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Scour and fill in a gravel-bed channel : observations and stochastic models Haschenburger, Judith Kay 1996

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SCOUR AND FILL IN A GRAVEL-BED CHANNEL: OBSERVATIONS AND STOCHASTIC MODELS by JUDITH K A Y HASCHENBURGER B.S., University of Nebraska at Kearney, 1984 M.A., Arizona State University, 1989 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Geography) We accept this thesis as conforming (te^ the required standard THE UNIVERSITY OF BRITISH COLUMBIA January 1996 © Judith Kay Haschenburger, 1996 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of o~tSo~ The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT This study investigates channel bed scour and fill as a result of individual flood events in a gravel-bed channel. Given the complexity of interactions between hydraulic force, the texture and arrangement of bed material, and input of sediment to a particular point of the channel bed, study objectives were pursued with the view that bed material movement is a stochastic phenomenon. A two-year field program was conducted in Carnation Creek, a small gravel-bed stream draining 11 km 2 on the west coast of Vancouver Island, British Columbia. In the 900 m study reach, an array of measurement techniques, including scour indicators, magnetically-tagged stones, and conventional survey, yielded information about the fluctuations of the channel bed elevation and movement of scoured material for individual flooding periods. Frequency distributions of scour and fill depths associated with individual flooding periods are adequately modeled by negative exponential functions over the range of flood peak magnitudes observed in Carnation Creek. Analysis of scour depths measured in streams on the Queen Charlotte Islands demonstrates the applicability of the exponential model to flooding periods and flood seasons. Further, exploratory analysis suggests that a regional scour depth model is possible. Power functions relating mean depths of scour and fill to flood peak discharge show that depth increases with an increase in peak magnitude. Observed maximum scour depths in flooding periods are linked, in general, to streambed conditions influenced by antecedent flow conditions. These patterns in scour and fill exist within an overall pattern of increasing variability in depths of scour and fill as peak discharge increases. Evaluation of a heuristic model for mean travel distance as a function of particle size proposed by Church and Hassan (1992) provides convincing evidence for its general merit. Mean travel distance decreases inversely with particle size as size increases beyond the median diameter of subsurface sediment. This trend is consistent in both individual flooding periods as well as flood seasons. The majority of material finer than the median diameter of surface sediment is supplied from subsurface material, which influences the travel distances of these finer fractions because of burial. ii Computation of volumetric transport rates of bed material, based on the active scour depth and width of the channel bed, the virtual velocity of particle movement, and sediment porosity, suggests the potential for building scale correlations with streamflow, which have usually been defined by bedload sampling during floods. Error analysis indicates that determination of active width contributes most significantly to the imprecision of transport rate estimates. Results underscore the stochastic nature of sediment transport in gravel-bed channels. iii T A M E OF CONTENTS Abstract ii Table of Contents iv List of Tables vii List of Figures viii List of Symbols xi Acknowledgements xii Chapter 1: Introduction 1 Previous Work 2 Overview of Study . 6 Chapter 2: Study Site 8 Basin Characteristics 8 Sediment Transport 10 Study Reach 11 Chapter 3: Field Methods 14 Scour Indicators 14 Deployment of Scour Indicators 15 Mechanics of Installation 19 Scour Indicator Measurement Procedures 20 Recovery of Scour Indicators 21 Magnetically-tagged Stones 21 Deployment of Tracers 26 Tracer Measurement Procedures 27 Recovery of Tracers 28 Channel Survey 28 Cross-sectional Survey 30 Mapping 30 Channel Sediment 31 iv Surface Sediment 31 Subsurface Sediment 31 Streamflow Measurement 32 Chapter 4: Mathematical Models of Scour and Fill Distributions 33 Exponential Models 34 Verification and Extension of the Exponential Model 39 Exponential Models for Regional Scour Depths 44 Discussion 44 Chapter 5: Influence of Discharge on Scour and Fill Depths 48 Functional Relation between Depth and Peak Discharge 48 Discussion 54 Chapter 6: Movement of Bed Sediment 64 Experimental Data for Analysis 65 Travel Distance by Particle Size 65 Functional Relation between Distance and Particle Size 70 Discussion 72 Chapter 7: Transport of Bed Material 80 Focus of Transport Calculations 81 Trends in Parameters 81 Particle Step Length 81 Virtual Velocity 87 Width of the Active Layer 89 Depth of the Active Layer : 91 Porosity of Bed Sediment 95 Transport Rates and Total Volumes 95 Transport Through the Study Reach 102 Volumes from Bedload Rating Curves 102 Discussion 104 v Chapter 8: Conclusions 110 References Cited 115 Appendix 1: Hydrologic and Bedload Transport Relations 124 Flood Frequency 124 Flow Duration 125 Bedload Transport 126 Appendix 2: Discharge Estimation at the UBC gauging site 127 Methods of Estimation 127 Ratio of Subbasin Areas 127 Rating Curve Extension 129 Subarea Contribution 129 Results 129 Appendix 3: Distributions of Scour and Fill Depths and Exponential Models, Carnation Creek and Streams on the Queen Charlotte Islands 133 Appendix 4: Field Program for Streams on the Queen Charlotte Islands 141 Program of Observation 141 vi LIST OF TABLES 3.1 Description of scour indicator deployment in subreaches 18 3.2 Timeline of scour indicator and tracer recoveries and channel cross-sectional survey... 22 3.3 Recovery rates of tracers 29 4.1 Exponential model parameters and goodness-of-fit results in Carnation Creek 38 4.2 Exponential model parameters and goodness-of-fit results for streams on the Queen Charlotte Islands 42 5.1 River parameters for scaled depth-discharge relation 53 6.1 Travel distances by size fraction and tracer generation 71 6.2 Mean travel distances for generation 1 tracers based on starting position prior to the 21.8 m 3s _ 1 flooding period 75 7.1 Parameters for calculation of volumetric bed material transport 82 7.2 Volumetric estimates of bed material transport 97 A4.1 Physical characteristics of streams of the Queen Charlotte Islands 143 vii TIST O F F I G U R E S 2.1 Basin map of Carnation Creek 9 2.2 Channel views of study reach 12 3.1 Examples of scour indicators 16 3.2 Map of study reach 17 3.3 Gauging station B hydrograph for 1991-92 flood season 23 3.4 Gauging station B hydrograph for 1992-93 flood season 24 3.5 Particle size distribution of magnetically-tagged stones deployed in study reach 25 4.1 Frequency distributions and exponential functions for the 5.7,11.2, and 21.8 m 3s _ 1 flooding periods in Carnation Creek 35 4.2 Frequency distributions and exponential functions for the 33.9 m 3s _ 1 flooding period in Carnation Creek 36 4.3 Frequency distributions and exponential functions for the 48.8 m 3s _ 1 flooding period in Carnation Creek 37 4.4 Frequency distributions of scour depth and exponential functions for two streams on the Queen Charlotte Islands 41 4.5 Seasonal scour depth distributions and exponential functions for two streams on the Queen Charlotte Islands 43 4.6 Regional scour distributions and exponential functions for streams on the Queen Charlotte Islands for three monitoring periods 45 5.1 Relation between mean depth and peak discharge 50 5.2 Relation between maximum depth and peak discharge 52 5.3 Relation between scaled scour depth and specific discharge 55 5.4 Variability of scour and fill versus peak discharge in Carnation Creek 57 5.5 Maximum scour depth versus peak discharge in Carnation Creek 58 5.6 Net change in channel bed elevation for flooding periods 60 5.7 Variability in cross-sectional area based on peak discharge in Carnation Creek 61 6.1 Trends in mean travel distance as a function of particle size 66 viii 6.2 Variability of travel distance as a function of particle size 68 6.3 Trends in mean travel distance as a function of particle size for refined analysis 69 6.4 Relation between scaled travel distance and grain size 73 6.5 Longitudinal starting positions and distances traveled by generation 1 tracers in association with the 21.8 m 3s _ 1 flooding period 77 7.1 Relation of step length and virtual velocity to stream power 85 7.2 Schematic illustrating different definitions of duration of sediment movement within a flooding period 88 7.3 Relation between active width and stream power 90 7.4 Active width by measurement technique 92 7.5 Relation between active depth and stream power 93 7.6 Active depth by measurement technique 96 7.7 Relation between transport rate and stream power 100 7.8 Transport rates by measurement technique 101 7.9 Relation between total volume and stream power 103 7.10 Relation between active width and specific discharge 105 7.11 Evolution of tracer size distributions over time 107 A l . l Flood frequency curve for Carnation Creek 124 A1.2 Flow duration curve for Carnation Creek 1 125 A1.3 Bedload rating curves for Carnation Creek 126 A2.1 Relation between stage height and discharge at the UBC gauge 128 A2.2 Extended rating curves 130 A2.3 Peak discharge estimated from five methods 131 A3.1 Frequency distributions and exponential density functions for Carnation Creek 134 A3.2 Frequency distributions and exponential density functions for two streams on the Queen Charlotte Islands 139 A3.3 Seasonal frequency distributions and exponential density functions for two streams on the Queen Charlotte Islands 140 ix A4.1 Location map of streams on the Queen Charlotte Islands 142 x LIST OF SYMBOL^ d f Depth of fill [cm] dfx Maximum depth of fill [cm] D n Particle diameter, where n is a given percentile [mm] d s Depth of scour [cm] d s x Maximum depth of scour [cm] d' Ratio of mean scour depth to median diameter of subsurface sediment D' Ratio of particle fraction size to the particle size fraction containing the median diameter of subsurface sediment L' Ratio of mean travel distance for particle size fraction to mean travel distance of fraction containing median diameter of surface sediment P Porosity of streambed sediment Qb Volumetric transport rate of bed material [m3 hr -1] Qp Flood peak discharge [m3s"1] q' Ratio of specific discharge to mean annual specific discharge Vb Mean virtual velocity of bed material movement [m hr 1] W s Active width of streambed [m] D s Active depth of streambed [m] co Specific stream power [W nr 2] xi A C K N O W L E D G E M E N T S This research would not have been possible without the intellectual and financial support provided by my research supervisor, M . Church. I also express my appreciation to committee members T. Hickin, D. Russell, and O. Slaymaker for their involvement and comments regarding this research. Field assistance during the winter flood seasons in Carnation Creek was provided by A. Collett and S. Tsang. During drier conditions S. Babakaiff, B. Eaton, D. Ham, B. Killam, C. Nistor, M . Oden, S. Sterling, S. Toller, and K. Trainor assisted with fieldwork. Data from the Queen Charlotte Islands were kindly supplied by D. Tripp. Fieldwork was conducted by B. Eccles and C. Rally. Special thanks are extended to J. Spinelli for adapting a goodness-of-fit statistic specifically for this research. Arclnfo assistance by A. Moy and K. Cook is gratefully acknowledged. P. Jance provided valuable cartographic assistance. This research was funded primarily by a National Science and Engineering Research Council of Canada operating grant awarded to M . Church. Additional support was provided by a student research grant from the Geological Society of America and the J. Hoover Mackin Research Award given by the Quaternary geology and geomorphology division of the same organization, both awarded to me. The British Columbia Ministry of Forests provided logistical support by operating the Carnation Creek field station. xii CHAPTER 1 INTRODUCTION The elevation of a streambed fluctuates in response to flood events. These changes, termed scour and fill, are the result of sediment transfers. They constitute the focus of this study. The characteristic depth and variability of bed activity, the differential movement of scoured bed material as a function of size, and resulting sediment fluxes are addressed in turn. When flow level increases, sediment is scoured, which lowers the channel bed elevation. Deposition at a particular location in the channel produces fill. The depth and spatial extent of scour and fill are both regulated by the magnitude of flow. Transport of bed material, which consists of widely graded sediment in gravel-bed channels, is the fundamental connection between scour and fill. Hence, this study encompasses not only specific questions on scour and fill but also closely related aspects of bed material transport. The process of scour and fill is the key link between bed material transport and net change in channel morphology. Virtually all aspects of morphological change in gravel-bed rivers are governed by the movement of bed material (Gomez, 1991). These changes arise from the imbalance between scour and fill at particular channel locations. The migration of bends in meandering streams (Leopold et al., 1964; Nanson and Hickin, 1980; Neill, 1983; 1987) and the formation and evolution of channel bars and islands in braided streams (Ashworth and Ferguson, 1986; Ferguson and Werritty, 1983; Goff and Ashmore, 1994) come about through the redistribution patterns of bed material over time. An understanding of and ability to predict scour and fill have practical value in the management of fish habitat and design of engineering works. Defining the relation between channel-bed scour and flow magnitude and duration would aid decisions regarding appropriate measures for the maintenance and enhancement of fish habitat. Although a substantial literature exists concerning scour around obstacles and within constrictions (Breusers and Raudkivi, 1991; Laursen, 1962), the design of engineering works, especially pipeline crossings, would benefit from a broader based understanding of open channel scour processes in gravel-bed rivers. Although 1 bedload constitutes a small portion of the sediment load in alluvial channels, it strongly influences channel stability through patterns of sediment transfer. PREVIOUS W O R K Early interest in scour and fill derived from the need to design unlined canals (Kennedy, 1895; Lindley, 1919). These empirical design equations, identified as 'regime theory', require that the canal slope and cross section be in equilibrium with flow conditions. Where sediment is introduced into a canal, effective design attempts to minimize scour and fill magnitudes by equalizing rates of sediment supply and transport. Maintenance of equilibrium conditions is judged on a seasonal basis and does not imply a static bed within the seasonal period. Attempts have been made to expand the generality of regime equations by incorporating factors that characterize sediment size (Lacey, 1930) and the relative cohesion of bed and bank materials (Blench, 1957) and by extending the database used in the analysis (Simons and Albertson, 1960). The adaptation of regime theory to natural channels through the development of hydraulic geometry relations (Leopold and Maddock, 1953) required the use of a dominant discharge, which is supposed to characterize unsteady flow regimes atypical of many canals. Downstream hydraulic geometry relations based on gauging station locations (Leopold and Maddock, 1953) sparked debate on the nature of scour and fill along river channels. These relations implied that patterns of scour and fill at constricted gauging station cross sections (Mitchell in Leopold and Maddock, 1952; Straub, 1934) characterize long channel reaches (Colby, 1964). Flow constriction, however, produces accentuated, systematic scour. An alternative proposal of downstream discontinuity, where constricted sections scour and wide sections fill, was derived from observations on the Rio Grande, New Mexico (Lane and Borland, 1954). This model lacked a rigorous quantitative basis since fill in wide sections did not necessarily preclude prior scour during a flood. In a subsequent study in the sandy Arroyo de los Frijoles, New Mexico (Leopold et al., 1966), depths of scour were directly measured using scour chains and these measurements documented that the channel bed was lowered, in general, during flood events over the 10 km long study reach. The channel thalweg constituted the major focus of scour chain 2 deployment over the study reach, but even within this homogeneous environment, the channel exhibited notable variation in the magnitude of bed scour. In an investigation of lateral patterns of scour and fill in the gravelly Nahal Og, Hassan (1990) reported differences as large as 40 cm between channel thalweg and gravel bar environments in the 9 m wide channel, with variability within channel sections between flooding events. Within a single gravel riffle in Flynn Creek (Jackson and Beschta, 1982), one side of the channel experienced scour while the other recorded fill during a flood event capable of disrupting channel armour. Local patterns of scour and fill may be influenced by streamside obstructions that stabilize the locations of bar-pool units (Lisle, 1986). Overall, the range of scour and fill depths appears to increase with flow level (Lisle, 1989). Concentrating on mean response rather than variability, Leopold et al. (1966) developed a power relation between scour depth and specific peak discharge for the Arroyos de los Frijoles, New Mexico, which explains 58% of the variance. A portion of data variability around the relation results from grouping scour depths from three different reaches within the basin. Given the sandy bed material, scour depths most likely reflect the migration of primary bedforms (Foley, 1978). In contrast, gravel-bed rivers lack these bedforms in general (Parker and Peterson, 1980) and scour results from the collective random movement of individual particles. What appears to be the most complete analysis developing power functions between scour and fill depths and peak discharge in gravel-bed rivers (Carling, 1987) actually characterizes net change in bed elevation rather than individual components of scour and fill (P. Carling, personal communication, 1995). Net change measurements underestimate the actual change that occurs within the active layer (Colby, 1964). Such a bias is evident in an evaluation of the mean scour and fill depths measured in the arid-region Nahal Og and the depth values predicted from Carling's equations for the corresponding peak discharges (Hassan, 1990). For the events with mean depths of 10 cm or more, predicted values account for only 22 to 50% of the observed values. Poor predictions were also obtained for the Nahal Hebron, however, they must be partially explained by the aggradational nature of the observed flood event (Hassan, 1990). This signals the important 3 influence of sediment continuity conditions in a channel, which are influenced by antecedent patterns of flow and sediment supply. Concomitant with the increase of scour and fill activity with flood magnitude is an increase of the channel width involved in such activity (Hollingshead, 1971). Laronne and Duncan (1989) illustrated this general trend with two different bankfull widths, where the relatively wide section displayed greater variability in width than the narrow section in a braided gravel-bed river. Carling (1987) formalized the relation between active channel bed area and peak discharge as a power function, although the actual active areas measured varied by as much as 60% at a given discharge. Depth-discharge relations characterize the magnitude but not the timing of the bed response. In constricted channels, such as the San Juan River, Utah (Leopold and Maddock, 1952; 1953), the flow scoured sandy material from the bed up to approximately the time of the flood peak, then filled during the recession limb. The occurrence of scour and fill periods were reversed in the riffle-like sections compared to pool-like sections of the largely sand-bedded East Fork River (Andrews, 1979; Leopold and Emmett, 1984). Here the discrimination of morphologic units satisfied an approximation of those hydraulic conditions expected in well-developed pool-riffle streams. Within a single riffle, initial periods of fill and scour prior to the flood peak were followed by a second round of fill and scour on the recessional limb in a small gravel-bed river (Jackson and Beschta, 1982). These real-time surveyed measurements of scour and fill document that greater complexity is indeed possible (Clifford and Richards, 1992). Nonetheless, most bed material deposited by a given flood event is apparently subsequently mobilized before additional incoming bed material is deposited in a gravelly braided river (Laronne and Duncan, 1989). Scour of the channel bed signifies the entrainment of sediment, which is a complex process in gravel-bed rivers. Fluctuating hydraulic forces impinge upon a variable channel boundary formed of distinctive morphological and sedimentological features. Textural characteristics of bed material vary within and between pools, riffles, and bars (Bluck, 1979; 1982; Hirsch and Abrahams, 1981; Keller, 1971). Gravel-bed channels exhibit vertical size segregation with a relatively coarse surface layer compared to subsurface material (Kellerhals, 1967; Parker and Klingeman, 1982). Within the coarse surface layer, relative exposure and geometric arrangement 4 of particles (Brayshaw, 1985; Laronne and Carson, 1976; Wolcott, 1990) delay the onset of scour by increasing flow requirements for sediment mobilization. Long periods between flood events allow gradual consolidation of the streambed,which retards the onset of scour and subsequent bed material transport at the rising stage of the next flood (Reid et al., 1985). Flume and field investigations suggest that the transport distance of individual particles is not, in general, an inverse function of size. Movements within a specific grain size fraction show a wide range of downstream displacements (Einstein, 1937; Laronne and Carson, 1976; Stelczer, 1981). Once scour occurs, individual grains collide with other particles, drop into scour holes, or enter areas of the channel where hydraulic conditions are insufficient to maintain motion. Changing conditions in the channel may reinitiate motion. The variable nature of these influences, combined with the complexity of entrainment, lead to variability in the length of particle displacements and duration of rest periods and an overall random movement of individual particles (Einstein, 1937; Stelczer, 1971). Thus, attempts to establish formal inverse relations between distance of movement and grain size have reported weak relations or none at all (Ashworth and Ferguson, 1989; Carling, 1987; Leopold et al., 1966). An upper limit to travel distance based on size does exist, however, when a sufficiently wide range of grain sizes is considered relative to the sediment size distribution (Hassan and Church, 1992). Thus, the range of travel distance for a given grain size provides the possibility of a trend in mean travel distance. Church and Hassan (1992) demonstrated the existence of such a relation through the evaluation of virtually all available data on the movement of unconstrained surface particles in gravel-bed rivers. Mean distance of travel decreases for sizes larger than the median diameter of surface sediment. The mobility of smaller grain sizes is reduced by hiding (Egiazaroff, 1965; Einstein, 1950) and burial within the subsurface sediment layer. Travel distances of individual particles over a known time period can be used to determine the rates of particle movement. Given that particles move downstream in a series of rest periods punctuated by periods of motion, the average rate of movement over a time interval describes a virtual velocity (Einstein, 1937). The product of mean virtual velocity and the dimensions of the active layer of the streambed, when adjusted for sediment porosity, forms a fundamental basis for 5 calculating the rate of bed material transport (Hubbell and Sayre, 1964). Transport of sediment derived from the bed and lower banks of a river channel does not require an assumption regarding the actual mode of transport. This method, which is relatively untested in the field (Laronne et al., 1992), directly incorporates the stochastic nature of particle movement through virtual velocity. It stands as an alternative to estimating rates from sampling bedload during floods. O V E R V I E W O F S T U D Y The first objective of this study was to characterize scour and fill depths produced by individual flood events. Two natural extensions of this objective form the basis of two further purposes, that of evaluating the differential movement of individual particles and estimating volumetric bed material transport. Both topics are closely interconnected with scour and fill processes in gravel-bed channels. Given the complexity of interactions between hydraulic force, the texture and arrangement of bed material, and the input of sediment to a particular point on the channel bed, these objectives were pursued with the view that bed material movement is a stochastic phenomenon (Einstein, 1937; Stelczer, 1981). While the importance of scour and fill is recognized in the longer term lateral evolution of alluvial channels, this study focused on the channel bed, which is the typical approach in investigations of storm period and seasonal sediment transport in gravel-bed rivers. In the absence of detailed and conclusive results from earlier studies in the areas of scour and fill, this study has attempted to build empirically-based generalizations. This course of action dictated extensive efforts of field data collection at a single study site. This study site is described in Chapter 2 and the field sampling strategy and data collected are detailed in Chapter 3. The interplay between hydraulic force and the channel boundary, expressed through its morphological and sedimentological character, results in a variable magnitude of bed activity over a channel reach. While previous studies have documented this variability, there has been no attempt to formally model the range of scour and fill depths that occur during individual flood events. In Chapter 4, the distributions of scour and fill depths are modeled using a specific mathematical function. 