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Temporal adjustments of a streambed following an episodic sediment supply regime von Flotow, Claudia 2013

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  Temporal Adjustments of a Streambed Following an Episodic Sediment Supply Regime  by Claudia von Flotow B.Sc., The University of British Columbia, 2011 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  Master of Science in THE FACULTY OF GRADUATE STUDIES (Geography) The University of British Columbia (Vancouver) August 2013 ? Claudia von Flotow, 2013  ii  Abstract The objective of this research is to evaluate temporal adjustments of a streambed surface due to changes in the sediment supply regime. To achieve the goals, laboratory experiments were conducted in an 18 m long, 1 m wide flume with a gradient of 0.0218. The bed was brought to an armored state by running water with no sediment feed before releasing a sequence of sediment pulses. Water discharge and grain size distribution of the sediment feed were held constant over the set of experimental runs, while supply input rates and magnitudes varied. Sediment flux at the outlet of the flume was continuously measured. At frequent time intervals, bed surface texture, 1 mm vertical resolution bed elevation, and microtopographical cluster features were measured over a two meter section of the flume bed. Instantaneous three-dimensional observations of flow velocities were made using an Acoustic Doppler Velocimeter. Surface texture adjustments in response to the sediment supply regime followed similar patterns between all runs involving pulses of sediment in that (1) the D16 ? the diameter at which 16% of the particles are smaller than ? was the most variable characteristic grain size value and (2) medium-gravel patch areas were least variable, likely due to higher relative mobility of fine material. Fine-gravel patch areas developed following sediment pulses and persisted over time even once the overall characterization of the bed had returned to an armored state. Increases in bed roughness, quantified by the standard deviation of bed elevations (?z), were consistently paralleled with increases in the number of identified clusters and their combined surface area. Cluster formation was seemingly random, but expansion occured only once surface texture became relatively coarse and bed roughness increased. These results inform about the degree of bed surface evolution complexity under conditions of variable sediment supply and can be linked to observations and predictions of sediment transport in field settings.    iii  Preface This thesis is based on experimental work completed in the fall of 2012 in the Mountain Channel Hydraulics Experimental Laboratory (MCHEL) at The University of British Columbia (UBC). None of the text is taken directly from previously published or collaborative articles. Figures 4.1 and 6.1 were used with permission from the applicable sources. The laboratory flume was designed by M.A. Hassan and built by Coanda Research and Development Corporation, with many hardware additions and modifications by M.A. Elgueta, T. M?ller, S. Chartrand, and me. Custom LabViewTM programs for bed topography data collection were written by A. Zimmermann and modified by M.A. Elgueta, T. M?ller, and me. The MATLAB function for computing grain size gradients was written by S. Chartrand. Analysis of the grain size gradient outputs is my original work. Semivariograms of bed elevation were computed in the open source statistical programming and graphics environment, R using a function written by E.J. Pebesma.    iv  Table of Contents Abstract ..................................................................................................................................... ii Preface...................................................................................................................................... iii Table of Contents ..................................................................................................................... iv List of Tables ........................................................................................................................... vi List of Figures ........................................................................................................................ viii Acknowledgements .................................................................................................................. xi Introduction ............................................................................................................................... 1 1.1.1 Flow Relations to Bed Sediment .............................................................................. 2 1.1.2 Spatial and Temporal Variability of Bedload Transport .......................................... 5 1.1.3 Sediment Transport in the Context of the Watershed............................................... 7 1.2 Research Objectives ................................................................................................... 9 Experimental Design ............................................................................................................... 10 2.1 Flume Design ........................................................................................................... 10 2.2 Experimental Procedure ........................................................................................... 13 Sediment Transport ................................................................................................................. 18 Surface Texture Representations ............................................................................................ 21 4.1 Bed Surface Texture Classifications ........................................................................ 21 4.2 Methods .................................................................................................................... 25 4.2.1 Data Acquisition ............................................................................................... 25 4.2.2 Surface Grain Size and Sorting ......................................................................... 26 4.2.3 Patch Delineation .............................................................................................. 28 4.3 Results ...................................................................................................................... 31 4.3.1 Surface Grain Size and Sorting ......................................................................... 31 4.3.2 Patch Delineation .............................................................................................. 52 Bed Topography...................................................................................................................... 60 5.1 Roughness Characterization and Spatial Statistics................................................... 60 5.2 Methods .................................................................................................................... 62 5.2.1 Data Acquisition ............................................................................................... 62 5.2.2 Data Preprocessing............................................................................................ 62   v  5.2.3 Statistical Roughness Analysis ......................................................................... 63 5.2.4 Sediment Storage .............................................................................................. 65 5.3 Results ...................................................................................................................... 65 5.3.1 Bed Roughness.................................................................................................. 65 5.3.2 Structure Functions of Bed Elevation ............................................................... 73 5.3.3 Temporal Evolution of Sediment Storage......................................................... 80 Microtopography..................................................................................................................... 85 6.1 The Influence of Microtopography on Sediment Transport..................................... 86 6.2 Descriptions of Clusters ........................................................................................... 87 6.3 Methods .................................................................................................................... 89 6.3.1 Cluster Identification ........................................................................................ 89 6.4 Results ...................................................................................................................... 92 6.4.1 Observations of Cluster Dynamics ................................................................... 92 6.4.2 Cluster Formation, Disintegration, and Expansion ........................................... 96 Discussion ............................................................................................................................. 109 7.1 Overall Bed Surface Evolution ........................................................................... 109 7.2 Limitations ............................................................................................................. 119 7.2.1 Surface Texture Derivation ............................................................................. 119 7.2.2 Patch Identification ......................................................................................... 121 7.2.3 Bed Topography.............................................................................................. 124 7.2.4 Structure Functions of Bed Elevation ............................................................. 124 7.2.5 Cluster Identification ...................................................................................... 126 Conclusions and Future Work .............................................................................................. 131 References ............................................................................................................................. 135      vi  List of Tables Table 2.1 Grain size fractions ................................................................................................. 12 Table 2.2 Initial experimental parameters............................................................................... 12 Table 2.3 Summary of the experiment .................................................................................... 16  Table 4.1 Surface measurements ............................................................................................ 26 Table 4.2 Queried patch types................................................................................................. 29 Table 4.3 Overall changes to grain size statistics ................................................................... 37 Table 4.4 Variability of grain size statistics ............................................................................ 39 Table 4.5 Summary values of surface texture for all runs ...................................................... 45 Table 4.6 Surface texture values for hours 10, 20, 30, and 40 for runs 2, 4, and 6 ................ 47 Table 4.7 Surface texture values for hours 10, 20, 30, and 40 for runs 1, 3, and 7 ................ 49 Table 4.8 Surface texture values for hours 1, 2, 4, and 7 for runs 1, 3, and 7 ........................ 51  Table 5.1 Statistical properties of PDFs for all runs ............................................................... 69 Table 5.2 Statistical properties of PDFs for hours 10, 20, 30, and 40 for runs 2, 4, and 6 ..... 70 Table 5.3 Statistical properties of PDFs for hours 10, 20, 30, and 40 for runs 1, 3, and 7 ..... 72 Table 5.4 Statistical properties of PDFs for hours 1, 2, 4, and 7 for runs 1, 3, and 7 ............. 72 Table 5.5 Storage differences within each run ........................................................................ 82 Table 5.6 Storage differences for runs 3, 4, and 5 .................................................................. 83  Table 6.1 Number and area of clusters ................................................................................. 106  Table 7.1 Summary of bed adjustments ................................................................................ 110   vii  Table 7.2 Fraction of each patch type relative to total patch area ........................................ 118     viii  List of Figures Figure 2.1 Working area of the flume ...................................................................................... 10 Figure 2.2 Cumulative GSD of the initial bed.......................................................................... 11 Figure 2.3 Light table at the outlet of the flume ....................................................................... 14 Figure 2.4 Summary of the experiment .................................................................................... 16 Figure 2.5 Side view of the flume ............................................................................................ 17  Figure 3.1 Light table output of sediment transport ................................................................. 19  Figure 4.1 Sample bed material map of coarse patches ........................................................... 23 Figure 4.2 Grid superimposed on bed photograph section ....................................................... 27 Figure 4.3 Cumulative GSD curves for hours 1 and 40 of all runs .......................................... 33 Figure 4.4 Cumulative GSD curves for sequential hours of all runs ....................................... 35 Figure 4.5 Evolution of GSD summary values ........................................................................ 38 Figure 4.6 Evolution of sorting parameter ............................................................................... 41 Figure 4.7 Evolution of fine surface material........................................................................... 43 Figure 4.8 Cumulative GSD curves for hours 10, 20, 30, and 40 for runs 2, 4, and 6 ............. 47 Figure 4.9 Cumulative GSD curves for hours 10, 20, 30, and 40 for runs 1, 3, and 7 ............. 49 Figure 4.10 Cumulative GSD curves for hours 10, 20, 30, and 40 for runs 1, 3, and 7 ............. 51 Figure 4.11 Grain size gradient variance and grain size values for run 3, hour 1 ...................... 53 Figure 4.12 Histogram of run 3, hour 1 grain size gradient variance values ............................. 54 Figure 4.13 Run 3, hour 1, P1 cells ............................................................................................ 55 Figure 4.14 Fraction of each patch type relative to total patch area .......................................... 57    ix  Figure 5.1 Run 2, hour 1 and run 4, hour 31 elevation plots .................................................... 67 Figure 5.2 Structure functions for each run .............................................................................. 74 Figure 5.3 Structure functions for hours 10, 20, 30, and 40 for runs 2, 4, and 6 ..................... 77 Figure 5.4 Structure functions for hours 10, 20, 30, and 40 for runs 1, 3, and 7 ..................... 78 Figure 5.5 Structure functions for hours 1, 2, 4, and 7 for runs 1, 3, and 7 ............................. 79 Figure 5.6 Evolution of cumulative and incremental changes in bed elevation ....................... 81 Figure 5.7 Evolution of mean, maximum, and minimum bed elevations ................................ 84  Figure 6.1 Cluster types............................................................................................................ 88 Figure 6.2 Potential anchor stones and cross-sections ............................................................. 90 Figure 6.3 Spatial boundaries of a cluster in run 3, hour 1 ...................................................... 91 Figure 6.4 A cluster and the cross-sectional profile through its anchor stone ......................... 93 Figure 6.5 Two clusters identified during successive observation windows ........................... 94 Figure 6.6 A cluster whose surface area diminished ................................................................ 95 Figure 6.7 Clusters whose surface areas grew ......................................................................... 96 Figure 6.8 Evolution of total number of clusters...................................................................... 98 Figure 6.9 Evolution of total number of expanded clusters ................................................... 102 Figure 6.10 Evolution of relative combined cluster surface area ............................................. 105  Figure 7.1 Evolution of percent change of total number of clusters and cluster area ............ 113 Figure 7.2 Two clusters identified during run 4, hour 10....................................................... 114 Figure 7.3 Examples of photographs and patch maps ............................................................ 116 Figure 7.4 Two cases of grain size recognition by color........................................................ 120 Figure 7.5 Medium gravel patches ......................................................................................... 122 Figure 7.6 Cluster identified on a bed photograph during run 3, hour 4 ................................ 127   x  Figure 7.7 Cross-section of the cluster identified in figure 7.6 .............................................. 127 Figure 7.8 Elevation of the cluster identified in figure 7.6 .................................................... 128 Figure 7.9 Streamwise elevation through the cluster identified in figure 7.6 ........................ 129     xi  Acknowledgements This thesis is the product of laboratory monkeying alongside wonderful people from many countries including Chile, Germany, Canada, Russia, the United States of America, Spain, and Palestine. My greatest debt of gratitude is to my tenacious comrades, Maria Alejandra Elgueta and Tobias M?ller, my supervisor and friend, Marwan Hassan, who has organized the last few years of my academic life, all the while insisting on my role as ?boss?, and my other supervisor and friend, Brett Eaton, who inspired the first few years of my academic life and made me feel capable and intelligent. Andr? Zimmermann spent untold hours revamping material that made this research possible. Lucy MacKenzie provided a shining example of the importance of taking breaks to eat lunch next to a water feature. Shawn Chartrand became a huge source of encouragement and revived my passion for the science at the most critical moments. I would also like to thank my family and loved ones. My dear father, Andy, reminded me that I do not know everything like I used to when I was 16 years old. I would like to thank my mother, Lucia, for being the best woman in the world and for feeding me and teaching me new dance moves. My parents bred into me curiosity and energy, from which, ventures such as this thesis result. I would like to thank my brother, Andreas, for his critical thinking assistances, which are annoyingly important, my brother, Fritz, for commenting on my research ideas with the indispensable honesty that only a sibling can muster, and my brother, Maurizio for visits to our windowless flume laboratory with pulled pork and snow reports. Finally, I owe a large portion of my strength and happiness to my loving adventure partner who whisked me away for extended periods, without my thesis. Thank you all.    1  Chapter 1 Introduction The entrainment, transport, and deposition of bedload largely determine channel morphology. Therefore, patterns of bedload transport and deposition are critical in maintaining habitat diversity (Lisle, 1989), understanding landscape evolution (Roering et al., 1999; Whipple and Tucker, 2002), predicting river reach adjustments for stable channel design (Griffiths, 1981), and quantifying bank erosion (Green et al., 1999). Though the importance of bedload transport has long been recognized, there remains limited understanding of the processes involved in entrainment and deposition. Discrepancies in bedload transport predictions are due to (1) the difficulty of characterizing flow and relating shear stress to grain size and channel geometry, (2) observations of bedload transport in the field that are bias due to spatial and temporal variability, and (3) the task of incorporating the history of the watershed into the formulae. Furthermore, transport formulas must account for the range of grain sizes available for transport and bed structures that dictate sediment mobility. This chapter addresses causes for discrepancies in sediment transport predictions with a focus on mountain channels. The research presented thereafter uses a physical model to examine the effects of varying frequency and magnitude of sediment supply on bed surface texture (Chapter 4), topography (Chapter 5), and microtopography (Chapter 6). At present, there is a paucity of research involving experimental sediment pulsing and its effect on bed surface evolution, structure development, and overall channel stability. This research contributes to the relatively few studies that have recorded the temporal evolution of a streambed in   2  response to an episodic sediment supply regime. The results can provide a basis for further identifying the effects of sediment pulsing on transport rates and associated morphologic changes over time. 1.1.1 Flow Relations to Bed Sediment Bedload transport is typically linked to the amount of geomorphic work done by a river (Wolman and Miller, 1960). The current theory for initiation of sediment transport follows the non-dimensional boundary shear stress, ?b*, exerted by the water flow:        (    )           (1.1) where ?g is the shear stress at the bed, D is the diameter of a particle, g is gravitational acceleration, r is the submerged specific density of sediment (r = (?s ? ?)/?), where ?s and ? are the densities of sediment and fluid, respectively), and u* is the shear velocity (u* = ??g/?) (Shields, 1936). The relation is simply a ratio of the bed stress of the flow on sediment to the weight of a grain; one would expect that larger grains require more force to move than smaller grains. Before sediment entrainment can occur, the shear stress exerted by the flow must exceed the critical shear stress, ?*c. Recent models show that ?*c for incipient motion can increase with an increase in channel slope (e.g., Lamb et al., 2008) due to turbulent fluctuations as the flow depth to grain size ratio decreases (M?ller et al., 2005; Lamb et al., 2008; Recking, 2009). Several other effects may explain the variation in ?*c with channel slope: grain emergence (e.g., Graf, 1979; Lamb et al., 2008; Recking, 2009), form drag (e.g., Buffington and Montgomery, 1997; Ferguson, 2012; Yager et al., 2012), particle interlocking (e.g., Grant et al., 1990; Church et al., 1998;   3  Zimmermann et al., 2010), and the presence of lag sediment deposits that are transported by non-fluvial processes (Church and Hassan, 2004). Incipient motion predictions in mountain streams are especially complicated by these factors and few studies have attempted to quantify their influence on ?