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On the development of bed surface structures in response to variable flow regimes Wang, Yinlue 2020

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On the development of bed surface structures in response to variable flow regimes   by  Yinlue Wang   A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Geography)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  November 2020 © Yinlue Wang, 2020 ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis entitled:  On the development of bed surface structures in response to variable flow regimes  submitted by Yinlue Wang in partial fulfillment of the requirements for the degree of Master of Science in Geography  Examining Committee: Marwan Hassan, Geography Supervisor  Michael Church, Geography Supervisory Committee Member   iii  Abstract  The objective of this research is to use flume experiments to investigate the formation and development of bed surface structures and their impact on channel stability in response to variable flow regimes. A wide range of bed structures (clusters, stone cells, and transverse ribs) was reproduced in five sets of experiments, and data of sediment transport, bed surface grain size, and channel bed topography were systematically collected. A semi-automated method was developed to identify the bed structures, and used to record their temporal evolution regarding numbers and areal coverage. After the initial period of bed coarsening, D50 and D84 of surface grain size remained almost unchanged. In contrast, ongoing bedform development, longitudinal grain segregation, and evolution of bed structures were observed throughout the experiments. Bed structures developed and coexisted, and they constantly formed, disappeared, and transformed into other structures. The bed structure dynamic cannot be simply explained by flow regimes, but was significantly driven by particle interactions. The dynamic behaviour of bed structures concurred with the fluctuation of grain stability on the bed surface. Despite the active evolution of individual structures, their overall bed coverage remained around 15-20% most of the time. It can be inferred that the dynamic development of bed structures can be linked fundamentally to increasing channel stability, and that the fluctuation of bed mobility is partly associated with the development of bed structures.     iv  Lay Summary  Extensive studies have been done on how channel beds will develop a coarsened bed surface to increase channel stability. However, more research is needed on how the formation and evolution of bed surface structures will influence channel stability. The objective of this thesis is to study the influence of bed structures by conducting flume experiments. The result shows that bed structures can form and evolve dynamically along with ongoing sediment transport while bed coarsening is only profound at the initial period of bed degradation. This study also shows that bed structure development is significantly driven by particle interactions and is fundamentally related to channel stability. This thesis highlights the importance of understanding bed structures in practical applications of fluvial geomorphology. v  Preface  This thesis is the results of a series of flume experiments conducted in the Mountain Channel Hydraulic Experimental Laboratory at the University of British Columbia designed in conjunction with my supervisor Dr. Marwan Hassan. I conducted the experiments with help from Rick Kelter and David Waine, and performed the data analysis. A paper with Dr. Marwan Hassan and Dr. Michael Church as co-authors is planned for publication, based on Chapters 2-5. vi  Table of Contents  Abstract ......................................................................................................................................... iii Lay Summary ............................................................................................................................... iv Preface .............................................................................................................................................v Table of Contents ......................................................................................................................... vi List of Tables .............................................................................................................................. viii List of Figures ............................................................................................................................... ix List of Symbols ............................................................................................................................. xi Acknowledgements ..................................................................................................................... xii Chapter 1: Introduction ................................................................................................................1 1.1 Research background ...................................................................................................... 1 1.2 Research questions .......................................................................................................... 3 Chapter 2: Experimental design and methods ............................................................................5 Chapter 3: Data Analysis ............................................................................................................12 3.1 Fractional sediment transport rates ............................................................................... 12 3.2 Bedform delineation ...................................................................................................... 