6 Bedload transport scales with flow magnitude (Schoklitsch, 1934). A similar relation is expected to hold for the magnitude of bed activity, but this has undergone limited development in previous work. Chapter 5 presents power relations for flood magnitude and depths of scour and fill. The connection between scour and fill in a channel is the downstream and lateral translation of sediment. In Chapter 6 the distance of movement of individual particles during individual flood events and over flood seasons is examined for a range of particle sizes. The heuristic model proposed by Church and Hassan (1992) relating mean travel distance to particle size is evaluated. In Chapter 7 volumetric bed material transport is estimated by considering the stochastic movement of individual particles, as characterized by virtual velocity, the delineation of the active layer in the channel and the porosity of sediment. Attention is given to the technique and precision of parameter measurements used in calculations because of the limited prior field application of this method in gravel-bed rivers. 7 CHAPTER 2 STUDY SITE Carnation Creek, a small gravel-bed stream, drains about 11 km 2 on the perhumid west coast of Vancouver Island, British Columbia [48°54' N , 125°GTW] (figure 2.1). The geographical location of the study basin ensures frequent floods during the winter rainy season. The high level of channel bed activity caused by these floods has been documented in several channel sections within the lower portion of the basin by Powell (1987). In 1970, Carnation Creek was designated an experimental watershed for a federal and provincial cooperative investigation of interactions between logging practices and anadromous fish populations. Chum (Oncorhynchus keta) and coho (Oncorhynchus kisutch) salmon and steelhead trout (Salmo gairdneri) use the lower 3.2 km of the stream network. After 6 years of pre-logging monitoring, prescribed harvesting occurred between 1976 and 1981, resulting in the removal of about 40% of the forest cover. Subsequent logging in the upper portion of the basin in the early 1990s increased the total forest removal to about 60%. BASIN CHARACTERISTICS A significant amount of information exists about the basin because of its experimental status. A brief basin description is provided below. Additional details are available in Hartman (1982), Chamberlin (1987), and Hartman and Scrivener (1990). The basin features rugged terrain influenced by glaciation during the Pleistocene Epoch. Elevation changes from sea level to approximately 900 m. In the lower portion of the basin (figure 2.1), the main channel meanders within a valley flat, that is wide relative to channel width, with adjacent valley slopes reaching gradients of 40 to 80%. A narrow bedrock canyon, extending from 3.2 to 4.2 km upstream from the basin outlet, separates the upper portion of the basin from the lower section and effectively limits further upstream migration of anadromous fish. Underlying bedrock is primarily Jurassic volcanics of the Bonanza Group (Oswald, 1982; Yorath and Nasmith, 1995). Lithology within this group ranges from basaltic and rhyolitic lava, tuff, breccia, and minor argillite, to greywacke. 8 % CJ c o •3 6 CCj U O CX, cd a c 00 9 Soils are primarily orthic ferro-humic podzols (Canada Soil Survey Committee, 1978) with coarse-textured, well-drained characteristics. Regosols prevail in more active alluvial areas and in steep rocky areas (Oswald, 1982). Frequent outcrops of bedrock signal the generally shallow development of soils, which averages 70 cm in depth. The basin supported a mature forest of western hemlock (Tsuga heterophylla), amabilis fir (Abies amabilis), and western red cedar (Thuja plicata) (Oswald, 1982) prior to logging. Vegetative patterns are closely associated with site moisture, which is influenced by aspect, slope, and soil depth and texture. Annual precipitation ranges from 2100 to 4800 mm, reflecting the sharp precipitation gradient from the mouth of the river to higher elevations induced by lifting convergence from increased onshore roughness formed in part from basin relief. Approximately 75% of annual precipitation occurs between October and March (Hetherington, 1982) delivered by frequent frontal storms. Snow is occasionally received at higher elevations but because the majority of the basin is below snow line, 95% of the precipitation falls as rain. The temporal pattern of streamflow closely follows precipitation (Hetherington, 1982). Given soil characteristics and macrochannel networks, following decayed tree roots, vertical transmission of water can reach rates greater than 40 cm h _ 1 (Hetherington, 1982). Overall, the hydrologic response to precipitation events is rapid, resulting in flood hydrographs with short time-to-peak characteristics as illustrated by flow data from the Water Survey of Canada stream gauging station B near the mouth of the basin (08HB048) and on tributary C, near its junction with the main channel (08HB069) (figure 2.1). At gauging station B, the largest instantaneous flood peak on record is 65.1 m 3s _ 1, which corresponds to a 30 year return period of an annual maximum series analysis (Gumbel type I) (Appendix 1). Sediment Transport Suspended load and bedload were measured for a limited time between 1973 and 1984 near gauging station B. Sampling details and analysis are reported by Tassone (1987). Further consideration of the transport of fine sediment is found in Church (in press). 10 Suspended sediment concentrations respond rapidly to increased stormflow in the channel (Tassone, 1987). Peak concentrations persist for short duration since suspended sediment concentrations are generally supply limited. Primary sources for pronounced concentration peaks appear related to major bank collapse, debris flow input from gullies, and log jam failure (Church, in press). During an instantaneous discharge of 27.5 m 3s _ 1, clay and silt comprised 9 and 55%, respectively, of sediment in suspension. The remaining portion of the distribution, derived from one set of depth-integrated sediment samples, consisted of sand less than 1 mm in size. The mean monthly suspended sediment load averaged over the monitoring period ranged from 0.07 to 1.76 tons day 1. Significant bedload transport, defined as 1 kg m _ 1min _ 1 (Tassone, 1987), generally occurs when discharge reaches 10 m 3s _ 1 at gauging station B. Sediment is mobile prior to this discharge threshold, as indicated in rating curves (Appendix 1), but transport is of low intensity. Measured bedload transport rates reached a maximum of 30 kg m^min"1 during a monitoring program of 20 flood events. Depending on flow conditions, the median diameter of sediment collected ranged from about 1 to 35 mm. Annual suspended load averaged 234 tons during the monitoring period. Mean annual bedload, derived from volumetric estimates of sediment removed upstream of the weir at gauging station B, averaged 290 tons. Given the low trapping efficiency of the weir, this is a lower bound estimate. Nonetheless, bedload apparently constitutes over 50% of the sediment transported in Carnation Creek. STUDY REACH Field measurements were concentrated in a 900-m long study reach (figure 3.2), located within 3 km of the basin outlet (figure 2.1). Channel planform consists of relatively straight reaches punctuated by sharp bends. Resistant bank material or bedrock outcrops frequently force the bend configuration. Pool-riffle morphology characterizes the channel bed configuration of the study reach (figure 2.2). Pool-riffle units are characteristic bedforms in gravel-bed rivers (Leopold et al., 11 Figure 2.2. Channel views of study reach: a) pool-riffle morphology in subreach 1 and b) streamside obstructions in upper portion of subreach 3. 12 1964). In single-thread rivers like Carnation Creek, riffles are the leading edge of depositional bar units that tend to alternate between channel banks. Hence, the fundamental unit of channel morphology is a pool-riffle-bar composite (Church and Jones, 1982; Parker and Peterson, 1980 among others). Reference to pool-riffle units herein includes the associated channel bar. Large organic debris is a common natural feature of coastal streams in British Columbia and Carnation Creek is no exception (Toews and Moore, 1982). Although the study reach is not completely devoid of organic debris, the selected section avoids the highly congested area of the channel near the basin outlet, where the concentration of organic debris dominates channel morphology. In the study reach, organic debris and bedrock outcrops appear to exert some influence on the location of pool-riffle units (Lisle, 1986). The channel spans an average width of 14 m between banks. Median diameters of surface and subsurface sediment are 47 and 29 mm, respectively (figure 3.5), for this very poorly sorted sediment. Di6 and Ds4 diameters are 18 and 97 mm for surface sediment and 3.5 and 88 mm for subsurface sediment. The gradient of the channel bed is 0.9% over the study reach. 13 CHAPTER 3 FIELD METHODS A major deterrent to investigating scour and fill in gravel-bed rivers is the difficulty of obtaining field observations, especially for individual flood events. The frequency of floods within a particular hydrologic regime may require an extended time commitment to document scour and fill over a range of flow magnitudes. In perennial regimes, elevated baseflow during flood seasons may restrict the actual channel area that can be monitored with the instrumentation currently used to measure scour and fill. The interval between flood events constrains the amount of time available to collect data before an additional flood confounds event-based data. Depending on the magnitude of bed activity and the number of deployed instruments, such as scour indicators, magnetically-tagged stones, and other supporting measurements, data collection after a flood event can span several days to several weeks. The field program, conducted over the two winter flood seasons of 1991-92 and 1992-93, employed a range of techniques to measure scour and fill, in part to compensate for limitations of individual techniques. A general criticism of scour indicator and magnetically tagged particle techniques involves the disruption of the channel bed during deployment and subsequent retrieval. Given that the structural integrity of the coarse surface layer has been disturbed, entrainment of sediment from these installation areas may precede that from adjacent undisturbed areas. Whether or not this expected result severely biases channel behavior remains to be documented. Scour indicators are small obstacles that may accelerate scour locally. Given the size of indicators relative to channel sediment, however, this effect is probably minimal, particularly when significant depths of scour and fill are involved. Although repeat sounding of channel cross sections using sonar avoids bed disruption, it demands the presence of personnel during flood events when working conditions can be quite dangerous. SCOUR INDICATORS Scour chains (Emmett and Leopold, 1964), and subsequent variations in the form of scour cords (Foley, 1978), scour monitors (Tripp and Poulin, 1986), and scour beads (Nawa and 14 Frissell, 1993), can be used to document scour and fill depths. Two types of scour indicators were employed in this study. Metal chains with 3.5 cm-long links comprise the scour chains (figure 3.1a). A 6-cm diameter aluminum washer wired to one end of the 1.25 m long chain sections facilitated installation and anchored the chain once installed in the bed. A portion of each chain was exposed on the channel bed surface to aid recovery. Scour monitors (figure 3.1b), the second type, were constructed using 25 perforated plastic balls strung on a 1.5 m length of fishing line. A plastic disc secured the exposed end of the monitor line and two large nuts served as the base. The ball diameter of 4 cm constrains measurement of scour and fill depths to increments of this length. To aid measurement procedures, white and orange colored balls were alternated along the monitor line. Comparable data of scour and fill depths are derived from both types of scour indicators. The scour depth measured is a maximum depth at the location of the indicator, whereas the fill depth is a net estimate because sediment deposition in the channel could be transient over the extent of a flood event. Scour indicators record only one apparent cycle of scour and fill. Deployment of Scour Indicators Five subreaches were instrumented with scour indicators. Selection criteria for these sections encompassed the spatial coverage of the study reach, channel planform, and local channel characteristics. Subreaches were distributed throughout the study reach (figure 3.2) to ensure representative measurements of the complete reach. Relatively straight reaches reduced complications due to bends. Moreover, the relatively deep pools in these bends precluded measurement in these areas during winter baseflow levels. Section 4, located in a curved reach, exerts a minimal influence on overall results because of the limited number of scour indicators installed in this section (table 3.1). In evaluating local channel characteristics, the limited number of suitable reaches exhibiting representative pool-riffle units required sampling near log jams in the study reach (figure 3.2). As mentioned previously, however, large organic debris is a natural feature in coastal streams. Within each section, positioning scour indicators within individual pool-riffle units maximizes the potential to transfer scour and fill information to similar segments of the channel as 15 Oro c jo s O C a *-< o g-0) Table 3.1. Description of scour indicator deployment in subreaches Distance of Section Downstream Length Standard Section Limit (m)1 (m) Cross sections* Number of Indicator Indicators Typet Comments 103 100 MP, LP, RC, RT 26 SC 392 90 UP, MP, LP, RC, RT 21 SC 599 100 RC, RT, MP, LP RC, RT, MP, RC 49 SM Two pool-riffle units 783 30 MP, RC SC Curved reach 840 40 UP, MP, RC 15 SC 1 Measured from the downstream boundary of the study reach * UP-upper pool; MP-mid pool; LP-lower pool; RC-riffle crest; RT-riffle terminus; f SC-scour chain; SM-scour monitor 18 well as to other rivers. Pools were divided into three equal areas, denoted as upper, mid, and lower, while riffles were divided into two equal areas, identified as crest and terminus. Cross sections for scour indicators were placed in the middle of each subarea. Positions were adjusted slightly to avoid channel obstructions where necessary. In each section a minimum replication of the mid pool and riffle crest standard cross sections was achieved. Difficulty in installing indicators because of coarse sediment and delays due to breakage of driving equipment prevented complete replication of all standard cross sections (table 3.1). Scour indicators were spaced at 2 m intervals along channel cross sections spanning the complete width between channel banks. In a limited number of cross sections scour indicators were spaced at 3 m intervals in bar environments. The top and side slope of channel banks were also instrumented along a few cross sections. The total number of scour indicators installed in the study reach was 120. Mechanics of installation A double pipe driver was forced vertically into the ground with a customized Cobra rock drill fitting to install scour indicators. Insertion of the pipe driver into the channel bed required 10 minutes to nearly 2 hours per site, the longer insertion times being associated with areas of coarser sediment. Occasionally the downward progression of the pipe driver prematurely terminated when, presumably, the driver was incapable of moving or breaking through stones in its path. Indicator insertion was reinitiated in a slightly offset position within the defined cross section. The leading edge of the indicators reached a depth of 1 m in most cases, which represents the maximum depth of scour that can be recorded by scour indicators in this study. The maximum depth is actually less for a few indicators because bedrock was probably encountered below the current bed surface. With the pipe driver in place, a scour indicator was lowered into the 6 cm circular opening created by removing the inner pipe. While the outer pipe was gradually twisted out of the ground the indicator was held taut by a length of PVC pipe. Sidewall sediment collapsed into the hole and was packed around the scour indicator with the PVC pipe to maintain the vertical position of the indicator. Sediment from the surface was added as needed. 19 The bed of the channel was disturbed during the installation process but the pipe driver minimized this disturbance compared to excavating a deep hole. Visual inspection of scour monitors during the first recovery indicated that the perforated balls were filled with sediment in response to preceding, relatively low magnitude floods. Scour Indicator Measurement Procedures The two types of scour indicators required slightly different measurement procedures during recoveries. A depthometer (figure 3.1a) was used to standardize measurement of scour chains. The 1-m long base of the depthometer rests on the average armour surface and is oriented parallel to flow in a consistent lateral position adjacent to each chain. Scour depth is determined from the change in total length of chain; measurements of exposed chain length before and after a flood provide the necessary information. Excavation preceded the post-flood measurement of chain length when fill occurred. Fill depth is a direct measurement from the exposed head of the scour chain to the base of the depthometer. Following fill measurements, the scour chain was held vertically while the excavation hole was refilled to the local bed surface. The additional measurement of chain length that followed served as the pre-flood measurement for the next event. Although changes in bed elevation may be surveyed (Leopold et al., 1966), a more expedient strategy seemed prudent given the number of indicators deployed and the difficult working conditions. Observations of scour and fill from scour monitors are derived by counting the number of balls liberated during a flood and replaced into the ground until the top ball is flush with the local bed surface. These counts are multiplied by the diameter of the perforated balls to give depth values. Occasionally the fishing line would break during a flood and prevent direct measurement of scour depth because scoured balls were not retained at the end of the monitor line. Scour ball color and net change to cross-sectional elevation, derived by repeated surveys, permitted estimation of scour depths for these indicators. Fill depth can always be measured if the top ball in the ground is located. Observations of partially exposed balls indicate that ball stability can be maintained with as much as 50% exposure. This stability is aided, in part, by the sediment that fills the scour balls. 20 Because observations are reported in 1 ball increments the depth corresponding with the partial exposure is incorporated into the next observation when appropriate. From these observations, measurement error appears to be in the range of + 2 cm. Repeat measurement of scour chains, unaffected by high flow levels, reveals a measurement error of + 2 cm. Recovery of Scour Indicators Scour indicators were recovered 15 times during the two flood seasons and these data characterize depths of scour and fill associated with individual flood events with peak magnitudes ranging from 4.1 to 48.8 m V 1 (table 3.2). The return period of the 48.8 m 3s _ 1 flood is about 7 years (Appendix 1). In most cases scour and fill depths characterize more than one flood hydrograph but, in general, the primary flood peak is preceded or followed by discharge peaks less than 10 m 3s _ 1 when only minor bedload transport occurs (Tassone, 1987) (figure 3.3 and 3.4). Notable exceptions include flooding periods 3, 7,15, and 16 (figure 3.3 and 3.4). Flooding period 3 is preceded by a 14.0 m 3s _ 1 flood peak and period 15 is followed by a peak discharge of 17.7 m 3s _ 1. Flooding periods 7 and 16 each consist of a series of two flood peaks of comparable magnitude, 25.8 m 3s _ 1 followed by 27.3 m3s"1 and 20.4 m 3s _ 1 followed by 16.2 m 3s _ 1, respectively. Given that deeper scour and fill are expected during larger magnitude floods, events are indexed according to the largest peak magnitude. M A G N E T I C A L L Y - T A G G E D STONES Magnetically-tagged stones have been used effectively to determine travel distances of individual particles (Hassan et al., 1991; Schmidt and Ergenzinger, 1992) and the depth of the active bed layer (Hassan et al., 1992) and, using this information, volumetric estimates of bed material transport (Laronne and Duncan, 1989). In Carnation Creek, tracers range in size from 16 to 180 mm (figure 3.5). The proportion of each size fraction corresponds to the particle size distribution of subsurface sediment in the study reach, beginning one phi fraction finer than the median diameter. About 200 additional stones of the two smallest size fractions were deployed to compensate for anticipated lower recovery rates due to their mobility. 