*c values. The variability of sediment supply, degree of surface armoring, and channel morphology across fluvial environments complicates correlations between shear stress or other flow variables (e.g., discharge or stream power) used to predict sediment transport. Furthermore, many modelers have used the same expressions for lower gradient gravel bed rivers to predict bedload transport in mountain channels, where sediment supply processes and ensuing effects on bed structure are different. Regardless of the channel context, values of shear stress cannot be measured directly and, instead, measurements of flow velocity directly above the point of interest on the streambed are used to back-calculate shear stress. This presents a problem because local shear stresses can vary considerably across and along a stream reach. Bed material transport is driven by nonlinear relations and average values of shear stress that are used in the formulae can produce large errors (Wilcock et al., 2009). To account for spatial and temporal averaging, flow non-uniformity, and drag partitioning, researchers have suggested that values of ?g be partitioned to extract the portion of ?g that produces transport, the grain stress (Wilcock et al., 2009). The concept of shear stress partitioning is based on the hypothesis that roughness elements can be characterized by additive components of shear stress (Einstein and Barbarossa, 1952). Accounting for the total boundary stress in a stream is difficult because energy can dissipate on morphologic features such as bars (e.g., Mosly and Tindale, 1985; Laronne and Duncan, 1992; Lisle and Hilton, 1999), woody debris (e.g., Buffington and Montgomery, 1999b; Haschenburger and Rice, 2004), or colluvial deposits (e.g., Yager,   4  2007). While there is no direct way to estimate the fraction of ?g that acts to do geomorphic work, an approach involving the characteristic grain size, D, channel slope, S, and flow velocity, V (which depends on flow discharge and channel size and shape) can be used:     (  )        (1.2) where ?? is the partitioned grain stress and a is a scaling constant (Wilcock et al., 2009). However, observations of mixed grain size beds indicate that coarser material can become entrained at similar, or even lower, boundary shear stresses than is required to move fine material (Parker and Klingeman, 1982). That is, specification of a value of D in (1.2) is difficult. Representation of D is complicated because the range of sizes in a gravel bed is broad. Furthermore, observations of surface sediment are often orders of magnitude different from what is observed in the transported load. Armored beds, for example, are typically coarser than the material that passes over them and as such, deterministic bedload predictors with a component of critical bed shear stress for incipient motion would erroneously yield low estimates of transport if D were to be represented by the surface grain size (Hassan and Church, 2000; Pitlick et al., 2008). Some bedload transport models have come to incorporate a range of grain sizes, with unique estimates of ?? for every size fraction (e.g., Parker, 1990; Wilcock and Crowe, 2003). Measures of partial transport, or the condition in which only a portion of the grains on the bed surface move over the duration of a transport event (Wilcock et al., 2009), have been defined in laboratory settings (e.g., Wilcock and McArdell, 1997) to show that fractional transport rates vary linearly with the proportion of each fraction in the   5  bed. To date, nonetheless, advances into the relations of shear stress to grain size and channel geometry are largely incomplete in the context of fluvial bedload transport. 1.1.2 Spatial and Temporal Variability of Bedload Transport Spatial and temporal variability of bedload transport rates have been linked to sediment supply to rivers and sediment storage changes through time (e.g., Trimble, 1981; Meade, 1982; Beschta, 1983). Various factors control the generation, movement, and deposition of material and they rarely act on the same spatial and temporal scales. In mountainous environments, where the channel is usually not bordered by a valley flat or a well-developed floodplain, sediment inputs come from small, frequent landslides (Benda et al., 1997a, 2005) and are said to be coupled to hillslope sediment processes (Campbell and Church, 2003) that deliver material large enough to reside in the channel on the order of hundreds of years (Dietrich and Dunne, 1978). By contrast, fine material supplied to armored beds can be readily transported, giving way to differences between characteristic grain sizes of transported and bed material. As such, predictions of transport rates in gravel bed rivers are constrained. To address the issue of transport rate variability, field studies have come to distinguish between two-phase (Emmett, 1976; Jackson and Beschta, 1982; Andrews, 1983) or three-phase (Ashworth and Ferguson, 1989; Warburton, 1992) modes of transport. Phase I of bedload transport consists of fine material passing over a stable bed during low flows. Phase II occurs during moderate flows with size-selective entrainment and transport of local material and phase III transport describes the extreme events that mobilize most of the sizes found in the bed. Characterization of transport regimes into three phases is useful, but the   6  relations between transport capacity and sediment supply in mountain streams that are responsible for such dynamics are difficult to incorporate into transport formulae. Variability of mass movement processes within a drainage basin, flow discharge, and channel geometry give rise to spatial and temporal variations in channel morphology (Montgomery and Buffington, 1999). Bed material particle size can vary longitudinally, across the stream, and vertically within the bed. Sampling of bed material with the objective of computing a characteristic D may thus be influenced by the location of the study site in relation to tributaries that supply sediment to the channel, bedforms within the channel, downstream fining as a result of local control of stream gradient (Surian, 2000), and other flow obstructions such as log jams that control local grade and bed scour (Rice and Church, 1996). Relating these factors of bed material variability to bedload transport processes is further complicated by the timescales over which they occur. For example, sediment deposited upstream of a log jam may scour and coarsen over time or suddenly be released as the jam is destroyed. Furthermore, the texture and amount of sediment supplied to the channel at one time may distort the vertical profile of a streambed by causing abrupt changes in the form of strata (Bunte and Abt, 2001). Bedform migration over time may also lead to overestimates of bedload transport predictions by mobilizing coarse particles in sequences (Iseya and Ikeda, 1987; Whiting et al., 1988). These observations of spatial and temporal variability are clear, but incorporating representative components of such processes into bedload transport formulae remains a challenge.   7  1.1.3 Sediment Transport in the Context of the Watershed An understanding of the dynamics of sediment supply and storage and the history of the watershed is necessary in order to provide a basis for the interpretation of sediment transport results from a given study reach. The timing and location of disturbances within the watershed as well as characteristics including hydrology, geology, and vegetation have a dominant and persistent influence on water and sediment supply and thus on sediment transport rates. Flow records and aerial photograph coverage are commonly available resources that can be used to reveal land-use changes over time and their implications for channel adjustments (e.g., Jacobson and Coleman, 1986; Trimble, 1995). With knowledge of sediment availability and flow capability, transport conditions can be qualitatively assessed. Such assessments of the relative trends in water and sediment supply on a watershed scale were first suggested by Lane (1955) with a balance proposed as:        (1.3) where Qs is sediment supply, D is the grain size of the sediment, Q is water discharge, and S is channel slope (presented by Wilcock et al., 2009). The relation is ambiguous as it lacks a quantitative interpretation, but it presents a framework that can be linked to bed degradation or aggradation given changes in Q or Qs imposed upon a reach of temporally constant slope. Relations have since been presented to represent the balance as a single proportionality. For example, Henderson (1966, p. 449) combined Brown?s (1950) approximation of the Einstein bedload transport equation with the Ch?zy flow resistance formula and conservation of mass and momentum for steady, uniform flow into:        (  )  (1.4)   8  where qS and q are the sediment transport rate and water discharge per unit width. For the purposes of interpreting channel changes, (1.4) can be rearranged to   ?         (1.5) and S can be interpreted as the slope required to transport sediment of a given grain size and with flow, q (presented by Wilcock et al., 2009). An increase in S indicates bed aggradation (rather than an increase in channel slope, which only happens over a long period of time) while a decrease in S represents the tendency for the channel to evacuate sediment (Wilcock et al., 2009). The function in (1.5) thus represents the balance in (1.3). The relations presented in this section can provide as reliable an estimate of aggradation or degradation as those that are based on detailed calculations using uncertain boundary conditions (Wilcock et al., 2009; Clark and Wilcock, 2000). Given the spatially and temporally variable flow relations to sediment in a stream, the impossibility of reliably characterizing bedload material, and the episodic nature of sediment supply, it is not surprising that there has been no widely accepted bedload transport formula in the years since Du Boys (1879). Meyer-Peter and M?ller (1948) and many others derived empirical formulas for bedload transport that have since proved useful when a prediction has to be made for a system with similar conditions as the laboratory or field measurements used to calibrate the formulae. However, there remains a knowledge gap in the role of watershed-scale sediment supply conditions on bedload transport.    9  1.2 Research Objectives The objective of this research is to evaluate the effects of an episodic sediment supply regime on temporal adjustments of a streambed surface using a flume. Laboratory flume experiments provide an opportunity to study channel responses under controlled conditions. Flume studies that investigate transport rates and bed surface texture usually use constant sediment feed rates until a state of equilibrium is reached. However, since mountain streams have variable rates and types of sediment input, this study focused on the impact of episodic sediment supply on sediment transport and bed surface evolution. The research addresses the temporal adjustment of the bed surface in terms of texture, patchiness, and bed surface structures. To achieve the goals, a constant flow regime and supply texture similar to the original bed mixture was imposed.    10  Chapter 2 Experimental Design 2.1 Flume Design The experiment was conducted in an 18 m long, 1 m wide flume with a channel gradient of 0.0218 in the Mountain Channel Hydraulics Experimental Laboratory (MCHEL) at UBC (figure 2.1). A 12 m working area of the bed was monitored throughout the experiment. To reduce the effects of inflow conditions on the section of the bed where measurements were made, an upstream 4 m length of sediment was epoxied to plywood and placed on top of the channel bottom. A 1 m long section at the downstream outlet was also excluded from the measurement area.  Figure 2.1: The flume with the 12 m working area and fixed bed indicated.   11  A generic model was developed with a prototype stream, East Creek, in the UBC Malcolm Knapp Research Forest, used as a guide to configure scaled dimensions. The grain size distribution (hereafter GSD) of material in the initial bed and of the sediment feed (figure 2.2) was calculated as a composite from two segments in East Creek. The GSD was geometrically scaled from subsurface samples in two riffle-pool reaches by 1:3. Sediment was sieved in ? phi intervals from 0.5 mm to 64 mm (table 2.1) and painted different colors for each grain size class to allow for easy surface grain size analysis. Initial sediment depth was 10 cm with a median geometric grain size of 3.64 mm. With the scaling considerations in mind and through a series of trial runs, water discharge was set to 65 L/s in the flume, similar to bankfull discharge in the prototype stream. Though water velocity profiles were taken using a multi-beam bi-static profiling system, the Nortek Vectrino-II, the results are not presented herein.  Figure 2.2: Cumulative GSD of the initial material in the bed of the flume. 10-11001011020102030405060708090100Cumulative Surface GSDGrain size (mm)Cumulative % finer  12  Table 2.1: Cumulative grain size fractions and corresponding colors. Size Range (mm) Cumulative % Finer Color 45.3 - 64 100 Dark blue 32 - 45.3 99.8 White 22.6 - 32 95.2 Light green 16 - 22.6 86.1 Black 11.3 - 16 75.4 Red 8 - 11.3 67.3 Yellow 5.66 - 8 60.1 Dark green 4 - 5.66 53.3 Light blue 2.83 - 4 42.6 Pink 2 - 2.83 32.0 No color 1.41 - 2 20.2 Natural white 1 - 1.41 10.0 Tan 0.701 - 1 4.0 Eggplant 0.5 - 0.701 2.2 Orange  Table 2.2: Summary of initial experimental parameters and hydraulic conditions. Parameter Value Units Water discharge 65 L/s D50 3.64 mm Sediment depth 0.10 m Flume slope 0.0218 m/m Mean flow depth 0.07 m Water surface slope 0.015 m/m Mean flow velocity 0.65 m/s Froude number 0.78 -- Boundary shear stress 10.3 Pa     13  2.2 Experimental Procedure To begin the experiment, bed material was mixed and leveled in the flume to ensure that there was no vertical sorting. The downstream end of the flume was equipped with a mesh sediment collection basket that hung from a 100 kg maximum capacity load cell. The load cell recorded submerged sediment weight at a rate of 10 samples per second. Throughout the 7 continuous 40 hour runs, the experiment was paused at set times to scan and photograph the bed and to change the sediment collection basket. In addition to the load cell outputs, a light table at the outlet of the flume tracked the texture and volume of material transported out of the flume (figure 2.3). A bedload-tracking concept presented by Frey et al. (2003) and modified by Zimmermann (2009) was used to video capture grain size-specific transport rates every second. The outputs included a GSD of sediment exiting the flume, thus eliminating the need to dry and sieve samples collected at set intervals. A sample of collected sediment from each run was used only to calibrate the light table output. The light table used 12V halogen bulbs to illuminate grains passing over its surface. A sheet of opaque plastic was positioned above the lights and below the surface over which the particles passed to blur the outlines of individual lights on the output image. Light diffusivity was designed in such a way that the difference between the smallest grain and the darkest part of the image was large enough to yield a useful subtraction image. Prior to the start of each run, a new background image of the light table was captured. Variations in light intensity were thus accounted for so that all subsequent images were subtracted from background images taken at proximate time periods.   14   Figure 2.3: The light table set-up at the outlet of the flume. To accommodate high flows, some of the water exiting the flume was routed away from the surface of the light table using pieces of sheet metal. Without this diversion of water, bubbles and standing waves may form on the light table and be mistaken as particles. A 4 Megapixel Prosilica GX2300 camera with a 16 mm lens was used to capture particles overhead the light table at 25-30 frames per second. The camera is a high resolution (2336 x 1752) charge-coupled device with Gigabit Ethernet output. Image sensitivity and low noise are crucial to obtain accurate GSD outputs. Therefore, the electronic gain of the camera had to be set so that the brightest areas in the image were not quite saturated and the smallest particles could be detected. To account for lighting changes in the room and those caused by changes in water depths, the video image acquisition algorithm maintains the mean pixel value within a narrow range (197-203).   15  The sequence of experimental runs is summarized in figure 2.4 and table 2.3. During run 1, water was supplied without sediment feed to bring the bed to an armored state. For each of the runs 2-6, the bed was supplied with a total mass of 300 kg of sediment, fed into the upstream end of the flume. The sediment input rate was the same during pulsed deliveries across runs 3-6. During the constant feed runs (2 and 6), sediment was supplied at a rate of 7.5 kg/hour. Within the first hour of run 3, 300 kg of sediment was supplied to the channel, followed by 39 hours of no sediment feed. Four pulses, each 75 kg, were supplied at a rate of 75 kg/15 minutes during run 4 at 10 hour increments. The fifth experimental run consisted of two 150 kg pulses, with 20 hours of no feed conditions between each input. The same conditions as runs 1 and 2, constant feed and starvation, were implemented during runs 6 and 7, respectively.   16   Figure 2.4: Summary of the experiment completed in the MCHEL at UBC with time (in hours) on the x-axis and sediment input magnitude (in kg) on the y-axis. Each of the seven experimental runs lasted for 40 hours for a total 280 experimental hours. The filled bars represent sediment input events. The bed was mixed at the beginning of run 1 and then continuously conditioned throughout the other runs. Table 2.3: Summary of the experiment completed in the MCHEL at UBC.  Run # Pulses Pulse Enter Time (h) Feed Rate Pulse Magnitude (kg) 1 -- -- -- -- 2 -- -- 7.5 kg/h -- 3 1 1 300 kg/h 300 4 4 1, 10, 20, 30 75 kg/15 min. 75 5 2 1, 20 150 kg/30 min. 150 6 -- -- 7.5 kg/h -- 7 -- -- -- --   17  Every half hour throughout the experiment, measurements of bed surface elevation and water surface elevation every 0.5 m along the flume were taken (illustrated in figure 2.5). In order to calculate unbiased average values, three minimum values and three maximum values were recorded. Other bed surface measurements are described in subsequent chapters.  Figure 2.5: Side view of the flume with three locations of bed and water surface elevation measurements indicated.   Flow direction   18  Chapter 3 Sediment Transport Sediment transport results recorded by the light table are presented over the duration of the experiment, smoothed using a running mean of 31 seconds such that each data point represents an average transport rate for 31 seconds of transport information, in which, the actual time is the central value (figure 3.1). The outputs of the load cell provide a similar trend to figure 3.1 and are thus omitted. This section is meant to provide a broad context of sediment transport evolution over the duration of the experiment. Detailed transport mechanisms and fractional transport rates are not presented herein, but rather observations of total sediment transport outputted by video capture results over the light table are described and linked to bed surface evolution results in subsequent chapters. Gaps in the data in figure 3.1 indicate time periods during which no data were recorded. Vertical lines represent observation windows at the beginning of each sediment input event (i.e., a vertical line drawn at hour 80 indicates the period immediately before the 300 kg sediment pulse was input).   19   Figure 3.1: Sediment output as detected by the light table over the duration of the experiment with vertical lines representing the observation window one hour prior to the beginning of each sediment input event. Arrows above the plot represent the hour following each sediment input event. Transport rates are given in g/m-2s-1 smoothed using a running mean of 31 seconds.   20  Initial transport rates were high, as fine sediment winnowed out of the flume, but over the course of run, transport rates declined rapidly until the bed stabilized (figure 3.1). Output rates during run 1 followed an exponential decay curve, reaching the lowest values over the entire experiment by about hour 30 (figure 3.1). Transport rates steadily increased and then leveled off about halfway through run 2 (figure 3.1). By hour 81 of the experiment, (indicated by the thick, downward-pointing arrow in figure 3.1), transport rates peaked as material from the 300 kg pulse exited the flume. The ensuing decrease and leveling-off of sediment transport rates over run 3 mimicked what was observed over the course of run 1 (figure 3.1). Run 4 was characterized by relatively constant overall sediment transport rates, with peaks about equal in magnitude one hour after each 75 kg sediment input (as indicated by four small, downward-pointing arrows in figure 3.1). Similarly, the 150 kg sediment inputs of run 5 induced slighter higher magnitude sediment transport rates one hour after each input event than those observed during run 4 (figure 3.1). Time elapsed between each of the sediment input events of runs 4 and 5 was not sufficient to observe a leveling-off of sediment transport rates similar to the pattern observed following the 300 kg sediment input (figure 3.1). With the advent of the second constant feed experimental run indicated during hours 200-240 on figure 3.1, transport rates increased for about 10 hours before leveling off to values similar to those observed during hours 50-80, during the last half of run 2 (figure 3.1). Immediately upon discontinuing the constant sediment feed of run 6, sediment transport rates dropped from hours 240-260 of run 7 (figure 3.1). The last 20 hours of the experiment, however, were characterized by a slight increase in transport rates, as a wave of sediment reached the outlet (figure 3.1).    21  Chapter 4 Surface Texture Representations Sediment patches have been loosely referenced as areas of relatively similar grain size, but they are so far not clearly defined. These morphological features are often delineated visually, which gives way to biases in picking out patterns. Recently, researchers have questioned whether rivers really exhibit discrete patchiness, or if patches are a simplification of patterns of continuous grain size variation (e.g., Nelson, 2010). Regardless, the influence of surface heterogeneity on local bed mobility, overall bedload transport rates, hydrodynamic roughness, and benthic habitat is best understood when variations in grain size are quantified using a categorical or hierarchical approach. Definable patch scales emerge on a river bed for a particular grain-size mixture and hydraulic conditions. Preliminary observations of patch formation and interaction should guide patch definitions. Visual delineation of patches should thus be preceded by a thorough study of the bed surface material and the changes it undergoes throughout the study period. The overall goals of this chapter are to (1) use photographs of the bed surface to generate a dataset of grain sizes of high spatial resolution as a field of point measurements and (2) draw boundaries on the field of grain sizes that delineate a set of meaningful patches. 