12 3.3 Longitudinal segregation of coarse particles ................................................................ 15 3.4 Semi-automated bed structure identification ................................................................ 16 3.5 Threshold of sediment transport ................................................................................... 22 Chapter 4: Observations .............................................................................................................24 4.1 Sediment transport and bedform development ............................................................. 24 4.2 Longitudinal coarse grain segregation and sediment texture ........................................ 31 vii  4.3 Development of bed structures ..................................................................................... 34 4.4 Threshold of particle mobility ...................................................................................... 41 Chapter 5: Discussion ..................................................................................................................44 5.1 Bed surface adjustment during degradation .................................................................. 44 5.2 Conditions and possible processes for bed surface structures ...................................... 45 5.3 Implication of bed structures for channel stability ....................................................... 48 5.4 Limitations and future work .......................................................................................... 49 Chapter 6: Conclusion .................................................................................................................52 References .....................................................................................................................................54  viii  List of Tables  Table 2.1 Flow magnitudes and durations used in the experiments ............................................. 10 Table 3.1 Summary of the quantitative measurements of bed structures ..................................... 20 Table 4.1 Summary of experimental data ..................................................................................... 25  ix  List of Figures  Figure 1.1 Various bed structures in gravel-bed rivers ................................................................... 4 Figure 2.1 5-metre flume used in this study. .................................................................................. 6 Figure 2.2 Grain size and flow used in the experiments ................................................................. 7 Figure 3.1 In-phase water and bed surface elevation profiles of the gravel antidunes formed in e03r06 and wavelength and corresponding spectral amplitude of the 1D longitudinal profiles of e03 after Fourier transform ............................................................................. 14 Figure 3.2 Data used to calculate longitudinal segregation of coarse particles ............................ 15 Figure 3.3 Procedure of bed structure identification after coarse particles are extracted ............. 21 Figure 3.4 Classification results using different R values ............................................................ 21 Figure 4.1 Grain mobility shown as the scaled fractional transport rates ..................................... 28 Figure 4.2 Longitudinal profiles and temporal development of bedforms according to Fourier transform ........................................................................................................................... 29 Figure 4.3 Longitudinal profiles of other experiments ................................................................. 31 Figure 4.4 Temporal evolution of coarse particle density on the bed surface with relatively high and low elevation showing the longitudinal segregation of coarse particles and the texture of the surface and bedload material .................................................................................. 33 Figure 4.5 Temporal evolution of bed structures identified in e03 ............................................... 35 Figure 4.6 Temporal evolution of bed structures identified in e02. .............................................. 36 Figure 4.7 Temporal evolution of bed structures identified in e04. .............................................. 37 Figure 4.8 Temporal evolution of bed structures identified in e05. .............................................. 38 Figure 4.9 Temporal evolution of bed structures identified in e06. .............................................. 39 x  Figure 4.10 Temporal changes in the numbers and areal coverage of each type of bed structure during the experiments. .................................................................................................... 40 Figure 4.11 Temporal evolution of critical shear stress ................................................................ 42 Figure 4.12 A comparison between the critical shear stress estimated by Wong and Parker (2006) and the critical shear stress estimated by channel slope based on Lamb et al. (2008). .... 43 Figure 5.1 Comparison between bed structures reproduced in the study and structures found in the field ............................................................................................................................. 