, D.R., Beamer, E.M., Pess, G.R., and Quinn, T.P. 1999. Channel type and salmonid spawning distribution and abundance. Canadian Journal of Fisheries and Aquatic Sciences, 56: 377-387. Mull, K.E. and Wilzbach, M.A. 2007. Selection of spawning sites by Coho salmon in a Northern California stream. North American Journal of Fisheries Management, 27(4): 1343-1354. Naghibi, A. 2011. Ph.D Thesis. Downstream environmental impacts of reservoir high outflows – with a focus on fisheries. University of British Columbia, Vancouver. Neilson, J.D and Banford, C.E. 1983. Chinook salmon (Oncorhynchus tshawytscha) spawner characteristics in relation to red physical features. Canadian Journal of Zoology¸61: 1524-1531. Olsen, N.R.B. 2011. A three-dimesional numerical model for simulation of sediment movements in water intakes with multiblock option: User Manual, Version 1 and 2. Norwegian University of Science and Technology. Parker, G., Klingeman, P.C., and McLean, D.G. 1982. Bedload and size distribution in paved gravel-bed streams. Journal of the Hydraulics Division, 108 (4): 544-571. Pickands, J. 1975. Statistical inference using extreme order statistics. 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Hydrogeomorphic effects on bedload scour in bull char (Salvelinus confluentus) spawning habitat, western Washington, USA. Canadian Journal of Fisheries and Aquatic Sciences, 67: 626-640. Shields, A. 1936. Application of similarity principles and turbulence research to bedload movement. Translated from Anwendung der Achnlichketis Geschiebebewegung. In: Mitt. Preuss. versAnst. Wasserh. Schifth by. W.D. Ott & J.C von Vcheten. Publication California Institute of Technology Hydrodynamics Lab. No. 167. Smiarowski, A. 2010. MASC Thesis: The evaluation of a two-dimensional sediment transport and bed morphology model based on the Seymour River. University of British Columbia, Vancouver. Steen, R.P. and Quinn, T.P. 1999. Egg burial depth by sockeye salmon (Oncorhynchus nerka): implications for survival of embryos and natural selection on female body size. Journal of Canadian Zoology, 77: 836-841. Steffler, P. and Blackburn. 2002. 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Journal of Hydraulic Engineering. 110 (12):1783-1797.  83  Appendix A– Wolman pebble count Wolman Pebble Count  Project site: Campbell River  Survey Date:  08Sep10    Size (mm) Count-1 Count-2 Count-3 Count-4 Count-5 > >256 13 1 8 1 3 < 256 3 1 3 0 0 < 180 15 5 7 6 3 < 128 7 3 6 4 7 < 90 2  8 8 8 < 64 1  6 11 15 < 45 1  5 14 7 < 32 0  2 6 3 < 22.6 3  2 0 2 < 16 0 2 1 0 2 < 11.3 1  0 0 0 < 8 2  0 0 0 < 5.6 0  0 0 0 < 4 2 1 2 0 0   50 13 50 50 50  Survey Date: 17Aug11  Size (mm) Bar 1 Bar 2 > >256 1 1 < 256 4 2 < 180 23 3 < 128 28 17 < 90 34 15 < 64 14 7 < 45 1 3 < 32 0 2 < 22.6 0 0 < 16 0 0 < 11.3 0 0 < 8 0 0 < 5.6 0 0 < 4 0 0   84   Appendix B– 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).  Upper tail percentage values (p-value) 0.25 0.15 0.10 0.05 0.025 0.01 A2 1.248 1.610 1.933 2.492 3.020 3.857 

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