4.1 Bed Surface Texture Classifications The classification of bed surface texture by Buffington and Montgomery (1999) provides a way to combine human identification of patches and grain-size measurements. The authors suggested visual patch delineation as a necessary first step in being able to discriminate   22  between statistically meaningful areas of bed texture. Their statistical application was less rigorous than the Crowder and Diplas (1997) scheme wherein local variations in the GSD of a streambed reach were identified by comparing arithmetic means of adjacent subsamples. Buffington and Montgomery (1999) applied two descriptive diagrams to facies maps to show (1) relative abundance of a texture class and (2) grain size composition of each texture class. They then sampled the surface material to update the initial two-part classification. By comparing GSD medians and variances within and between textural categories, the method indicates a ?reasonable? statistical discrimination of texture. However, with a component of visual identification, the method does little to advance objectivity of patch delineation. Patch delineation analyses have nonetheless largely followed the Buffington and Montgomery (1999) method or some variation of it with acceptable results. For example, Yuill et al. (2010) conducted multiple trials of patch delineation at a stable location with resulting variation of patch area up to 10% of the mean (figure 4.1).     23   Figure 4.1: A sample bed material map of coarse patches. Adapted from ?Coarse bed material patch evolution in low-order, ephemeral channels,? by B. Yuill, M. Nichols, and E. Yager, 2010, Catena, 81 (2), p. 129. That Crowder and Diplas (1997) and Buffington and Montgomery (1999) had been the most notable workers to attempt to make patch delineation more objective was motivation for Nelson (2010) to investigate automated methods about a decade later. Nelson et al. (2012) tested automated methods on densely-sampled grain size data from a laboratory experiment. They implemented four clustering algorithms to produce patches that resulted in better-separated GSDs than results from visually-delineated patches on the same dataset. The approaches were deemed successful on the basis that intra-patch similarity was maximized and between-patch similarity was minimized using all four algorithms (Nelson et al., 2012). Various other methods of automated grain size characterization have been reported, but none attempt to draw boundaries around meaningful areas of grain size. Statistical methods of grain size characterization may use autocorrelation (e.g., Rubin, 2004; Warrick et al., 2009)   24  or semivariance or fractals of image ?texture? (e.g., Carbonneau et al., 2004, 2005; Buscombe and Masselink, 2009). Spatial autocorrelation in geostatistics has the potential to provide a wealth of other ways to classify bed texture. Assuming that the spatial distribution of grain size data is continuous, autocorrelation techniques can be used to describe spatial dependence of point data. For example, Moran?s I, a spatial statistic tool in ArcGIS (ESRI, 2006), measures feature similarity based on feature location and feature values simultaneously. Such methods have not been widely implemented in geomorphologic applications. There have been attempts to work backwards in patch delineation analysis by describing patches that are already drawn, similar to methods used by landscape ecologists wherein indices of spatial heterogeneity are used to quantify population richness and diversity. The total number of patch types and their relative proportions to the landscape along with patch configuration, or the spatial pattern of patches in the landscape, can be used to quantify landscape diversity (Li, 1989). Geomorphologists have adopted some patch composition and configuration indices for riverbed and flume data. For example, Yarnell et al. (2006) computed the Shannon?s Diversity Index (SHDI) to describe the spatial complexity of patches to relate relative sediment supply to geomorphic diversity. The SHDI was used to describe predefined habitat units from field data following the definitions of Hawkins et al. (1993) and Wohl (2000) and facies maps from a flume experiment (Yarnell et al., 2005). The technique is attractive in that it is automated and universal, but patches can only be described, rather than defined. Some workers have explored the possibility of characterizing scales of variability in bed morphology without actually delineating patches. On a landscape scale, periodicity of physical phenomena has been demonstrated using Fourier analysis (e.g., Rayner, 1972;   25  Hanley, 1977; Gallant, 1997; Perron et al., 2008). Such a method, when applied to grain size data, may result in spectral peaks at a bar or pool scale (about 10 m) and at a bedload sheet or dune scale (about 1 m). While implications of results for fractal descriptions of landscapes of riverbeds are wide, scaling properties and topographic patterns can only be described using these methods. That is, for the purposes of automated patch delineation, Fourier analysis may only provide a measure of the amplitude of bed features at particular wavelengths, not spatial separation of distinct patches. 4.2 Methods 4.2.1 Data Acquisition For 79 surface observation windows of the experiment, the flume was drained (apart from a shallow, about 1 cm, layer of water to maintain sediment saturation) and wooden markers were placed about every 0.5 m along the bed from the outlet of the flume to the upstream end before photographing the surface. A camera mounted 1 m above the bed on a motorized cart was used to photograph the surface. The camera used was a Canon PowerShot G12 with the following settings: F-stop = f/5, exposure time = 1/80 sec, ISO speed = 2500, focal length = 6 mm, with flash. Each image was 3648 x 2736 pixels with bit depth = 24. A sequence of 16 bed photographs was taken along the flume by moving the cart in 70 cm increments. Each photograph covered about a 1 m long by 1.3 m wide area of the bed with about 0.2 m of overlap on adjacent photographs. The photographic method provided for a quick and non-destructive visual documentation of the bed surface. The bed surface texture analysis was conducted on a 2 m area in the middle of the flume in order to generate a high temporal resolution dataset of surface evolution. Area-by-number   26  grain size distribution results from the photographs were extracted for each observation window. Grain size classes were painted different colors so that the manual GSD analysis would not be affected by grain shape, burial, orientation, or imbrication. To obtain the full image of the 2 m middle area for analysis, four of the 16 photographs from each observation window were merged together and their overlapping areas were cropped using a custom template in Adobe Illustrator. The sides of the images, where the glass walls of the flume were visible, were also cropped out of the panel of merged photographs. Table 4.1: Surface measurements taken during each of the seven experimental runs. Run Hours Measurement 1 1, 10, 20, 40 Full length scans; bed photographs 1 2, 4, 7, 15, 30 2 m-long scans; bed photographs 2 1, 10, 20, 40 Full length scans; bed photographs 2 2, 4, 7, 15, 30 2 m-long scans; bed photographs 3 1, 10, 20, 40 Full length scans; bed photographs 3 2, 4, 7, 15, 30 2 m-long scans; bed photographs 4 1, 10, 11, 20, 21, 30, 31, 40 Full length scans; bed photographs 4 2, 4, 7, 12, 14, 17, 22, 24, 27, 32, 34, 37 2 m-long scans; bed photographs 5 1, 10, 20, 21, 30, 40 Full length scans; bed photographs 5 2, 4, 7, 15, 22, 24, 27, 35 2 m-long scans; bed photographs 6 1, 10, 20, 40 Full length scans; bed photographs 6 2, 4, 7, 15, 30 2 m-long scans; bed photographs 7 1, 10, 20, 40 Full length scans; bed photographs 7 2, 4, 7, 15, 30 2 m-long scans; bed photographs  4.2.2 Surface Grain Size and Sorting Bed surface GSD was derived using a point count technique (Wolman, 1954) by identifying particle size at the intersection of a grid superimposed on each photograph (figure 4.2). At each node of the grid, grain size and location were recorded as (x, y, D) to produce GSD maps for every observation window. Due to the resolution of the photographs, individual   27  grains were identifiable based upon their color for all size fractions coarser than 2.83 mm. Material finer than 2.83 mm was grouped in the same class. Two different sizes of grids were used to identify grains, 5 cm and 10 cm. From the 5 cm grid maps, 946 observations were made on each 2 m image panel. From the 10 cm grid maps, 221 observations were made. A careful decision about grid spacing was necessary in order to prevent double counting of large particles. Graham et al. (2005) recommended that grid spacing be twice the maximum grain diameter to prevent repeat counts on the same stone instead of sampling based upon a predefined number of grains. Though the largest stones on the bed were between 45.3-64 mm, grid spacing for the subsequent analysis was chosen to be 5 cm after finding that only five or fewer stones were repeat sampled in each observation window of the first run. As well, each bed texture analysis was tested using (x, y, D) data from the 10 cm grid spacing results of the first run before the decision to use the 5 cm grid was made.  Figure 4.2: A section of the bed with the 5 cm grid superimposed. Cumulative GSDs were plotted on a run-by-run basis to examine the overall change in texture of the bed. That is, the GSDs after one hour of run time and after 40 hours of run time were plotted together. Cumulative GSDs were also plotted on a pulse-by-pulse basis in order to relate the magnitude of the input event to bed recovery. Two-sample Kolmogorov-  28  Smirnov (KS) goodness-of-fit hypothesis tests (Zar, 1999) were performed to determine if GSDs were drawn from the same underlying continuous populations at a significance level of 0.05. To summarize the temporal evolution of bed texture in the 2 m middle section of the flume, the D16, D50, and D84 of surface GSD for each of the grain size maps unique to the 79 observation windows were calculated. Bed sorting, ?, was estimated using the modified geometric Folk and Ward (1957) sorting parameter:                                            (4.1) where Di is the grain size diameter in mm of the ith percentile. The results were plotted over the duration of the experiment. The cumulative percent of fine material on the surface was summarized in two ways: (1) as the sum of fractions corresponding to grains finer than 5.66 mm and (2) as the fraction corresponding to grains finer than 4 mm to encompass fine material and sand fractions. Percent of fine material on the surface was plotted for each observation window over the duration of the experiment. 4.2.3 Patch Delineation A function that computes the grain size gradient using eight neighboring cells surrounding a central grain was developed in MATLAB (The MathWorks, Inc.). Missing observations were handled by using the NaN marker (an arithmetic representation for not-a-number) in the input matrix of grain size observations. The gradient was computed as the difference in grain size divided by the distance of separation in each of the eight directions. Thus, the grain size gradient was output as a vector. Gradient sum, average, median, and variance were then calculated at each grid node. Gradient variance describes how far values lie from the mean gradient and provides a relatively sensitive way to examine the results. For example, when a   29  large particle is surrounded by small particles, high grain size gradients will be output. The values are exaggerated by displaying their variance, computed as the average of the squared differences from the mean. The distribution of gradient variance values for each observation window was divided into five geometrical intervals. Geometrical intervals were selected because their divisions are created by minimizing the sum of squares of the number of elements in each class. This classification technique ensures that each class range has approximately the same number of observations within each class and that the change between intervals is consistent. Three patch types were then defined by querying both the underlying grain size observations and the gradient variance. For each patch type, gradient variance below or equal to the value of the third geometrical interval (in most cases about the median value of gradient variance) was extracted. Patch type 1 (P1) was then determined by querying out all grain size observations below or equal to 5.66 mm to define fine gravel patches. The query for patch type 2 (P2) included medium gravel, between 5.66 and 16 mm. Patch type 3 (P3) queried all grain size observations greater than or equal to 16 mm to delineate coarse gravel patches. Patches were only delineated where both the grain size observation query and the variance of gradient values were extracted at the same location together. Table 4.2: Summary of patch types queried out of grain size observations and variance of grain size gradients. Patch Type Observed D (mm) Description P1 ? 5.66 Fine gravel surrounded by fine gravel. P2 > 5.66 and < 16 Medium gravel surrounded by medium gravel. P3 ? 16 Coarse gravel surrounded by coarse gravel.    30  To present the results of surface texture evolution, GSDs are plotted for the beginning and end of each run to examine the overall effect of the sediment supply conditions. Within each run, the overall change in each of the grain size statistics and the maximum variability, or the difference between the maximum and minimum of each within-run grain size statistic, are summarized (tables 4.3 and 4.4). To investigate the temporal evolution of surface texture, curves are drawn for hours 1, 2, and 40 for runs 1, 2, 3, 6, and 7, for hours 1, 2, 10, 11, 12, 20, 21, 22, 30, 32, and 40 for run 4 (photographs were not taken during the run 4, hour 31 observation window), and for hours 1, 2, 20, 21, 22, and 40 for run 5. The KS test returned no significant differences in GSD between any of the curves presented in the following section. That is, the results of the test were not true ?enough? to meet the confidence level of 95% and reject the null hypothesis that the data are from the same continuous distribution. The 0.05 level of significance was chosen in order to reduce the chances of rejecting the null hypothesis that is actually true. Following each sediment pulse in run 4, surface GSDs are plotted at hours 10, 20, 30, and 40. As run 4 was characterized by the highest frequency, lowest magnitude sediment pulses of the three sediment pulsing runs, a comparison between surface GSD curves for the constant feed runs (2 and 6) is made at hours 10, 20, 30, and 40. Surface GSDs for runs 1, 3, and 7 are also compared at hours 10, 20, 30, and 40 and again at hours 1, 2, 4, and 7 to examine the duration of the effect of the 300 kg sediment pulse as a bed disturbance. Summary values of bed texture are given as D16, D50, D84, and the fraction of fine material on the surface for each of the observation windows whose GSDs are plotted. The sorting parameter and fine material fraction on the surface are also presented over the duration of the experiment and linked to results of the GSD curves. Section 4.3.1 provides a   31  preliminary study of surface texture evolution that was used to guide the patch delineation process in terms of patch scale and composition. Results of the grain size gradient patch delineation analysis are presented in section 4.3.2. To summarize the results, relative patch area, defined as the number of cells occupied by one of the three patch types as a fraction of the total number of cells identified as patches, is plotted over the duration of the experiment. Examples of outputted patch maps are presented alongside photographs of corresponding observation windows. A discussion of the results of surface texture representations in chapter 7 links the sediment supply regime to stages during which the largest or most prevalent patches developed. 4.3 Results 4.3.1 Surface Grain Size and Sorting Figure 4.3 displays GSD curves computed for observation windows at the first and last hour of each run. After 40 hours of no feed conditions during run 1, the surface exhibited a coarser texture than its initial condition (figure 4.3 A). The difference in GSD between hours 1 and 40 in run 1 is most exaggerated for material finer than the D50 (figure 4.3 A). With constant sediment supply (7.5 kg/hour) in run 2, the GSD curves exhibit similar shapes at hours 1 and 40 (figure 4.3 B). During the time between the first and last observation windows of run 3, the bed surface coarsened with increases in all representative grain sizes (figure 4.3 C). The sediment supply regime of run 4 caused a slight fining of the bed, seen as an overall increase in representative grain sizes below the D50 and almost no change in coarser material (figure 4.3 D). The surface became coarser from hour 1 to hour 40 of run 5, with the largest differences observed in the fine fractions (figure 4.3 E). Overall surface texture results of run   32  6 were similar to those of run 2, both under constant feed conditions, with distribution curves maintaining relatively similar shapes over the respective 40 hour runs (figure 4.3 F). Finally, the no feed regime of run 7 brought the surface to exhibit a coarser texture after 40 experimental hours (figure 4.3 G).  33        Figure 4.3: Cumulative GSD curves for the first and last hours of each experimental run (A-G). 1001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 1, Hour 1Run 1, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 2, Hour 1Run 2, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 3, Hour 1Run 3, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 4, Hour 1Run 4, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 5, Hour 1Run 5, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 6, Hour 1Run 6, Hour 40100101102010203040506078910Grain size (mm)Cumulative % finer  Run 7, Hour 1Run 7, Hour 40A B C D E F G   34  Figure 4.4 displays GSD curves computed during the initial two hour progression after each run or after each pulse. The first two hours are plotted along with the last hour in order to compare between rates of surface evolution following each input event. After two hours of no feed conditions in run 1, little change in surface texture occurred (figure 4.4 A). There was little difference between the GSD curves of hours 1 and 2 drawn for run 2 in the fine material fraction (figure 4.4 B). The surface became finer then slightly coarser from hours 1 to 2 during run 2. Figure 4.4 C displays a rapid coarsening of bed texture from hour 1 to hour 2 of run 3. By hour 2, characteristic grain sizes increased to about half of their values observed during hour 40 of run 3. Very little change in surface texture occurred between the first and second hours following each sediment pulse of run 4 (figure 4.4 D-G). Nor was there a clear pattern in the first two hours of bed surface texture evolution between each 75 kg pulse; only two hours after the second pulse of run 4, characteristic grain size values had recovered to those observed eight hours later. The curve drawn from the hour 2 observation window following the first 150 kg pulse of run 5 exhibits a shape more similar to hour 20 of that run than to hour 1 (figure 4.4 H), indicating that, similar to run 3, bed texture responded quickly to relatively large sediment inputs. This behavior is less marked in run 5, hour 22 (figure 4.4 I). Run 6, hours 1, 2, and 40 show similar GSD curves while bed texture during the first hours of run 7 seems to evolve in a manner similar to run 1, with little change occurring between hours 1 and 2 and a relatively coarse final bed surface state (figures 4.4 J and 4.4 K).   35     1001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 1, Hour 1Run 1, Hour 2Run 1, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 2, Hour 1Run 2, Hour 2Run 2, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 3, Hour 1Run 3, Hour 2Run 3, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 4, Hour 1Run 4, Hour 2Run 4, Hour 101001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 4, Hour 11Run 4, Hour 12Run 4, Hour 201001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 4, Hour 21Run 4, Hour 22Run 4, Hour 30A B C D E F   36     Figure 4.4: Cumulative GSD curves for hours 1, 2, and 40 for runs 1 (A), 2 (B), 3 (C), 6 (J), and 7 (K), for hours 1, 2, 10, 11, 12, 20, 21, 22, 30, 32, and 40 for run 4 (D-G), and for hours 1, 2, 20, 21, 22, and 40 for run 5 (H and I).   1001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 4, Hour 32 (missing 31)Run 4, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 5, Hour 1Run 5, Hour 2Run 5, Hour 201001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 5, Hour 21Run 5, Hour 22Run 5, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 6, Hour 1Run 6, Hour 2Run 6, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 7, Hour 1Run 7, Hour 2Run 7, Hour 40G H I K  I J  I   37  To summarize the GSD curves of figures 4.3 and 4.4, D16, D50, and D84 values for each observation window are plotted over the duration of the experiment (figure 4.5). Of the three grain size statistics plotted, the largest overall difference between the first and last observation windows of a run was observed in the D16 values of run 3 (table 4.3); at hour 1, the D16 was 3.91 mm and by hour 40, the value had increased to 8.08 mm (a change of 4.17 mm). The only decrease in D16 from the first and last observation windows of a run was observed during run 2 (table 4.3). The largest magnitude changes in those values were also observed during run 3 with the D50 increasing by 3.67 mm and the D84 by 2.27 mm from hour 1 to hour 40. Overall, decreases in each of the grain size statistics were minor (<0.50 mm). Table 4.3: The overall changes (in mm) to each grain size statistic between the first and last hours within each experimental run. Run D16 final ? D16 initial (mm) D50 final ? D50 initial (mm) D84 final ? D84 initial (mm) 1 3.13 2.53 1.52 2 -0.50 1.10 0.76 3 4.17 3.67 2.27 4 2.55 -0.05 -0.39 5 2.28 1.39 0.80 6 0.02 -0.04 0.01 7 1.62 2.02 1.30    38   Figure 4.5: Experiment time (in hours) on the x-axis and GSD summary values on the y-axis, D16, D50, and D84 (in mm). Vertical lines represent the observation window one hour after the beginning of each sediment input event.  