50  xi  List of Symbols  tb bed shear stress tc* critical shear stress lr rib wavelength 1D one-dimensional 2D two-dimensional D grain diameter D50s 50th percentile of bed surface particles D84s 84th percentile of bed surface particles DEM digital elevation model Fr Froude number h water depth hb minimum barrier height for flow regime changes NL degree of non-linearity Q discharge Qs sediment discharge S bed surface slope S0 effective bed slope for sediment transport T flow duration W channel width  xii  Acknowledgements  I am deeply indebted to my supervisor Marwan Hassan, who gave me the opportunity to work in his lab, guided me through this research, and deepened my understanding of fluvial geomorphology. I am also sincerely grateful to my committee member Michael Church, who spent immense time helping me with this study and writing. I cannot express how much I have learned from them. I must thank the Department of Geography staff members, especially Rick Ketler and David Waine, for helping with my experiments, and Vincent Kujala for saving my computer when it crashed. I also wish to thank my fellow students in the Hassan research group for the countless valuable advice and enjoyable discussions. Thanks also to my friends who cheered me up all the time during the time of this program. Finally, I would like to express my deep and sincere gratitude to my family for their continuous and unparalleled support.   1  Chapter 1: Introduction  1.1 Research background Degrading gravel streambeds develop an armoured surface as a result of sediment starvation. A long history of flume experiments shows that a coarsened bed surface inhibits further bed erosion in the absence of abundant sediment supply (e.g., Harrison, 1950; Gessler, 1970; Little and Mayer, 1972; Dietrich et al., 1989). Despite relatively comprehensive investigations on the coarsened bed surface (e.g., summarized by Parker, 2008), understanding of bed structures on the coarsened surface remains limited (Venditti et al., 2017).  Bed structures are developed by the arrangements of coarse particles (e.g., Figure 1.1). They are meso-scale features that are larger than individual coarse particles and smaller than channel-scale features such as bars (Hassan et al., 2008). The presence of bed structures can significantly influence sediment transport and channel morphology in intermediate streams (Lisle and Church, 2002; Hassan et al., 2008). Furthermore, bed structures change dynamically even though the overall surface texture does not change much (Hassan et al., 2020a, 2020b). Bed structures influence flow dynamics, particle mobility, sediment availability for entrainment and transport rates, and introduce additional complexity to understanding and predicting sediment transport, channel morphology and morphodynamics in gravel-bed rivers (e.g., Morris, 1955; Hassan and Reid, 1990; Church et al., 1998; Hassan and Church, 2000; Marion et al., 2003; Heays et al., 2014; Hassan et al., 2020a, 2020b; Vázquez-Tarrío et al., 2020). Therefore, improving understanding of bed structures is critical for scientific advance and practical applications of fluvial geomorphology. 2   Hassan et al. (2008) and Venditti et al. (2017) summarized that bed structures emerge in low sediment transport regimes and that there is a wide range of bed structures such as stone clusters, stone cells, transverse ribs, and steps. Although stone clusters (e.g., Dal Cin, 1968; Brayshaw, 1984; De Jong, 1991; Wittenberg, 2002; Heays et al., 2014; Hassan et al., 2020a, 2020b; Hodge et al., 2020) and steps (e.g., Whittaker and Jaeggi, 1982; Chartrand and Whiting, 2000; Hasegawa, 2005; Church and Zimmermann, 2007; Zimmermann et al., 2010; Golly et al., 2019; Saletti and Hassan, 2020) have been extensively studied, little is known about transverse ribs and stone cells. Only a few experiments (e.g., Church et al., 1998; Hassan and Church, 2000) have reproduced stone cells. For transverse ribs, none of the theories of rib formation (Gustavson, 1974; Boothroyd and Ashley, 1975; Koster, 1978; McDonald and Day, 1978; Allen, 1983) have been tested by experiment. Only some kinematic simulation results (Tribe and Church, 1999; Malmaeus and Hassan, 2002) have improved understanding. They suggest that sediment structures, including transverse ribs and stone cells, are related to grain interactions, especially particle collisions, rotations, and proximity rules (Tribe and Church, 1999), and that particle interactions are controlled by resistance fields rather than solely by direct contact (Malmaeus and Hassan, 2002).  On top of limited understanding of individual types of some bed structures (especially cells and ribs), there is relatively little information about the coexistence and interaction among a variety of bed structures. Despite many important insights into how certain types of bed structures develop and affect channel stability and sediment transport, most prior studies have focused on a particular type of bed structure, in contrast to the diversity of bed structures in natural channels (e.g. Figure 1.1a). Understanding whether or how the formative conditions of 3  different types of bed structures will affect each other still remains very limited (Venditti et al., 2017)  1.2 Research questions The general goal of this study is, therefore, to investigate the development of the variety of bed surface structures. Based on current understanding of bed structures, two specific research questions are proposed:  (1) What are the conditions and possible processes for the formation of various bed surface structures (e.g., clusters, cells, and ribs), and do the conditions and processes of one type of bed structure oppose that of other bed structures?  (2) What is the implication of bed surface structures for channel stability?  