21 cu tS CU U cd • M CO Q ° B co •4-» CO Q a CU a o U ^ .2 o C ° «£ eu cS o cu cu o CO o CN ON <3 CN 73 CU •s CO <U , t-i f = fe CO CN eu cu & 3 -co co x: o CO cu 3 CO OQ & cu > 8 cu )-l U l cu o CO CN CN CU CO eu CH 3 CO u cu > 8 cu CD co CO eu CO cu eu 6; £ 3 3 CO CO CU CH 3 CO cu CJ CU +3 £ =5 3 3 CO fe cu I 3 CO i -H 4-* cu CO >. cu > Ci 3 CO Q CU > o o CU I H CN l_ 4 H CU CU cj co CO >> * H CU l -H £ 3 3 fe CO cu CO >> CU £ 3 CO cu £ 3 co CN cu co cu £ 3 co CO CN CO cu •s CO CU I H £> 3 co w cr cu I cu cu o cd CN 42 cu CO >•> cu £ 3 CO fe" cu > cu o cd cu cu CH t: 3 3 CO CO CO* I H « cu > >-» cu > >> CU > CO* I H « 2 >> 8 > CU :ers, ers, trac c 3 co c 3 co C 3 CO trac 2 CH H 3 £3 to £ 3 co CJ c j CO CO 43 43 CO CO co" co" CO to" </? co co" CO co~ CO co* co" O 2 O O O O o O o o 2 O O o o 1 CO CJ « CJ CO CJ ea o s CO o "CO o 1 1 CO CJ to o to CJ 1 1 e -a indi indi indi indi indi indi indi •a -o a a indi indi indi .a .a Tracei Scour Scour Scour Scour Scour Scour Scour Scour Scour Scour Scour Scour Scour Scour Scour CN C O T H T H I - H C N tN ( N ON o CN 0 0 p \ O \ O > O \ 0 0 l n © CN CN CN CN O T T CO VO ^ d Ci r> CN CN r H T - H C N m r f i n v o r - O O O N O ^ H C N c r i T f U~) VO 22 T3 C CO VO 00 CN CO TI-CS VO 00 § a H a i/5 T 3 6 .3 i 1 •<-> i s I-I eg S.8 <u Q-a, . •73 "O •a o o O <u fl •4-» .fl o o C <D OX) .fl -3 o o <a o 59 o <u D -V5 fl ,° 0 ^ cn fl cd o CJ - . -» tj 8 1 CN & a, 2 § So o 8 3 * 53 m .9 a w •2 I fl° •5 CN t»0 ON 1 2 cn & cn £ u a b GO 23 T 3 fl CO 00 o cn -*fr VO oo 00 o CO cn •*fr vo fN H 00 ( s^ui) aSreqosiQ s in) aSxeqasiQ u fl fl <u Oi 03 cn bO •s cn 3 3 -S cd ti am o <a a, o o a cn fl O ii a CS a" o oo •d o •c CD CL, (so .3 - a o o « 9 Q o <u cn C L , CO g X t « « 0 § ? l CN O OS ° ON cd S ° a. o « 2 (SO (5-S a, "a 6 £ 8 w £ fl ^ .2 -2 cd c co _ cn • (so > cn •S I cn cd < 3 cn ^ ^ & S cn r H p 1 ^ * >—> cn 24 Particle size (mm) Figure 3.5. Particle size distribution of magnetically-tagged stones deployed in the study reach. Particle size distributions of surface and subsurface sediment represent average distributions for the field program and are shown for reference. 25 Production of tracers in the 32 through 180 mm size fractions involved inserting ceramic magnets into natural stones as outlined by Hassan et al. (1984). The two smallest size fractions, 16 and 22 mm, were fabricated with fiberglass resin using aluminum molds. Tracer density was standardized to 2.65 g m~3 by adding proportional amounts of lead shot to the fiberglass resin during the fabrication process. Tracers provide estimates of scour depth at their place of origin, which is equal to or less than the maximum scour depth, and net fill depth at their place of deposition, which is equal to or less than net fill estimates from indicators. Magnetically-tagged stones can register scour and fill depths over greater spatial areas of the channel than can scour indicators in fixed cross sections. As well, recording longitudinal positions of tracers yields vital information about the travel distances of individual particles, and hence virtual velocities over various measurement periods. Deployment of Tracers Approximately 2000 magnetically-tagged particles were seeded in total in the study reach. Deployment at this order of magnitude was recommended by Hassan et al. (1991) to unambiguously identify the distributional form of particle displacements based on a statistical criterion. Although this study does not directly evaluate the distribution of displacements, this general recommendation was adopted because an overall large sample translates into relatively large sample sizes for individual particle size fractions. Al l fractions except the 180 mm size are represented by more than 45 tracers per season. The pattern of declining recovery rates of tracers over time also called for larger samples than the usual total of 100-300 tracers. Prior to the first flood season, 1007 tracers were deployed in area A (figure 3.2) in two groups. Each group consisted of four rows that spanned the entire channel width. Rows were separated by 0.7 m to avoid stone wake effects (Leopold et al., 1966). Tracers in group 1 were placed on top of the bed surface whereas group 2 tracers were substituted for a stone of similar size in the four cross sections. Tracers in the latter group represent more natural positions of surface stones because of their incorporation into the bed surface. Although the groups were separated by 1.65 m, they were located in the same pool area of the channel bed morphology. A subsequent deployment of 157 tracers increased the number in the largest size fraction, which 26 satisfied the proportional requirement based on the subsurface particle size distribution, and in the smallest five fractions, which compensated for illegible identification labels discovered during the first tracer recovery in September. For the second flood season, 991 tracers were deployed in two areas of the study reach (figure 3.2). An upper group was positioned about 6 m upstream of the 1991 start line in deployment area A, while a lower group was released in deployment area B (figure 3.2). Each group of tracers was deployed in four rows, separated by 0.8 m. Rows of tracers that were placed on the top of the bed surface were alternated with rows where tracers were substituted for stones of similar sizes. The deployment strategy used in the second flood season expedited tracer dispersion into the lower portion of the study reach. Field observations indicated that the sediment trapping efficiency of the log jam upstream of deployment area B was perhaps increasing and would retard tracer movement into the lower reach. Further, recovery of tracers after the first flood season highlighted the difficulty associated with high tracer density near the start line in deployment area A. Overlap of burial depth information was reduced by the divided deployment. Tracer Measurement Procedures Tracers were located using a magnet detector with a depth detection limit approaching 1 m. In practice the detection limit was probably closer to 0.8 m. The probability of locating deeply buried tracers increases in areas of high density because recovery of near surface tracers lowers the streambed elevation and effectively extends the detection limit. Overall, distributions of burial depths are most likely biased toward an underestimation of mean depth because of the deeply buried tracers that are not detected. Burial depths were measured to the bottom of tracers using the depthometer, which references depths to the average armour surface. The depthometer provides consistency in measurements, particularly in the more difficult, deeper portions of the flow channel. The diameter axis of the tracer oriented parallel to the vertical dimension of the streambed was noted whenever the tracer was not disturbed because this axis comprises part of the depth of burial. Tracers found in the subsurface were reburied at the recorded burial depth for continued tracing. 27 Surface tracers were distinguished as free or locked, the latter requiring coverage of at least 30% of the planview surface area by other stones. Spatial coordinates and associated channel morphology for each stone were recorded from a central tape running the length of the study reach. Tracers that moved beyond the downstream limit of the study reach represent lost information but the degree of bias introduced into the estimation of particle travel distances is not known. The finer fractions that are relatively mobile would be more susceptible to this potential bias. Judging by tracers that remained stationary between subsequent recoveries, measurement error associated with longitudinal distances is approximately + 0.5 m due to slight shifts in the positioning of the central measuring tape. Overestimation of burial depth is minimized by frequent monitoring with the magnet detector as digging proceeds. Brightly painted natural stones and dyed artificial tracers substantially aid the searching process as liberated tracers can be visually identified. Measurement errors in depth estimates are probably largest for tracers recovered in flowing water, where visibility and sidewall stability of excavated holes are reduced. Error is estimated as + 4 cm. Recovery of Tracers Recovery of tracers proceeded after large magnitude flood events when feasible (table 3.2). A total of 6 recoveries was conducted, three during each flood season. Associated recovery rates are found in table 3.3. In the first flood season, a full search of the study reach was accomplished in the first and third recoveries. Although the first recovery longitudinal search length is truncated compared to the full study reach, it is considered a complete search because very few stones were found in the final 100 m of the search length and a 93% recovery rate was attained. The second recovery focused on only subreach 3 and consisted of a 100 m long search. In the second field season, the first and third recoveries constituted complete searches, while searching procedures were restricted to three sections containing scour indicators, namely subreaches 1, 2, and 3, in the second recovery (figure 3.2). C H A N N E L SURVEY Differences in the magnitudes of scour and fill depths produce net changes in channel bed elevation. Within a defined reach, these changes provide important contextual information for 28 Table 3.3. Recovery rates of tracers Recovery Total Number Deployed Generation* Number Recovered Percent Recovered Distance Searched (m) Comments A 1007 1 941 93.4 360 B 1165 1 191 16.4 100 Subreach 1 C 1563 all 1088 70.0 760 1165 1 973 83.5 384 0 115 29.9 D 2554 all 1533 60.0 760 Only surface 1165 1 745 63.9 stones recovered 991 2 693 69.9 in deployment 384 0 96 25.0 areas A & B E 2554 all ' 222 8.7 300 Subreaches 1,2,3 1165 1 86 7.4 991 2 100 10.1 384 0 36 9.4 F 2554 all 1589 62.2 800 1165 1 792 70.0 991 2 674 68.0 384 0 123 32.0 * Generation 0 consists of two generations of 16-180 mm tracers deployed prior to this study (1989 and 1990). Deployment consisted of 384 tracers released from deployment area 0 (figure 3.2), about 100 m downstream of deployment area B. 29 patterns of scour and fill. These elevational changes were quantified by a survey of set channel cross sections and detailed mapping of the study reach. Cross-sectional Survey Two sets of channel cross sections were established for repeat surveys to record net changes in bed elevation. The 22 channel cross sections containing scour indicators comprise the first set. Survey of these cross sections provided bounds for scour and fill depths derived from scour indicators. A second set of 19 channel cross sections, spaced at approximately three times the average bankfull width, extended spatial coverage over the length of the study reach. These cross sections, positioned in pool and riffle areas, were originally installed by personnel of the British Columbia Ministry of Forests. Using an automatic level and stadia rod, bed height readings, to the nearest centimeter, were recorded at major breaks in bed slope and at standard positions, such as the flow thalweg, and scour indicators, where appropriate. Over the two flood seasons cross sections in sets 1 and 2 were surveyed 9 and 6 times, respectively (table 3.2), primarily after large magnitude flood events. Survey of cross sections after flood peaks smaller than 10 m3s"l in the first flood season showed insignificant changes in bed elevation so resurvey after smaller magnitude floods was not routinely undertaken. Mapping Complete spatial coverage of net change in channel bed elevation was achieved by mapping the study reach. Channel bed height was recorded between channel banks using a theodolite and stadia rod. Bed heights were recorded to the nearest centimeter at major breaks in bed slope along cross sections spaced approximately 5 m apart. Supplemental sights were taken as needed. Channel bed morphology and large channel obstructions, such as logs, were incorporated into the mapping survey. The majority of the study reach was mapped during the late summer and early fall of 1991. Due to time constraints a 90 m reach, upstream of the large organic debris located between subreaches 1 and 2 (figure 3.2), was not mapped before a large magnitude flood event occurred in winter 1991-92. In the summer of 1992 and 1993 the study reach was mapped in full. The two 30 series of set cross sections and the study areas monitored in association with the fish/forestry experimental program (figure 2.1), which continue to be surveyed annually, form two portions of the mapping database. C H A N N E L SEDTMENT Surface and subsurface sediment textures in the channel were characterized by sampling seven gravel bars, approximately every other bar in the study reach (figure 3.2). The break • between pool and riffle bed configuration served as a consistent sampling location between bars. Repeat sampling was conducted during summer months in 1991,1992, and 1993. An additional gravel bar, sampled in 1989 for other work (Hassan and Church, 1992), was resampled in 1992 and 1993 (site 0, figure 3.2). Surface Sediment Grain size distributions of surface sediment were determined from particle count collected from a grid (Wolman, 1954). Adjustment of grid spacing to a minimum of two times the diameter of the largest size fraction avoided multiple sampling of stones from sediment clusters. A 0.6 m grid spacing met this criterion except on gravel bar G, which required a 0.8 m interval. Selected stones were classed into 0.50 increments using a template in the field. Particles less than 8 mm were discarded and replaced for the 100 count samples. Subsurface Sediment Subsurface sediment samples were extracted to a depth of approximately 0.3 m after removal of the surface layer. The 0.5% criterion for minimum weight (Church et al., 1987) dictated the sample size at each bar. At two sites, A and D, an 800 kg sample, achieved by collecting 500 and 300 kg samples in series, approximated the weight criterion. Sample weights much larger than 500 kg are very difficult to adequately mix and split. Sediment samples were sieved to a 32 and 22 mm threshold for the first and second flood seasons, respectively. After hand templating the coarse portion of the sample in 0.50 increments, a 0.1% criterion split of the fine portion was returned to the laboratory for automated particle size analysis. 31 In the laboratory, oven dried field splits were sieved into 0.50 intervals using a sieve shaker that operated for 20 minutes (Folk, 1974). Given that silt- and clay-sized sediment was not of major interest, sieving procedures followed a dry sediment method down to 0.063 mm. STREAMFLOW M E A S U R E M E N T A supplemental stage recorder installed near the upper boundary of the study reach (figure 3.2) provided monitoring of flood hydrographs at this point in the channel. A Stevens stage recorder registered water level within a 0.4 m diameter culvert pipe installed adjacent to the stream channel to a depth of about 1 m. Changes in stage height depend on water transmission through near channel sediment, where the coarse nature of sediment should not significantly delay the response. An essentially continuous record from mid-November 1991 to September 1993 exists for the UBC stage recorder. A limited rating curve, established in the first flood season, spans discharges from 0.4 to 2.7 m 3s _ 1. Discharge was determined using the velocity-area method. Velocities were derived from 1 minute samples measured with an Ott laboratory meter positioned at 0.4 depth from the channel bottom. Discharge calculations are based on a minimum of 10 measurement sites along a standard cross section in subreach 3. The flood of January 24,1993, which peaked at 48.8 m3s*1, substantially lowered the channel bed in the vicinity of the stage recorder, as evidenced by cross-sectional survey, and eroded a nearby tree stump, which supported a staff gauge, from the bank. After this event, one discharge measurement was completed with stage height referenced to a second staff gauge located near the standard measurement cross section in subreach 3. Discharge values reported are based primarily on flow measured at gauging station B, given the limitation of the rating curve at the UBC gauging site. When sediment entrainment conditions must be assessed, however, flow information gathered at the UBC site is preferred for determining flow depth estimates in the study reach. Procedures used to estimate discharge at the UBC site are outlined in Appendix 2. 32 CHAPTER 4 M A T H E M A T I C A L MODELS OF SCOUR AND F I L L DISTRIBUTIONS Depths of scour and fill in gravel-bed rivers exhibit variability in space and time (Hassan, 1990; Jackson and Beschta, 1982; Lisle, 1986), confirming a phenomenon found previously in sand-bed rivers (Andrews, 1979; Colby, 1964; Foley, 1978; Leopold et al., 1966). Local variability in flow conditions, sediment characteristics, and channel configuration give rise to a range of scour and fill depths within a channel. During a flood event a limited area of the channel bed scours or fills relatively deeply and a larger spatial area of the bed experiences little, if any, sediment transfer. Empirical observations from magnetically-tagged stones expose this pattern because some tracers remain stationary on the bed surface while others, beginning in buried positions, are located downstream after a flood event (Hassan et al., 1991). The probability of exposure of the channel bed at different depths controls the vertical distribution of tracer burial depths (Galvin, 1965). Hassan et al. (1994) demonstrated that the negative exponential model describes the proportion of marked particles found in a given stratum of the gravel sediment body, and hence the distributions of burial depths of tracers in gravel-bed rivers. Scour indicators record the maximum depth of exposure of the channel bed during flood events. Maximum depths of exposure might also be described by the exponential model by considering a substitution of space for time. Another reason can be offered, however. The underlying processes of transport in gravel-bed rivers have been modeled by Poisson distributions (Einstein, 1937; Hurley, 1992; Sirangelo and Versace, 1984; Todorovic and Zelenhasic, 1970). For example, in a two-stage process of particle rest and motion, Einstein (1937) described the distributions of step lengths by a gamma distribution and the rest periods by a Poisson distribution. Further, the occurrence of bedload transport events has been described as Poisson distributed (Hurley, 1992) because hydrologic forcing follows the Poisson distribution (Todorovic and Zelenhasic, 1970). The Poisson distribution describes point processes that derive from consideration of random variables, each distributed as a negative exponential density function (Olkin et al., 1980). Since scour and fill result from sediment transfers, the depth distributions are 33 random variables for the Poisson process, which is the movement of bed material. Hence the negative exponential function is a candidate mathematical model to describe the phenomenon of scour and fill. Specifically, the exponential density function is expressed by f{x)-0e-* where f(x) equals the proportion of the channel scouring or filling to a given depth increment x and q is the model parameter derived from mean scour or fill depth over a channel reach. EXPONENTIAL MODELS Frequency distributions of scour and fill depths clearly show the single peak, asymmetrical nature of depth distributions for flooding periods that occurred in Carnation Creek (figure 4.1, 4.2 and 4.3; Appendix 3). The range of depths experienced in the channel increases with flow level, as evidenced by the elongation of the right tail of these distributions, and consequently mean depths of scour and fill increase with flood peak magnitude as expected. Maximum observations of scour and fill depths equal 99 and 61 cm, respectively, and occurred during the 48.8 m 3s _ 1 flooding period. Frequency distributions of scour and fill depths were fit by exponential density functions (figure 4.1, 4.2 and 4.3; Appendix 3). Parameters, determined by a Newton-Raphson iteration, are maximum likelihood estimates (Lawless, 1982) for 4-cm increment frequency distributions, given the measurement resolution of scour indicators. Actual parameter values vary between 0.0640 and 0.791 (table 4.1). As flood peak discharge increases over the range of discharge magnitude, the parameter of the exponential function decreases. The corresponding distributions describe a channel that experiences an increasing depth of activity over an increasing proportion of the bed as a function of peak discharge. Within individual flooding periods, nearly 70% of the paired scour and fill parameters differ by less than 0.10. The largest differences are associated with relatively small magnitude flood peaks rather than the five largest flood peaks. Collectively, the differences between scour and fill parameters are not statistically significant at a level of 0.05 judged by the Wilcoxon signed-rank statistic (Neter et al., 1982). 34 35 36 Table 4.1. Exponential model parameters and goodness-of-fit results in Carnation Creek Scour Relations Fill Relations Flood Peak n* Model Parameter W 2 probability n* Model Parameter W 2 probability 4.1 108 0.700 0.805 108 0.595 0.999 5.7 108 0.617 0.985 108 0.700 0.664 7.3§ 67 0.788 0.936 68 0.791 0.0906 7.9 108 0.736 0.852 108 0.558 0.0739 8.6 108 0.512 0.994 108 0.512 0.690 9.2 108 0.576 0.516 108 0.426 0.792 9.6 106 0.522 0.981 106 0.378 0.882 11.2 105 0.569 0.333 105 0.506 0.153 11.5 104 0.368 0.240 105 0.493 0.126 12.7 105 0.535 0.894 105 0.458 0.00707t 20.4 103 0.169 0.210 103 0.173 0.999 21.8 108 0.275 0.747 108 0.193 0.0204t 27.3 104 0.214 0.878 105 0.159 0.720 33.9 108 0.160 0.266 107 0.108 0.684 48.8 108 0.0640 0.168 107 0.0670 0.664 * Scour indicators located on top of channel banks excluded f Observed and expected distributions statistically different at 0.05 significance level § Flood event prior to complete installation of scour indicators in the study reach 38 Similarity between fitted and observed distributions was assessed using the Cramer-von Mises statistic (W2) (Spinelli and Stephens, 1994) adapted specifically for an exponential density function when parameter estimation derives from empirical grouped data (J. Spinelli, personal communication, 1995). In general, statistics based on empirical distribution functions give a more powerful test of the null hypothesis than x2 (Stephens, 1974). Further, use of this statistic circumvents difficulties of insufficient degrees of freedom and minimum expectation requirements encountered using %2. Only the fill relations for the 12.7 and 21.8 mV 1 flooding periods are not adequately fitted by the exponential model at the significance level of 0.05 (table 4.1). Both frequency distributions are deficient in the 4 to 8 cm category (Appendix 3). Overall, the scour relations are more consistent than fill relations, as indicated by the probability range of the statistic. It is worth noting that many theoretical distributions would adequately fit distributions described by only two categories. Four distributions, the scour relations for the 4.1,7.3, 7.9, and 9.2 m 3s _ 1 flooding periods, are described using only two bins (Appendix 3). These results are shown for completeness. Verification and Extension of the Exponential Model It is possible to verify the mathematical model and to explore a possible application at a regional scale based on data collected from gravel-bed streams on the Queen Charlotte Islands, British Columbia, in association with a fish/forestry interaction research program in the early 1980s. A physical description of the 12 study streams and details of the field program are contained in Appendix 4. Four streams, Haans, Riley, Sachs, and Tarundl Creeks, were selected for evaluation of the exponential model for scour depths in two flooding periods (October to December and December to February) and a single flood season (October to February). Selection of these streams satisfied two criteria, maximizing the number of functional scour indicators over the study period and the geographic coverage within the Islands. The absence of detailed hydrological records for the study streams prevents a direct assessment of scour depths as they relate to magnitude of flood events. 