39  Maximum variability between grain size statistics calculated for each observation within every run is summarized in table 4.4. Run 3 exhibited the highest variability across each of the grain size statistics (table 4.4). Across all runs, D16 values were most variable on average. However, variability within run 2 was relatively constant across each grain size statistic. Average variability of D84 values within each run was 1.34 mm, the lowest average variability of the grain size statistics. Table 4.4: The maximum variability (in mm) of each grain size statistic between all hours of each experimental run. Run D16 max. ? D16 min. (mm) D50 max. ? D50 min. (mm) D84 max. ? D84 min. (mm) 1 3.21 2.53 1.69 2 1.58 1.43 1.41 3 4.17 3.67 2.27 4 2.55 1.49 1.36 5 3.03 2.64 1.02 6 0.85 1.04 0.33 7 2.32 2.49 1.30  A few patterns in characteristic grain size emerged over the course of the experiment. The D16, D50, and D84 values would decrease following inputs of sediment and recover back to values similar to those observed before the sediment input within a short period (figure 4.5). Surface grain size values throughout run 4 evolved in two distinct ways: the D16 of the bed increased from 6.29 mm in hour 1 to 8.84 mm in hour 40 while D50 and D84 values decreased slightly (from 17.2 to 17.1 mm and 29.5 to 29.1 mm, respectively). The D16, D50, and D84 increased by 23%, 2%, and 1.3%, respectively by the end of the first 10 hours of run 4. Two hours after the second 75 kg pulse of run 4, however, the surface texture changed considerably relative to the bed state observed after the first 75 kg pulse. Surface D16, D50, and D84 had nearly reached the values observed at the end of 20 hours of run 4 by hour 12 of   40  run 4. That is, the advent of a 75 kg pulse on a highly armored bed (pulse 1 of run 4) triggered a relatively slow response in bed texture evolution whereas after the second 75 kg pulse of run 4, the bed responded quickly to become almost as coarse at hour 12 as observed at hour 20. Two hours after the third 75 kg pulse, surface D16 increased from 6.94 mm to 7.54 mm and further increased to 7.78 mm by hour 30 of run 4. Surface D50 and D84 decreased two hours after the third 75 kg pulse and then increased to values 2.3% and < 1 %, respectively, larger than those observed one hour after the third 75 kg pulse. The bed eventually became coarser after the third 75 kg pulse, but large material seemed to have entered and exited the 2 m middle section of the flume periodically throughout the observation window. The bed sorting parameter, ?, is plotted in figure 4.6 over the duration of the experiment. Higher values represent a poorly-sorted bed. Since the formula includes the smallest and the largest material on the bed, it is sensitive to changes on the grain size scale. The highest value of ? was observed during run 3, one hour after the 300 kg sediment pulse. Each pulse of sediment brought about a peak in ?, with no apparent scaling pattern in pulse magnitude to parameter value (figure 4.6). Values of ? fluctuated throughout runs 2 and 6, when a constant supply of sediment was input to the bed. Overall, the bed became more sorted over the duration of the experiment.  41   Figure 4.6: The sorting parameter, ?, plotted over the duration of the experiment with vertical lines representing the observation window one hour after the beginning of each sediment input event. Higher values of ? represent a relatively poorly-sorted bed surface.  42  Figure 4.7 shows the percent of surface material below 5.66 mm and the percent of surface material below 4 mm in the 2 m middle section of the flume over the duration of the experiment. The 4 mm fraction contains all material finer than 4 mm and is therefore plotted separately from the 5.66 mm fraction. Over the course of run 1, surface material < 5.66 mm decreased from 27.3 to 12.3% and material < 4 mm decreased from 8.8 to 3.2%. Constant sediment feed conditions of run 2 initially renewed the surface with fine material and over 40 hours, the bed maintained a nearly equal fraction of material < 5.66 and 4 mm. From the end of run 2 to the first hour after the 300 kg pulse of run 3, bed material < 5.66 mm increased by 27% and material < 4 mm increased by about 14%. Two hours after the 300 kg pulse, much of the fine material had already been transported out of the 2 m middle section of flume and by the end of run 3, material < 5.66 mm had decreased by 30% and material < 4 mm had decreased by about 14% relative to the first hour of run 3.  43   Figure 4.7: Percent of surface material < 5.66 mm and < 4 mm over the duration of the experiment with vertical lines representing the observation window one hour after the beginning of each sediment input event.  44  The first 75 kg pulse brought another increase of fine material to the surface that persisted for about two hours. Following the last three 75 kg pulses, increases in fine surface material were observed at approximately the same scale. The 150 kg pulses of run 5 yielded sand fraction changes similar to each other with initial increases, followed by a winnowing of fine sediment out of the surface and then a short (about eight hour) period of sand fraction increase. During run 6, fine surface material appeared in the bed surface periodically, but overall, diminished. Finally, run 7 produced a relatively constant fine material fraction decline on the bed surface.    45  Table 4.5: Summary values of D16, D50, D84, percent fine material, and the sorting parameter, ?, for hours 1, 2, and 40 for runs 1, 2, 3, 6, and 7, for hours 1, 2, 10, 11, 12, 20, 21, 22, 30, 32, and 40 for run 4, and for hours 1, 2, 20, 21, 22, and 40 for run 5. Run Hour D16 (mm) D50 (mm) D84 (mm) % < 5.66 mm % < 4 mm ? 1 1 5.24 14.8 27.9 27.3 8.85 1.13 1 2 5.21 14.9 28.1 27.4 8.75 1.14 1 40 8.36 17.4 29.4 12.3 3.20 0.93 2 1 7.24 16.2 28.7 14.7 2.24 0.97 2 2 6.02 16.1 28.6 16.4 1.49 1.04 2 40 6.74 17.3 29.4 16.3 3.72 1.02 3 1 3.91 14.4 28.5 43.3 17.5 1.26 3 2 5.14 15.8 29.3 29.1 10.6 1.16 3 40 8.08 18.1 30.8 13.0 4.0 0.97 4 1 6.29 17.2 29.5 20.4 6.2 1.07 4 2 6.62 17.0 29.9 20.7 7.6 1.07 4 10 8.14 17.5 29.9 12.3 2.7 0.94 4 11 6.87 17.0 29.3 17.2 4.3 1.01 4 12 8.01 17.2 29.2 13.2 3.3 0.94 4 20 8.06 17.3 29.5 13.3 4.0 0.95 4 21 6.94 16.7 29.1 18.5 6.1 1.03 4 22 7.54 16.4 28.9 16.0 5.2 0.98 4 30 7.78 17.1 29.3 12.7 4.5 0.96 4 32 6.57 16.2 28.7 18.0 5.0 1.02 4 40 8.84 17.1 29.1 9.9 2.0 0.88 5 1 6.22 16.1 28.4 20.1 5.9 1.05 5 2 7.86 16.6 28.7 14.4 3.4 0.94 5 20 8.27 17.1 29.1 10.6 2.6 0.91 5 21 5.84 15.0 28.4 22.1 6.8 1.08 5 22 6.48 16.0 28.3 19.1 6.0 1.03 5 40 8.51 17.4 29.2 8.7 1.9 0.89 6 1 6.71 16.4 28.7 17.4 4.46 1.01 6 2 6.99 16.3 28.7 16.8 5.02 1.00 6 40 6.73 16.3 28.7 13.0 3.29 0.99 7 1 6.73 16.00 28.1 10.2 1.27 0.96 7 2 7.14 16.4 28.6 8.16 1.59 0.94 7 40 8.35 18.0 29.4 4.57 0.32 0.87     46  In order to investigate whether the frequency and magnitude of sediment delivered to the bed during run 4 had a similar effect on bed texture as the constant feed experimental runs, cumulative GSDs are plotted for hours 10, 20, 30, and 40 in figure 4.8. Within runs 2, 4, and 6, the curves exhibit similar shapes, overlapping the four unique observations that represent bed texture nine hours after each 75 kg pulse (figure 4.8 B) or at the corresponding observation windows of the constant feed runs (figures 4.8 A and 4.8 C). Between runs, there is little difference in representative grain size. Summary values that correspond to the GSD curves of runs 2, 4, and 6 are presented in table 4.6. Run 4 consistently produced the highest D16 values at hours 10, 20, 30, and 40 (table 4.6). The D50 and D84 values were similar between runs at each corresponding observation window (table 4.6). The constant feed conditions of runs 2 and 6 sustained higher fractions of material < 5.66 mm on the surface than what was observed during run 4 at hours 10, 20, 30 and 40. However, as the fraction of the finest material on the bed was relatively different between runs 2, 4, and 6, values of ? were relatively similar.    47   Figure 4.8: Cumulative GSD curves for hours 10, 20, 30, and 40 for runs 2 (A), 4 (B), and 6 (C). Table 4.6: Summary values of D16, D50, D84, percent fine material, and the sorting parameter, ?, for hours 10, 20, 30, and 40 for runs 2, 4, and 6. Run Hour D16 (mm) D50 (mm) D84 (mm) % < 5.66 mm % < 4 mm ? 2 10 6.82 17.1 28.8 17.5 4.35 1.01 2 20 7.17 17.1 29.2 14.9 2.77 0.99 2 30 6.15 17.1 29.8 16.7 2.33 1.05 2 40 6.74 17.3 29.4 16.3 3.72 1.02 4 10 8.14 17.5 29.9 12.3 2.67 0.94 4 20 8.06 17.3 29.5 13.3 4.05 0.95 4 30 7.78 17.1 29.3 12.7 4.47 0.96 4 40 8.84 17.1 29.1 9.90 2.02 0.88 6 10 6.74 16.1 28.5 14.7 3.96 1.00 6 20 6.14 15.3 28.6 16.9 3.51 1.03 6 30 6.70 16.1 28.4 12.0 2.33 0.98 6 40 6.73 16.3 28.7 13.0 3.29 0.99   1001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 2, Hour 10Run 2, Hour 20Run 2, Hour 30Run 2, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 4, Hour 10Run 4, Hour 20Run 4, Hour 30Run 4, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 6, Hour 10Run 6, Hour 20Run 6, Hour 30Run 6, Hour 40A B C   48  Another comparison of bed recovery is made between runs 1, 3, and 7. Figure 4.9 displays cumulative GSD curves for hours 10, 20, 30, and 40 of each run. The bed gradually became coarser during runs 1 and 3 (figures 4.9 A and 4.9 B), but grain size values below the D50 show an increase at hour 30 of run 7 (figure 4.9 C). Values of D16, D50, and D84 at hour 40 between the runs were similar (table 4.7), but the fraction of material < 5.66 mm observed on the bed surface during the final hour of run 7 was less than half as much as what was observed at the end of runs 1 and 3. Material < 4 mm had almost completely winnowed out of the frame by the end of the experiment (table 4.7).    49    Figure 4.9: Cumulative GSD curves for hours 10, 20, 30, and 40 for runs 1 (A), 3 (B), and 7 (C). Table 4.7: Summary values of D16, D50, D84, percent fine material, and the sorting parameter, ?, for hours 10, 20, 30, and 40 for runs 1, 3, and 7. Run Hour D16 (mm) D50 (mm) D84 (mm) % < 5.66 mm % < 4 mm ? 1 10 6.97 16.5 29.1 17.7 5.43 1.02 1 20 8.43 17.2 29.6 11.7 3.09 0.93 1 30 8.29 16.9 29.5 12.5 3.74 0.94 1 40 8.36 17.4 29.4 12.3 3.20 0.93 3 10 6.38 17.1 29.5 18.0 4.37 1.05 3 20 7.09 16.9 29.7 16.4 5.02 1.02 3 30 7.44 17.7 30.5 15.1 4.58 1.01 3 40 8.08 18.1 30.8 13.0 3.95 0.97 7 10 7.94 17.3 28.6 6.79 0.85 0.89 7 20 9.04 18.5 29.3 3.82 0.64 0.82 7 30 8.80 18.1 29.3 3.82 0.32 0.84 7 40 8.35 18.0 29.4 4.57 0.32 0.87 1001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 1, Hour 10Run 1, Hour 20Run 1, Hour 30Run 1, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 3, Hour 10Run 3, Hour 20Run 3, Hour 30Run 3, Hour 401001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 7, Hour 10Run 7, Hour 20Run 7, Hour 30Run 7, Hour 40A C B   50  To compare the initial progression of bed texture between runs 1, 3, and 7, GSD curves are plotted for the first four observation windows of each experimental run (figure 4.10). Within two hours of the introduction of the 300 kg pulse, the bed became coarser and proceeded to coarsen until hour 4 (figure 4.10 B). Curves for hours 4 and 7 from run 3 overlap at every point except for the finest fraction (figure 4.10 B). Overall, bed texture responded rapidly to the 300 kg pulse as much of the fine material was evacuated within the first four hours. Bed coarsening also progressed quickly during the first four hours of run 1 (figure 4.10 A).Though less fine material remained on the bed during hours corresponding to run 3, characteristic grain sizes were similar at hours 2-7 (table 4.8). Characteristic grain sizes calculated for the first seven hours of run 7 were overall similar to those calculated for corresponding hours of runs 1 and 3, but less fine material remained on the surface during the first seven hours of the last experimental run (table 4.8). The residual effect of the 300 kg sediment pulse was thus most evident in the finest fractions of bed surface material. However, the initial conditions of the experiment were not quick to produce a well-sorted coarse surface as what was observed during hours 1-7 of run 7.    51    Figure 4.10: Cumulative GSD curves for hours 10, 20, 30, and 40 for runs 1 (A), 3 (B), and 7 (C). Table 4.8: Summary values of D16, D50, D84, percent fine material, and the sorting parameter, ?, for hours 1, 2, 4, and 7 for runs 1, 3, and 7. Run Hour D16 (mm) D50 (mm) D84 (mm) % < 5.66 mm % < 4 mm ? 1 1 5.24 14.8 27.9 27.3 8.85 1.13 1 2 5.21 14.9 28.1 27.4 8.75 1.14 1 4 6.09 16.2 28.5 20.9 6.20 1.07 1 7 6.72 16.2 28.8 18.1 4.79 1.02 3 1 3.91 14.4 28.5 43.3 17.5 1.26 3 2 5.14 15.8 29.3 29.1 10.6 1.16 3 4 5.52 16.5 29.6 26.5 9.97 1.14 3 7 5.97 16.3 29.3 20.4 5.53 1.08 7 1 6.73 16.0 28.1 10.2 1.27 0.96 7 2 7.14 16.4 28.6 8.16 1.59 0.94 7 4 7.54 17.2 28.7 7.31 1.17 0.91 7 7 7.39 17.4 28.8 7.43 1.06 0.92 1001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 1, Hour 1Run 1, Hour 2Run 1, Hour 4Run 1, Hour 71001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 3, Hour 1Run 3, Hour 2Run 3, Hour 4Run 3, Hour 71001011020102030405060708090100Grain size (mm)Cumulative % finer  Run 7, Hour 1Run 7, Hour 2Run 7, Hour 4Run 7, Hour 7A B C   52  4.3.2 Patch Delineation As an example of the process described in section 4.2.3, a map of the outputted grain size gradient variance values computed during the run 3, hour 1 observation window is overlain on the observed grain size values (figure 4.11). Small, light purple-colored hexagons represent low values of gradient variance. In this case, the third geometrical interval value of gradient variance is 0.04, as indicated by the red vertical line on the histogram of all run 3, hour 1 gradient variance values (figure 4.12). In locations where this variance threshold value is overlain on observations of grain size smaller than or equal to 5.66 mm, P1 is output. Patch types 2 and 3 (P2 and P3, respectively) are output in locations where this variance threshold value is overlain on observations of grain size between 5.66 and 16 mm (P2) and those 16 mm and above (P3). An example of a resulting P1 map is displayed adjacent to a panel of bed photographs from run 3, hour 1 (figure 4.13).  53   Figure 4.11: Run 3, hour 1 grain size gradient variance values (displayed as purple hexagons) overlain on grain size values (displayed as brown squares). Flow direction goes from left to right. The image represents the 2 m long by 1 m wide middle section of the flume bed.  54   Figure 4.12: The histogram of run 3, hour 1 grain size gradient variance values. To delineate patches, cells where the value of gradient variance was less than or equal to the third geometrical interval were extracted where values of observed grain size were smaller than or equal to 5.66 mm (P1), between 5.66 and 16 mm (P2), and 16 mm or above (P3). The threshold value of gradient variance is unique to each observation window because the distribution of values changes.  55   Figure 4.13: Run 3, hour 1, P1 cells (fine sediment patches) represented by brown-colored squares adjacent to the corresponding bed photograph. Flow direction goes from left to right. The image represents the 2 m long by 1 m wide middle section of the flume bed.  56  To summarize the results of the patch delineation analysis, figure 4.14 displays three curves, each of which represent the fraction of area identified as P1, P2, or P3 as a proportion of the total identified patch area. The solid red curve represents the summed fraction of area of each patch type as a proportion of the total area in the 2 m middle section of the flume (figure 4.14). The total patch area relative to the total area in the frame never reaches 100% because some locations did not fall into one of the three patch type categories. Gradient variance threshold values unique to each observation window ranged from 0.02 ? 0.04. The P3 cells encompassed the largest relative area and fluctuations to P2 areas were the least variable across each experimental run (figure 4.14).  57   Figure 4.14: Fraction of area identified as P1, P2, or P3 as a proportion of the total identified patch area (black curves) and the total identified patch area as a fraction of the total area in the 2 m middle section of the flume (red curve) over the duration of the experiment with vertical lines representing the observation window one hour after the beginning of each sediment input event.  58  The initial no feed conditions of run 1 resulted in a gradual increase in the area of the bed classified as P3, while the area composed of P1 decreased (figure 4.14). Further examination of these results, however, revealed that by hour 10 of run 1, cells identified as patches were dispersed. That is, aggregations of fine, medium, or coarse material that would typically be identified as patches were actually isolated cells that fit the patch delineation query. The initial response of the bed to the introduction of constant sediment supply was a decrease in P2 and P3 and an increase in areas identified as P1 (figure 4.14). By hour 4 of run 2, however, fractional P1 and P3 areas attained a relatively steady value and P2 continued to decline in area over the remainder of the run. One hour after the 300 kg sediment pulse, P1 and P3 made up the majority of the bed (figure 4.14). The total area identified as one of the three patch types relative to the total area of the bed also peaked one hour after the 300 kg pulse (figure 4.14). Over time, the area of the bed delineated as P1 diminished with a slight increase halfway through run 3. The increase in P1 during run 3, hour 20 coincided with a decrease in P3 and almost no change from the previous observation window to areas identified as P2 (figure 4.14). The number of cells identified as P2 was the least variable of all three patch types. The P2 cells were also the least aggregated of the three patch types over the duration of run 3. Patch delineation over the course of run 4 was variable, but overall, P1 and P3 areas decreased while P2 area increased after four 75 kg sediment inputs (figure 4.14). The total patch area relative to the area of the bed fluctuated throughout run 4, with a declining trend (figure 4.14). One hour after each sediment input, P3 decreased and P1 increased. However, the time between sediment pulses brought about decrease in the area identified as P1. There were no detectable patterns in the fluctuation of area identified as P2 from pulse to pulse.   59  Similarly, run 5 induced immediate increases in P1 area and decreases in P3 area following each of the 150 kg sediment pulses (figure 4.14). By the end of the run, the bed was characterized by a relatively low total patch area as a fraction of the area of the bed, with a largely coarse material presence (figure 4.14). The second constant feed experimental run brought about a marked increase in P1 relative to those areas identified as fine material patches over runs 3, 4, and 5 (figure 4.14). The P2 and P3 areas declined, but attained a relatively constant value over the duration of run 6. The increase in P1 area induced by the constant sediment feed resulted in a relatively high total value of patch area as a fraction of the entire bed area. Finally, the no feed conditions of run 7 resulted in the lowest values of P1 and an increase in P3 (figure 4.14). The final 20 hours of the experiment, however, saw an increase in P1 area, while other patch types remained constant.    60  Chapter 5 Bed Topography In fluvial hydraulics, a parameter of bed roughness is needed to determine flow resistance and mean flow velocity (Clifford et al., 1992). Statistical analyses can be conducted on high resolution three-dimensional (3D) Digital Elevation Models (DEMs) to acquire such a parameter. Surface elevation is assumed to be a random field, z(x, y), where z is surface height at coordinates (x, y) (e.g., Aberle and Nikora, 2006). In this study, the topography of the 2 m bed section was acquired with a laser profiler. This chapter presents a review of the methods used to characterize bed roughness, the measurement techniques used in this study, and the statistical and spatial-statistical analyses of bed elevation. The focus is to use Probability Distribution Functions (PDFs) and two-dimensional (2D) second-order structure functions (semivariograms) to characterize bed roughness. Sediment storage in the bed is then linked to results of the bed roughness analyses. 5.1 Roughness Characterization and Spatial Statistics Conventionally, bed roughness was represented by percentiles of the GSD (e.g., Bathurst, 1985), a technique that stemmed from work of Nikuradse (reported in Nikora et al., 1998). However, the conventional characterization of gravel bed roughness is made under the assumption that the GSD, particle arrangements on the bed, grain shape and orientation, bed sorting, clustering, and other features of bed topography are constant at all observation windows and locations along a reach. These assumptions have been criticized as long as the method has been in place (e.g., Bray, 1985; Hey and Thorne, 1986; Furbish, 1987; Kirchner   61  et al., 19990; Robert, 1990; Carling et al., 1992). As an alternative, researchers have come to use the random field approach to quantify gravel bed roughness. The description of gravel bed roughness has emerged in two categories: small scale particle roughness and large scale form roughness. Flow energy lost on particles occurs due to viscous drag on the bed surface and form drag due to small scale roughness elements of particle size, shape, and arrangement (Aberle and Nikora, 2006). Advancements in spatial resolution of 3D measurements in laboratory settings are vital to the study of particle and form-scale variations in bed topography. Scales of roughness with 1 mm precision can be identified using spatial statistics of bed surface elevations. The method most recognized to date to represent the vertical roughness length is to compute the standard deviation of bed elevations, ?z (usually given in mm) (e.g., Nikora et al., 1998; Aberle and Nikora, 2006), to show how elevation varies from the mean. In addition to ?z, PDF skewness (Sk) and kurtosis (Ku) of bed elevation provide measures of evenness and intermittency between DEMs (Coleman et al., 2011). One way to further characterize the spatial structure of a river bed surface is based upon the idea that sediment structure signatures have typical dimensions within which maximum variability occurs. The spatial arrangement of grains on a bed and the degree of self-organization that occurs can be quantified using a structure function (Marion et al., 2003). Spatial dependence between pairs of elevation points is analyzed by estimating the correlation between elevations at different distances and in different directions. In geomorphology, the use of 2D structure functions, or semivariograms, is becoming a robust way to model the geometric properties of surface structures in relation to parameters such as   62  flow intensity (e.g., Robert, 1988, 1991; Nikora et al., 1998; Butler et al., 2001; Marion et al., 2003; Smart et al., 2004; Aberle and Nikora, 2006). 5.2 Methods 5.2.1 Data Acquisition At the same 79 observation windows as those made for bed surface photographs (table 4.1), a programmable laser scanner mounted 1 m above the bed on a motorized cart was used to obtain topographic scans of the bed. A matrix of bed elevations was produced from a sheet of green (532 nm) laser light and a video camera that recorded where the laser reflected off the bed using LabViewTM image processing software. Bed scans were composed of cross-sections with 1 mm vertical and horizontal resolution. Cross-sections spaced 2 mm apart were then stacked together to construct DEMs that covered the width and length of the flume. Each meter of flume length took about 15 minutes to scan. To continue a run after recording bed surface properties or to begin another run, flow was slowly restarted in order to minimize influence on bed topography. 