Based on a hypothesis that a combination of little or no sediment supply and various flow regimes will produce a wide range of bed structures, five sets of no-feed flume experiments were conducted. A semi-automated method was also developed to identify the diverse bed structures reproduced in the experiments and used to quantify the temporal evolution of bed surface structures. In this study, particular attention was paid to transverse ribs because understanding of them has not been significantly improved since the 2000s. Despite widely accepted agreement on the description in McDonald and Banerjee (1971), ribs are sometimes mixed up with steps (e.g., Whittaker and Jaeggi, 1982; Hasegawa, 2005; Yokokawa et al., 2010; Venditti et al., 2017) and stone clusters with limited transversal extent (e.g., Lamarre and Roy, 2008). The description of McDonald and Banerjee (1971) was adapted by suggesting that transverse ribs in gravel-bed rivers are channel-spanning linear structures that can have appendages with limited streamwise 4  extent in this research. Furthermore, transverse ribs are proposed to be different from steps because the relatively large ratio between channel width and rib particles (as shown by comparing Figures 1.1a-1.1b to Figure 1.1c) implies that the effect of particle interactions leading to a jammed state (Church and Zimmermann, 2007) is low or absent during rib formation and therefore, transverse ribs impose less robust gradient control compared to steps.  Figure 1.1 Various bed structures in gravel-bed rivers: (a) Bed surface structures in Harris Creek showing transverse ribs and stone cells reported by Church et al. (1998). Both are notable bed structures in Harris Creek; their collective shape can be visualized as reticulate cells. Figure is reproduced with permission of Wiley. (b) Transverse ribs in Eggleshope Brook, North Yorkshire, UK. Photo courtesy of Michael Church. (c) Steps in East Creek, BC, Canada. Photo courtesy of Matteo Saletti. The comparison between the ribs and steps in this figure demonstrates that steps have larger keystones and more control on channel gradient. 5  Chapter 2: Experimental design and methods  Five sets of no-feed flume experiments (e02-e06) were conducted in the Mountain Channel Hydraulic Experimental Laboratory at the University of British Columbia. The goal of the experiments is to study the formation and evolution of bed surface structures under sediment starvation. The flume is 5 m long, 0.4 m wide, and 0.8 m deep (Figure 2.1). The initial flume slope was set at 3%, as a generic simulation of mountain rivers. The bed material (Figure 2.2a) was composed of poorly-sorted material ranging from 0.5 mm to 45 mm and scaled in the ratio of 1:3 from composite samples collected in East Creek (Elgueta‐Astaburuaga and Hassan, 2017; 2019), a forest stream near Vancouver. All the stones with b-axes coarser than 2 mm were painted according to grain size by half-phi intervals. In this study, the “coarse” portion of sediment includes the green (22.6-32 mm, from the 87th to the 98th percentile) and white (32-45 mm, coarser than the 98th percentile) stones. They are important because they can be anchor stones for bed structures (e.g., Brayshaw, 1984; Hassan and Reid, 1990; Hendrick et al., 2010; Hassan et al., 2020a). Bed structures usually characteristically contain the largest stones on the bed surface (McDonald and Banerjee, 1971). The ratio between channel width and the coarsest particles is 8.9-12.5, which is notably larger than the ratios observed in step formation (cf. Zimmermann et al., 2010; Saletti and Hassan, 2020), indicating that the grain mobility in this research was less constrained by channel width and potentially higher than the grain mobility in the aforementioned experiments related to steps. The relatively mobile particles combined with the 6  absence of width variation in the flume (cf. Golly et al., 2019; Saletti and Hassan, 2020) discourage the formation of jammed structures and thus encourages fewer stable structures.  Figure 2.1 5-metre flume located in the Mountain Channel Hydraulic Experimental Laboratory, UBC used in this study.   7   Figure 2.2 Grain size and flow used in the experiments: (a) Cumulative grain size distribution (plotted as geometric mean) of the bed material and (b) hydrograph used in the experiments. In e03, the highest flow lasted for another three hours after the hydrograph shown in the figure. e04-06 are three constant flow experiments using one flow magnitude selected from the hydrograph.  The flow information of the experiments in this study is summarized in Figure 2.2b and Table 2.1. The experiment sets e02 and e03 used the same stepped hydrograph: e03 was a repeated experiment of e02, while the other three sets (e04-06) were experiments with individual constant flows (Figure 2.2b). The stepped hydrograph experiments were utilized to investigate sequential adjustments of a channel bed to increasing flows. The stepped hydrograph was determined based on preliminary experiments and divided the hydrographs into successive runs 60 300Time (min)020406080Flow usedin e041 10 20 40Particle grain size (mm)200406080100Percnet finer thanDischarge (L/s)D98D87Green stonesWhite stones(a)(b)120 180Flow usedin e05240 360Flow usedin e068  of one hour. For example, e02 consisted of six runs (e02r01-e02r06); e02r01 denotes run 01 of the experimental set e02. Based on a couple of preliminary experiments, a flow of 19.4 L/s (r01) was used to form a coarsened surface from the initially well-mixed bed in the hydrograph experiments. Afterwards, flow discharge was increased by 25% every run to ensure the flow increments were gradual while also great enough to mobilize additional sediment and noticeably alter the preceding bed surface. For e03, flow was extended for an additional three hours (e03r07-09) after the flow reached the maximum value of the hydrograph (59.2 L/s) to see how the increase of flow duration might cause further bed adjustments and whether the bed structures formed by the preceding flows were stable.  