39 A stream gauging station in the general study area, however, indicates that several floods occurred within each monitoring period. Frequency distributions of scour depth adhere to a consistent configuration similar to depth distributions from Carnation Creek (figure 4.4; Appendix 3). Sample sizes are smaller than in Carnation Creek, ranging from 18 to 27. Scour depths from Tarundl and Riley Creeks include right censored data because some scour monitors were completely eroded from channel beds. The maximum depth of measurement of these scour monitors equals 38 cm. Exponential models describe depth distributions constructed for the two flooding periods (figure 4.4; Appendix 3). Model parameters are maximum likelihood estimates for grouped data (table 4.2). In the first flooding period, parameters varied between 0.14 and 0.47. Corresponding mean scour depths ranged from about 2 to 7 cm, indicating that channel beds experienced similar scour activity. Model parameters for the second flooding period exhibit a wider range, 0.024 to 0.34. During this period mean depth of scour varied between 3 and 41 cm. The latter mean exceeds the maximum depth of measurement of scour monitors because in the calculation the actual depths of censored data were approximated based on the observed frequency distribution conforming to an exponential model. Confidence in this mean value is clearly reduced. Parameters decrease in value as the geographic location of the stream translates eastward, which reflects the strong west-east precipitation gradient in the region. Riley Creek, located on the west coast, exhibits the largest change in parameters, decreasing from 0.35 to 0.024 from the first to second flooding period (table 4.2). The Cramer-von Mises statistic for grouped data indicates that fitted and observed distributions do not differ at the 0.05 significance level (table 4.2) except for the second flooding period in Sachs Creek. The increase in parameters between the first and second flooding period, counter to expectation, most likely reflects the method of deriving depth observations for this flooding period (Appendix 4). Frequency distributions of cumulative scour depths for the flood season are also well described by exponential models (figure 4.5). Models do not differ statistically from observed distributions at the 0.05 significance level, as determined by the Cramer-von Mises statistic for 40 CO CO -a CD o co a <u U Aonanbajj. 9ATJBT3^[ 41 co CD CD C T l CO 8 2 E .9 Table 4.2. Exponential model parameters and goodness-of-fit results for streams on the Queen Charlotte Islands Number of Stream Scour Indicators Recovery Periodt Model Parameter W 2 probability Haans Ck 17 1 0.474 0.579 17 2 0.336 0.838 17 Flood season 0.265 0.994 Riley Ck 18 1 0.347 0.708 18 2 0.0245 0.761 18 Flood season 0.0232 0.896 Sachs Ck 18 1 0.167 0.903 18 2 0.207 0.00335* 18 Flood season 0.109 0.725 Tarundl Ck 27 1 0.137 0.659 27 2 0.0859 0.855 27 Flood season 0.0568 0.436 Region 279 1 0.570 <0.001* 240 2 0.287 <0.001* 279 Flood season 0.162 0.0139 f Recovery 1 conducted in December; recovery 2 conducted in February * Observed and expected distributions statistically different at the 0.01 significance level 42 u - z I 1 1 1 i 1 1 1 r Sachs Creek Seasonal Scour § n = 18 cr CD Riley Creek Seasonal Scour 0 8 16 24 32 40 Depth (cm) Figure 4.5. Seasonal scour depth distributions and exponential functions for two streams on the Queen Charlotte Islands. Censored data indicated by greater than and equal to symbol above far right column. See text for explanation. 43 grouped data (table 4.2). Extremes in streambed response to a season of floods are illustrated by Haans and Riley Creeks, where parameters reflect mean cumulative scour depths of 4 and 43 cm, respectively. The latter value involves the depth approximation for censored data described previously for flooding periods. Exponential Models for Regional Scour Depths Exploratory analysis was pursued at the regional scale for the three monitoring periods. Regional frequency distributions were derived by scaling scour depth observations from the 12 individual streams on the Queen Charlotte Islands by their respective median diameter of surffcial sediment. Median diameters range from 43 to 72 mm. Sediment size indexes the relative mobility of channel sediment, and hence scour, given similar sedimentologic and hydrologic characteristics. Frequency distributions indicate an approximate exponential form (figure 4.6) Secondary peaks reflect right censored data. The upper limit of depth measurement was reached, and most likely exceeded, at 121 of the indicators by the end of the study period. Maximum likelihood estimation of model parameters incorporates censored data. The Cramer-von Mises statistic for grouped data was used to evaluate the distributions. The success of the exponential model in describing regional distributions is mixed (table 4.2). For the first and second flooding periods, observed and expected distributions are statistically different, whereas for the flood season empirical and theoretical distributions are not statistically different, all judged at the 0.01 significance level in this exploratory analysis. DISCUSSION Modeling results suggest collectively that exponential functions describe scour and fill depths in gravel-bed rivers. In Carnation Creek, frequency distributions of scour and fill depths conform to this mathematical model over a range of flood magnitudes. Although scour depth distributions from streams on the Queen Charlotte Islands are based on fewer scour indicators, modeling results from a representative subset of streams verify the applicability of the exponential model. Exploratory development of a regional scour depth model suggests that larger spatial scale models are possible by incorporating channel sediment characteristics into the model. Overall, 44 1 2 3 4 5 6 Scour depth/Median diameter Figure 4.6. Regional scour depth distributions and exponential functions for streams on the Queen Charlotte Islands for three monitoring periods. Censored data indicated by greater than and equal to symbol above far right column. See text for explanation. 45 these results illustrate empirically that different spatial and temporal scales can be described by the same mathematical form. This result is expected theoretically because the summation of exponential density functions produces an exponential density function (Johnson and Kotz, 1970). The systematic inverse relation between model parameters and discharge level indicates that the channel is scoured and filled more deeply with increasing flow levels, as expected. Observations of scour and fill depths record bed activity at the largest peak when a flooding period consists of multiple events if streambed conditions do not change. In the more likely case of bed adjustments, distributions of depth include mixed observations in some unknown combination. Although change to streambed conditions was documented in the study reach, the averaging of scour and fill depths from multiple flood peaks appears not to significantly distort the underlying pattern. The relation between depths of scour and fill and flood magnitude is explored formally in Chapter 5. Insights into conditions of sediment continuity in a channel reach may be gleaned from the relative magnitude of exponential model parameters. In Carnation Creek, scour and fill models for a given flood exhibit comparable model parameters, which indicates an approximate symmetry between the amount of sediment scoured and filled over the study reach during the monitoring period. Systematic differences between exponential model parameters would be expected in a stream experiencing net aggradation or degradation. With net aggradation, for example, the parameter for the fill model would be systematically smaller than that of the scour model, but both depth distributions would be exponential. Depending on the magnitude of the aggradation, the fill distribution would show a more elongated right tail relative to the scour distribution. Symmetry between scour and fill distributions does not imply a static channel bed as changes to channel morphology may occur without the bed undergoing mean elevational change. Pooling scour indicator data, and thereby disregarding local variability in bed response, increases the statistical rigor of the analysis but concomitantly limits interpretation to the scale of the study reach. Net change or asymmetry between scour and fill on a smaller spatial scale is revealed by focusing on a spatially refined grouping of scour indicators. Data from scour indicators characterize relatively straight subreaches distributed throughout the study reach. Scour and fill 46 activity associated with bends has not been directly considered because of practical field constraints. Given the state of knowledge, however, a first analysis with the simple case of the relatively straight channel seemed appropriate. Exponential models are advantageous in that only one parameter is required to articulate a model and this parameter can be estimated from observations. Eventually, development of a more complex and, hence, complete model that incorporates channel and hydrologic characteristics would facilitate prediction. The collapse of individual stream scour depth distributions into a regional distribution underscores the importance of channel sediment in controlling scour depth. Although only sediment size is directly incorporated into the regional relation, the structural tightness of surface particles is known to exert control over the mobility of channel sediment (Andrews and Parker, 1987; Hassan, 1992) and can affect scour depth by reducing the total time available for scour to occur in the channel. It remains for the effect of surface sediment structure to be quantified before it can be incorporated into regional models of scour depth. In any analysis of quantitative data, specifying the underlying probability distribution of random variables of interest is a major step forward (Olkin et al., 1980). In this present analysis, scour and fill depths have been described by an exponential density function. The theoretical implications stem from the close mathematical relation between the exponential and Poisson distributions. Hence, successful modeling of scour and fill depths with the exponential density function lends support to the idea that the underlying processes of transport in gravel-bed rivers are Poisson distributed. 47 CHAPTER 5 INFLUENCE OF DISCHARGE ON SCOUR AND FILL DEPTHS The depth to which a channel bed becomes active is a function of the interactions among flow and sediment characteristics within the context of channel morphology. A relation must therefore exist between the magnitude of flow and scour and fill depths given specific sediment and morphological characteristics and superimposed sediment supply conditions. Empirical evidence covering a limited range of flow conditions (Hassan, 1990; Lisle, 1989; Madej, 1984; Slaymaker, 1972) reveals the expected positive correlation between flow and scour and fill depths in gravel-bed rivers. An attempt at formalizing depth-flow relations (Carling, 1987) employed net change in bed elevation rather than the separate components of scour and fill depths. The relations are identified as scour or fill through a negative or positive net change in bed elevation. Scour and fill depths characterized by net elevational change, however, underestimate the vertical dimension of the active layer (Colby, 1964). Moreover, given a channel bed that maintains an essentially constant mean elevation, the active layer would show no detectable response to increasing discharge levels. Leopold et al. (1966) developed a power function for scour depth in ephemeral sand-bed channels. This mathematical function was also adopted in the analyses of net change and flow magnitude in gravel-bed rivers noted above. Church and Mark (1980) provide compelling reasons why power functions, in general, are worthy of pursuit in the empirical study of proportional relations. FUNCTIONAL RELATION BETWEEN DEPTH AND PEAK DISCHARGE Functional analysis is the appropriate method (Kendall and Stuart, 1963; Mark and Church, 1977) to determine coefficients for the depth-flow relations because the regression assumption of an error free independent variable (Draper and Smith, 1966) is violated. Observations of scour and fill depths from both types of scour indicators were grouped together using a 4-cm interval because of the measurement resolution of the indicators. Mean depths based on these grouped data are more appropriate. Moreover, the underlying exponential distribution of scour and fill 48 depths argues for use of mean depths derived from an iterative maximum likelihood technique; direct calculation of means from frequency counts of grouped data leads to biased parameters for exponential density functions (Lawless, 1982). Curve fitting procedures yielded the result log ds = -0.94 + 1.20 log Qp for mean scour and log df = -0.89 + 1.21 log Qp for mean fill in Carnation Creek, where ds and af/indicate mean scour and fill, respectively and Qp denotes the maximum peak discharge of the flooding periods. These models are principal axis functional relations with coefficients determined by adjusting least squares regression results as outlined in Mark and Church (1977). Mean depths for the two smallest peak discharges were excluded from analyses because they appear to characterize a lower limit biased by the measurement resolution of scour indicators. Otherwise mean scour and mean fill increase with flood magnitude as expected. Coefficients of determination equal 0.91 and 0.95 for the mean scour and fill relations, respectively. Alternative arithmetic and exponential models explain, in general, less variation and residuals exhibit curvature in contrast to those from power function models. Confidence limits constructed for the exponents are ± 0.20 and ± 0.16 for scour and fill relations, respectively, and indicate that these relations are not statistically different at the 0.05 significance level. Analysis of means computed from ungrouped data yields the same general result. The power function for the scour relation is expressed by ds = 0 . 1 2 Q / 2 0 while the fill relation is described by df = 0.13Qp121 where backtransformed parameters are corrected for transformation bias (Miller, 1984) (figure 5.1). Indices of determination (Ezekiel and Fox, 1959) for these power functions equal 0.90 and 0.98, respectively. 49 Figure 5.1. Relation between mean depth and peak discharge: a) scour and b) fill. Open circles indicate data not included in analysis. See text for explanation. 50 Maximum depths of scour and fill achieved during flood events provide additional insight into fluctuations of the active layer. Curve fitting procedures yielded the result l o g ^ = -0.54 + 1.51 log Qp for maximum scour, dsx, and log dp = -0. O i l + L 07 log Qp for maximum fill, dfe. Residual patterns are similar in both relations and show more pronounced scatter in the mid-range of peak discharge. Coefficients of determination are 0.73 and 0.94 for scour and fill, respectively. Confidence limits of ± 0.53 and ± 0.15 constructed for exponents indicate that these maximum relations are not statistically different at the 0.05 significance level. The power function for the maximum scour relation is expressed by </« - 0 . 3 0 ( £ 5 1 while the maximum fill relation is given by ^ = 0 . 9 8 G j 0 8 where coefficients are corrected for backtransformation bias (figure 5.2). Indices of determination are 0.69 and 0.94 for maximum scour and fill, respectively. Further analysis of the ephemeral sand-bedded Arroyos de los Frijoles data (Leopold et al., 1966) allows a comparison with the mean scour relation in Carnation Creek. Only data from the Main Project reach (Leopold et al., 1966, table 4) are utilized to achieve a similar spatial scale with the study reach in Carnation Creek. The Main Project reach exhibits a wider channel and steeper bed gradient than Carnation Creek (table 5.1). The median diameter of sediment in Carnation Creek is about 40 times larger than the median diameter of sediment in Main Project reach. In this exploratory analysis, the separate means reported for subdivisions of scour chains into two subreaches and the channel thalweg environment in the Main Project reach are maintained, which gives, in general, three mean values per flood event. Mean depths are based on a total of only 33 scour chains. Scour depths were measured for about the same number of flooding periods in both streams (table 5.1). 51 Figure 5.2. Relation between maximum depth and peak discharge: a) scour and b) fill. Open circles indicate data not included in analysis. See text for explanation. 52 111 3 «S OH CN fl e CO CO 00 o e w _ .2 i> fl u 8 B S --3 w O ON CN CD O S3 3^ | | B c i i CO W a ^•v 3 a s a a 3 a -a .a CO CN i f O So CJ (-7 cx cd ^ fj CO cn © m o o © r-CN CN co CO o Hi? 73 w 00 ON o « ^ a CO CN 1 1 1 C M W VO © © .3 cd I 8 1 0\ CN co CD > co O <o T3 • co O > . o <D CD u fl o •«—» cd a fi Scaling data from each river facilitates comparison, given different hydrologic regimes and channel sediment (table 5.1). Specific discharge scaled by the mean annual flood accounts for differences in recorded flood magnitudes within specific regimes. Mean scour depth scaled by the median diameter of channel sediment standardizes scour depth in terms of the number of layers scoured, one median diameter thick, by a particular flow level. Coefficients are estimated using functional analysis, to properly compare between empirical relations. The original Arroyos de los Frijoles equation derived using least squares regression gives an exponent of 0.5 and a coefficient of determination of 0.58. Curve fitting procedures for the Main Project reach give a coefficient of 1.94, exponent of 0.63, and coefficient of determination of 0.84. Residual analysis indicates that the power function is a suitable model as no diagnostic patterns of lack of fit emerge in the residuals. Confidence limits equal ± 0.09, which substantiates that the two scaled relations differ statistically at the 0.05 significance level. The scaling procedures modify the equation coefficient to 0.40 in the scour relation for Carnation Creek; the slope, 1.20 ±0.20, of the functional relation remains unchanged. The Main Project reach power relation, backtransformed and corrected for related bias, is expressed by d' = 86.57 q' 0 , 6 3 where d' = the ratio of scour depth to median diameter and q' = the ratio of specific discharge to the specific mean annual flood. The index of determination equals 0.78. For Carnation Creek the scaled power function is given by d' = 2.54 q'120 These relations are illustrated in figure 5.3. DISCUSSION The development of power functions relating flood peak magnitude and mean scour and fill depths indicates that predictive relations for scour and fill based on streamflow are indeed 54 1000 100 =o 10 1—t— i ! . 4 L c 3 ! O 1 C } o 1' ...... ... .:_ x>. :::::.}:::: -* o 1 1 r i i 1 I j i -H* c r --}••• - [• i .Q c j i ...„.._„.[._.... j _0O-~> 3 C °° 1 j j j i - ^> t- i |- - t 1 j _ a i 0 ! . p. • i i < • i :: : —.f—, L i r ! ; j | ! i i u u Li U LI u LL j ! i i u LL 0.01 0.1 1 10 100 Figure 5.3. Relation between scaled scour depth and specific discharge. Upper relation based the Arroyos de los Frijoles (Main Project reach) and lower relation based on Carnation Creek. 55 possible for gravel-bed rivers. The relation between maximum scour depth and peak discharge presents a potentially powerful tool for the management of fish habitat, where the survival of eggs depends on the severity of scour during flood events. Although insight into the exact timing of scour and fill during a flood event is not provided, the nature of the active layer over the sequence of individual events provides critical information for calculation of volumetric sediment transport. This topic is discussed in Chapter 7. The variability of scour and fill within a flooding period increases with peak discharge in Carnation Creek (figure 5.4). The coefficient of variation changes from about 40 to 80% over the range of small flood peaks. For peak discharges larger than 13 m 3s _ 1, variability continues to increase for scour but levels off for fill. Pre-flood streambed conditions exert control directly over scour but not fill. Once sediment is mobile in the channel, deposition depends on the interplay between hydraulic conditions and the channel boundary. The amount of fill is constrained by the magnitude of scoured material if other inputs of sediment do not occur in the channel reach. If maximum scour depth is used as an index of streambed conditions, some additional insight is possible. Maximum scour exhibits a greater level of variability than maximum fill (figure 5.2). The most pronounced deviation in maximum scour is associated with the 20.4 m 3s _ 1 flooding period (figure 5.5). The 20.4 m 3s _ 1 flood peak followed by about 6 weeks the maximum flood peak of the field program, which suggests that a more disrupted streambed, as evidenced by morphological change, facilitated the deeper maximum scour. Further, the first significant flood peak in each of the two flood seasons, numbers 3 and 10, show negative deviations from the relation due to a relatively long period of inactivity that allowed the bed to consolidate (Reid et al., 1985). The deviations in flooding periods 6 and 7, however, defy explanation based on likely bed conditions. These two flooding periods share a common characteristics; each consists of two flood peaks of very similar magnitude. Similarity in the exponents of the depth-flow relations in Carnation Creek indicates that the bed of the channel scours and fills to similar magnitudes within specific flood events. This can be confirmed, in a general sense, by examining net change in bed elevation derived from cross-sectional surveys. Patterns of net change for periods dominated by the five largest flood 56 —' fl _o cd ca > fl CD CD o u fl o • »-< •*-» .2 cd > fl CU • »-( o o u 10 20 30 Peak discharge (m s ) Figure 5.4. Variability of scour and fill versus peak discharge in Carnation Creek: a) scour b) fill. 57 1000 1 10 100 Peak discharge (m'V1) Figure 5.5. Maximum scour depth versus peak discharge in Carnation Creek. Numbers indicate flooding periods. Open squares indicate first large peak of season (with scour indicator data available), crossed squares indicate first flood following maximum peak of each flood season, and open circles indicate data excluded from power function analysis. 