5.2.2 Data Preprocessing Inspection of the DEM data revealed several outliers that were physically impossible in the flume setting, such as values much greater than the depth of sediment in the flume. To account for other obscure measurements that were likely generated from reflections on the sides of the flume, DEMs were masked by removing 96 mm on the left back and all values past the 1066 mm mark on the right bank. To ensure that unrealistic bed elevation points were removed (e.g., negative or very large values), maximum and minimum elevation threshold values were set at 200 and 0 mm, respectively.   63  Before analyzing the DEMs, detrending surfaces unique to each elevation plot were created to remove trends with scales larger than the scale of sediment patterns, such as bed slope or undulations. In previous studies, linear or higher degree polynomial trend surfaces have been fitted to elevation matrices (e.g., Clifford et al., 1992; Marion et al., 2003) or constructed through the application of a moving filter (e.g., the 1.25D90 filter in Smart et al., 2002) to determine the spatial extent of trends that should be removed from the data. In this study, unique detrending surfaces were generated by averaging bed elevation values at every cross-section and then constructing planar surfaces with slopes calculated from best-fit least squares linear regressions of longitudinal profiles from each 2 m long section. Detrending surfaces were then subtracted from the original DEMs to make an unbiased surface from which to measure grain roughness (Goring et al., 1999). 5.2.3 Statistical Roughness Analysis Histograms were obtained to display empirical distributions of surface elevations for DEMs at each observation window. Three functions were used to calculate the ?ideal? number of bins for each histogram: (1) Freedman-Diaconis, which is based upon the interquartile range and number of data, (2) Scott, which is based upon the sample standard deviation and number of data, and (3) Sturges, which is based upon the number of data (Cotton, R., 2008 MATLAB script). The functions used to calculate the numbers of bins were simply guides to the definitive human eye. Distribution plots of bed elevation values were generated using the histfit function in MATLAB with 30 bins and a superimposed fitted normal density curve. Each detrended DEM was converted from a matrix to an array before Sk, Ku, maximum, minimum, mean, median, and ?z of surface elevations were extracted. Values of ?z were used   64  as a surrogate for vertical roughness length, as prompted by Nikora et al., 1998, Aberle and Nikora, 2006, and Cooper and Tait, 2009. Generalized 2D second order structure functions, or semivariograms, were used to further investigate bed topography. The function, D(lx, ly), of bed elevation, z, is an average squared increment: {z(x + ?x, y + ?y) ? z(x, y)}2 that can be generalized to DG (Nikora et al., 1998) by summing the difference in elevations between all pairs with a given spacing to produce one observation of semivariance, ?: DG(lx, ly) = [1 / (N ? n)(M ? m)]?N-ni = 1 ?M-mj = 1{|z(xi + n?x, yj + m?y) - z(xi, yj)|}2     (5.1) Where n and m are lags, or horizontal distances between point pairs of elevation, in the N and M directions (corresponding to the x and y directions, respectively) and lx = n?x, ly = m?y, ?x, and ?y are the sample intervals. The goal is to express the semivariance of a surface between the elevation of point pairs as a function of the horizontal distance or lag between the pairs. Semivariograms were calculated in the open source statistical programming and graphics environment, R (R Development Core Team, 2009). A function built into the gstat package (Pebesma, 2004) was used. At lags n and m greater than half of x and y, respectively, it was assumed that there were insufficient pairs of points to calculate ? accurately (e.g., Hodge et al., 2008). The maximum distance at which pairs of observed elevations points were considered for inclusion in semivariogram estimates was thus set at 10 (called the ?cutoff? in the variogram command in gstat) and lag width, or step size of distance intervals for variogram estimates, was set at 1. The units for both cutoff and width correspond to the coordinate system of the original bed   65  elevation matrix. Each matrix is 471 points x 1001 points, indicating that there is an elevation value every 2 mm along and across the 2 m section of the flume. 5.2.4 Sediment Storage Geomorphic Change Detection (GCD) maps were produced to estimate the net change in sediment storage in the 2 m middle section of the flume. The maps were produced for each run, that is, bed elevations from the first hour of each run were subtracted from subsequent hours within the same run. Cumulative values of sediment storage were also calculated over the entire experiment whereby bed elevations from the first hour of the experiment were subtracted from every subsequent hour of observation in the experiment. Finally, the temporal evolution of sediment storage was plotted as the difference in elevation from one observation window to the next across all runs of the experiment. 5.3 Results Tables 5.1-5.4 are presented in this section as well as select DEMs and PDFs in order to compare bed topography to surface texture results from sections 4.3.1 and 4.3.2. Semivariograms computed for observation windows corresponding to the values presented in tables 5.1-5.4 are plotted in section 5.3.2. Finally, the results of the GCD analysis are presented. 5.3.1 Bed Roughness Well-mixed or freshly-screeded gravel beds typically produce tall, narrow, symmetrical PDFs, which indicate that the deviation of surface elevations for the mean bed elevation is small. After a period of flow, grains reorganize and PDFs display wider, shallower curves.   66  Skewness of a PDF can be used to assess the general shape or form of the bed surface; positive Sk coefficients are typical for armored gravel beds (e.g., Nikora et al., 1998; Smart et al., 2004; Aberle and Nikora; 2006; Coleman et al., 2011). As the bed evolves to an armored state, fine particles winnow out or fill surface depressions and the magnitude of surface elevations below the mean bed level reduces (Aberle and Nikora, 2006; Nikora et al., 1998). Kurtosis describes the variation of variance of the PDF. Visually, Ku is a description of the tailedness and peakedness of the distribution. Large values of Ku indicate a heavy-tailed, narrow-peaked PDF while uniform, compact PDFs take on lower Ku values; a normal distribution has a Ku of 3. Figure 5.1 illustrates the effect of surface armoring on PDFs of bed elevation. These two observation windows were selected to contrast PDFs of beds characterized by different roughness states. After 40 hours of no sediment feed and one hour of constant sediment feed, the elevation plot of run 2, hour 1 displays low values, ranging from 27.09-90.22 mm (figure 5.1 A). The Sk value of the run 2, hour 1 PDF was 0.74, indicating a higher degree of armoring than what the surface elevations of run 4, hour 31 exhibited (figure 5.1 B). After the third 75 kg pulse of run 4, that is, the PDF of bed elevation was close to normal, as indicated by the solid black curve on figure 5.1 D. The Ku value of the run 4, hour 31 PDF was 3.07 and Sk was 0.26. Though the PDF of bed elevations of run 4, hour 31 exhibited a more normal shape, overall bed roughness was higher than that of run 2, hour 1 (table 5.1). The value of ?z for the armored bed of run 2, hour 1 was 8.79 mm, while ?z was 11.03 mm immediately following the third 75 kg pulse of run 4 (table 5.1).   67    Figure 5.1: Run 2, hour 1 (A and C) and run 4, hour 31 (B and D) elevation plots and PDFs of bed elevation with normal curves overlain. A B C D   68  Statistical properties for PDFs from hours 1, 2, and 40 for runs 1, 2, 3, 6, and 7, for hours 1, 2, 10, 11, 12, 20, 21, 22, 30, 32, and 40 for run 4, and for hours 1, 2, 20, 21, 22, and 40 for run 5 are presented in table 5.1. In all experimental runs except for run 5, Sk values were lower at hour 40 than hour 1. Overall, Sk decreased throughout the experiment, ranging from 0.01 to 0.77. As the values of Sk were consistently positive, all PDFs were skewed to the right, attributed to surface armoring. Values of Ku were relatively constant throughout the experiment, hovering around the value that a normal distribution would take on (2.82-3.76). There was no apparent within-run variability observed in Ku values.     69  Table 5.1: Statistical properties for PDFs from hours 1, 2, and 40 for runs 1, 2, 3, 6, and 7, for hours 1, 2, 10, 11, 12, 20, 21, 22, 30, 32, and 40 for run 4, and for hours 1, 2, 20, 21, 22, and 40 for run 5: Sk, Ku, and zmax, zmin, zmean, zmedian, and ?z (all in mm). Run Hour Sk Ku zmax (mm) zmin (mm) zmean (mm) zmedian (mm) ?z (mm) 1 1 0.64 3.12 91.98 29.26 55.58 54.23 9.01 1 2 0.68 3.23 91.68 8.62 54.93 53.39 8.93 1 40 0.43 2.96 89.88 21.62 51.22 50.25 9.85 2 1 0.74 3.29 90.22 27.09 52.83 51.17 8.79 2 2 0.77 3.37 90.48 20.02 52.95 51.26 8.77 2 40 0.45 3.33 107.71 28.50 63.90 63.13 9.81 3 1 0.20 3.25 110.63 31.42 69.68 69.41 10.20 3 2 0.60 3.76 114.96 46.14 71.33 70.49 8.71 3 40 0.23 2.99 112.81 31.63 70.51 70.03 11.14 4 1 0.37 3.29 116.55 46.93 74.98 74.51 9.62 4 2 0.41 3.29 115.26 45.29 73.53 72.72 10.15 4 10 0.19 2.95 112.05 36.82 71.96 71.46 10.86 4 11 0.29 2.92 114.44 51.95 77.20 77.04 9.39 4 12 0.28 2.96 113.86 46.74 77.03 76.90 9.40 4 20 0.18 2.82 115.44 42.66 74.45 74.24 10.78 4 21 0.25 3.08 119.24 45.42 77.07 76.98 9.40 4 22 0.19 2.83 113.69 46.21 76.72 76.67 9.92 4 30 0.08 2.99 131.14 38.21 76.01 76.20 10.89 4 31 0.26 3.07 127.22 41.18 79.76 79.32 11.03 4 32 0.32 2.87 120.50 47.35 78.72 78.23 10.78 4 40 0.15 2.91 117.26 36.11 78.16 77.97 11.16 5 1 0.15 3.11 125.90 44.27 81.01 80.84 10.79 5 2 0.21 3.13 124.78 46.97 80.81 80.41 10.94 5 20 0.26 3.15 124.76 41.25 78.97 78.42 10.83 5 21 0.40 3.20 124.74 50.58 81.93 81.28 9.91 5 22 0.28 3.25 124.36 26.41 80.00 79.39 10.15 5 40 0.42 3.13 127.01 44.09 81.96 81.00 10.39 6 1 0.42 3.19 127.02 45.07 82.07 81.13 10.36 6 2 0.68 3.39 127.02 54.33 82.82 81.26 9.56 6 40 0.13 3.45 128.23 53.02 88.59 88.38 9.65 7 1 0.08 3.46 129.26 49.66 88.76 88.97 9.80 7 2 0.06 3.49 128.23 51.88 88.97 89.22 9.87 7 40 0.01 3.42 128.74 47.83 87.50 87.59 10.33   70  Table 5.2 summarizes the between-run bed roughness and elevation statistics for hours 10, 20, 30, and 40 from runs 2, 4, and 6. Consistently low values of Sk and Ku were computed during hours 10, 20, 30, and 40 of run 4, but bed elevation values increased from run to run (table 5.2). Over time, values of ?z increased, (except for the last observation window of run 6, when ?z decreased to 9.65 mm), indicating more extreme variations in bed elevation and therefore, a rougher bed. Corresponding hours between experimental runs did not exhibit similar bed elevation characteristics as those described for bed texture in sections 4.3.1 and 4.3.2. Table 5.2: Statistical properties for PDFs from hours 10, 20, 30, and 40 for runs 2, 4, and 6: Sk, Ku, and zmax, zmin, zmean, zmedian, and ?z (all in mm). Run Hour Sk Ku zmax (mm) zmin (mm) zmean (mm) zmedian (mm) ?z (mm) 2 10 0.69 3.30 86.56 15.74 52.99 51.65 8.12 2 20 0.38 3.11 90.76 22.01 53.16 52.46 9.25 2 30 0.77 4.08 93.39 36.12 59.32 58.55 7.18 2 40 0.45 3.33 107.71 28.50 63.90 63.13 9.81 4 10 0.19 2.95 112.05 36.82 71.96 71.46 10.86 4 20 0.18 2.82 115.44 42.66 74.45 74.24 10.78 4 30 0.08 2.99 131.14 38.21 76.01 76.20 10.89 4 40 0.15 2.91 117.26 36.11 78.16 77.97 11.16 6 10 0.24 3.13 127.05 49.57 84.10 83.62 10.33 6 20 0.28 3.22 133.73 49.65 85.16 84.75 10.75 6 30 0.27 3.38 135.85 55.22 87.86 87.75 10.02 6 40 0.13 3.45 128.23 53.02 88.59 88.38 9.65  Overall roughness and bed elevation statistics between runs 1, 3, and 7 are summarized in tables 5.3 and 5.4. Values of Sk were generally different between corresponding observation windows, with a progressive decline from runs 1 to 3 to 7, but steady values of Ku were observed over the hours summarized in tables 5.3 and 5.4. Maximum bed elevation grew   71  increasingly larger from runs 1 to 3 to 7, but maintained constant values within each run. A similar increasing ?stair-step? pattern was observed for values of zmean and zmedian. Bed roughness, however, resulted in variable results with the highest values of ?z observed over each observation window of run 3 (table 5.3).    72  Table 5.3: Statistical properties for PDFs from hours 10, 20, 30, and 40 for runs 1, 3, and 7: Sk, Ku, and zmax, zmin, zmean, zmedian, and ?z (all in mm). Run Hour Sk Ku zmax (mm) zmin (mm) zmean (mm) zmedian (mm) ?z (mm) 1 10 0.64 3.06 91.47 6.35 53.61 52.19 9.46 1 20 0.51 2.90 89.61 17.08 51.77 50.74 9.73 1 30 0.84 3.78 89.26 32.71 54.17 52.90 7.74 1 40 0.43 2.96 89.88 21.62 51.22 50.25 9.85 3 10 0.19 3.09 110.49 29.72 69.87 69.77 10.84 3 20 0.28 3.11 121.44 35.85 70.50 70.29 11.14 3 30 0.23 2.99 121.48 33.34 70.54 70.05 11.15 3 40 0.19 3.09 112.81 31.63 70.51 70.03 11.14 7 10 0.05 3.76 132.61 50.92 88.73 88.84 10.13 7 20 0.01 3.50 128.23 52.78 88.21 88.27 10.17 7 30 0.45 3.55 128.23 38.58 88.84 88.10 9.04 7 40 0.01 3.42 128.74 47.83 87.50 87.59 10.33  Table 5.4: Statistical properties for PDFs from hours 1, 2, 4, and 7 for runs 1, 3, and 7: Sk, Ku, and zmax, zmin, zmean, zmedian, and ?z (all in mm). Run Hour Sk Ku zmax (mm) zmin (mm) zmean (mm) zmedian (mm) ?z (mm) 1 1 0.64 3.12 91.98 29.26 55.58 54.23 9.01 1 2 0.68 3.23 91.68 8.62 54.93 53.39 8.93 1 4 0.68 3.20 136.77 3.63 54.59 52.93 9.08 1 7 0.83 3.91 92.18 11.73 57.36 56.22 7.68 3 1 0.20 3.25 110.63 31.42 69.68 69.41 10.20 3 2 0.60 3.76 114.96 46.14 71.33 70.49 8.71 3 4 0.57 3.77 110.79 45.06 72.13 71.32 8.50 3 7 0.22 3.08 110.60 32.27 69.51 69.12 10.31 7 1 0.08 3.46 129.26 49.66 88.76 88.97 9.80 7 2 0.06 3.49 128.23 51.88 88.97 89.22 9.87 7 4 0.02 3.57 129.33 52.99 88.86 88.85 10.01 7 7 0.36 3.48 128.24 42.75 89.49 89.18 9.16    73  5.3.2 Structure Functions of Bed Elevation Semivariograms, or 2D second-order structure functions, were computed for the first and last hour of each experimental run and for observation windows corresponding to those explored in detail in sections 4.3.1, 4.3.2, and 5.3.1. In order to compare between experimental runs, spatial lags, or separation distances between pairs of binned data points, were normalized by the D50 of surface material at each respective observation window and ? was normalized by ?z2. The results show that at values of the normalized spatial lag, the gradient of the structure function is approximately linear in log-log space (figure 5.2). Robert (1988) found that semivariograms of gravel bed profiles present two distinct linear increases of ? with lag distance that correspond to grain scale and form scale roughness. It is difficult to say that the results of this study follow the same pattern. Instead, it can be interpreted that at the range where the curves level off, there is no spatial dependence after respective lag distances. The ?scaling region?, or the linear relation up to the leveling-off point is thought to increase up to < 0.5D50 as the bed becomes more armored (Marion et al., 2003; Nikora and Walsh, 2004). The scale of topographic variation at the range of lags in each semivariogram plot is presumably determined by a particular process regime. For the same relative lag, bed surfaces that exhibit relatively high normalized ? can be attributed to relatively high elevation differences brought about by the presence of large, protruding grains. In contrast, relatively low values of normalized ? at the same relative lag may be due to a bed surface made up of relatively well-embedded or small particles (Hodge et al., 2009).    74      Figure 5.2: 2D second-order generalized structure functions for hours 1 (dash-dotted curve), 2 (solid curve with ?+? symbol), and 40 (solid curve) for each experimental run (A-G).  10-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 1, Hour 1Run 1, Hour 2Run 1, Hour 4010-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 2, Hour 1Run 2, Hour 2Run 2, Hour 4010-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 3, Hour 1Run 3, Hour 2Run 3, Hour 4010-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 4, Hour 1Run 4, Hour 2Run 4, Hour 4010-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 5, Hour 1Run 5, Hour 2Run 5, Hour 4010-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 6, Hour 1Run 6, Hour 2Run 6, Hour 4010-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 7, Hour 1Run 7, Hour 2Run 7, Hour 40A B C D E F G   75  The scaling region occupied about the same range of normalized lag values for hours 1, 2, and 40 of run 1 (figure 5.2 A). The variogram curve for run 2, hour 40 was shifted up to higher values of ? at the same relative lag compared to run 1 and hours 1 and 2 for run 2 (figures5.2 B and 5.2 A). After 40 hours of starvation conditions followed by 40 hours of constant sediment supply, the 2 m middle section of the flume came to exhibit high elevation differences and therefore higher values of ? relative to former oberservation windows. Semivariogram plots for run 3, hours 1, 2, and 40 occupy shorter scaling regions than those displayed in figure 5.2 A and 5.2 B (figure 5.2 C). Even by hour 40 of run 3, when the bed surface returned to a relatively well-armored state, the linear relation leveled-off a lower point of normalized lag than that of runs 1 and 2. That is to say that spatial autocorrelation was detected at shorter relative lag distances for hours 1, 2, and 40 of run 3 than those for structures that evolved over the course of runs 1 and 2. Hours 1, 2, and 40 of run 4 reached similar values of normalized lag to the same observation windows of runs 1, 2, and 3, but values of normalized ? were lower (figure 5.2 D). The range of normalized ? values at the same value of normalized lag was also greater than those of runs 1, 2, and 3, indicating that surface structures became more variable at a particle scale following the four 75 kg sediment pulses (Hodge et al., 2009). Correspondingly, the bed became rougher from hour 1 to hour 40 of run 4 (from ?z = 9.62 to 11.16 mm). Run 5 semivariogram curves exhibited similar attributes as those for corresponding observation windows of run 2 (figure 5.2 E). Little change in normalized ? was detected at the same value of normalized lag from hours 1 to 2 to 40 (figure 5.2 E) and roughness values were calculated as 10.79, 10.94, and 10.39 mm, respectively (table 5.1).   76  By the end of run 6, a relatively low value of normalized ? was output at the same normalized lag as those computed from the first two sets of elevation data in run 6 (figure 5.2 F). Bed structures were thus dissimilar to those that evolved over the course of run 2. As well, roughness decreased over the second constant feed experimental run from 10.36 to 9.65 mm (table 5.1). Finally, figure 5.2 G displays three overlapping semivariogram curves of hours 1, 2, and 40 for run 7. Little change in surface structure was detected throughout the final sediment starvation run (figure 5.2 G).    77   Figure 5.3: 2D second-order generalized structure functions for hours 10 (dash-dotted curve), 20 (solid curve with ?+? symbol), 30 (dotted curve), and 40 (dashed curve) for runs 2 (A), 4 (B), and 6 (C). The resulting structure functions plotted for runs 2, 4, and 6 at hours 10, 20, 30, and 40 can be used to supplement the general results in table 5.2 (figure 5.3). As the bed became increasingly rougher over the course of run 4, values of normalized ? decreased at the same relative value of normalized lag in comparison to run 2 (figures 5.3 B and 5.3 A). The ranges over which autocorrelation of spatial structure were detected were similar across each observation window in runs 2, 4, and 6. In other words, spatial dependence of bed structure is similar at similar lag distances, but lower values of normalized ? in runs 4 and 6 compared to run 2 may have been brought about by the general embedding of grains on the surface or by 10-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 2, Hour 10Run 2, Hour 20Run 2, Hour 30Run 2, Hour 4010-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 4, Hour 10Run 4, Hour 20Run 4, Hour 30Run 4, Hour 4010-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 6, Hour 10Run 6, Hour 20Run 6, Hour 30Run 6, Hour 40A B C   78  the presence of smaller grains. There are no marked similarities between corresponding observation windows of each run.   Figure 5.4: 2D second-order generalized structure functions for hours 10 (dash-dotted curve), 20 (solid curve with ?+? symbol), 30 (dotted curve), and 40 (dashed curve) for runs 1 (A), 3 (B), and 7 (C). 10-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 1, Hour 10Run 1, Hour 20Run 1, Hour 30Run 1, Hour 4010-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 3, Hour 10Run 3, Hour 20Run 3, Hour 30Run 3, Hour 4010-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 7, Hour 10Run 7, Hour 20Run 7, Hour 30Run 7, Hour 40A B C   79   Figure 5.5: 2D second-order generalized structure functions for hours 1 (dash-dotted curve), 2 (solid curve with ?+? symbol), 4 (dotted curve), and 7 (dashed curve) for runs 1 (A), 3 (B), and 7 (C). Figures 5.4 and 5.5 display semivariogram curves for runs 1, 3, and 7 at hours 10, 20, 30, and 40 (figure 5.4) and hours 1, 2, 4, and 7 (figure 5.5). Similarities between corresponding observation windows are once again, not marked. For all curves computed for run 3, ranges of normalized lag were shorter than those computed for runs 1 and 7. Values of normalized ? were similar across all observation windows plotted in figures 5.4 and 5.5, perhaps surprising, given that the introduction of the 300 kg sediment pulse in run 3 resulted in increased bed roughness in the 2 m middle section of the flume (tables 5.3 and 5.4).  10-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 1, Hour 1Run 1, Hour 2Run 1, Hour 4Run 1, Hour 710-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 3, Hour 1Run 3, Hour 2Run 3, Hour 4Run 3, Hour 710-210-1100101100Lag / D50Semivariance ( ? / ?2 z )  Run 7, Hour 1Run 7, Hour 2Run 7, Hour 4Run 7, Hour 7A B C   80  5.3.3 Temporal Evolution of Sediment Storage Overall results of the within-run GCD values are given in table 5.5. Figure 5.6 summarizes the average net change in sediment storage (in mm) in the 2 m middle section of the flume. The solid curve represents incremental changes in sediment storage, that is, differences in elevation from one observation window the next across all runs of the experiment. The cumulative change in bed elevation is represented with a dashed curve on figure 5.6. Bed elevations from the first hour of the experiment were subtracted from every subsequent observation window and then averaged to produce the dashed curve.  81   Figure 5.6: Cumulative (dashed curve) and incremental (solid curve) changes in bed elevation (mm) in the 2 m middle section of the flume over the duration of the experiment with vertical lines representing the observation window one hour after the beginning of each sediment input event.  