For a reason similar to the maximum flow extension in e03, three constant flow experiments (e04-06) were conducted to see whether a different flow history (constant flow vs stepped hydrograph) and duration would result in different bed surface adjustments. Three flows were selected from the stepped hydrograph to represent the results caused by low (30.0 L/s in e05), medium (47.4 L/s in e04), and high (59.2 L/s in e06) flows, and the discharge remained constant throughout each entire experiment. The same notation was utilized for constant flow experiments (e.g., e04r01 represents the run 01 of e04). However, the duration of each run was not constant during e04-06 because of the assumption that most of the changes would happen at the beginning of the constant flow. Therefore, r01 and r02 were as short as 15 minutes; r03 and r04 lasted for 30 and 60 minutes respectively, and the duration of r05 and r06 was 2 hours (Table 2.1).  The bed was thoroughly mixed before each set of experiments and levelled with an initial depth of 15 cm. After the first run, in which the first flow, r01, formed a coarsened bed surface from the well-mixed bed, the subsequent runs started from the previous bed condition. A pump 9  recirculated the flow and controlled the discharge around the desired rate with little fluctuation (smaller than 0.5 L/s, so <3% of the lowest applied flow). Before each run, water was slowly added to expel the air from the bed and then the flow was increased to the desired rate to mobilize sediment. Flow hydraulics, bed properties, and sediment transport were systematically measured. Longitudinal profiles of water and bed surface (except in e02) were measured by using a point gauge. The point gauge measured the water and bed surface elevation in the middle of the cross-section every 10 cm along the flume plus two boundary points (at 0.5, 1, 1.1, 1.2, …, 3.9, 4.0, 4.5 m from the outlet) once the water surface and bed surface were overall stabilized. After each run, the flume was drained and bed properties were measured with photo and laser scans. Orthogonal photos of the whole bed surface were obtained with a digital camera. Digital elevation models (DEMs) were generated by recording the reflective location of a green laser beam. The DEMs consisted of 2 mm x 2 mm cells with a vertical resolution of 1 mm. In order to obtain information of surface grain size, a sample grid was superimposed on each photo and a Wolman count was conducted based on the color of grains on the grid. 400 particles were counted for each run to determine the entire grain size distribution (Rice and Church, 1996). All the coarse particles (green and white stones) were mapped based on their properties of color and size (Müller, 2019) because this study has a particular interest in the arrangement of coarse particles on the bed surface and the locations of coarse particles are critical to bed structures. Bedload output was collected in a trap at the flume outlet, and was sampled and sieved to determine the sediment texture of bedload material.  10   Table 2.1 Flow magnitudes and durations used in the experiments Run Name Q (L/s) T (min) e02r01 19.4 60 e02r02 24.0 60 e02r03 30.0 60 e02r04 37.9 60 e02r05 47.4 60 e02r06 59.2 60 e03r01 19.4 60 e03r02 24.0 60 e03r03 30.0 60 e03r04 37.9 60 e03r05 47.4 60 e03r06 59.2 60 e03r07 59.2 60 e03r08 59.2 60 e03r09 59.2 60 e04r01 47.4 15 e04r02 47.4 15 e04r03 47.4 30 e04r04 47.4 60 e04r05 47.4 120 e04r06 47.4 120 e05r01 30.0 15 11  e05r02 30.0 15 e05r03 30.0 30 e05r04 30.0 60 e05r05 30.0 120 e05r06 30.0 120 e06r01 59.2 15 e06r02 59.2 15 e06r03 59.2 30 e06r04 59.2 60 e06r05 59.2 120 e06r06 59.2 120       12  Chapter 3: Data Analysis  3.1 Fractional sediment transport rates Fractional sediment transport rates during each run were calculated because the development of bed structures is critically related to the mode of sediment transport, especially partial transport (Church et al., 1998; Hassan and Church, 2000). During full mobility, the fractional transport rate is independent of particle grain size, while in partial mobility the factional transport rate declines as grain size increases. The degree of partial transport can be estimated by calculating the scaled fractional transport rates of each particle size group, Qspi/fi where Qs is the bedload transport rate, pi indicates the proportion of each grain size in the bedload material from sieving the bedload samples, and fi indicates the proportion of each grain size in the surface material according the Wolman count results. Surface material was used to calculate fi because sediment is transported from the coarsened bed surface and the availability of fine particles on the bed surface is greatly reduced after bed coarsening. Particles between 2.8 and 22 mm were divided into six groups based on half-phi intervals. Particles finer than 2.8 mm were grouped because those particles are difficult to capture by Wolman count, and particles coarser than 22 mm (green and white particles) were combined to reduce the bias related to the small quantity of the coarsest particles in the bedload samples.  3.2 Bedform delineation The flow was either near-critical or supercritical in all cases according to the Froude number (further information can be seen Fr, Table 4.1). Continuous longitudinal bedforms in the form of quasi-regularly spaced undulations were observed. Nascent antidunes were assumed in low 13  flows, and they became more marked during high flows (e.g., Figure 3.1a). To test the antidune conjecture and quantify the bedform as a background for bed structure development, a 1D Fourier transform was performed on the longitudinal bed profiles to capture the bedform changes because the features showed no significant cross-stream variation (as shown by the DEM in Figure 5b). Before the transform, the upstream and downstream boundaries of the mean longitudinal profiles were removed and the longitudinal profiles were detrended by removing the mean gradient. A moving average filter with a 4 cm window was further applied on the mean longitudinal profiles to smooth the signal related to grain-scale. Then, the Fourier transform was performed after the longitudinal profiles were tapered with a Tukey window to prevent spectrum leakage. The raw outcome (Figure 3.1b) shows distinct spikes when there were developed bedforms. Once the wavelength of the highest spectral amplitude is smaller than the length of the longitudinal profile subjected to the Fourier transform, quasi-regularly spaced bedforms are considered detected and the amplitude is further used to record the bedform development. 