58 peaks demonstrate that some sections of the channel experienced net fill while others experienced net scour (figure 5.6). An approximate equality between the two states of change prevailed except for the period with the largest flood peak when scour exceeded fill (figure 5.6d). The corresponding mean depth for this period displays a positive deviation from the scour relation as expected (figure 5.1a). An approximate balance between areas of scour and fill in the channel was reestablished in the following flooding period (figure 5.6e), although at a relatively lower elevational baseline in some sections. As flow level increases the channel expands vertically and laterally. During the smallest flood events scour and fill are restricted to a few scour indicators. Larger magnitude flows, with an increased level of mobilized sediment, present the most probable conditions for morphological change. Significant adjustment to bed elevation requires the physical movement and deposition of large quantities of sediment. For example, the low-flow channel shifted from the right to left bank in subreach 1 over the study period. The four cross sections in this subreach registered from 1.6 to 3.1 m 2 of net scour that was accompanied by 1.4 to 2.7 m 2 of net fill, leading to a minimal net change in channel bed elevation, during the 48.8 m 3s _ 1 flooding period. Overall, the most widespread and notable changes in morphology occurred during this flooding period as the baseflow channel shifted laterally, eroding the channel bank, with concomitant migration of a portion of the riffles by about 8 m. In a few channel sections net change surpassed about 3.0 m 2 of cross-sectional area. The variability in net change in cross-sectional area increases with peak discharge (figure 5.7). The individual components of net fill and net scour follow the same general trend with the former less variable than the latter. The relatively large variability in net change suggests that the channel undergoes numerous shape adjustments to the active cross section through differential net scour and fill. These adjustments occurred, in general, within the confines of the current planview configuration. The similarity between net change and net scour indicates that adjustments are dominated by the scour process. Documenting adjustments in Carnation Creek required relatively frequent measurement of channel bed elevation. Coarser temporal resolution would likely mask this phenomenon in active streams. 59 3 i i i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i _2 r • • • • i • • • i i • • • • i • • i • i i i • • i • • • • i • • i • i • • • • i • 0 5 10 15 20 25 30 35 40 Cross section number Figure 5.6. Net change in channel bed elevation for flooding periods: a) 33.9 m3s"1, b) 27.3 m3s"1, c) 21.8 m V 1 , d) 48.8 m V 1 , and e) 20.4 m V 1 . Flooding periods shown in temporal sequence. Cross section numbering begins from downstream boundary of study reach. Locations of cross sections shown in figure 3.2. 60 10 .6. ca cu ca "ca a o '•6 CU co co co O o a o •r-H 13 • r-H > <U T3 T3 • a c/3 0.1 1 1 1—1—1 1 i 1 i i ! 1 1 1 • i i l l o Net scour • Net fill + Net change 4 c -—u. -"O" T J * a o * , __| • i i i ( > 10 Peak discharge (m3s 1 ) 100 Figure 5.7. Variability in cross-sectional area based on peak discharge in Carnation Creek. 61 The largest flood in Carnation Creek left an historic imprint on the channel by modifying sections but assessing this effect definitively is difficult given the singularity of particular events couched within a long series of antecedent events. Residual analysis of the mean depth-flow relations reveals a slightly increasing temporal trend to deviations from the models but the Runs statistic indicates that these trends are not statistically significant at the 0.05 level. These factors remain to be rigorously investigated. Insights into these influences may be achievable through laboratory flume experimentation, where control can be exerted over flow magnitude and sequence of flood events. The analysis employs peak discharge as the index of magnitude for a scale correlation with mean depth. Hydrograph shape, and hence the duration of flow levels competent to scour the channel bed, may influence scour and fill relations. In Carnation Creek the mean duration of flood peaks greater than 15 m 3s _ 1 equals 14.3 hr with a standard error of ± 2.2 hr. In general, duration is systematically tied to flood magnitude. The ratio of peak magnitude to duration of live-bed conditions (elaborated in Chapter 7) approximates 2 for all but two floods, where the ratio equals about 1. These floods, with peak magnitudes of 25.8 and 27.3 mV 1, both occurred in the seventh flooding period. Although the mean depths of scour and fill do not deviate radically from the general trend (figure 5.1), the double-peaked nature of the flooding period may have convoluted the pattern. For a given peak magnitude, hydrographs of longer duration may produce deeper scour to supply more sediment for transport than is achieved during shorter duration flood events, particularly in situations where the supply of bed material is limited. The relatively longer maintenance of flow at levels competent to mobilize sediment would provide a longer time period for disruption of the armour layer typically found in gravel-bed rivers. Power relations between flow magnitude and mean scour and fill depth provide models for changes in the vertical dimension of the channel bed in response to flood events. Refined analysis of mean scour depths measured in the Arroyos de los Frijoles allows a more general statement about the appropriateness of the power function as a model. Moreover, an exploratory comparison of scour relations demonstrates that sand- and gravel-bed streams occupy distinct fields in a scaled diagram, the sand-bed relation positioned above the gravel-bed relation. These two models are 62 statistically different with the rate of change being about two times larger in Carnation Creek than in the Arroyos de los Frijoles. This result remains tentative until additional empirical data permit further analysis. 63 CHAPTER 6 M O V E M E N T OF BED SEDIMENT The necessary connection between scour of the streambed in one location and fill in a downstream location is the movement of sediment. The influx of sediment from side tributaries or collapsed banks may be transported over a stable bed surface but when sediment is supplied from the channel bed this connection is fundamental. Bed material transport consists of a collection of individual grains that are entrained, propelled downstream by unsteady flow over a rough and variable boundary, and deposited. Entrapment in scour holes or behind stationary particles, transport into zones of relatively low shear stress, or recession of flow below that necessary to maintain motion may serve to temporarily delay or completely terminate individual grain movement. The collection of particles in a gravel-bed channel is a heterogeneous mix of sizes. The majority of work investigating the transport of individual grains reports that sediment size does not strictly control distance of movement (Ashworth and Ferguson, 1989; Carling, 1987; Einstein, 1937; Hassan et al., 1991; Laronne and Carson, 1976; Leopold et al., 1966; Stelczer, 1981) but that a range of travel distances exists for particles within a particular size fraction. Given the complexity of sediment movement, it seems virtually impossible that all individuals within particular particle size fractions would travel similar distances. Given a sufficiently wide range of grain sizes however, an upper limit to the distances particles move based on size is apparent (Hassan and Church, 1992). Rather than concentrating on variability in travel distance, Church and Hassan (1992) proposed a heuristic, nonlinear relation between mean travel distance and grain size through the evaluation of unconstrained surface tracers from numerous gravel-bed rivers. The Church-Hassan (C-H) relation is expressed by V = 1.77 (1-logJD') 1 3 5 where L' = the ratio between fractional mean travel distance and mean travel distance of the particle size fraction encompassing the median diameter of surface sediment and D' = the ratio 64 between grain size fraction and the median diameter of subsurface sediment. The model is based on rivers exhibiting a wide range of bed textures, presumed bed surface structures, and hydrologic regimes and hence scaling normalizes specific river characteristics. The suitability of the C-H model for other rivers remains to be evaluated. EXPERIMENTAL DATA FOR ANALYSIS Distance of travel for individual stones derives from four recoveries of tracers where field searching procedures extended over the study reach. These distances characterize the general movement of coarse bed material. The temporal sequence of recovery provides data for two flooding periods, one dominated by a 21.8 m3s"1 peak and the other by a single 28.3 m 3 s - 1 peak, and the two flood seasons. Travel distances are characterized by the two different tracer generations for the 21.8 m 3s _ 1 dominant peak and the second field season. The deployment of a large number of magnetically-tagged tracers and minimum recovery rates of 60% provide sample sizes ranging from 670 to 963. The magnitude of these samples is atypical for a single river. Only one other database of comparable deployment magnitude is known to exist for gravel-sized tracers (Laronne and Duncan, 1989) but these data have yet to be used to evaluate the travel distance-grain size relation. Bias may be introduced into travel distance estimates through the failure to recover tracers that move beyond the study reach or those that reside deeper than the detection capability. Any effect should be minimal, however, because of the large sample sizes. T R A V E L DISTANCE BY PARTICLE SIZE Mean travel distance varies systematically by particle size for individual flooding periods and flood seasons, the latter displaying steeper gradients than the former (figure 6.1). In general, the 22 mm size fraction, the fraction that includes the median diameter of subsurface sediment, travels the greatest distance. As particle size increases beyond 22 mm travel distance decreases (figure 6.1). Only the 16 mm fraction deviates from this trend with a travel distance, on average, less than the 22 mm fraction. The Kruskal-Wallis statistic indicates that in both individual flooding periods and in both flood seasons travel distances differ between size fractions at the 0.05 significance level. 65 200 10 20 50 100 Size fraction (mm) Figure 6.1. Trends in mean travel distance as a function of particle size: a) flooding periods and b) flood seasons. 66 A general trend in mean behavior prevails in the context of variability within size fractions (figure 6.2). The characteristic scatter of all distances below an upper envelope was also found by Hassan et al. (1994). Although not without exception, maximum travel distance declines with particle size for flooding periods and flood seasons. The two flooding periods display similar upper envelopes, although the 21.8 m3s"l flooding period is dominated by the relatively more mobile generation 2 tracers that began exclusively from the bed surface. Travel distances by the end of the second flood season show reduced differentiation between size fractions (figure 6.2d). Mean distances for flooding periods are systematically larger for the period dominated by the larger flood peak until an approximate convergence of the three largest size fractions (figure 6.1a). The Wilcoxon signed rank statistic indicates that mean trends differ between maximum flood peaks at a 0.05 significance level. Given that both tracer generations are used to derive travel distances for the 21.8 m3s"1 flooding period, a more strict comparison, to evaluate the control of discharge magnitude over mean travel distance, is afforded by examination of tracer data from only the second tracer generation so that tracer starting positions are uniform. Further, only tracers released from the upper deployment area are used to avoid introducing any effect from the split deployment (figure 6.3a). Comparison of these travel distances with distances from the 28.3 m 3s _ 1 flooding period corroborates the initial result. Seasonal trends in fractional travel distance display a more complex pattern. Distances for the 16-45 mm fractions in the first flood season exceed the second flood season while the relative magnitude reverses in the remaining, larger size fractions. The Wilcoxon signed rank statistic indicates that mean trends do not differ between flood seasons at the 0.05 significance level even though the two seasons are composed of a different series of flood magnitudes and frequencies. Flow exceeded 10 m 3s _ 1 for 112 hr during the first flood season compared to 56 hr during the second flood season. Comparison of the seasonal trends may be conducted on a refined level given that travel distances derive from two tracer generations in the second flood season. By segregating travel distances by tracer generation, a distinct differentiation in the trend of mean travel distance becomes evident (figure 6.3b). Travel distances are significantly reduced for generation 1 tracers 67 > / 1 / a / ° a D a>"om / n , S H H • pc 11 m m -H-1 • a + I I o o (ui) aoireisip P A B J X 8 8 8 8 8 VO IT) Tj- CO CN (Ul) 30UBJSip 68 CN VO u I E a o •a I-I D a u Figure 6.3. Trends in mean travel distance as a function of particle size for refined analysis a) flooding periods and b) flood seasons. 69 in the second flood season compared to the first flood season. The second tracer generation, with a greater proportion of tracers remaining on the surface before the maximum flood peak of the season, shows a trend of larger mean distances. When the Wilcoxon signed rank statistic was used to evaluate differences between mean travel distances in the first flood season with each generation in the second flood season, differences are revealed at the 0.05 significance level. The initial result appears to be simply an artifact of tracer generations undergoing different behavior as conditioned by residence time in the channel. FUNCTIONAL RELATION BETWEEN DISTANCE AND PARTICLE SIZE General trends in travel distance as a function of grain size support formal evaluation of the C-H travel distance-grain size model using Carnation Creek data. The specific travel distance data used in the generation of three different models (table 6.1) avoid potential convolution of results from the influence of different tracer generations. Scaling procedures followed those outlined by Church and Hassan (1992). Individual tracers were grouped into size fractions based on a 0.50 interval. A template measurement rather than a b-axis diameter determined tracer size class. Particle size fractions, indexed by geometric means, were scaled by the median diameter of subsurface sediment, which reflects the size distribution of mobile sediment. Mean travel distance calculated for each size fraction was scaled by the mean travel distance of the size group that includes the median size of surface material, which is a measure of flood event size. Least squares regression generated coefficients for the travel distance-grain size relation and yielded the result logV. = 0.22 +1.60 log (1 - logD') when distances characterize unconstrained surface stones for the two flooding periods. For size fractions predetermined through the production of tracers, regression is the appropriate technique for parameter estimation. The coefficient of determination is high, 0.90, and larger than the C-H relation by 0.18. Residual analysis revealed no systematic deviations diagnostic of a lack of model fit. The backtransformed equation, corrected for bias in the coefficient (Miller, 1984), is expressed by 70 8 is ' a CO s a •4-1 o cd £ .a 03 5 CD 4-* o ex a o U o 00 00 CN o ON VO in C N cn C N C N VO a o 'ts ca I-I 8 CD o a a M >< S " <u s a CO CU CJ 3 co cu co ON O O 00 ON VO 1-H VO cn d cn cn o C N in >n VO o S C N ON t> cn cn d S C N ^ VO VO d cn cn C N i-i CN o\ d T f vo in C N C N oo Tf cn + + i-H C N cn oq oo i-5 C N C N O CN Ov in d C N 00 00 ON q in oo d CU e a to 1 00 C N cn r- o vo r- r-ON VO VO VO o q in VO 00 cn cn in vo s CU I CJ .3 .8' <3 c t>3 ON cn cn T T VO H VO* VO Tj" vo cn in vo oo « 00 i-H VO CN i-H i-H rH 00 vo cn C N O C N i-H cn vo C N in C N T T i-H C N C N ON vo cn o oo cn T T i-i d i-H r-~ cn vq q rH ON I-H C N •<t 00 00 in ON oq oo in cn C N vo vo i-H C N 00 00 71 V = 1.70 (1- log D')160 and is illustrated in figure 6.4a along with the C-H relation. The index of determination (Ezekiel and Fox, 1959) for this transformed relation equals 0.69. A relation for tracers resident in the channel for one complete flood season (table 6.1), and thus more integrated within channel sediment than surface tracers, was determined for the 21.8 m 3s _ 1 flooding period and is expressed by log V = 0.045 + 1.58 log (1 - logD') where the coefficient of determination equals 0.96. Residuals display minor departures from the fitted relation. The scaled travel distance of the 90 mm fraction exceeds the predicted value while the 16 mm fraction falls below the predicted value. The backtransformed relation (figure 6.4b), corrected for bias, is given by V = 1.12 (1- logD')1-5 8 where the index of determination equals 0.86. When seasonal displacements for tracers are considered (table 6.1), the travel distance-grain size relation is given by log!/ = 0.051 + 1.15 log (1 - logD') where coefficient of determination equals 0.75. The exponent differs by about 0.5 from specific relations based on flooding periods. Residuals indicate a tendency for increasing variance with particle size. The corrected backtransformed relation (figure 6.4c) is expressed by V - 1.16 (1- logD') 1 1 5 The index of determination equals 0.80. The three relations specific to Carnation Creek are not statistically different from the C-H relation at a significance level of 0.05. DISCUSSTON The travel distance-grain size relations developed herein provide convincing evidence for the general merit of the heuristic model proposed by Church and Hassan (1992). The relation for 72 unconstrained surface stones exhibits a larger exponent than the C-H relation, indicating that mean travel distance decreases more sharply with size in Carnation Creek. The potential influence of tracer generation has been circumvented in the functional relation analysis because of the scaling procedures, which subsume relative differences in flow magnitude, and the nature of data selected for model development (table 6.1). This circumstance permits an exploration of the C-H model based on tracers other than unconstrained surface stones to evaluate how well the model describes travel distance of tracers beginning from natural bed positions. Particle burial and incorporation into the surface sediment structure delays entrainment and limits the potential time for movement, leading to an overall reduction in travel distances compared to those derived from unconstrained surface stones (Hassan and Church, 1992; Reid et al., 1992). The relation developed for mixed stones is not statistically different from that for the unconstrained surface stones at the 0.05 significance level; the exponents are virtually identical. The smaller coefficient indicates a shift in the magnitude of fractional mean travel distances. Moreover, the exponent for the flood season relation is less than those of both the individual flooding period relations, which illustrates that larger particles experience a relative gain in travel distance compared to finer sizes over a flood season. Differentiation between particle size lessens as tracers, particularly the smaller fractions, are increasingly mixed in channel sediment. Burial of an increased proportion of a particle size class as an inverse function of size has been suggested as a mechanism controlling the relative rate at which smaller particles travel downstream (Church and Hassan, 1992). Buried tracers must be exposed before transport is possible so with a larger proportion of buried particles the overall mean travel distance would be reduced. Proportional trends for the 21.8 m 3s _ 1 flooding period substantiate that smaller fractions are buried to a greater degree (table 6.2). In the four smallest fractions a minimum of 61% resided within the subsurface. Burial was about 90% for the two smallest sizes. Corresponding trends in mean travel distance, however, do not strictly corroborate the expected lower travel distance due to increased burial. Travel distances achieved by subsurface stones exceeded those of surface stones in the two smallest size fractions, but the sample size is relatively small for surface tracers 74 Table 6.2. Mean travel distances for generation 1 tracers based on starting position prior to the 21.8 mV 1 flooding period. Surface Subsurface Particle size fraction* (mm) Mean travel Number distance (m)t recovered %of total in class Mean travel Number distance (m)t recovered %of total in class 16 5.3 13 8.5 10.9 140 91.5 22 8.7 19 9.6 15.7 180 90.4 32 11.4 27 37.5 8.3 45 62.5 45 11.6 35 39.3 4.7 54 60.7 64 4.5 47 63.7 5.2 28 37.3 90 1.4 52 81.2 3.8 10 19.2 128 1.2 37 94.9 1.9 2 5.0 180 0.5 19 100.0 - 0 0.0 * Lower bound of particle size fraction t Includes tracers that did not move 75 (table 6.2). Mean distances traveled by the 32 and 45 mm fractions appear to be regulated by burial (table 6.2). It appears that overall mean trends are strongly influenced by travel distances of subsurface tracers. Once tracers begin from natural positions, the majority of the four smallest size fractions come primarily from the subsurface (table 6.2). Although data are presented only for the 21.8 m 3s _ 1 flooding event, a similar pattern in the proportion of buried particles exists for the second flood season, when the most highly mixed generation 1 tracers are considered. That a significant amount of sediment derives from the subsurface verifies that the relatively poorly developed armour layer is disrupted in numerous locations in the channel (figure 6.5). In the first 300 m downstream from deployment area A (figure 3.2) a substantial number of tracers experienced no movement during the 21.8 m 3s _ 1 flooding event but are in close longitudinal proximity to areas of the bed that scoured. Overall results strongly suggest size-preferred transport. Mean travel distances decrease for particle sizes larger than a scaled diameter of about 1. The 22 mm fraction traveled the greatest mean distance of the sizes characterized by tracers. Considering the three smallest size fractions, the relative magnitude of travel distance consistently is 32 mm < 16 mm < 22 mm. On a statistical basis, however, travel distances of these fractions do not differ at the 0.05 significance level based on the Kruskal-Wallis statistic. This result applies to flooding periods and flood seasons. Hence, the peak in travel distance for the 22 mm fraction, although pronounced, appears to be statistically insignificant. When the larger size fractions are included, however, mean travel distances are statistically different at the 0.05 significance level using the same statistic. When the ratio of particle size fraction to median diameter is less than 5, particles of different sizes are expected to display little difference in mobility based on the arguments of equal mobility (Andrews, 1983). Accordingly, grain sizes less than 128 mm should be equally mobile in Carnation Creek. When fractional transport rates are calculated based on tracers that moved and scaled by the respective fractional proportion in the particle size distribution of subsurface sediment, fractional rates vary between these size fractions. Fractional transport rates derived from tracing marked particles constitute an assessment based on frequency-by-number, which is 76 a CD t-i SO fl o 8 'S •4-t 5 o o CN o o CN o oo o 1 1 s 1 1 1 o a CN X 0 cn X B X i 0 _ X 8. X* X o o o X o o 0 o tr X X X 0 # X x_ X ~ o X >? K X 1 1 1 1 o o o 00 "* o o cn o V) CN