82  The effect of no sediment feed during runs 1 and 7 resulted in average bed elevation degradation of 2.52 mm and 1.38 mm, respectively (table 5.5). The sediment pulsing regimes of runs 3, 4, and 5 also induced negative changes in average bed elevation over the course of each run, the largest of which, was calculated over run 5 with degradation of 7.84 mm (table 5.5). The highest average value of aggradation was calculated over run 2, with an increase of 2.89 mm (table 5.5). Table 5.5: Overall bed elevation or storage differences (mm) between hours 1 and 40 within each experimental run. Run Overall GCD (mm) 1 -2.52 2 2.89 3 -5.55 4 -7.19 5 -7.84 6 0.49 7 -1.38  By the end of the experiment, cumulative sediment storage increased up to about 33 mm (figure 5.6). Each of the sediment input pulses resulted in cumulative and incremental aggradation, but the bed tended to immediately degrade before reaching a stable level of elevation after each input event (figure 5.6). Table 5.6 summarizes the effect of each pulse on sediment storage, with values of average cumulative bed elevation difference and sequential bed elevation difference (in mm). Overall, cumulative sediment storage increased from runs 3 to 5, except for the observation window following the third 75 kg pulse, when the bed accumulated slightly less material relative to the initial conditions of the experiment (table 5.6). Average sequential values of sediment storage were highest following the 300 kg pulse and the first two 75 kg pulses. That is to say that between 40 hours of constant feed   83  conditions and the first hour following the 300 kg sediment pulse, the bed aggraded 5.69 mm of material (table 5.6). Between the end of run 3 and the first 75 kg pulse of run 4, the bed aggraded 4.09 mm and after nine hours of water flow with no sediment feed and the second 75 kg pulse of run 4, 4.94 mm (table 5.6). Bed material aggradation from each preceding observation window to the next listed in figure 5.5 decreased over time. Over the entire experiment, however, values of sequential changes in bed elevation were relatively constant around zero. Table 5.6: Overall (between runs 3, 4, and 5 and hour 1 of run 1) and sequential (from the observation window preceding each of the hours listed) bed elevation or storage differences (mm). Run Hour Cumulative GCD (mm) Sequential GCD (mm) 3 1 14.57 5.69 4 1 19.73 4.09 4 11 21.97 4.94 4 21 21.80 2.44 4 31 24.76 3.62 5 1 26.12 2.72 5 21 26.92 2.85  With an increasingly aggraded bed, average bed elevation values became increasingly higher over the course of the experiment (figure 5.7). Initially, the bed maintained a relatively constant value of average elevation within the 2 m middle section, with increases detected only 20 hours after the introduction of constant sediment supply (figure 5.7). The advent of a 300 kg sediment input spiked the value of minimum, maximum, and mean bed elevation as the highest increase in aggradation across all experimental runs also resulted (table 5.4). Minimum values of bed elevation were in fact the most variable over the duration of the experiment, with fluctuations occurring within each run (figure 5.7).   84   Figure 5.7: Mean, maximum, and minimum bed elevations (mm) in the 2 m middle section of the flume over the duration of the experiment with vertical lines representing the observation window one hour after the beginning of each sediment input event.   85  Chapter 6 Microtopography It is widely known that clusters, a type of microform, play a role in the function of natural gravel bed streams. Laronne and Carson (1976) and Brayshaw et al. (1983) were among the first to relate the formation of clusters to particle interlocking, near-bed flow characteristics, sediment availability and transport, and channel slope. However, the most recent bedload transport equations that relate hydraulic parameters to surface sediment distribution in poorly sorted gravel bed streams do not directly take into account the effect of neighboring particles on stability. Some transport equations incorporate a hiding function (e.g., Einstein, 1950; Parker and Sutherland, 1990; Wilcock and Crowe, 2003) to indirectly model the incipient motion of mixed-size sediment. Because clusters tend to form and disintegrate in high flow conditions, field observations are impractical (Strom and Papanicolaou, 2002; Wittenberg et al., 2007). Nonetheless, studies of cluster dynamics are emerging in natural and flume settings (e.g., Papanicolaou and Kramer, 2006; Papanicolaou and Schuyler, 2003; Papanicolaou et al., 2003; Strom and Papanicolaou, 2002; Strom et al., 2004; Strom and Papanicolaou, 2006). The results of this study add to the body of knowledge by relating cluster development, formation, and disintegration to the sediment supply regime. In this chapter, a cluster identification method is presented following a summary of previous cluster descriptions, namely those of Strom et al. (2005) and the modifications by Hendrick et al. (2010). Cluster formation, disintegration, and surface area are then summarized over the duration of the experiment.   86  6.1 The Influence of Microtopography on Sediment Transport Clusters have been identified as microforms in gravel bed streams that generate turbulent flow structures and increase flow resistance (Teisseyre, 1977; Brayshaw, 1984; Hassan and Reid, 1990; Reid et al., 1992; de Jong, 1995; Buffin-Belanger and Roy, 1998; Hassan and Church, 2000; Roy et al., 1999; Roy and Buffin-Belanger, 2001; Tan and Curran, 2012). These sorts of structures play a role in the stability of the bed (Reid et al., 1992) and bedload transport rates (Strom et al., 2004) and can delay sediment entrainment by entrapping sediment particles along their perimeter or within their structure. Early observations of cluster dynamics reported that the so-called anchor stone increases bed stability by preventing transport of particles within the cluster until the anchor stone is entrained (Brayshaw, 1984; Hassan and Reid 1990; Reid et al., 1992). Theoretically, entrainment of the anchor stone would occur at high flows and therefore, material finer than the anchor stone grain size would require higher shear stresses to become entrained than the values predicted under typical empirical or physical relations. However, Billi (1988) and De Jong (1991) suggested that microform stability does not depend upon characteristics of the anchor stone. Hendrick et al. (2010) determined that both scenarios could occur; they attributed higher dimensionless Shields stress values (0.08) to graded clusters and cited disintegration of clusters in uniform bed material to require lower values (0.06). Interactions between the flow field and the bed that produce grain size-scale structures are equally as complex as those that are responsible for patch formation. Surface structure development, such as clusters, in laboratory flumes has been observed during periods of bed armoring and water-working without sediment feed (e.g., Parker and Sutherland, 1990; Tait and Willetts, 1991; Hassan and Church, 2000; Marion et al., 2003). Armored streambeds are   87  characterized by large surface clasts relative to subsurface material. A so-called static armor layer protects fine grains from entrainment (Parker and Sutherland, 1990). Throughout the armoring process, large surface grains can form clusters (Brayshaw, 1984; Church et al., 1998; Oldmeadow and Church, 2006) by way of protrusion into the flow, which affects local hydrodynamic forces in the water and induces upstream and downstream deposition of smaller particles (Brayshaw et al., 1983). 6.2 Descriptions of Clusters Since the description by Brayshaw (1984) of closely nested groups of particles aligned parallel to the flow, clusters have been broadly defined as ?discrete, organized groupings of particles that sit above the average elevation of the surrounding bed surface? (Strom and Papanicolaou, 2008, p. 138). Through the work of Strom et al. (2005) and modifications by Strom and Papanicolaou (2008) and Hendrick et al. (2010), various cluster shapes have been identified and used to describe microtopography in field and flumes. Pebble clusters consist of an anchor stone surrounded by fine material in the stoss (upstream) zone and coarse material in the wake (downstream) zone. Line clusters on the other hand, lack stoss and wake zones and are composed of material of similar size linked together parallel to the direction of flow. Comet clusters are similar to pebble clusters, but normally occupy a wider cross-stream area and form two tails of medium-sized particles. Comet clusters collect fine material in the middle of the structure, similar to the less-commonly observed ring cluster formation. Heap clusters are loosely defined as piles of the largest particle sizes on the bed. Upstream triangle-shaped clusters exhibit the similar streamline shape as pebble clusters and are typical of newly-formed clusters. Downstream triangle, transverse line, and diamond clusters are   88  uncommon, perhaps due to their complex shapes, but nonetheless documented (Hendrick et al., 2010).   Figure 6.1: Cluster types from (A) ?Characterization of particle cluster bedforms in a mountain stream,? by Strom, K.B. Papanicolaou, A.N., Billing, B., Ely, L.L., and Hendricks, R.R., 2005. In: Proceedings of the ASCE/EWRI World Water and Environmental Resources Congress, pp. 399. Resont, Virginia: ASCE, and (B) ?The role of hydrologic processes and geomorphology on the morphology and evolution of sediment clusters in gravel-bed rivers,? by Hendrick, R.R., Ely, L.L., and Papanicolaou, A.N., 2010. Geomorphology, 114 (3), 483-496. Such a plethora of cluster types is guided by the fact that the selection of clasts that comprise a cluster can vary. The 2D cluster categorization presented above has proved robust. Fractal modeling of field and flume-created clusters by Papanicolaou et al. (2012) and Tsakiris and Papanicolaou (2008) and the application of second-order Kolmogorov structure functions to analyze bed elevation correlations over a range of longitudinal and transverse scales by Goring et al. (1999), Marion et al. (2003), and Cooper and Tait (2009) represent advances in streambed texture analysis. Nevertheless, there remains a place for qualitative, gestalt methods of cluster identification. A B   89  6.3 Methods 6.3.1 Cluster Identification The cluster identification process was conducted on the 2 m reach in the middle of the flume for each of the 79 observation windows. Guided by the observation that formations most typically observed in this study resemble pebble clusters, all potential anchor stones (? D80) were identified on bed photographs. The relative protrusion (P) of each potential anchor stone was examined in the DEMs. To calculate protrusion, an area surrounding the potential anchor stone with a 64 mm radius (equal to the D100 grain size of the original bed) was delineated and the cross-sectional elevation through the centroid of the potential anchor stone was plotted. The mean bed elevation was plotted as a straight line superimposed on the cross-sectional diagram of each potential anchor stone and protrusion was calculated by subtracting the mean elevation of the cross-section from maximum bed elevation: P = zmax. x-sec. ? zmean. x-sec. (6.1) Embeddedness (E) was then calculated as E = 1 ? (P/D) (6.2) where D is the grain size (mm). Initially, stones that were relatively well-embedded were discarded as potential anchor stones. However, over the course of the analysis, it was found that embedded particles could still function as anchor stones and no threshold for anchor stone protrusion was made. Potential anchor stones that were neither protruded nor in a structure similar to the pebble cluster illustration of Strom et al. (2005) were not delineated as clusters.   90    Figure 6.2: (A) and (C) Potential anchor stones in a run 3, hour 1 photograph within a 64 mm surrounding area (flow from top to bottom). The lines drawn through the centroid of the potential anchor stones represent the location of cross-sections in (B) and (D). (B) and (D) Cross-sections through the centroids of the potential anchor stones from (A) and (C) with mean bed elevation superimposed. In (B), E = 1 ? ((110.63 mm ? 79.70 mm) / 45.3 mm) = 0.32 and in (D) E = 0.54. The potential anchor stone in (C) was discarded as a cluster. To delineate spatial boundaries of each cluster, all particles larger than gravel material (>= 8 mm) in contact with each other and upstream of the anchor stone were considered part of the stoss zone. Small particles (< 8 mm) downstream of each cluster were drawn as part of the wake zone. Side boundaries of clusters were delineated within the width of the anchor stone under the assumption that shear stresses are high on either side of the anchor stone and deposition is discouraged (Brayshaw et al., 1983). When the majority of a large particle in A C D  A B  A zmax. x-sec  = 110.63 mm zmean. x-sec  = 79.70 mm   91  the stoss zone fell within the lateral extent of a cluster, the boundary was extended to include it in the overall area of a cluster.  Figure 6.3: Spatial boundaries of a cluster in run 3, hour 1 (flow from top to bottom). Stones whose centroids do not fall within the lateral boundaries of the anchor stone are not included in the boundaries of the cluster (e.g., the black stone on the left side of the cluster).     92  6.4 Results Results from the cluster identification procedure can be summarized to address questions of cluster dynamics in response to the sediment supply regime. The results presented herein include an anecdotal description of cluster formation, disintegration, and expansion using examples from neighboring observation windows. A run-by-run record of the total number of clusters and their surface area is then provided to summarize the results graphically. 6.4.1 Observations of Cluster Dynamics No measurements of flow surrounding clusters were made to conclude whether the anchor stone must be slightly protruded in order to influence the surrounding flow field to the point where cluster development is initiated. Anchor stones that became more embedded following an input of sediment maintained both a stoss-side accumulation of imbricated particles 8-16 mm in size and a wake tail of fine material. Figure 6.4 shows a cluster identified during run 2, hour 2. In this example, the anchor stone is relatively well-embedded (E = 0.33), yet a distinguished cluster has formed around it.     93            Figure 6.4: (A) A cluster identified during run 2, hour 2 (flow from top to bottom) and (B) the cross-sectional profile through the anchor stone of the identified cluster illustrating a relatively high value of embeddedness.  As the bed armored to a relatively high degree during periods of no sediment supply, distinct cluster boundaries became less pronounced. In some cases, the bed appeared as one conglomerate of clusters as fine sediment winnowed out and cluster boundaries merged. Gaps between large stoss zone particles would fill in with other large stoss zone particles and the identification procedure would require the cluster boundary to extend to include all touching particles. Though the anchor stones of each formerly independent cluster may influence the behavior of particles located some threshold distance away from their centroid, no streamwise threshold was set. Figure 6.5 shows two independent clusters merging together to become one large cluster. A B   94   Figure 6.5: (A) Two clusters identified during run 4, hour 32 and (B) during run 4, hour 34 that merged to become one large cluster according to the identification procedure used for this analysis (flow from top to bottom). As cluster boundaries merged during conditions of no sediment supply, wake zones composed of fine particles (< 8 mm) tended to disappear. Characteristics of the stoss zone upstream of anchor stones, however, were seemingly random and unrelated to the size or orientation of the anchor stone. The size of the wake zone relative to the total surface area of the cluster fluctuated more than the size of the stoss zone over all runs. Size fluctuations of cluster zones could be linked to the definition used to identify clusters. There was a relatively high supply of potential stoss zone particles over the entire experiment, but potential wake zone particles winnowed out of the surface almost immediately upon introduction. In other words, the mere availability of cluster zone material may have been what was responsible for size fluctuations of the stoss and wake zones of clusters. A B   95  Overall, there was no detectable pattern of the same clusters persisting over time, but rather clusters would develop and disintegrate randomly. In a few cases, clusters were identified and in a subsequent observation window, the anchor stone remained while all stoss zone particles had been transported (e.g., figure 6.6). The same anchor stone would entrap material in the wake and stoss zones later in the run. Cluster formation and disintegration around the same anchor stone thus occurred sporadically during most observation windows. The only systematic, yet inconclusive pattern of cluster disintegration began to emerge upon identification of anchor stones before and after sediment input events. In many cases, particles making up the stoss zone of a cluster would disappear one hour after a pulse (e.g., figure 6.6). The size of the pulse did not dictate the number of disintegrated clusters nor could it be correlated to a systematic reduction in cluster surface area.  Figure 6.6: (A) A cluster identified during run 4, hour 40 and (B) during run 5, hour 1 (immediately after the 150 kg sediment input) whose surface area diminished as the large grains in the stoss zone started to become separated by small grains (flow from top to bottom). A B   96  Clusters that persisted over at least seven hours during a run tended to grow in surface area and number of particles in the stoss zone. Anchor stones marked in figure 6.7 as C41, C42, and C43 identified from run 3 illustrate cluster growth over time. A trend of average cluster area increasing over time was observed. The most variation in cluster area was observed during run 4, with the introduction of four 75 kg pulses. Any given cluster would shrink or grow at no remarkable time during the run.    Figure 6.7: (A) Clusters identified during run 3, hour 4 and (B) during run 3, hour 7 grow in the number of particles in the stoss zone and in surface area (flow from top to bottom).  6.4.2 Cluster Formation, Disintegration, and Expansion The total number of newly-formed clusters, disintegrated clusters, and expanded clusters from one observation window to the next is presented in this section. In figure 6.8, for each observation window, the number of newly-formed clusters is displayed in blue and the number of clusters that disintegrated is displayed in red. The bars are stacked and colors can be used to visualize cluster dynamics in that red indicates negative and blue indicates positive cluster formation. The superimposed curve in figure 6.8 represents the total number of A B   97  clusters in a given observation window. Empty circles represent the time each bed photograph was taken.  98   Figure 6.8: Experiment time (in hours) on the x-axis, bars representing the number of newly-formed (blue) and disintegrated (red) clusters, and the total number of identified clusters superimposed. Vertical lines represent the observation window one hour after each sediment input event. Generally, clusters form anew and disintegrate at random, but each sediment input triggers a decrease in the total number of clusters.  99  Over the course of the first run, with no sediment feed, the total number of identified clusters increased two fold (figure 6.8). Only four of the original seven clusters remained intact by the end of run 1. A total of 37 clusters formed over the course of the first constant feed experimental run (indicated by the peak in the curve at hour 80 in figure 6.8). In a few cases, clusters re-formed on an abandoned anchor stone from run 1, but for the most part, clusters formed from new anchor stones that had either been transported into the study area or that had remained stable over the first 40 hours of the experiment. During the last 10 hours of run 2, 27 new clusters formed and 16 disintegrated. Within one hour of introducing the 300 kg pulse of sediment, 11 clusters from the previous observation window had disintegrated (indicated by the drop in the curve at hour 81 in figure 6.8), but by hour 2 of run 3, 11 newly-formed clusters appeared. A decrease in the total number of clusters was observed up to hour 20 of run 3, but the late half of the run was marked by the existence of 16 stable clusters as illustrated by the nearly level curve from hour 100 to hour 120 in figure 6.8. The dynamics of cluster formation and disintegration during the late half of run 3 were similar to those observed during run 1, in that most identified clusters remained stable in existence. The pattern of cluster dynamics between each 75 kg pulse in run 4 reveals large numbers (up to seven) of disintegrated and newly-formed clusters at each observation window. Immediately following each of the 75 kg sediment inputs, the total number of identified clusters decreased by 10-14% of the total number from the previous observation window (indicated by the steep drops in the curve overlain by vertical lines that represent the observation windows one hour after each 75 kg sediment input in figure 6.8). Similarily, the 300 kg sediment input of run 3 brought about a 30% decrease of the total number of observed   100  clusters from the previous observation window (from 37 identified in run 2, hour 40 to 26 identified one hour after the 300 kg pulse). The total number of identified clusters increased from 16 to 29 over the duration of run 4. In contrast, the total number of identified clusters over the course of run 3 decreased from 26 to 17. The two sediment input events of run 5 caused dissimilar patterns in cluster dymanics. After the first 150 kg pulse, a 24% decrease in the number of clusters from the previous observation window was observed (from 29 to 22 observed clusters). By hour 7 of run 5, the total number of clusters on the bed had peaked at 28 (the highest value plotted for run 5 in figure 6.8) and by the end of the first half of the run, 21 clusters remained. There were only 5% fewer clusters on the bed following the second 150 kg pulse, with three newly-formed and four disintegrated clusters from the previous observation window. The last 20 hours of run 5 were marked by relatively stable microtopography; few new clusters formed or disintegrated. Cluster dynamics during the prolonged period of no sediment supply following the second 150 kg pulse of run 5 progressed similar to the late half of runs 1 and 3, in that most identified clusters remained stable in existence. Toward the end of the experiment, the total number of clusters on the bed fluctuated between 16 and 22 during run 6 and between 15 and 18 during run 7. In contrast to run 2, the total number of clusters decreased over the duration of run 6 and the highest number of newly-formed clusters observed was only four (compared to 27 newly-formed clusters during run 2, hour 40). Run 7 also brought about dissimilar changes in comparison to cluster dynamics of run 1. The last 40 hours of the experiment was characterized by relatively stable microtopography, contrary to the variability and overall increased density of bed structures   101  observed during run 1. The curve representing the total number of identified clusters thus exhibits a decreasing trend over the last 80 hours of the experiment (figure 6.8).  