14   Figure 3.1 (a) In-phase water surface elevation (WSE) and bed surface elevation (BSE) profiles of the gravel antidunes formed in e03r06. Note the large vertical exaggeration. (b) Wavelength and corresponding spectral amplitude of the 1D longitudinal profiles of e03 after Fourier transform. Distinct spectral peaks can be observed when there are regular bedforms (e.g., r06)  10 2 3 4 5Distance from the outlet (m)Wavelength (mm)152025303540WSEBSE5000 1200 800 400 200024681012r01r02r03r04r05r06r07r08r09Elevation (cm)Amplitude(a)(b)15  3.3 Longitudinal segregation of coarse particles It is important to quantify the longitudinal segregation effect of coarse particles on bedforms because the development of bed structures is highly correlated with the distribution of resident coarse particles. A high density of coarse stones can promote the formation of bed structures because of more frequent interaction between bedload material and coarse particles acting as anchor stones.  To calculate the coarse particle density on the surface with relatively high and low elevation, all the coarse particles were first detected from the orthogonal photos based on their colour and size (Figures 3.2a and 3.2b) by using Müller's (2019) method. Then the trend line of longitudinal profiles derived from the DEM (Figure 3.2c) was used to divide the bed surface into areas with relatively high and low elevation. The density of coarse particles on the high elevation areas was calculated as the particle number divided by the area of the relatively high bed surface. Similarly, coarse particle density on the relatively low areas is the ratio between coarse particle number and the area of the relatively low bed surface.  Figure 3.2 Data used to calculate longitudinal segregation of coarse particles: (a) orthogonal bed surface photo, (b) coarse particles extracted from the orthogonal photo, and (c) bed surface DEM. 16  3.4 Semi-automated bed structure identification Bed structures can be identified visually according to the coarse particle concentration and bed topography. For example, Church et al. (1998) mapped the stones coarser than D84 and visually identified transverse ribs and stone cells. However, manual identification can be time-consuming and subjective, especially for transverse ribs (Gustavson, 1974; Martini, 1977). Although there are methods using quantitative means to identify bed structures such as clusters (e.g., Heays et al., 2014; Wu et al., 2018; Hassan et al., 2020a) and steps (Zimmermann et al., 2008; Saletti and Hassan, 2020), there are no quantitative methods proposed to identify transverse ribs. Furthermore, no quantitative methods have been developed to identify a variety of bed structures (consisting of stone clusters, stone cells, transverse ribs and partial ribs) reproduced in the experiments of this research. In order to reduce subjectivity when identifying the bed structures and record their evolution in a consistent way, a semi-automated method using the concept of overlapping resistance fields was introduced to identify bed structures, including ribs. The identification method consists of selecting the large particles that generate resistance fields, delineating the fields around the selected particles, extracting overlapping resistance fields as units for identification, and developing a bed structure classification scheme to identify the units as stone clusters, stone cells, transverse ribs or partial ribs (Figure 3.3 and Table 3.1). Overlapping resistance fields were identified by adopting the concept introduced by Malmaeus and Hassan (2002). The overlapping resistance field method in this study assumes that individual particles generate resistance fields that alter the flow around them and, when two or more individual resistance fields overlap, they form a much more stable resistance field more extensive than the field generated by individual grains. If an overlap exists among the resistance fields of a group of individual particles, the interaction among those particles can be considered 17  to enhance the stability of all of the grains significantly, and therefore the sum of overlapping individual resistance fields can be treated as a unit for structure identification. To transfer the overlapping resistance field concept into a practical structure identification method, the particles that are stable enough to generate resistance fields (used for structure identification) and the extent (i.e., size and shape) of the fields need to be determined. Although particles of all grain size are able to generate resistance fields, only the particles that are coarse enough to be anchor stones were chosen because they are more stable as individual particles and their resistance fields would have greater continuing impact on the flow. Thus, white and green stones were first mapped (as shown in Figure 3.2b). The spatial distribution of coarse particles and bed topography were further combined to specify the particles used for structure identification; Only the exposed coarse particles (Figure 3.3a) were selected because those particles are able to significantly interact with flows and moving sediment. Those particles were selected as particles with higher elevation compared to