CN s cd CO O o •o 8 o cd 4 ^ co Q o (m) aouBjsip P A B J J . (m) 90UBJSip T3ABIJL 77 T3 CO <D O CO peri Cros OJO Cros g CO a o o *4-» 'to O 1 CX CO e o cd oq t i CN 3 CO CD a ithth gfro tartin on' tartin * CO cd co '3 CD O CO O cd >. J3 i—^ OJ » .a & ara CO o CD -3 CD CO T3 o .3 to les CD 4- i r H les cd a *4-» cd Open circ illustr enei Open circ ions <: 4-» >% CJ cd •O cd < f l T3 CD CD .a JD S3 "cD * CO :> a 4-1 cd CD CO ces tr t 3 a ex 3 cd CD O 4-» CO - a •3 CO a O cd g o Cd 4-* • f l tions from posi 'CO -a uried od 8 a uried CD tartin refer from Vi CD <H "cd cd fl CO tudi 8 9 '5b '5b Cd 4-» 22 be Q -3 CO U l i—1 a? cd O 6.5. udin e tra CD Figur Long india compatible with the standard approach of assigning fractional proportions based on size-by-weight of a volumetric sample of bedload (Kellerhals and Bray, 1971). Other workers have reported varying degrees of departure from equal mobility (Ashworth and Ferguson, 1989; Church et al., 1991; Komar, 1987; Wilcock, 1993; Wilcock and Southard, 1989). The C-H relation suggests grain mobility approaches zero at a scaled diameter of 10. In Carnation Creek, the largest size fraction of subsurface sediment is the 180 mm fraction, which constitutes only 1.9% of the size distribution. This fraction scales to 7.3 and travels, on average, about 1 m per event. It appears then that all sediment sizes are mobile in Carnation Creek during flood events with a minimum return period of about 1 year. In the development of the C-H relation, data characterizing the limit of mobility cover the full range of the confidence bands. Further investigation of the limit to sediment mobility is needed over a range of particle size distributions and surface structure development. The evaluation of the C-H model presented herein employed a more limited range of diameter sizes than was analyzed in its development. Tracers deployed in Carnation Creek, however, cover a relatively wide range of the bed material in comparison with most other individual studies, where tracer sizes consist, in general, of sediment coarser than the median diameter of surface sediment (Church and Hassan, 1992, table 1). In Carnation Creek three 0.50 interval size classes below the median diameter of surface sediment have been traced. In gravel-bed rivers with particle size distributions similar to Carnation Creek, a wider coverage of the size distribution requires careful attention in tracing smaller particle sizes, including size constraints to tracer fabrication and magnitude of deployment necessary to ensure adequate retrieved sample sizes. These smaller sizes would likely experience lower recovery rates due to a lower probability of detection as the result of propensity for deeper burial and greater probability of transport beyond a delimited study reach. A confirmation of the model over the full diameter range may be accomplished more readily in gravel-bed rivers with coarser size distributions. Development of travel distance-grain size relations shows some sensitivity to scaling procedures. For example, if a slightly different median diameter is used, scaled travel distances shift systematically to the right or left depending on the relative change in particle size. Hence 78 representative sampling of gravel is an important component for successful model development. In this study, the median diameter is based on 21 subsurface gravel samples, averaging about 580 kg each, collected over 3 years. Annual distributions show little change between years. Further, particle size scaling is based on the subsurface sediment distribution, justified as being representative of the sediment sizes in transport. A relation with different parameters may result if the median diameter of surface sediment is used instead, which could be defended on the basis that this distribution represents the material exposed for initiation of motion. Finally, in the development of the C-H relation the b-axis measurement was used to group tracers into size fractions. If generation 1 tracers are regrouped based on a b-axis measurement rather than a combined b and c axis, which is what results from template classification, the scaled travel distance of the four largest size fractions increases with the 180 mm rising by an order of magnitude. The slope of the travel distance-grain size relation would be adjusted accordingly. The analysis of mean travel distance as a function of grain size included all tracers. As such the reported travel distances do not strictly describe travel distances of scoured sediment. General trends computed from only tracers that experienced movement, however, are similar to those reported herein. Within the development of the travel distance-grain size relation this point is, in general, of no consequence as long as the relative behavior between fractions is fairly consistent because travel distances are scaled by the relative magnitude of the particular event. In investigations aimed at computing bed material transport, however, a more appropriate characterization of mean travel distance excludes static tracers. This topic is addressed in the next chapter. 79 CHAPTER 7 TRANSPORT OF BED M A T E R I A L A fundamental equation for the volumetric transport of bed material, Qt,, is Qb = VbDsWs(l-P) where Vt> = mean virtual travel rate of bed material, Ds = active depth of the streambed, Ws = active width of the streambed, and P = porosity of channel sediment. Virtual velocity derives from considering periods of rest and motion experienced by individual particles; it is calculated as the total distance traveled over multiple steps divided by total time elapsed (Einstein, 1937). Given that bed particles are not in continuous motion this velocity is necessarily less than the actual velocity of particle movement. Virtual velocity directly incorporates the random aspect of particle* movement into the estimation of transport rates. Transport estimates include bed material that moves relatively short distances by traction, saltation, or in suspension. The above equation constitutes an alternative to seeking a scale correlation between shear stress (Andrews, 1994) or stream power (Reid and Frostick, 1986) and bedload transport, measured during flood events using portable hand-held samplers (Engel and Lau, 1981; Helley and Smith, 1971) or pit traps (Emmett, 1980; Reid et al., 1980; Tacconi and Billi, 1987). Spatial and temporal variability in the patterns of bed material transport (Ergenzinger, 1988; Gomez, 1991), in part influenced by the random movement of individual particles, dictates that extensive and laborious sampling programs are necessary to characterize bedload rates during flood events. Errors associated with sampler-derived data may commonly be greater than ± 100% (Hubbell and Stevens, 1986). An advantage to pursuing the alternative method is that information on fundamental transport processes, such as rates of movement and dispersion of sediment sizes (Hubbell and Sayre, 1964), can be gained by tracing individual particles. Although direct measurement of transport at multiple cross sections in a particular river reach can yield information about mobile particle size distributions and any differences at cross sections, little insight is gained about particle exchange within the channel bed, an important component in understanding the evolution of a 80 heterogeneous and variable streambed. The limited number of studies that have explored bed material transport rates in the field using the above equation (Carling, 1987; Hassan et al., 1992; Kondolf and Matthews, 1986; Laronne et al., 1992; Mosley, 1978) suggests the need for further investigation. FOCUS OF TRANSPORT CALCULATIONS Determination of bed material transport concentrates on three of the subreaches instrumented with scour indicators. Subreaches 1, 2, and 3 are located downstream of tracer deployment areas (figure 3.2) so that estimates of virtual velocity are obtainable. Tracers considered included generations 1 and 2 and those deployed prior to this study identified as generation 0. Working within these three channel subreaches also permits two independent delineations of the active cross section using scour indicators and tracers. For subreaches 1 and 2, transport estimates were computed for three individual flooding periods (table 7.1). The most extensive database is associated with subreach 3, where transport estimates were possible for six individual flooding periods (table 7.1). In addition to subreach estimates, transport rates were determined in the entire study reach over two flooding periods (table 7.1), which provide a context for subreach transport rates. TRENDS IN PARAMETERS Particle Step Length Mean step lengths range from 6.1 to 129.1 m in the three subreaches with 83% larger than 40 m (table 7.1). Means derive from more than 30 tracers in 75% of the cases; three means are based on over 145 tracers. Subreach 1, which is the greatest distance from deployment areas, exhibits low tracer counts but trends are consistent with expectations based on flood magnitude (table 7.1). Distances represent either sediment fluxes into and within a subreach or fluxes within and out of a subreach because of the sequence and extent of tracer recoveries (table 3.2). To determine the step length of an individual particle, tracer position must be known before and after a flood event. When recoveries were limited only to subreaches during flooding periods B and E, , 81 Table 7.1. Parameters for calculation of volumetric bed material transport. Flooding periodst A B C D E F Peak discharge (m3 s-l)+ 24.5 30.4 21.9 17.7 36.3 17.9 Duration of sediment movement Maximum flood peak [mfp] (hr) 15.6 14.5 18.5 8.8 16.2 10.3 Total competent period [tcp] (hr) 15.6 28.5 67.5 12.6 25.8 17.5 Subreach 1 Stream power (W nr 2) 104.8 215.2 106.0 Number of tracers 15 29 8 Mean travel distance (m)§ 44.44 125.94 42.74 Mean virtual velocity [mfp] (m hr - 1) 5.0 7.8 4.2 Mean virtual velocity [tcp] (m hr 1 ) 3.5 4.9 2.4 Scour indicators Active width (m) 8.0 16.1 9.7 Active depth (m) 0.04 0.17 0.11 Tracers Active width (m) 4.3 7.4 7.0 Active depth (m) 0.19 0.15 0.12 Subreach 2 Stream power (W nr 2) 180.4 370.4.2 182.4 Number of tracers 146 55 39 Mean travel distance (m) 51.43 43.44 47.15 Mean virtual velocity [mfp] (m hr - 1) 5.8 2.7 4.6 Mean virtual velocity [tcp] (m hr 1 ) 4.1 1.7 2.7 Scour indicators Active width (m) 2.8 10.6 9.2 Active depth (m) 0.04 0.19 0.04 Tracers Active width (m) 2.6 3.1 2.7 Active depth (m) 0.06* 0.05 0.07 82 Table 7.1 (continued) Flooding periodst A B C D E F Subreach 3 Stream power (W nr 2) 147.9 183.8 132.7 107.1 219.7 108.2 Number of tracers 50 180 161 25 50 51 Mean travel distance (m) 129.13 104.64 54.15 28.75 67.74 6.15 Mean virtual velocity [mfp] (m hr - 1) 8.3 7.2 2.9 3.3 4.2 0.6 Mean virtual velocity [top] (m hr 1) 8.3 3.7 0.8 2.3 2.6 0.4 Scour indicators Active width (m) 4.5 5.6 6.0 6.6 4.5 Active depth (m) 0.05 0.04 0.03 0.05 0.03 Tracers Active width (m) 3.4 4.8 4.6 3.7 4.2 4.4 Active depth (m) 0.06* 0.06 0.08 0.05 0.07 0.11 f Shown in temporal sequence; see table 3.1 for corresponding date + Peak discharge based on UBC gauging station * Based on tracer fill depth § includes tracers deployed prior to this study 3 Tracers incoming to subreach 4 Tracers incoming and within subreach 5 Tracers within and outgoing from subreach 83 positions of tracers beyond subreach boundaries were not available for subsequent floods. Thus for flooding periods C and F mean travel distances had to be based on tracers moving within and out of subreaches. These estimates are possible because recoveries limited to subreaches were always followed by recoveries of the full length of the study reach to provide the necessary post-flood tracer positions. Inclusion of tracers that moved within subreach boundaries incorporated the internal rearrangement of particles stored within subreaches, a component of transported sediment. Distances based on the first flood event after tracer deployment are, by necessity, based only on tracers moving into subreaches. Figure 7.1a illustrates the tendency for step length to increase with specific stream power. Specific stream power, defined as the product of fluid density, acceleration due to gravity, specific discharge, and channel slope, is preferred as the flow magnitude parameter because it subsumes differences in channel width and bed gradient between subreaches. Gradients of 1.2,1.2, and 0.6% describe subreaches 1, 2, and 3, respectively. Gradients were estimated between the upstream and downstream riffle crests in each subreach using thalweg sightings of the mapping survey. The largest peak discharge, which occurred in flooding period E, induced relatively large step lengths in subreaches 1 and 3,125.9 and 67.7 m, respectively. In subreach 2, the relatively small travel distance is the prominent outlier (figure 7.1a). The maximum travel distance achievable by individual tracers moving into this subreach constrains the mean value. The maximum distance between deployment area B and the downstream end of subreach 2 is 100 m. Although tracers deployed in area A will eventually enter subreach 2, the majority of tracers originated from deployment area B during this study. Hence, individual observations did not exceed 100 m during this flooding period. Similarly, in subreach 3, a maximum distance of 190 m defines the distance between deployment area A and the downstream boundary of the subreach. In subreach 1, travel distances of tracers scoured from the subreach can not exceed 128 m because this distance separates the downstream boundary of the subreach from the downstream limit to tracer recovery in the overall study reach. These operational constraints limit some of the mean travel distances to lower bound estimates (table 7.1). 84 1000 100 J 3 o > 3 10 0.1 100 a, (so c <u Oh CO 4—1 C/3 10 ~ A Subreac • Subreac • Subreac A h :h 1— :h 2 :h3 I i i i .4.4-i o *- • k #-~ --r-j— i „_Jft_D j A " ] j D ! i j ; -! -• -1 • | ! j i ! i j i i U i j i ! j 10 100 Stream power (W m"'6) -2s 1000 ! ... L I i ; j f 1 1 f _„ j. r ^ i i j 1 i I \— h 1 i — 'T -*-T 1 t 1 i • i • i j i i i H i ~ j i j j ""•"1 —j---. ..j. j-i 1 4.L _ + ! | ; f H (-i u LJJ 1 i 1 j 1 i j j — t C i ! i j i i. 1 i j ...j... i ! T 4 j 1 --r - o— T l A ; i : i r( m ! i i i * • m ! 1 i i | • i " T ! i i • 1 JjJ 10 100 Stream power (W m" ) 1000 10 100 - 2 s 1000 Stream power (W m" ) Figure 7.1. Relation of step length and virtual velocity to stream power: a) mean step length, b) mean virtual velocity based on maximum peak, and c) mean virtual velocity based on total competent flow. Open symbol indicates first flood after tracer deployment; open symbol with vertical slash indicates mixture of first flood after generation 2 deployment and other resident tracers. 85 The maximum travel distance recorded, 129.1 m in subreach 3, represents the initial flood after tracer deployment, when elevated travel distances are expected from the unconstrained surface position of all tracers. In subreach 2, the slightly elevated mean at oo = 180 W nr 2 (flooding period D) (figure 7.1a) is also associated with the initial flood after deployment, but of generation 2 tracers released from the lower deployment area. The positively biased effect of unconstrained surface tracers is modulated, however, by the proximity of the study reach to the deployment area discussed above. The deployment of generation 2 tracers did not significantly affect mean travel distances in subreaches 1 and 3. In the former, step length observations do not include any generation 2 tracers, and in the latter only 13% of the observations are based on generation 2 tracers. The shortest step length, 6.1 m, appears to be biased downward by the particular subpopulation of tracers comprising the estimate. Only 2% of tracers that moved out of subreach 3 are incorporated, the remaining observations being derived from internal rearrangement of tracers within this subreach. This percent of tracers exchanged outside the subreach boundaries is the lowest of the mean estimates. During the same flooding period, subreaches 1 and 2 experienced tracer exchange at a rate of 12 and 33%, respectively. Estimates of travel distance based on incoming versus outgoing tracers may convolute the relation between step length and stream power because both estimates were used because of field procedures. For example, tracers transported into a subreach from upstream could represent more deeply buried particles, and hence, travel distances would be relatively reduced compared to distances from tracers exiting the subreach from shallow burial positions. During flooding period D, marked particles traveling into and within subreach 3 moved a mean distance of 28.0 m, while tracers moving within and out of the subreach traveled a mean distance of 28.7 m. The distribution of burial depths for these two groups of tracers prior to the flooding period are similar. This direct comparison suggests that using the two different estimates of mean travel distance should have little effect given approximate similarity in the vertical distribution of tracers for both estimates. Nonetheless, some bias in travel distances may be introduced through those tracers not included in estimates as previously mentioned. 86 Virtual Velocity Mean virtual velocity varies from a minimum rate of 0.4 m h r - 1 to a maximum rate of 8.3 m h r T h e two sets of velocity estimates (table 7.1) reflect different period definitions of the flow responsible for transporting coarse sediment. The maximum peak definition assumes that the flood event with the largest peak discharge in a flooding period mobilizes the majority of sediment. Total competent time is defined by the total period during a flooding period when flow is theoretically competent to transport coarse sediment. In the figure 7.2, the maximum peak definition considers only peak 1, while the total competent time definition includes both flood peaks. Both definitions consider only live-bed conditions by delineating a baseline flow level that induces general sediment movement (figure 7.2). A10 m 3 s"1 discharge was used as an approximation for this flow level, which corresponds generally to low transport activity as documented by mean scour depths of about 2 cm in the study reach (figure 5.1a) and bedload transport rates of about 1 kg nr 1 hr _ 1 near gauging station B (Tassone, 1987). The 10 m 3 s_ 1 discharge translates to about 8 m 3 s_ 1 at the UBC gauging site (Appendix 1). This reach-based discharge is theoretically capable of transporting bed material up to 33 mm when determined for reach averaged cross-sectional dimensions, study reach gradient, and a critical Shields parameter of 0.06. Asymmetry between the initiation and cessation of sediment transport in a gravel-bed channel documented by Reid and Frostick (1984) was not investigated in Carnation Creek. This phenomenon was assumed negligible in the estimation of virtual velocity. The relation between velocity and stream power generally reflects travel distances (figure 7.1b, c) with velocities based on the maximum flood peak hydrograph exceeding those derived from total period of competent flow conditions as expected (table 7.1). The highest velocity, 8.3 m hr - 1, reflects the elevated mean travel distance of unconstrained surface tracers in subreach 3. The next largest velocity of 7.8 m hr 1 , which occurred in subreach 1, resulted from a large mean step length associated with the flooding period containing the maximum flood peak of the field program of 48.8 m 3s _ 1. The outlier pattern reflects, in general, such trends in mean step lengths. The additional low estimate of 0.8 m hr 1 for total competent flow (figure 7.1c) is associated with 87 Figure 7.2. Schematic illustrating two definitions of duration of sediment movement within a flooding period. The maximum peak definition includes only ti while the total competent flow definition includes ti and t"2. 88 the flooding period with the longest duration of live-bed conditions, 67.5 hr, which significantly lowers the virtual velocity. Width of the Active Laver Mean active width based on scour indicators ranges from 2.8 to 16.1 m for the three subreaches (table 7.1). Definition of the active width invoked the assumption that when scour activity was measured by an indicator it continued midway toward an adjacent inactive indicator or to the bank edge. Most scour indicators are spaced 2 m from channel banks and adjacent indicators. Active width increases with stream power (figure 7.3a). In subreach 3, the mean width associated with a stream power of 184 W nr 2 (flooding period B) falls slightly below the expected trend because scour was not recorded at any of the scour indicators in a single cross section. The more pronounced outlier, representing subreach 2, can not be explained. Overall, the trends between subreaches progress in the descending order of subreach. The average width between channel banks equals 9.0,11.2, and 19.8 m in subreaches 3,2, and 1, respectively. The trend in active width follows the trend in average channel width. Mean active widths exhibit a smaller range, 2.6 to 7.4 m, when defined by tracer position (table 7.1). Averaging 10 measurements of width derived from channel maps displaying tracer positions produced mean values. Overall, confidence in active width delineation increased with the number of tracers discovered within a subreach. Figure 7.3b illustrates active width based on tracers in reference to stream power. The most notable disparity between estimates occurred in subreach 1, where a flood peak of about 18 m3s*l produced an active width of 4.3 m in flooding period D and 7.0 m in flooding period F. In general, active widths in subreach 1 are based on the least numbers of tracers, which reduces the level of confidence in width estimation. If the 4.3 m active width of subreach 1 is considered an underestimate, the widths in the individual subreaches roughly parallel each other. A steeper reach gradient, combined with a more pronounced elevational difference between the low flow channel and adjacent bar, may produce more laterally concentrated movement of tracers in subreach 2 compared to the other two subreaches. 89 100 CU > o 10 — •! ! 1 ! J 1 A SiiVw.nr.Vi 1 ! - .4... —- • Subreach 2 • Subreach 3 ...... . . . . . • . A • • • • • • . . . . . 100 <a > o 10 1 B 1-i J i A A *• • • • • • • 10 100 Stream power (W m ) 1000 Figure 7.3. Relation between active width and stream power: a) scour indicators and b) tracers. 90 The Wilcoxon signed rank statistic indicates that the two measurement techniques yield different active widths at the 0.05 significance level. Mean active width based on scour indicators exceeds, in general, the active width derived from tracers (table 7.1 and figure 7.4). This is true in all subreaches. Although the assumption regarding termination of scour activity may upwardly bias widths based on scour indicators, major differences between techniques are associated with large magnitude floods, when the additional width potentially incorporated by the assumption can not account for the approximate doubling of width estimates between techniques. Depth of the Active Laver A direct proportional relation between mean scour depth and flood peak discharge using scour indicator data was presented in Chapter 5 (figure 5.1a). The positive correlation with flow strength prevails in depth estimates based on scour indicators located within the active width of the channel with definition of outer boundaries of inactivity where appropriate (figure 7.5a). Flooding period E, which included the largest flood peak of the field program, induced a mean scour depth of 0.17 and 0.19 m in subreaches 1 and 2, respectively, but a depth of only 0.05 m in subreach 3. The relatively large depth of 0.11 m that occurred in subreach 1 during flooding period F probably reflects concentrated scour in the low flow channel as a further adjustment to bed elevation associated with a shift of the flow channel to the right bank. Active depths determined from tracers form a less consistent pattern with maximum flood peak than those from scour indicators (figure 7.5b). The active depth for a particular flooding period is based on tracers that were scoured from known burial depths during the flooding period. In subreach 3, mean depths for flooding periods C and F are larger than for flooding periods B and E, respectively, even though the relative flood peaks are less (table 7.1). Subreach 2 displays a similar trend between flooding periods E and F. These reversals in the expected trend appear to reflect the sequence of flood peak magnitude. The reported active depths were defined by tracers scoured during given floods, the depth values being derived from the burial depths of tracers resident in the subreach prior to the flooding period of interest. Given the direct proportional relation between flood peak and mean scour depth, peak magnitude controls tracer burial depths in a channel with a relatively stable bed elevation and dictates the maximum scour depths that can be 91 2 4 6 8 10 12 14 16 18 Active width (m) from scour indicators Figure 7.4. Active width by measurement technique. 