102   Figure 6.9: Experiment time (in hours) on the x-axis, bars representing the number of newly-formed (blue) and disintegrated (red) clusters, and the total number of clusters that expanded from one observation window to the next. Vertical lines represent the observation window one hour after the beginning of each sediment input event. Typically, clusters that existed for at least seven hours at any point during a run would increase in surface area. Following each sediment input event, the number of expanded clusters tended to decrease. Within two hours, however, existing clusters would expand in surface area.   103  Overall, the number of clusters that expanded over the course of run 1 increased, with the most marked period of cluster expansion during hour 30 (figure 6.9). Of the relatively stable clusters observed during the late half of run 1, most expanded in surface area (figures 6.8 and 6.9). The increase in the total number of clusters identified during run 2 was paralleled by an overall decrease in the number of expanded clusters (figures 6.8 and 6.9). As new clusters formed toward the end of run 2, few existing clusters expanded. Most newly-formed and existing clusters observed during hour 2 of run 3 increased in surface area after the initial period of cluster disintegration immediatley following the 300 kg sediment input. The number of expanded clusters, however, decreased over run 3, aside from a small peak during hour 30, when nine clusters expanded from the previous observation window, seen as a peak in the late half of run 3 in figure 6.9. The number of expanding clusters was most variable during runs 4 and 5 (figure 6.9). With the total number of clusters and the number of expanded clusters increasing over the duration of run 4, a systematic decrease in both values occurred one hour after each 75 kg sediment pulse (figures 6.8 and 6.9). Few clusters observed during run 4 remained stable between sediment pulses, instead, existing clusters would either grow in surface area or disintegrate all together. The variability in cluster expansion observed during run 5 mirrored that of run 4 in a few ways: of the clusters that remained intact following a sediment input, few expanded (figure 6.9). The temporally stable clusters observed following the second 150 kg pulse of run 5 fluctuated in surface area in no detectable pattern. The number of expanded clusters observed during run 6 evolved in a similar manner to run 5. A highly variable and overall decrease in the number of expanded clusters during the first half of the run (seen as a decreasing curve from hours 202-215 in figure 6.9) followed by   104  mostly stable cluster sizes over the last 20 hours of the run was observed. Variability in the number of clusters that expanded from one observation window to the next was observed during the final experimental run as few formed anew or disintegrated (as indicated by short blue and red bars beneath the curve in figure 6.9). Clusters formed by the same anchor stone gained and lost particles in both the stoss and wake zones over the last 40 hours of no feed conditions. That is, microtopography evolved to become relatively stable in space, yet sustained dynamic expansion and shrinkage within each cluster feature. Figure 6.10 shows the ratio of the total number of clusters in a given observation window to the total area that all clusters in that observation window cover plotted over the duration of the experiment. When the combined area of a relatively high number of clusters is small, the value on the curve is relatively higher than when the combined area of clusters is large. Over time, the number of clusters relative to their combined surface area decreased (figure 6.10). Though the total number of clusters increased over the duration of the experiment (which, in itself would lead to a decreasing curve), the curve in figure 6.10 is also attributed to an increase in combined cluster area. Table 6.1 includes the within-run values of the number of clusters and their combined area used to calculate the ratio plotted in figure 6.10.   105   Figure 6.10: Experiment time (in hours) on the x-axis and the ratio of the total number of clusters to their combined surface area on the y-axis. Vertical lines represent the observation window one hour after the beginning of each sediment input event.  106  Table 6.1: The total number of clusters and their combined surface area (cm2) at select observation windows of the experiment. Run Hour # Clusters Surface Coverage (cm2) 1 1 7 521.15 1 40 14 1231.59 2 1 13 1161.98 2 40 37 2927.82 3 1 26 1156.37 3 40 17 1629.73 4 1 16 1343.58 4 10 21 1856.23 4 11 19 1542.13 4 20 23 2599.90 4 21 20 2081.58 4 30 28 3111.61 4 32 24 2806.42 4 40 29 3155.81 5 1 22 2151.10 5 20 21 1901.88 5 21 20 1522.55 5 40 20 1949.12 6 1 21 2025.47 6 40 16 1758.77 7 1 16 1906.67 7 40 16 1845.78  As the number of clusters doubled over the first experimental run, total cluster area increased by 136%, giving rise to a disproportionate result seen as a decrease in the ratio plotted in figure 6.10. The reverse was observed over run 2: the total number of clusters increased from 13 to 37 (a 185% increase) while combined cluster area only increased by 152%. Overall, more, smaller clusters were produced as a consequence of constant sediment supply conditions in contrast to run 1. Run 2 was also characterized by a 42% increase in the total   107  number of identified clusters between hours 30 and 40. That is, the increase in the total number of clusters was observed during the late half of run 2. Within one hour of the 300 kg sediment input in run 3, there was a 30% decrease in the total number of clusters; the total surface area occupied by clusters decreased by 61% between run 2, hour 40 and run 3, hour 1 (table 6.1). Clusters quickly re-formed following the 300 kg sediment input and the combined cluster area increased to reach a peak value in the experiment by run 3, hour 2. Overall, run 3 was characterized by a 41% increase in combined cluster area and a 35% decrease in the number of identified clusters (table 6.1). Results of run 4 and 5 were highly variable, but the ratio between the total number of clusters and their combined surface area was relatively constant over both runs (figure 6.10). Overall, there was a 135% increase in combined surface area of clusters identified between hours 1 and 40 of run 4. Table 6.1 gives values for each 10 hour increment within which a 75 kg sediment pulse was introduced to the bed during run 4. Cluster surface area increased by 38% within the first 10 hour increment, then by 69%, 49%, and 12% between the following three sediment pulses, respectively. The total number of clusters identified between hours 1 and 40 of run 4 increased by 81%, with between-pulse increases of 31%, 21%, 40%, and 21%. Combined cluster surface area increased by greater proportions than the total number of clusters throughout run 4, except for the last 10 hour increment, and a downward trend was observed in the ratio plotted in figure 6.10. Both the total number of clusters and the combined cluster area observed during run 5 decreased by 9% from hours 1 to 40. Within the run, more variability was observed, with a 12% decrease in cluster area, and a 5% decrease in the number of identified clusters 20 hours   108  after the first 150 kg pulse. One hour after the first 150 kg sediment pulse, combined cluster area and the number of clusters decreased by 32% and 24%, respectively (from run 4, hour 40 to run 5, hour 1). By run 5, hour 2, clusters had already re-formed with combined cluster area and the number of clusters increasing by 16% and 18%, respectively. A different pattern emerged following the second 150 kg pulse of run 5; from hour 21 to 40, cluster surface area had increased by 28%, but there was no change in the number of clusters (table 6.1). The initial evolution of microtopography following the second sediment delivery of run 5 mimicked the first few hours of the run, but to a lesser degree; cluster surface area and the number of clusters decreased by 20% and 5%, respectively (from run 5, hour 20 to run 5, hour 21). As new clusters emerged and existing clusters accumulated particles, the values of cluster area and the total number of clusters increased by 17% and 5% from hours 21 to 22 of run 5. Cluster dynamics within runs 6 and 7 are dissimilar to what was observed during the first two experimental runs, but overall, a decrease in the ratio between the number of clusters and their combined surface area was observed (figure 6.10). Twenty-four percent fewer clusters were identified between hours 1 and 40 of run 6, while surface area of those clusters decreased by 13% (table 6.1). Though the number of cluster observed during the final experimental run remained constant over 40 hours, surface area of all combined clusters shrunk by 3% (table 6.1).    109  Chapter 7 Discussion A comprehensive link between bed surface adjustments in response to the sediment supply regime is presented in this chapter (section 7.1). Changes to bed surface texture and patchiness within and between experimental runs are linked to the evolutionary process of formation, persistence, disintegration, and the associated morphologic characteristics of surface clusters. Section 7.2 then summarizes the major limitations of the analyses presented in chapters 4, 5, and 6. 7.1 Overall Bed Surface Evolution Table 7.1 summarizes overall bed evolution results on a run-by-run basis including surface GSD and patchiness, bed roughness and sediment storage, and the number of clusters and their combined area. In general, coarser, rougher bed states were matched by increases in the number of clusters identified and their combined area. During periods of bed fining or relatively consistent values of surface grain size statistics, so long as the bed became more rough and aggraded material, the number of clusters and their combined surface area generally increased. Sediment input events caused immediate break-up of clusters or shrinking of their areas, but one or two hours following each event, clusters would form, re-build, and increase in total combined area. Overall, clusters formed, remained stable, and disintegrated at the same average flow rate. The bed did, however, aggrade material and gain elevation (as summarized in chapter 5) over the duration of the experiment. An in-depth, run-by-run examination of these processes is discussed herein.   110  Table 7.1: A run-by-run summary of the overall evolution of bed texture, topography, and microtopography. Run Texture Topography Microtopography Surface GSD Patchiness Roughness Sediment Storage # Clusters Cluster Area 1 Increasingly coarser, more sorted, and less fine material. Decrease in area of fine patches; increase in area of coarse patches. Increasingly rougher. Relatively consistent storage; increase in zmin. Overall increase. Overall increase. 2 Relatively constant texture, sorting range, and fraction of fine material. Decrease in area of medium gravel patches; initial increase/decrease in area of fine/coarse patches followed by relatively constant values. Initial decrease followed by increasing roughness. Increase in storage; variable zmin values. Overall increase. Overall increase. 3 Initial fining, poor sorting, and increase in fine material; bed recovery similar to run 1 two hours following sediment input. Initial increase/decrease in area of fine/coarse patches followed by steep decrease/increase in area of fine/coarse patches. Initial increase then rapid decrease followed by increasing roughness. Large increase followed by relatively consistent storage; variable zmin values. Overall decrease. Overall increase. 4 Overall decrease in fine material fractions; more sorted. Consistent D50 and D84 values; increase in D16. Overall increase/decrease in area of medium/coarse patches; relatively consistent area of fine patches. Overall increasingly rough. Overall increase in storage and values of zmin, zmax, and zmean. Overall increase. Overall increase. 5 Overall coarsening; more sorted; full recovery in fine material fractions following each sediment input. Relatively consistent areas of all patch types with initial increase/decrease in area of fine/coarse patches following each sediment input. Overall consistent values of roughness. Overall increase in storage and values of zmin, zmax, and zmean. Relatively consistent (decrease of two). Relatively consistent (small decrease). 6 Relatively constant texture and overall sorting; decrease in fine material. Increase in area of fine patches; relatively consistent areas of medium and coarse patches. Decrease in roughness. Overall increase in storage; relatively consistent values of zmin, zmax, and zmean. Overall decrease Overall decrease. 7 Increasingly coarser; relatively constant sorting; decrease in fine material. Increase in area of coarse patches; relatively consistent area of medium patches; variable area of fine patches. Increasingly rougher. Overall decrease in storage and values of zmin, zmax, and zmean. Consistent. Relatively consistent (small decrease).    111  Over the course of run 1, the bed evolved from a hand-mixed, relatively fine state to a coarser, armored state (from D50 = 14.8 mm at run 1, hour 1 to D50 = 17.4 mm at run 1, hour 40). Surface texture evolution progressed gradually throughout run 1 as fine material winnowed out and the bed became increasingly well-sorted and rough, coinciding with an increase in the total number of identified clusters and their combined area. Surface texture results over run 7 were similar to run 1, except for the slight increase in material < 5.66 mm on the surface toward the last 10 hours of the run. As well, bed coarsening during run 7 progressed more slowly than what was observed during run 1, possibly due to previous hours of bed conditioning. That is, because the bed was not re-mixed between experimental runs, the results of run 7 were a product of morphologic evolution via episodic sediment inputs whereas the results of run 1 were simply due to a prolonged period of no sediment feed. The impact of bed conditioning and complex structure development over the duration of the experiment may also lend insight into the contrasting observations of cluster dynamics between runs 1 and 7. The bed maintained a consistent number of clusters and total combined cluster area during the final 40 hours of the experiment while other aspects of bed surface evolution were similar to run 1. It can therefore be inferred that grains became interlocked into stable positions over hours of water-working and sediment introduction to the bed, resulting in more stable microtopographical features and a smaller overall sediment flux compared to run 1. Additionally, the increase in fine surface material at hour 20 of run 7 coincided with an increase in the surface area identified as fine material patches. Periodic downstream translation of fine sediment released as sediment structures upstream of the 2 m middle section of the flume disintegrated may be responsible for the fluctuations in P1 area. This   112  introduction of fine sediment to the study area manifest as dispersed areas identified as fine patches, but did not characterize the overall texture of the bed during run 7. Instead, the final state of bed texture during both runs 1 and 7 can be described as armored, though run 7 contained more stable bed topography and microtopography. Dispersed areas identified as coarse patches during run 7 and in few cases during which the bed became increasingly armored (e.g., over the course of run 1 and during the latter half of run 3), coincided with a decrease in the number of clusters and their total area from one observation window to the next (figure 7.1). In these instances, it is possible that the dominate microtopographical features were not clusters, but rather cellular structures that appeared to grow into a reticulate structure, sparsely blanketing the bed surface. Hassan and Church (2000) described cellular structures as features approximatley 1 m in diameter with boarders consisting of pebble to boulder-sized material larger than the D84. The steep decreases in percent change in cluster area over the last 20 hours of runs 1 and 3 (figure 7.1) add to the interpretation that, rather than the bed growing in cluster area, it came to be characterized by cellular structures.   113   Figure 7.1: Experiment time (in hours) on the x-axis and the percent change in the total number of clusters (red) and the cluster area (black) from one observation window to the next on the y-axis. Vertical lines represent the observation window one hour after the beginning of each sediment input event.   114  Clusters would lose clasts or disappear altogether and morph into particle lines and eventually into a network of structures that occupied a smaller area of the bed surface than the combined cluster area. In most cases, cluster break-up following sediment introduction was characterized by stoss zone particle entrainment (e.g., figure 7.2). A look into this observation may be worthwhile for future analysis as cellular structures generally act to stabilize the bed, provided that flow does not exceed twice the Shields? threshold (Marion et al., 2003). As well, their presence may play a role in the life cycle of clusters.   Figure 7.2: (A) Two clusters identified during run 4, hour 10 and (B) the remaining anchor stones identified during run 4, hour 11, after a 75 kg sediment input (flow from top to bottom). Remaining anchor stones may seed new clusters or develop into cellular features.  The effect of a 300 kg sediment pulse during the first hour of run 3 followed by 39 hours of no feed conditions can be compared to runs 1 and 7. Surface texture evolution progressed relatively quickly during run 3. The bed fined and became poorly sorted after the introduction of the 300 kg pulse, but within one hour, grain size statistics and patch areas had recovered to values closer to those observed during the hour 40 observation window of run 3. A B   115  Material < 5.66 mm increased from the end of run 2 to the hour following the 300 kg pulse from 16.3% to 43.3%. However, the effect of the 300 kg sediment pulse was short-lived on surface texture; material < 5.66 mm had decreased to 29.1% on the bed surface by hour 2 of run 3. Bed texture recovered to an armored state about 10 hours after the introduction of the 300 kg pulse. Hour 10 of run 3 also marked the beginning of a relatively stable period of patch existence. From hours 1 to 7, the number of cells identified as P1 decreased as fine material exited the frame. Conversely, P3 area increased up to hour 4 and then reached a stable value by hour 7 with minor fluctuations throughout the final 30 hours of run 3. The stable value of P3 area could be representative of an armored bed patch type or the existence of cellular structures similar to the results of runs 1 and 7. Values of D16 during run 3 were lower than those observed during runs 1 and 7, indicating that the presence of a fine patch could retain much of the fine material. Bed texture evolution between runs 1, 3, and 7 exhibited many similar characteristics despite the introduction of the 300 kg sediment pulse in run 3 and the effect of remnant bed properties on the surface observed during run 7, but the spatial distribution of patches was slightly different (figure 7.3). Though the bed became armored once again, the spatial effect of the 300 kg pulse had not quite disappeared by hour 10, as demonstrated by the patch of fine material in the upstream left bank (figure 7.3 B). However, grain size statistics, the value of the sorting parameter, and the overall relative patch type areas were similar to hour 10 of runs 1 and 7 (as summarized in table 7.1). In other words, overall bed texture evolved to a similar state, but the spatial distribution of bed texture maintained differences between the no feed runs and run 3.   