their local longitudinal profiles (from 6 cm upstream to 6 cm downstream) measured from DEM (e.g., Figure 3.2c). Malmaeus and Hassan (2002) used ellipsoidal resistance fields to avoid the formation of artificial features. Schmeeckle et al. (2007) showed that particles can influence the flow velocity sufficiently within 2r from their centres, where r is the particle radius. In this study, a circular resistance field shape was used as an average effect of particle-introduced resistance. For the area of a resistance field, the radius was assumed to be equal to one b-axis accordingly (2r with an approximation assuming that particles are spherical). The assumption of the critical distance is also supported by the field study conducted by Lamarre and Roy (2008), in which bed structures entrapped particles within the median distance of around 2 keystone diameters, indicating the average resistance field radius is around 2r. 18  After delineating the resistance fields around individual particles, it was straightforward to determine whether two individual fields are overlapping. If two particles have overlapping resistance fields, the distance between their centroids is smaller than the sum of their resistance radii. Therefore, every individual resistance field was examined and the resistance fields that were not overlapping with others (i.e., isolated, single particle fields without enhanced stability) were eliminated. After this process, only overlapping resistance fields remained, and every overlap was considered as the unit for bed structure identification, as shown in Figure 3.3b. Each overlapping resistance field was used as the basic unit for identification. A classification scheme similar to Weichert et al. (2008), Hassan et al. (2008), Hendrick et al. (2010) was applied to divide the bed structures developed in the experiments into four categories: stone clusters, stone cells, transverse ribs and partial ribs according to a series of empirical parameters (Table 3.1). In this study, full transverse effect to alter the flow is considered to be associated with structures wider than 75% of channel width while structures with transverse extent between 50% and 75% of channel width are considered to have partial transverse effect. The structures containing transverse ribs were first detected based on the fraction of channel span (> 75% channel width). Stone clusters were then extracted as they are the smallest bed structures in the category. To isolate stone clusters, an upper areal threshold of the overlapping fields was applied by considering stone clusters to have areas smaller than 4 resistance fields generated by green particles because Hassan (2005) found each cluster to have three or four particles. Afterwards, partial transverse ribs were identified as 1D structures with some degree of channel spanning (50-75% channel width). The degree of non-linearity (noted as NL in following text) calculated as the ratio between the area and longest axis based on eight extrema of the resistance field was used to differentiate between 1D and 2D structures. The 19  longest axis is calculated as the longest distance between two points of the eight extrema points of the resistance fields (detailed information shown in Table 3.1). For a linear feature, the NL calculated should be close to the diameter of the resistance field (4r) while the value of a 2D resistance field would be constantly larger than the resistance field diameter. The NL of partial ribs was defined empirically to be smaller than 1.25× the diameter of the resistance field generated by the coarsest particles (25% was added as room to account for partial ribs with imperfect linear shapes). The remaining structures have a similar degree of channel span compared to partial ribs. However, different from the 1D shape of partial ribs, they have 2D cellular morphology with closed or open shapes. Hence, those structures were regarded as stone cells. The classification results based on the semi-automated method (Figure 3.3c) are similar to judgments from visual inspection of the surface, but the semi-automated method greatly enhances the consistency when delineating the boundaries of bed structures. Slightly different parameters would lead only to minor changes in the identification results. In order to test the effect of a different resistance field area, 1.5r and 2.5r as the radius were tried for comparison (Figure 3.4). The comparison in Figure 3.4 shows that larger resistance areas lead to more large-scale structures scaled with channel-width (ribs and cells) and smaller resistance areas lead to more grain-scale clusters.  The numbers and coverage of each type of bed structure during each run in the experiments were calculated after applying the semi-automated method for bed structure identification. The extent of the overlapping resistance fields was assumed to be the extent of bed structures’ effect as the overlapping resistance fields shelter finer sediment within the resistance field. Therefore, the fractional areal coverage of each type of bed structure was calculated as the sum of the overlapping resistance field areas divided by the area of flume surface.  20  In order to compare the results to previous research related to transverse ribs (e.g., Koster, 1978; Allen, 1983), the rib wavelength (l r) in this thesis was calculated as the average distance between two adjacent ribs once two or more ribs formed in a run of the experiments.  Table 3.1 Summary of the quantitative measurements of bed structures Structure type Scale Definition and parameters used in the identification Plan form sketch Stone clusters D Few coarse stones surrounded by multiple smaller particles; distance between two coarse stones within one cluster should be very short if not in direct contact. Their areas should be smaller than four green particles.  