92 Cu CJ 4j ..! ! ! ! ! J A Subreach 1 • Subreach 2 • Subreach 3 0.1 0.01 :A=P B O H <U 73 O > 0.1 0.01 10 100 Stream power (W m ^ ) 1000 Figure 7.5. Relation between active depth and stream power: a) scour indicators and b) tracers. Open symbol indicates first flood after tracer deployment; open symbol with vertical slash indicates mixture of first flood after generation 2 deployment and other resident tracers. 93 actually recorded by the presence of tracers for the next flood in sequence. In the recovery series, the relatively small flood that preceded a large flood peak, as in the case when the active depth trend reverses in subreaches 2 and 3, defined the lower limit to depth measurement through the tracers found within the subreaches. If tracers have been subjected to a sufficient number of large magnitude floods, a proportion of tracers would be found deeply buried within channel sediment. These buried tracers could then define the upper bound of active depths for relatively small peak discharges. However, this is not the case for generation 1 and 2 tracers, and hence the existent limitation to measurement. That this limitation can lessen with time, as tracers are subjected to a wider range of flows within a hydrologic regime, is illustrated in subreach 1. Flooding period D, with a relatively small flood peak, resulted in the largest active depth in this subreach (table 7.1). Mean active depth is based primarily on burial depths derived from generation 0 tracers, which have resided longer in the channel and have been dispersed by a greater number of larger magnitude flows. In some cases, these tracers represent particles temporarily marooned through shifts in the location of the active layer between stable channel banks. Active depth defined by tracers may be biased toward a lower bound estimate because tracers buried deeper than the detection capability will not be included. This bias should not significantly alter means calculated from large samples, however, because relatively few tracers are deeply buried (Hassan et al., 1994). In the first flooding period after deployment, when some tracers were not distributed in subreaches, burial depths of incoming tracers were assumed to be representative of the active depth. These depths, however, actually characterize scour in the channel upstream of subreaches. Overall, considering active depth as an average of both scour and fill in a reach (Laronne et al. 1992) might circumvent some of the above issues. Mean depths from scour indicators exhibit smaller depths, in general, than depths derived from tracers that moved (table 7.1). Mean depths based on tracers represent a more extensive spatial sampling of scour depths, particularly because of the large number of deployed tracers. The movement of tracers is concentrated within a relative narrow width of the channel, as shown by differences in active widths between techniques. The concentration of tracer movement appears to 94 produce the relative larger mean values because tracers move within the main zone of bed activity. About half of the depth estimates are relatively similar between technique but the remaining estimates show wide divergence (figure 7.6). Although the Wilcoxon signed rank statistic indicates that mean depths are not different at the 0.05 significance level the failure to reject the null hypothesis is fairly marginal (p = 0.098). The statistical testing is further convoluted by the biased depths from tracers. Porosity of Bed Sediment Porosity is a poorly defined parameter in sediment flux calculations. Komura (1961) developed a relation between porosity and particle size for well-sorted, recently deposited river sediments, which is given by P = 0.245 + 0.0864 D5Q0-21 where P = porosity and D50 = median diameter size in mm. Carling and Reader (1982) characterized the porosity of very poorly sorted, consolidated channel sediments by P = -0.0333 + 0.466 D5Q0-21 Estimation of the porosity of Carnation Creek sediment from the relations gives values of 0.29 and 0.21, respectively, a difference of about 28%. The estimate derived from the latter relation is probably more representative of Carnation Creek sediment because it is very poorly sorted, and therefore, a porosity of 0.21 was used throughout calculations. A porosity of 0.29 would lead to lower estimates of volumetric bed material transport. TRANSPORT RATES AND T O T A L VOLUMES Transport rates range from 0.45 to 16.9 m 3 hr -1 for the maximum flood peak when the active layer is defined by scour indicators (table 7.2). The largest transport rate of 16.9 m 3 hr _ 1 occurred in subreach 1 during flooding period E. Although the rate for the same flooding period in subreach 2 is the second largest at 4.3 m 3 hr - 1, it is most likely an underestimate due to the bias associated with the maximum distance between the subreach and tracer deployment area discussed in the Step Length section. The lowest rate associated with subreach 3 results from a virtual velocity that is an order of magnitude less than the virtual velocity measured in subreaches 1 and 2 95 Figure 7.6. Active depth by measurement technique. 96 0\ co vd co r-" Ov ON VO t-; T f o o CN in m CN CO CN T T r H oi r H CN r H d d d © +i •H •H •H +i •H +1 +1 o in in o CO ON CN l> © vq r H ON CN CO ON VO r H CN TJ- in CN CO CN* «n co oi r H l> CN r H © oi r H © © wo CN ON CN CO ON r H CN T f ON ON in in o CO o in CO r H r H © © © d •H +1 +1 +1 +1 +1 +l +i CS ON CN VO 00 ON 00 ON CN 00 VO co co CN t » 00 r H in CO CN CN 00 vq VO r H © r H CO r -CN VO T f d r H r H TT CN d o © © in CN ON VO © CO O vq CO CN VO r H ON o VO © © © CN r H © © © © •H •H •H +1 +1 +1 +1 +1 CN r H ON 00 00 oo CN © CO r H ON m CN CO r -ON ON VO oo 00 © r H © ON CO CN 00 CN © d CO d d vo ON r H CN PQ © co in CN TJ O •c ii PH oo a -3 o o m oo co s , BP CO -s M CO <u> C M 1 CO T3 C col JS co co B B ^ C X CJ ^ r H OH B 2 Q » | » g Is2 £ 52 8 5 LH ja -C CO CO g OH CJ C ^ r H OH B 2 Q v 1 ° I 97 CN 3 co Ui O 4 H CO o •3 n 3 col J H CO CO B B & ^ g CJ 4-» I M i 8 a I s £ 2, 8 • CO E-H L -a J H CO OH CJ CO Is £ C N ± 0.017 T"H © •H ± 0.017 r H d o d ON >o +1 +l «n co o o v© C N d d d d d CN CN VO r H d ON CN CN <n vO wo ON CN r H r H O d d d d •H •H +1 +1 ON 00 o NO o o © NO NO ON NO in d t> d d in H CN ON co ON i—I O O d d d d +i +i +i +1 m CN NO NO CN O TT CO ON CO o d d CO* d d 00 ON ON vo NO d d od r-- C N rS d CN CN CN ON 00 r-5 r H CN u m CN CO r H o r H o d d d d •H •H •H •H m 00 m co WO i—i ON 00 CN d d ON* d d o in ON co l > r H vo r-ON 00 CO r H CN i—i d d d d +i •H •H +i o CN r H CN VO uo VO 00 T-H d r H d <n oq CO CN CO CN d d r H CN CN CN CN CN T3 <U 1 G CN t> CD I co T3 O •d a, so a '-3 o o m co •5 co IH B cS O *6 001 s ^ 3 Q CU »2 o o o +i o +1 >n >n co co in © r H CN CO a u m d | e ^ 3 Q » .15 I > 00 CN ON -Si r H ON co g •* g » u u « ^ d, tu cn 1 I 6 1 8 o > co co S & a a 3, o 0 > > CU ^ % 8 a « & 1 s '9 1 98 for the same flooding period (table 7.2). The very small step length (figure 7.1a), and hence velocity, dominates the transport rate in subreach 3. Transport rates generally reflect the magnitude of stream power, although scatter is particularly evident at the lowest value of stream power. Rates derived using virtual velocities based on the maximum flood peak (figure 7.7a) show minor differences compared to those based on the duration of total competent flow (figure 7.7b) when the active layer is defined by scour indicators. Subreach 1 exhibits the largest transport rates but the largest errors are associated with this subreach (table 7.2). Relatively large standard errors in velocity and active width due to small samples sizes of tracers (n < 30) and cross sections defining the active width (n = 4) combine to produce this outcome. Error analysis followed general rules for the propagation of error when deriving a quantity from multiple measured quantities (Beers, 1957). Deviations in the three parameters of velocity, width, and depth were assumed independent, which seems justified given that different measurement techniques and procedures were used to derive observations for these three parameters (Chapter 3). Although all parameters exhibit a general correlation with discharge, the focus of error calculations is on individual estimates, when discharge is constant for all parameters. Transport rates based on tracers exhibit a narrower range, 0.24 to 6.8 m 3 hr _ 1 , when maximum flood peak estimates are considered. As might be expected from the discussion of parameters based on tracers, transport rates show less well defined trends within subreaches and collectively with stream power (figure 7.7c). Evident deviations can be traced back to individual parameter deviations by comparing figures 7.1,7.3, and 7.5 with 7.7. Rates derived using the duration of total competent flow display minor differences compared to maximum flood peak rates (figure 7.7d). Rates in subreach 1 again display the largest errors, being an order of magnitude larger than other subreaches. In this case, however, variation in all three parameters contribute to the error. Active depth is based on relatively few tracers in this subreach (table 7.1). The Wilcoxon signed rank statistic indicates that maximum flood peak transport rates based on the two measurement techniques do not differ at the 0.05 significance level. The most notable discrepancy arises in flooding period E in both subreaches 1 and 2 (figure 7.8a), where 99 100 10 CD •*-» CO (-1 ti o cu oo a CO 0.1 0.01 10 cn CD ts o O H OO U 0.1 I-I H 0.01 A Subreach 1 • Subreach 2 • Subreach 3 A3 111 i — ••1L~. s i 1 L I — — f TT ^— n r r r t .. ..j. 1" 1 J i l | i I ] | J I i -4-1 1 i | j — j ' i" '—t ' | j - !l i i ! j | j | i l ' j \ f—- 1 — ! i ' p — 1 1 i | j 1 1 ; i j | 1 ui i I _.. i j ; j | T i • Ii !i i l j — j -!-!- — j — r ~ j " —i --H-i j '- 4--- Hj..„ | ii > | i | ii i j | i i i i i i 1—1 i i i 1. 11 i j i i i i LJ .j. . J rr-i a - n r r TT —L.„ - 7 D T l -r "T L | 'I j 4 — -J. 4 . y »_ ... n 11 — i — • i i j — \ i j 1 ! i t 10 100 2 Stream power (W m ) 1000 10 100 1000 Stream power (W m ) Figure 7.7. Relation between transport rate and stream power: a) scour indicators and maximum peak, b) scour indicators and total competent flow, c) tracers and maximum peak, and d) tracers and total competent flow. Open symbol indicates first flood after tracer deployment; open symbol with vertical slash indicates mixture of first flood after generation 2 deployment and other mixed tracers. 100 Figure 7.8. Transport rates by measurement technique: a) maximum peak and b) total competent flow. Open symbols indicate first flood after tracer deployment. 101 differences equal 10.1 and 4.0 m 3 hr _ 1 . In most other flooding periods the two methods yield comparable rates. The relation between measurement techniques for total competent rates is more compact (figure 7.8b). The Wilcoxon signed rank statistic returned the same decision as in the case of the maximum flood peak rates. Total volumes of bed material transported during flooding periods range from about 0.6 to 274 m 3 (table 7.2). Deviations in volumes arise directly from deviations in rates (figure 7.7). Combining results for all three subreaches, the total volume tends to increase with stream power as expected (figure 7.9). Subreach 1 exhibits larger volumes compared to the other subreaches, which correspond to the prominent outliers in figure 7.9. The subreach underwent net scour during these two flooding periods, which explains the large sediment transfers. A similar situation exists for subreach 2 at a stream power of 370 W nr 2 . Subreach 3 maintained a relatively constant bed elevation with a slight tendency for net fill, which corresponds with lower volumes of bed material transport in this subreach. Transport Through the Study Reach A larger spatial context for subreach estimates was derived for flooding periods A and D. Using all available tracers, the volume transported during flooding period A equals 20.0 m 3 , which is very similar to the estimated volume from subreach 3 (table 7.2). Given that subreach 3 is located toward the end of the study reach searched for tracers, similarity in volumetric results is not surprising. In flooding period D, the volume estimated for the study reach is 8.6 m 3 , which is larger than individual estimates for subreaches 2 and 3 but not subreach 1 (table 7.2). When the subreach volumes are averaged to subsume local variability, the mean volume of 13.0 m 3 approaches the volume derived from data characterizing the complete study reach (table 7.2). Volumes from Bedload Rating Curves Total volumes of transported bed material derived by extrapolation from rating curves (Appendix 1) that characterize bedload transport near gauging station B (Tassone, 1987) permit a gross but independent check on estimates based on the virtual velocity method in the study reach. Volumes derived from rating curves generally exceed subreach estimates, although in some flooding periods estimates are comparable (table 7.2). For example, flooding periods B and E 102 1000 F 100 s I 1 0 > 13 E2 o.i J .i.-i.i-.i i in A Subreach 1 • Subreach 2 • Subreach 3 •p-A r q 10 100 Stream power (W m 4-n 7 —i~ i I III 1 | j i i i i i i fc . i ] j i -T-i ; i i ] i 1 i * • o j— i • • i • ! i i i W i • i ! i ! —f_ i ! h ! 1 i ! i i | u j 1 i ] I_LL ! j -2s 1000 10 100 Stream power (W m ) 1000 Figure 7.9. Relation between total volume and stream power: a) scour indicators and b) tracers. Open symbol indicates first flood after tracer deployment; open symbol with vertical slash indicates mixture of first flood after generation 2 deployment and other resident tracers. 103 show volumetric departures of an order of magnitude for subreaches 2 and 3 but estimates within the range of subreach 1. These comparisons involve displacing in time and space the basis of the rating curve. Further, in considering the accuracy of volumes derived from rating curves, it is worth noting that rates were strictly applied from relations that are based on data displaying substantial variability. DISCUSSION The estimation of volumetric bed material transport based on virtual velocity and the active cross section is a technique that has recently been applied in gravel-bed rivers. Results presented herein comprise one of the few investigations in which virtual velocity and active cross section were measured directly in the field. Hassan and Church (1992) reported a transport rate of 10 m 3 hr _ 1 in the Nahal Hebron for a 49.8 m 3 s_ 1 flood peak and 2 m 3 h r 1 in the Nahal Og for a flood peak of 5.7 m 3 s_1. From information provided by Laronne et al. (1992) the transport rate in the Never Never River was approximated as 2 m 3 h r 1 at a discharge peak of 150 m 3 s"1. Similar transport rates were derived for most flooding periods in Carnation Creek. Total volume of sediment transported over these flood events equaled 112 m 3 in the Nahal Hebron, 49 m 3 in the Nahal Og, 641 m 3 in the Never Never River, and 120 m 3 for the largest peak flooding period in Carnation Creek, averaging subreach volumes defined by scour indicators. In these flooding events the mean active depth for the four rivers averages 0.15 ± 0.01 m. The different volumes arise from variation in the active width or flood duration at the particular flood peak magnitudes. In the Never Never River, the active width is 2 times wider and flood duration extends approximately 5 times longer than in Nahal Og and Carnation Creek. The Never Never River and Carnation Creek have similar peak specific discharges (q = 3.5 m 2 s_1) but in the Nahal Og it is only 0.63 m 2 s_1. The specific discharge equals 12.5 m 2 s - 1 in Nahal Hebron, which exhibits the coarsest surface sediment of the four rivers with a median diameter of 70 mm. Median diameters range between 25 and 37 mm in the other three rivers. Further evaluation requires additional site specific information regarding hydrologic regimes. A more extensive examination of active width in Carnation Creek is afforded by considering all scour indicator recoveries (figure 7.10). Active width increases in proportion to 104 F M-M-- r - i — — ^  TP FF3 |__J TT T i p r ^ iJ i j 1 j 1 I i ! i T i j k i i i 1 ! i 1 j i BIN i i I i i 1 1 I ! i B i i t i ^ ° f "T 1 i i • j : i 1 r J f ~\~-! -4- ._ — CA , £ . ; • j | •-- —j— i , i . J —• — -— — — j i JU i | LL <u 00 Ul CO -5 on T J o o co cx, CO 2 T J •S CA CO 3 C T 1 CA T J CD </} CA 8 u C O -S CO -§ CA / C J N T J 44+J-+-4-J 1 ! T I t"H j J 1 I : i ; ; i a ™i ! ! ] rh\ i : i ! 1 1 1 i * \ 4^  ! i i i 1 l I ; i i i i i i i | i i i t t t J L . ... ] u i . —t-— -i-4—i ,—4- 1 tr" t 4_T~ — 1 — i i J 1 -U i i j r 1 \ Ij... \ + j i "r" CO | ! C j | 1" ! 1 J ! i ! i i i 1 j ^ j ...p.. •1 j • • 1 1 1 1 1 1 j I ii j i i i i i ! i _ L _ l 1 1 j IL. .J_J ) t i i u_i l_J 1 1 II 1 1 1 1 I in P Fl p p i p-1 j ._ 1— 4 1 r T~ i _ j _ r ! m \ — i i j i j i i i — 4 - £ CO t J •• 1 — 3-| 1 I j - p...x c . . . • i • i i t i r _ j_ i ! Ji j i I i i i (va) m p i M 9Aipv CM cu SP C O •8 CA T J CJ C M •5 CD a, CO CN B, CU SP CO •8 C A • t-l T J CJ •s u OH C/3 CS -8 CO -§ CA CO < CU C T J •2 ° 3 -r< CA 53 * 60 ai .S 00 TJ o ta .00 b, T J «S T J C CO T J C J o CO a CJ <D 2 CO T J _ U . C O cO O 8 C A PH Tj . -c O cj r H OH t-^  60 cu .5. 3 "2 C J . O 105 discharge magnitude in each subreach and a power function appears to describe the general trend as reported previously by Hollingshead (1971). The variability of width exhibited in the lower discharge range reflects, in part, localized sediment movement, which is documented by variable patterns of scour indicator activity. In a given flooding period, scour activity may not occur at a single indicator in some of the cross sections in a subreach. As flow increases, however, sediment originates from a greater area of the bed, although how far the activity radiates from active indicators is not strictly known. The assumption used in determining active width could bias estimates for these lower magnitude flows to a greater degree and a refined criterion of the active width definition could possibly eliminate some, but probably not all, of the evident variability. The maximum channel width does not become fully engaged even during the highest discharge peak but rather the majority of sediment movement is concentrated in 81, 95, and 73% of the channel width for subreaches 1 through 3, respectively, based on width estimates from scour indicators. Smaller flow levels activate about 50% of the potential channel width. Moreover, for the flooding periods that included the five largest flood peaks, scour indicators record bed activity over a greater proportion of the channel width than tracers, which suggests that transport of the coarser portion of the bed material occurs in a relatively concentrated zone of the channel. The probability of tracers moving toward the margins of the transport zone is reduced because of lower shear stresses in these relatively straight channel reaches. Estimates of virtual velocity for subreaches are influenced by several factors that control tracer step length. The physical distance between tracer deployment area and the subreach of interest and the longitudinal extent of searching procedures dictate the possible range of distances incorporated into mean values. Careful consideration of the field sampling strategy, however, can minimize any major effect. The longitudinal distance from deployment area also controls the size distribution of tracers recovered within and adjacent to a subreach and how quickly it evolves over time. Smaller sizes flush through the channel more rapidly and, over time, mean travel distances are gradually dominated by the movement of larger, slower particles. This is particularly true when the subreach is relatively close to the deployment area, such as subreach 2 (figure 7.11b). The fining trend in 106 Size fraction (mm) Figure 7.11. Evolution of tracer size distributions over time: a) subreach 1, b) subreach 2, and c) subreach 3. Flooding periods indicated by letters. 107 the size distributions for subreach 1 reflects the introduction of new tracers, from generations 1 and 2, into this reach of the channel. The initial size distribution is based primarily on generation 0 tracers. Size fluctuations in subreach 3 illustrate how the release of new tracers modulates size distributions. New deployment, however, reintroduces the bias associated with unconstrained surface stones. A simple, though laborious alternative, would be to deploy tracers by burying them at known depths. In Carnation Creek, the tracers that replaced similar sized stones in natural positions actually traveled farther than those simply placed on the surface in the first flood event. The respective mean distances of 36.5 and 27.7 m are statistically different at the 0.05 significance level, according to the Kolmogorov-Smirnov statistic. A streambed with a more developed armour layer, however, may return a different result. The major issue is ensuring that the tracers used to estimate virtual velocity represent the general movement of particles in the streambed. The evaluation of mean active depth and width by two different techniques highlights the differences that can result from the method of field measurement. When the mean active cross section is considered, however, the Wilcoxon signed rank statistic indicates that the two techniques do not result in statistically different estimates at a significance level of 0.05 when subreaches are pooled. The two definitions of duration of sediment mobility yielded similar rate estimates except for flooding period C, which exhibits the largest deviation between the two definitions. Error analysis indicates that more precise transport estimates would have been achieved in Carnation Creek with an increased number of active width observations. For both techniques, the active width exhibits the largest standard error. The assessment of virtual velocity contributes significantly to the overall error in subreach 1 because of the small sample sizes. Field sampling strategies should be designed accordingly. Further improvement in rate estimates, in general, may derive from a more thorough evaluation of sediment porosity in river channels. The two available relations lead to a rate disparity of 28%, assuming that one is an appropriate characterization. The trends in parameters and rates have not been evaluated rigorously because of the limited number of observations. Estimates appear to be internally robust, however, because the level of response scales to stream power associated with the dominant flood peak magnitude, even given factors related to tracer deployment and flood magnitude sequence that induced most of the 108 apparent deviations. Comparison of volumes extrapolated from bedload transport rating curves returned some favorable results, considering the difficulties associated with the actual rating curve extrapolation. Overall results call for the continued pursuit of this approach to estimating bed material transport. 