116   Figure 7.3: Runs 1 (A), 3, (B), and 7 (C) photographs and patch maps for the hour 10 observation window of each run. Flow direction goes from left to right. The images represent the 2 m long by 1 m wide middle section of the flume bed. Patch maps display differences in the spatial distribution of each patch type.  117  Between sediment pulsing runs, the least dramatic observations of cluster dynamics were made during run 5, while, simultaneously, the bed maintained relatively consistent values of roughness. However, the sediment supply regime of run 5 induced similar effects on bed texture as those observed during run 3. One hour after the introduction of the first 150 kg pulse, most of the fine material had winnowed out of the bed. The pattern was less marked after the second 150 kg pulse, as hour 22 of run 5 did not exhibit texture as coarse as observed during hour 2 of the run, perhaps due to a residual effect of the first 150 kg pulse on bed surface evolution 20 hours later. Despite the fluctuations in surface texture after each sediment input event, microtopography was relatively stable during run 5. The fact that the bed had been previously conditioned by an armoring run, constant feed conditions, one large pulse, and four small pulses could once again be linked to cluster persistence during run 5 similar to what was observed during run 7. The four 75 kg pulses of run 4 induced smaller magnitude changes in grain size statistics than those observed following the sediment pulses of run 5. However, the fraction of fine material on the surface during run 4 was similar to the range of values observed during run 5. Residual sand from the 300 kg pulse seemed to have combined with material from the 75 kg pulses to produce high sand content bed surface texture throughout run 4. Patch development following each sediment pulse of runs 3, 4, and 5 also exhibited similar patterns between runs. The relative area of each patch type one hour (or two hours in the case of the last 75 kg pulse of run 4) after the sediment inputs is summarized in table 7.2. The largest proportion of P1 between the observation windows in table 7.2 was observed one hour after the 300 kg pulse. Fractions of the bed identified as P1 following the 75 kg and 150 kg sediment inputs of runs 4 and 5 ranged between 17.4-24.9% of the total patch area (table 7.2). During the hours   118  following each 75 kg sediment input, the bed maintained the highest P3 areas between runs 3, 4, and 5. These results suggest that the effect of sets of sediment pulses was scalable one hour following each input. Table 7.2: The fraction of each patch type relative to the total patch area for runs 3, 4, and 5, following each sediment input event. Note that the bed was not photographed one hour following the last 75 kg sediment input of run 4. Run Hour % P1 % P2 % P3 3 1 36.3 19.4 44.3 4 1 21.9 24.8 53.2 4 11 17.4 28.4 54.3 4 21 19.5 28.6 51.9 4 32 21.2 30.2 48.6 5 1 22.2 32.5 45.3 5 21 24.9 28.6 46.5  Comparisons between runs 2, 4, and 6 lend further insight to the effect of small, frequent sediment pulses on bed texture evolution. Due to the nine hour spacing between pulses during run 4, fine material fractions on the bed surface were consistently lower than those during runs 2 and 6, when material was constantly supplied to the bed. In fact, fine material fractions observed during hours 10, 20, 30 and 40 of run 4 were more similar to those that characterized the armored beds of hour 40 during runs 1, 3, 5, and 7 and hour 20 during run 5. The effect of each of the four 75 kg pulses on bed texture and patchiness lasted no more than two hours. Despite differences in the frequency and magnitude (or even the presence) of sediment inputs, adjustments in GSD followed similar patterns between all runs in that (1) the D16 was the most variable characteristic grain size value and (2) medium-gravel patch (P2) areas were least variable, likely due to higher relative mobility of fine material. However, marked   119  differences were observed between the constant feed runs, 2 and 6 (as summarized in table 7.1). Decreasing bed roughness observed over the duration of run 6 was matched by decreases in the number of clusters and their combined area while run 2 was characterized by an increase in roughness and increases in the number of clusters and their combined area. It is possible that cluster break-up during run 6 was caused by similar fine sediment translation processes as observed during run 7, resulting in an increase in the area of fine patches. In any case, no matter what the sediment supply regime, cluster disintegration consistently coincided with decreases in roughness and increases in P1 area. 7.2 Limitations 7.2.1 Surface Texture Derivation Technical or set-up limitations were minor in the data collection of bed texture information. However, certain analytical constraints had to be imposed. Those constraints are discussed in this section in regards to the surface grain size and sorting analysis. Figure 7.4 illustrates the main technical limitation of the surface grain size analysis. The resolution of bed photographs imposed a lower limit of 2.83 mm on reliable identification of grain sizes. All grains 4 mm (light pink in color) and finer were marked as 4 mm such that all sand grains were classified in the same grain size class. This truncation at small sizes may not make much of a difference in the interpretation of surface texture evolution, but sand signatures in fractional transport results may require calibration to higher resolution bed photographs. Truncation at a lower bound is necessary in field sampling (e.g., Wolman, 1954) because worker bias can result in underrepresentation of fine particles (e.g., Diplas and Fripp, 1992;   120  Fripp and Diplas, 1993). However, in a laboratory setting, particle recognition can be of higher resolution.  Figure 7.4: Bed photographs showing two cases of grain size recognition by color. (A) An easily recognizable particle in the red identification box. The stone is red, which corresponds to 11.3-16 mm. (B) shows what could be a light pink, light blue, white, or natural colored particle. Methodological criticism of surface grain size derivation has been widely discussed in regards to field and flume studies. Kellerhals and Bray (1971) showed that GSD by number obtained by the grid method is equivalent to GSD by mass obtained by bulk sampling and sieving. However, various photosieving studies (e.g., Butler et al., 2001; Graham et al., 2005) have found that grain size distributions derived from photographs always undercount the number of grains than those from a surface sieve sample. Graham et al (2010) manually digitized all visible grains in photographs of a study site and compared the results to paint-and-pick surface samples collected after taking the photographs. In all cases, the photographic analyses identified fewer grains in all size classes than in the paint-and-pick samples. Since undercounting was uniformly distributed, the precision of the grain size distributions was considered acceptable. In this study, it was not possible to confirm A B   121  similarities between methods because no surface samples of the bed were taken during the experiment. 7.2.2 Patch Identification Though patches delineated using the variance of grain size gradients resulted in visually similar areas on bed photographs, various amendments to the analysis could improve the results. For example, patches were identified on a cell-by-cell basis, meaning that significantly different areas of grain size manifest on 25 cm2 areas. The mixture of sediment used in this study includes grains of the same minimum patch area. This means that patches can be one grain size large, an unreasonable supposition. Instead, identified patches that only occupy one cell should not be included in the final patch map. The lack of aggregation is illustrated in figure 7.5, where the photograph taken during run 3, hour 30 is displayed next to the outputted patch map of medium gravel sediment (P2). In the cases where high proportions of P3 were identified, but cells were scattered instead of aggregated in patch-like areas, the results could be interpreted as surface armor or ?cell? structures that develop simultaneously with the armor layer, as discussed in section 7.1 (Church et al., 1998; Hassan and Church, 2000). Those cells identified as coarse patches could instead be interpreted as dispersed blankets of coarse material.   122   Figure 7.5: (A) Run 3, hour 30, P2 cells (medium gravel patches) represented by brown-colored squares adjacent to the corresponding bed photograph (B). Flow direction goes from left to right. The image represents the 2 m long by 1 m wide middle section of the flume bed. Patch definitions may also be modified to accommodate the distribution of grain size observations, much like the queried gradient variance values are. For example, values of D16, D50, and D84 unique to each observation window could be used to identify P1, P2, and P3, B A   123  respectively. Results would then include patch types that are unique to a given observation window or location on a flume or natural stream bed. That is, patch types would not be universally transferable, but rather characteristic of one moment in time or one location. Instead, this study uses threshold values of observed grain size based upon Wentworth (Wentworth, 1922) scale divisions in order to place the results in the broader research context. Though high resolution bed elevation data is not always available, another amendment to improve the patch delineation analysis could include information on bed topography. Patches are loosely defined as areas of similar grain size, but it has been shown that bed elevation (used as a surrogate for bed roughness) interacts with surface heterogeneity, or patch formation. Roughness feedbacks due to bed sorting are important when considering hydrodynamic mechanisms involved in patch formation (Seminara et al., 1996). To explore the surface grain size to roughness feedback, a correlation between those values within each identified patch could be made. This correlation would not advance the delineation procedure, but rather provide information on patch dynamics. Finally, the surface grain size analysis in this study was based on raw (x, y, D) data, which is subject to undercounting. An alternative method of objectively delineating patches could instead use subset groups of grain size observations. That way, differences between areas of similar GSD would be distinguished instead of differences between point data. The use of GSDs rather than point data would need to adhere to a few rules. Enough grains would need to be included in each sub-sampled GSD area so that all grain sizes in the population are represented. This rule would constrain the minimum size of the sampling area to be used in   124  the patch delineation analysis and may not be wise to implement in a study that examines only a 2 m2 area of the streambed. 7.2.3 Bed Topography The limitation of a GSD-based approach to sediment surface quantification has been highlighted in many studies. In particular, the influence of reach-scale bedforms appears to override grain-size effects on roughness parameterization. High resolution bed elevation data in the study allowed for a preferred alternative; the random field approach to characterizing bed roughness is independent from sample size and has thus been adopted in analyses of roughness elements in place of representations by the GSD. However, apart from the common lack of high resolution 3D bed elevation data, a few issues may arise. Laboratory settings are imperfect and reflections on the sides of flume walls can cause obscure measurements of elevation to be recorded when using laser devices. In this study, all DEMs were pre-processed to eliminate measurements lower than 0 mm and greater than 200 mm. Despite the procedure adopted to remove errors and trends in the bed elevation data, DEMs are not an absolute representation the bed surface. Any conclusions drawn from the preceding analysis should thus be coupled with a broad interpretation of surface processes. 7.2.4 Structure Functions of Bed Elevation While structure functions of bed elevation are useful, interpretation of the results is subject to worker bias. For example, fitting theoretical model semivariograms such as exponential, spherical, guassian, or matern to empirical results requires visual checks of the semivariogram. Fit statistics from each model are dissimilar so there is no way to compare between theoretical models. Some workers have used curved profiles to describe   125  semivariogram curves, citing multifractal behavior of bed structure (e.g., Butler et al., 2001). However, arbitrary choices of models that have been deemed appropriate for decades (Hohn, 1988) facilitate suspicious results of spatial structure. In this study, empirical semivariogram results between runs were visually similar and it was therefore not necessary to fit and test various theoretical models. However, a few further analyses of surface structure could be carried out to examine the high resolution bed elevation data. For example, 2D semivariogram surfaces may be constructed to display contour shapes of lag in multiple directions along the streambed. For example, Hodge et al. (2009) indicated isotropic surface structure through circular contours in the center of two semivariograms computed from field data. Increases in lag distance were correlated with increasingly ellipsoidal contour shapes, a reflection of the dominant grain orientation. Preferential alignment of grains (for example, with the long axis perpendicular to the flow direction in a riffle feature or with the long axis parallel to the flow direction in a pool feature) could then be extracted. Periodicity of surface structure may be further explained using scaling analysis. There are many ways this can be accomplished (see Klinkenberg and Goodchild, 1992) and all methods describe how the elevation change of a surface varies as a function of scale. Though 2D structure functions may be able to improve predictions of bulk flow velocity by providing an estimate of roughness height as f(?z, lx, ly) (Wohl, 2000), the results of the semivariogram analysis did little to describe gravel bed roughness at the individual particle level. Surface structure semivariograms in this study displayed different values of ? at similar normalized lag values, which could be interpreted as differences in grain shapes, orientation, and packing. Such sedimentological variations could be further linked to spatial hydraulic   126  variations and the spatial distribution of critical entrainment shear stress. However, the models ignore hydraulically important particle clusters. Differences in surface structure as a result of the sediment supply regime are thus best explored by identifying cluster or cluster-like features. 7.2.5 Cluster Identification Quantification of cluster development, persistence, and shape has been addressed in a number of studies using idealized glass beads or natural river bed situations (Brayshaw, 1984; Hendrick et al., 2010; Papanicolaou and Schuyler 2003; Reid et al., 1992; Strom and Papanicolaou 2002; Strom et al., 2004; Strom and Papanicolaou, 2008). The main objective of this study was not to induce cluster formation, but rather to link insights of cluster development to other bed adjustments. Some technical limitations of the initial bed photograph analysis posed constraints on the analysis of microtopography. It is possible that photograph distortion caused errors in the results of cluster area calculation because the photographs were not rectified. Of primary focus in this section, however, are the limitations of cluster identification. By eliminating a component of elevation in the cluster identification method, the surface area of each feature was reduced. If all areas elevated above a certain threshold were to be included in cluster extent, values of cluster surface area would have been much larger. This point is illustrated in figures 7.6-7.9, an example of a cluster identified during the run 3, hour 4 observation window. Figure 7.6 displays the outline of a cluster (in red) identified using the rules described in section 6.3. The lateral and streamwise extents of the feature are confined based upon the width of the anchor stone and the arrangement of stoss and wake zone   127  material, respectively. Figure 7.7 shows the cross-sectional elevation of the feature identified in figure 7.6.  Figure 7.6: A cluster identified on a bed photograph taken during run 3, hour 4 based upon the identification procedure described in section 6.3 (flow from top to bottom). The red line indicates the location of the cross-section plotted in 7.7.  Figure 7.7: The cross-section of the cluster identified in figure 7.6 including the maximum possible lateral extent of the feature (64 mm to the left and to the right from the centroid of the anchor stone).   128  Figures 7.8 and 7.9 display an alternative approach to identifying the spatial boundaries of the cluster in 7.6. In figure 7.8, an elevation map of the microform, the overlain red boundary highlights areas of relatively high elevation. That is, a third dimension is brought in to identify the surface area of the cluster feature. Figure 7.9 gives the streamwise elevation through the centroid of the highest point in the elevation map of figure 7.8. The stones protrude above the average elevation of the surrounding bed surface (figure 7.9), a concept that was not included in the 2D cluster identification method of this study.  Figure 7.8: Microform elevation (given in the colorbar in mm) for the cluster identified in figure 7.6 (flow from top to bottom). The red boundary is drawn around the relative high areas of elevation in the image.   129   Figure 7.9: Streamwise elevation through the centroid of the cluster anchor stone identified in figure 7.6 (flow from right to left). The inclusion of a third dimension in the cluster identification process branches into the idea that many types of cluster morphologies may exist simultaneously. To explore microtopographical evolution in terms of different cluster types, information on the orientation of anchor stones or other clasts that make up each feature should be extracted using bed photographs.  Identification of other microtopographical structures may lend insight to their function at a broader scope. Not only would the definition of a streamline extent of clusters prevent infinite extension of each feature, but flow field measurements around clusters would add a component of cluster identification. It has been suggested, for example, that the minimum size of all potential anchor stones be revised given information on their relative disturbance to the surrounding flow field (Strom and Papanicolaou, 2008). In particular, larger stones create larger low pressure zones downstream of the stone where the wake sediment deposits (Strom and Papanicolaou, 2008). Where recirculation flow paths upstream or downstream of   130  anchor stones become elliptical in shape, the streamwise extent of clusters could then be defined. Using components of cluster function to better define their extent is motivated by previous studies that have shown coarse, graded river beds to exhibit an armored surface layer due to selective entrainment of fine material (Chin, 1985). Those armored surfaces tend to be characterized by large surface particles that assemble into cluster structure such as the ones observed in this study. Field and laboratory studies have steered the theory of bed stability dependence on microforms to suggest that clusters provide higher form resistance and complicate sediment transport by interlocking with stones that would normally become entrained (e.g., Hassan and Reid, 1990; Church et al., 1998; Schuyler and Papanicolaou, 2000). Increases and decreases in transport rates have been observed as particles are trapped into clusters and released as the clusters disintegrate. A detailed link between cluster dynamics and sediment transport could be made in this study to better understand cluster function.    131  Chapter 8 Conclusions and Future Work The objective of the present study was to investigate the effects of variations in the magnitude and frequency of sediment deliveries on bed texture and topographical evolution. This goal has been accomplished through seven experimental runs involving pulsed and constant sediment inputs. Three components of the systematic changes in bed surface adjustments over the duration of the experiment were examined: (1) surface texture and patchiness, (2) topography, and (3) microtopographical cluster features. ? Bed texture recovered to a relatively armored state within hours following each input event, with little detectable temporal dependence on sediment input magnitude. Simultaneously, however, areas of fine gravel patches existed on the bed over relatively long time periods even once the overall characterization of the bed returned to an armored state. For example, a fine material patch that developed within the first hour after the 300 kg sediment input had no overall influence on bed surface texture within four hours after the input, but persisted in the same spatial arrangement throughout the remainder of the run. A residual effect of the fine material patch formed during run 3 was not marked in subsequent runs. ? Bed surface structures exhibited similar degrees of spatial dependence across all runs as indicated by the results of 2D structure functions of bed elevation. These observations were made despite the fact that the bed continously aggraded material and became more rough over the duration of the experiment. It is likely that the   132  method of surface structure characterization was simply not robust enough to encompass aspects of grain orientation and arrangement. ? Cluster expansion occured only once surface texture became relatively coarse (in terms of surface grain size) and rough (in terms of surface elevation). Cluster disintegration was consistently induced by the introduction of fine material, via sediment pulsing or translation of upstream material. This study also showed that the role of particle size in cluster formation was consistent across all runs. The light green and white stones (retaining sieve size 22.6 and 32 mm, respectively) acted as anchor stones while finer material formed the stoss and wake zones of clusters. ? Differences between runs 1 and 7, both without sediment feed to the bed, were most apparent in the level and rate of surface coarsening. Bed conditioning caused by 200 hours of a sediment supply regime caused surface texture evolution during run 7 to coarsen to a lesser extent than what was observed during run 1. As well, dispersed areas of coarse patches characterized the bed surface during run 7, a condition that may be better represented by cellular structures, rather than patches. ? The three runs during which sediment was supplied in pulses exhibited results scalable to the input magnitude across all surface representations. The main difference between the runs was observed in the high stability of cluster features and consistent values of bed roughness during run 5. ? Constant sediment supplied to the bed during runs 2 and 6 induced dissimilar topographical results. Run 2 was characterized by an increase in bed roughness and the number and surface area of cluster features, while the opposite evolutionary   133  response was detected over the course of run 6, possibly due to waves of fine sediment entering the study area during run 6. In the pursuit of a complete study of the temporal adjustments of a streambed under an episodic sediment supply regime, it is necessary to explore other aspects of gravel bed texture and structure. Relations between structure formation, sediment supply, and the surrounding flow field are complex, and further work on the existing data remains to define the mechanics of these phenomena. Therefore, recommendations for future analyses into bed surface evolution and other aspects of this study are presented below followed by recommendations for further research. ? Analysis of translation and dispersion dynamics as described by Sklar et al. (2009) was omitted in this study. If this could be carried out on the entire length of the flume, the addition of sediment wave migration information, downstream fining patterns, and large scale bedform development to the wealth of information provided by localized results would be useful. ? To add to the results of surface structure, directional semivariograms could be computed. A level of organization between cross-stream and downstream directions may then be detected, suggesting anisotropic structure signatures in bed elevation, an argument that has been presented in regards to water-worked surfaces (i.e., flow imparts a direction upon the surface during the armoring process). ? Flow information around clusters could shed light on the formation and function of the features. The pressure distribution around isolated clasts of clusters has been shown to induce scour patterns. In this study, those pressures were not measured, but   134  the theory that greater bed roughness requires greater shear stress to initiate motion of a particle can be tested. ? The contrasting results between runs 1 and 7 and between runs 2 and 6 suggest that bed conditioning influences textural and topographical dynamics. As well, residual effects of sediment pulses may have had an effect on subsequent experimental runs. On this basis, randomized sequencing of the experimental runs may provide a viable avenue for future experimentation. Changes to the flow regime and the texture of the material supplied to the bed could also be incorporated.   135  References Aberle, J. and Nikora, V., 2006. Statistical properties of armored gravel bed surfaces. Water Resources Research, 42 (11), W11414. Aberle, J., Nikora, V., Henning, M., Ettmer, B., and Hentschel, B., 2010. Statistical characterization of bed roughness due to bed forms: A field study in the Elbe River at Aken, Germany. 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