109 CHAPTER 8 CONCLUSIONS The first aim of this study was to develop a model that describes the variability of scour and fill depths over a channel reach. The negative exponential density function effectively models these depths in response to flood events and is robust over a range of discharges in Carnation Creek. The use of existing scour depth data from streams on the Queen Charlotte Islands demonstrates the applicability of this mathematical function at the time scale of a flooding period and flood season. An ability to model the distributions of scour and fill depths opens the possibility for prediction of the proportion of the channel bed that scours or fills to a particular depth. Such a model would serve a valuable role in the management of fish habitat. A successfully confirmed model could be used as a guide to disrupt a certain proportion of the bed to flush fine sediment without significant destruction of fish eggs buried in the substrate. Discharge peaks associated with exponential models can be derived from power functions because the parameter of the exponential density function is the inverse of mean depth. Conservative management practice would consider the variability exhibited in scour and fill depths in final prescriptions. The exponential models require empirical observations for calibration, but such a necessity is not atypical. For example, bedload transport equation performance can also be improved through the use of locally-based empirical data in parameter calibration. The exploratory development of a regional scour depth model, however, suggests that incorporation of additional information, such as particle size, may broaden potential predictive capabilities to situations where only physical characteristics of rivers that are relatively easy to measure are required for a first approximation. Power functions relating flood peak discharge to mean depths of scour and fill were developed in the second portion of this study. The entirety of this analysis is unmatched by previous work, although the expected positive correlation has been noted. The two mean relations indicate a general balance between the magnitude of scour and fill within flood events in Carnation Creek, which generally maintained its mean bed elevation over the field program. Within a 110 particular flooding period, however, the channel exhibited longitudinal variability in the net adjustment of bed elevation over the study reach. Documenting that the channel boundary fluctuates systematically in response to the magnitude of flood events is of importance in the determination of bed material transport, as shown in chapter 7. In sediment routing algorithms (e.g. Parker and Sutherland, 1990), information is also needed regarding the active layer thickness. This thickness is sometimes assumed a constant 2D84 of the active layer grain size (Hoey and Ferguson, 1994). Subsurface sediment in Carnation Creek exhibits a Ds4 of 88 mm. If subsurface sediment is taken as representative of the active layer grain size, the criterion is approached only for the flooding period with the largest peak discharge, when the channel scoured to a mean depth of 16 cm. For the flow magnitudes considered in this study, the 2D84 assumption is not valid. Furthermore, mean scour depth is not a constant quantity. An initial evaluation of the scour depth-discharge relations of a sand-bed river and of Carnation Creek suggests that a generalized relation could be developed for a wide range of river characteristics through scaling procedures that subsume differences in particle size and hydrologic regime. Such a relation would be useful, in general, for defining the thickness of the active layer in the modeling of sediment transfers. The general merit of the heuristic model for mean travel distance as a function of particle size proposed by Church and Hassan (1992) has been demonstrated in the third objective of this study. Although the characteristic variability of travel distance as a function of particle size is clearly evident in Carnation Creek, the relation between mean travel distance and grain size is consistent for individual flooding periods. The decrease in the mobility of grain sizes coarser than 2D50 of subsurface sediment documents the dominance of size-selective transport in Carnation Creek over the range of flows observed. Although the mean travel distances of the three smallest fractions were shown to be not statistically different, the remaining particle sizes within this general range are not equally mobile. Varying degrees of departure from equal mobility have been reported previously (Ashworth and Ferguson, 1989; Church et al., 1991; Komar, 1987; Wilcock, 1993; Wilcock and 111 Southard, 1989). Ashworth and Ferguson (1989), in examining several channel reaches within three different rivers, found the degree of size-selective transport reflected the magnitude of flood events. Smaller magnitude floods resulted in transport more markedly influenced by grain size. Size-selective transport dominates Carnation Creek transport patterns in two flood seasons, one of which included a flood peak with a 7 year return period. The largest size fraction was mobile during the relatively small floods for which tracers were recovered. This mobility implies that the armour layer was limited or nonexistent in the channel because there is no longer the necessity to segregate fines to equalize weights between size fractions during bedload transport events. The armour ratio of 1.6 in Carnation Creek is near the lower limit of the range of armour ratios typically reported for gravel-bed rivers (Andrews and Parker, 1987). Differential transport is still exhibited in Carnation Creek. In the examination of the proportion of tracers buried as a function of size, it was found that relatively small sizes reside mainly in the subsurface. Specifically these fractions range from 16 to 45 mm, which includes the median diameters of subsurface and surface sediment. Travel distances of these size fractions are therefore influenced by those particles that begin from buried positions. This result is in accordance with the idea of macroscopic hiding (Parker and Klingeman, 1982). The movement of these finer fractions depends upon the entrainment of relatively coarse particles at the surface, which then releases the finer particles as they are exposed to the flow. The overlying coarse surface layer has been shown to be disrupted in disjointed areas over the channel bed in Carnation Creek. The hiding mechanism of the coarse surface layer, however, does not completely counteract the relative mobility of grain sizes based on size. The vertical exchange of sediment must be accounted for in models of bedload transport. Volumetric transport rates determined in the fourth set of analyses incorporate the differences between individual particle size fractions. Conversion of volumetric rates to a mass-based quantity allows comparison of sediment exchange processes in Carnation Creek. Transport rates, as a weighted average of subreach estimates, range from 0.0077 to 0.25 kg nr 1 s*1, which is not atypical of other work reported (Andrews, 1983; Andrews and Erman, 1986; Ashworth and Ferguson, 1989; Parker et al., 1982). 112 Overall the computation of bed material transport rates using a parameterization of virtual velocity and the active channel cross section demonstrates that a scale correlation can be developed comparable with those derived from bedload sampling during flood events. In this study, the active width contributes most significantly to the imprecision of rate estimates within a given discharge, which should guide future field sampling programs pursuing this alternative approach to bed material transport. Variability is an inherent quality of scour, transport, and fill at the scale of the channel reach. Variability in scour and fill was found to increase with peak discharge in Carnation Creek. Inspection of maximum depths observed within events illustrates the more pronounced variability in scour compared to fill, which has been linked to pre-flood streambed conditions that are influenced by antecedent flood characteristics. Net change in bed elevation over the study reach suggests repeated adjustments of the active layer due to the variable redistribution of bed sediment. Given this variability, the investigation of bed material transport as a random phenomenon presents a promising avenue for fundamental insight. Progress in describing the kind of stochastic process has been made in the description of individual particle movement (Einstein, 1937; Hurley, 1992; Sirangelo and Versace, 1984; Todorovic and Zelenhasic, 1970). Although alternative models for scour and fill depth distributions were not evaluated, the overall success of the exponential model in describing these distributions supports the description of sediment transport in gravel-bed channels as a Poisson process. The generalizations formulated herein are based upon empirical observations gathered primarily from one small gravel-bed stream with certain hydrologic and channel characteristics. As illustrated by the travel distance-grain size model proposed by Church and Hassan (1992), however, data from rivers covering a wide range of environments can be described, in general, by one function. Likewise, differences in hydrologic regime and channel characteristics are not expected to significantly alter the general findings of this research. Differences that exist between rivers, as reflected in variable model coefficients, may reflect the present inability to quantify the modulating effect of surface sediment structure on sediment transport. When it is possible to do so, some of these differences may be eliminated from model development. Further, the general 113 relations reported herein would be expected to hold for a similar investigation in a river channel larger than Carnation Creek, although at present difficulties in data collection using scour indicators and magnetically-tagged stones would arise when baseflow depths are significantly deeper and spatially extensive over the streambed. 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Flood frequency curve for Carnation Creek. 124 F L O W DURATION Development of a flow duration curve for mean daily discharge is based on streamflow records from calendar years 1973 to 1989. 100 Q I I I I I I I I I I I I I • ' .01 .1 1 5 10 2030 50 70 80 90 95 99 99.9 99.99 Exceedence probability (%) Figure A1.2. Flow duration curve for Carnation Creek. 125 BEDLOAD TRANSPORT Rating curves for bedload transport measured near gauging station B from 1973 to 1984 were developed by Tassone (1987). 100 10 s 'a i SP O uO T3 T3 0.1 cd m o.oi 0.001 ' M l A ; I i i i • j i I • J • / • i ; •— • Jr • » • i ~ - i • ... i > y / ~* r1 p. • j —T* 1 j j j i L L i j i JJ. 10 c i T H ~ i I ! 1 [ r ' 1 1 ' h | j I , t — i j • • f j!j i ' i M ' T U - l - ! • /• i L L • 41... : 1 i ! | / | \\ i >•""/" f 0 ..... . . . . : j j j i i ! i i —r —^— '•• i f • i i ii < i li i | / f 1 * • I' < f i 1 i zzzz — t 'i — ( . . # [/ . . . I I i i r ! •••)• •4— T | I ! 1 ! / 1 i i : i i I j | • •! 1 B l l | | 1 j I . .4.-1. \ i 1 i 1 1 i t 1 J . 1, i # I 1 ! 1 X 1_ ! -• j 1 '"i"" j-! 1 i 1 I i i i ! I 1 i l i I ' I I ! J J 1 100 1 10 100 3 1 3-1 Instantaneous discharge (m s~ ) Instantaneous discharge (m s ) Figure A1.3. Bedload rating curves for Carnation Creek: a) rising stage and b) falling stage. Redrawn from Tassone (1987). 126 APPENDIX 2 DISCHARGE ESTIMATION AT THE UBC GAUGING SITE Continuous discharge at the UBC gauging site must be estimated by means other than typical gauging practice because of the limitation of the rating curve established for the site (figure A2.1). An order of magnitude extrapolation of the rating curve would be required to estimate the expected range of discharge values. Such estimates lack certainty. METHODS OF ESTIMATION Three different methods were used to estimate discharge at the UBC gauge. Ratio of subbasin areas, rating curve extension, and subarea contribution approaches involve use of continuous flow records from gauging stations B and C (figure 2.1), operated by the Water Survey of Canada. These methods rely upon the assumption of equal unit discharge in the drainage basin. Preliminary procedures included computing subbasin area and standardizing the UBC gauge stage height record. First, subbasin areas in Carnation Creek, required by two of the methods, were determined by digitizing subbasin boundaries delineated on a 1: 5,000 topographic map (Ministry of Forests, 1991) and calculating areas within the digitizing software. Second, least squares regression relating stage height readings between the upper and lower staff gauges permitted the UBC stage height record to be standardized to one staff gauge. The 48.8 m 3s _ 1 flood peak destroyed the upper staff gauge, located about 10 m downstream from the stage recorder, while the lower staff gauge, near the discharge measurement cross section in subreach 3, remained intact. Subsequent chart traces were referenced to the lower staff gauge during field procedures. Ratio of Subbasin Areas The ratio method employs a ratio between subbasin drainage areas as an adjustment factor for known hourly discharge. Discharge at the UBC site, Qu, is calculated by Qu " Qr ~i~ Ar where the hourly discharge and basin area draining the reference gauge are denoted by Qr and A r 127 Figure A2.1. Relation between stage height and discharge at the UBC gauge. Rating curve shown for illustrative purposes only. 128 and the basin area upstream of the UBC gauge is indexed by Au- Two estimates of discharge are possible referenced to the B and C gauging stations. Rating Curve Extension Stage height information at the UBC gauge and corresponding discharge values, derived by the above ratio method, permit extension of the rating curve. Stage height and discharge values were extracted from recessional limbs of hydrographs when a consistent runoff response in the basin could be reasonably assumed due to soil saturation. Periods characterized by multiple, closely spaced flood events satisfy this condition most readily. Rating curves referenced to the B and C gauging stations were visually fit through 61 and 57 points, respectively (Herschy, 1985) (figure A2.2). Subarea Contribution The method of subarea contribution computes discharge by subtracting the flow contribution from the portion of the basin located downstream of the UBC site from discharge measured at gauging station B. The basin area of tributary C and the lower section of the main channel comprise the two contributing areas. Discharge exiting tributary C is known independently by flow records at the C gauging station. Given that the area above the C tributary and the lower basin are essentially identical, a similar contribution of flow is assumed for the latter. Discharge at the UBC site is then expressed by Qu-Qb-iQc where Qb and Qc equal the hourly discharges at gauging sites B and C, respectively. RESULTS Comparison of discharge estimates focuses on high flow levels because of the emphasis in this research. Accordingly, estimates for the majority of flood peaks that occurred during the field program are presented in figure A2.3 referenced to gauge B discharge. Flood peaks derived from the subarea contribution method are systematically larger than the other four methods once flood peaks exceed 4 m 3 s_1. Peak discharges based on the B gauge surpass C gauge estimates. For a particular reference gauge discharge similarity between the ratio and rating curve extension 129 o o B • I I i I I I I I I—I—I—I—I—I—I—I—i—I— 0 5 10 15 20 25 30 3 -1 Discharge (m s ) Figure A2.2. Extended rating curves: a) gauge B and b) gauge C. Solid circles indicate actual discharge measurements. Rating curve for gauge B shown as dashed line in gauge C diagram for ease of comparison. 130 50 T T T CO 40 • Ratio: Gauge B Ratio: Gauge C ' Rating curve: Gauge B ' Rating curve: Gauge C Subarea contribution <D a ao U PQ P ? •8 M a <u PH 30 20 h 10 10 20 30 40 50 3 -U Peak discharge, B gauge (m s ) Figure A2.3. Peak discharge estimated from five methods. See text for description of methods. 131 is not surprising given that curve extension relies upon discharge computed from the ratio method. Flood peak estimates derived from the five methods are statistically different at the 0.95 confidence level as evaluated by the two-way Friedman analysis of variance statistic (n = 76, X 2 = 49.0; x 2* = 9.5). Departures from a normal distribution in arithmetic and log transformed data and expression of unequal variance invalidated use of the F test. Further, the Wilcoxon signed-rank test revealed that only the paired comparison of the ratio to curve extension method based on gauge C does not exhibit a significant difference at the 0.95 confidence level. Flood peak values at the UBC gauge are influenced by the estimation method and reference gauge used in computations. Given the differences between methods, selection of the most appropriate discharge values must rely upon evaluation of the underlying assumption of equal unit discharge. Mean annual precipitation increases by 755 mm from the basin outlet to the headwater area of tributary C (figure 2.1). Although a consistent runoff response may be expected with saturated soil, an unequal distribution of precipitation would lead to increased contribution per unit area toward the upper limits of the basin. The drainage area upstream of the UBC gauge is 5.8 km 2, which constitutes 59.7% of the total basin above gauge B and is located in the headwater area (figure 2.1). A larger discharge contribution per unit area would be expected in UBC gauge subbasin, given its location, and resulting flow patterns would likely dominate flow at gauge B, given its relative size. Discharge input from gauge C is relatively minor, reaching a maximum contribution of only 15% during the largest flood peak hydrograph. Hence, it seems reasonable that discharge estimates for the UBC gauge are based on gauge B records. The subarea contribution method allows some flexibility in unit discharge from different subbasins and is therefore selected for use. This method does not explicitly incorporate information derived directly from the UBC gauge but the similarity in hydrograph shape recorded at the B and UBC gauges implies little loss of information. Further, subarea method calculations are more expedient than the rating curve extension because of the nature of curve fitting procedures. 132 APPENDIX 3 DISTRIBUTIONS OF SCOUR AND F I L L DEPTHS AND EXPONENTIAL MODELS. CARNATION C R E E K AND STREAMS ON THE QUEEN C H A R L O T T E ISLANDS The following figures display frequency distributions and corresponding exponential models not shown in the main text. Figure A3.1 displays 20 diagrams illustrating scour and fill depth distributions in Carnation Creek arranged in ascending magnitude of flood peak. Parameter values and goodness-of-fit test results are found in table 4.1. Frequency distributions and exponential models for streams on the Queen Charlotte Islands are contained in figure A3.2 (flooding periods) and A3.3 (flood season). Table 4.2 includes parameter values and goodness-of-fit test results. 133 d d o d d d d o d o d o d d Xou9tib3.iT. a A i j B p y Xonanb9Ji aAireja^i 136 i fouanbai j . a A p B p ^ i M a ii a a o 5 6 co a o S a CO a o a co CO a _o 3 •8 § 3 cr 138 5 CU CO CN <—I O CO CN T H O d d d d o d o d 139 m CN rH o © © co co in T 3 140 APPENDIX 4 FIELD PROGRAM FOR STREAMS ON T H E QUEEN C H A R L O T T E ISLANDS Twelve gravel-bed streams were selected for investigation of scour depths in the early 1980s in a Fish/Forestry Interaction Program completed in the Queen Charlotte Islands, British Columbia (Poulin, 1984; Tripp and Poulin, 1986). Six of the streams are located on the west and southwest coasts of Graham Island and six are situated on the northeast coast of Moresby Island (figure A4.1). Basins range from 4 to 47 km 2 in size (table A4.1) and receive about 1,600 to 4,200 mm precipitation annually. A strong precipitation gradient, from west to east, is induced from increased onshore roughness and topographic relief, producing lifting convergence. Study reaches selected within each basin typically begin at the mouth and extend upstream for distances up to 880 m (table A4.1). The downstream boundary is displaced upstream from the basin mouth in Bonanza, Riley, and Tarundl Creeks but these distances do not exceed 6 km. The 10 to 23 m wide channels are characterized by pool-riffle bed morphology. Study reach gradients range from 0.7 to 4.0%. PROGRAM OF OBSERVATION The length of indicators and the depth to which they are vertically inserted into the channel bed determines the maximum depths of scour that can be measured. In the streams of Queen Charlotte Islands a maximum of 38 cm was achieved, in part due to the difficulty of driving indicators into the coarse sediment. Three scour indicators of the scour monitor type were positioned in the low flow channel along transects crossing the pool-riffle transition in channel bed morphology. Individual streams were instrumented with 18 to 30 indicators (table A4.1) and collectively the streams in the Queen Charlotte Islands contained 288 indicators. Recovery of scour indicators in the 12 streams of the Queen Charlotte Islands characterize cumulative scour depths for two time periods, late October to early December 1983 and late October 1983 to late February 1984. Scour depths associated with the December to February period were derived by subtracting the depths of the December recovery from the February 141 1 3 f W re A4.1. Location map of streams on the Queen Charlotte Islands. 142 0 1 3 55 V- Q 3 O o co O T J a a> -is T J CO CO oo Q CO + H T J H ca 3 CO CO 1 * _ a CO T J 0) CO 2 ^ .9 c a r ? a CO CO o o o o o o o c » o o o o o o o o r ~ T ^ r H > — I C O r H r O r H T — I f O C O C O C N o c » r H c » r ~ i n c N v o c N r ~ O f O U O r r r - V O V O V O t ^ T j - t ^ T t V O - ^ J -r O O N O r o O O O r o r ^ C N O O C N CN T—I CN r H CN T—I CN T—I T — I T — I T - I T — I O N O C ^ r H r H C N i r ^ C X J l / ^ r H r ^ O O r H d c o c o c N r H O c o c N ' r o ^ i -T - H t N O O O v o t ^ - O C N t ^ O r O T - H T - H O O O V O O - ^ - O C J N O V O t ^ c o c o - ^ - ^ o ^ o o o c N i / o c N w o c N - r j -t ^ O T - H V O C N ^ O N O O V O r ^ - ^ -CO CN CN CN rH * CA T J CO 6 a co 3 a CO CO U co CO CO CH co a o m u CA a CO CO K CU > o eo a CO CO CO a * _ co Q co CO I H S I 8 ^ I co 3^ D , >H O s s - * CO CO CO CO Ui CO CO co u .a u I H CO a. a £ JS . „ . „ CO o „ C H P C CO CO CO CO CO CO U a, a M 3 CO P CO I H U CO £> T J JS a 3 S O CO H oo o ON © o o ON M co U a B CO U 143 recovery. Detailed hydrological records for the study streams are not available but a stream gauging station in the general study area indicates that several floods occurred within each monitoring period. Surficial bed material was sampled along the 6 to 10 transects containing scour indicators in each stream and sediment size information from these transects was pooled for each stream to derive particle size distributions (0.50 size intervals). A minimum particle count of 150 was achieved in 83% of the streams. In only one stream the count was 5 observations less than the typical sample size of 100. 144 

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