Transverse ribs D/W Channel spanning or nearly channel-spanning linear organizations of coarse stones lying transversely to the flow direction. The transverse extent should be longer than 75% W.  Partial ribs D/W Similar to transverse ribs but the structures are less channel-spanning. The degree of non-linearity (NL) is smaller than 1.25 D. The transverse extent is between 50% and 75% W.   Stone cells D/W 2D organizations of coarse stones; the distance between two coarse stones should be within one-grain diameter; the outline of the structures can be either open or closed. NL is larger than 1.25 D.   W denotes the channel width and D denotes the diameter of the largest particles. The sketches of partial ribs and stone cells are accompanied by simplified shapes showing how the longest axis we used is determined based on 21  eight extrema system (left-top, top-left, right-top, top-right, right-bottom, bottom-right, bottom-left, left-bottom). The eight extrema are computed by using an official function (regionprops) in MATLAB.  Figure 3.3 Procedure of bed structure identification after coarse particles are extracted: (a) selecting the coarse particles with relatively high local exposure, (b) drawing resistance fields with R = 2r around the particles with high local exposure and extracting overlapping resistance fields for structure identification, and (c) applying the classification scheme based on Table 3.1.   Figure 3.4 Classification results using different R values: (a) R = 2r, (b) R = 1.5r, and (c) R = 2.5r.  (a)(b)(c)500 1000 1500 2000 2500 3000 3500 4000 4500Distance from the outlet (mm)Transverse rib Partial rib Cluster Stone Cell(a) R = 2r(b) R = 1.5r(c) R = 2.5r(c)(d)(e)(f)50100150500 1000 1500 2000 2500 3000 3500 4000 4500Distance from the outlet (mm)Transverse rib Partial rib Cluster Stone Cell22  3.5 Threshold of sediment transport To test the hypothesis that the formation of bed structures influence the channel bed stability, and that the effect can be seen as fluctuations of the overall critical shear stress, critical shear stress (tc*) was calculated by first adopting the method developed by Hassan et al. (2020b) following Wong and Parker (2006): 											"!∗ = 3.97()∗ − )#∗)$.&																			                                    (3.1) where qs* is the non-dimensional sediment transport rate per channel width, and t* and tc* represent non-dimensional shear stress and critical shear stress, respectively. In Wong and Parker (2006), tc* is equal to 0.0495 according to the best fit line of their database. Hassan et al. (2020b) calculated tc* by using their measured qs* and t* during each run and suggested the change in critical shear stress can reveal the evolution of bed mobility as a result of bed structuring. As bedform development was observed in the experiments, using the reach-averaged slope cannot yield accurate estimation of shear stress used for sediment transport due to the local acceleration and deceleration caused by bedforms. Chiari and Rickenmann (2011) showed that the effective slope for sediment transport is much lower than the topographical slope in steep channels. Thus, the method used in Hassan et al. (2020b) was further modified to separate the skin friction by implementing the methods of Chiari and Rickenmann (2011) based on effective slope (S0): ''!"! = 0.07-().*+                                                            (3.2) -) = -( ''!"!)$.,                                                               (3.3) 23  where n/ntot is the ratio of the channel roughness related to skin friction to the total channel roughness, and S and S0 represent the overall slope and effective slope for grain transport, respectively. Chiari and Rickenmann (2011) determined the constants in Equations 3.2 and 3.3 by applying a sediment routing model (Chiari et al., 2010) to steep streams with substantial sediment transport. S0 was used to calculate t* in Equation 3.1 and estimate tc* based on the skin friction.   24  Chapter 4: Observations  4.1 Sediment transport and bedform development e02 and e03, two repeated experiments with the same stepped hydrograph, have a similar pattern in terms of sediment transport (Qs in Table 4.1, and partial sediment transport shown in Figures 4.1a and 4.1b), longitudinal profiles (Figures 4.2a and 4.3a) and bedform development (Figure 4.2c). The flow was always near-critical or supercritical (according to Fr in Table 4.1). The first flow (r01, with a magnitude of 19.2 L/s for one hour) caused a significant amount of sediment transport and bed degradation (according to Qs in Table 4.1) and the channel slope was reduced from 3% to 2% in both e02 and e03 (S in Table 4.1). As the flow was increased, subsequent bed degradation (Qs and S in Table 4.1) was observed and longitudinal profiles (Figures 4.2a and 4.3a) evolved from nascent undulations located mainly upstream (e.g., r01) to antidunes occupying the whole channel bed (e.g., r06). The bedform development is captured by Fourier transform; as Figure 4.2c suggests, both e02 and e03 exhibited significant bedforms after r04 (37.9 L/s). According to the Fourier analysis, the bedforms of both e02 and e03 decayed in r05 (47.4 L/s) and redeveloped to their highest peak in r06 (59.2 L/s), consistent with the visual impression of the longitudinal profiles (e.g., Figure 4.2a). After r06, well-developed undulations spread throughout the entire length of the flume (Figure 4.2a), and the hand gauge survey showed that the water surface and bed surface were in-phase during that flow magnitude (Figure 3.1a).    25   Table 4.1 Summary of experimental data Run Name h (cm) S (%) S0 (%) tb (Pa) Fr Qs (kg/min) D50s (mm) D84s (mm) tc* (W-P) tc* (L) tc* (W-P-S0) l r (mm) l rA (mm) l rK (mm) hb (cm) e02r01 - 2.27 - - - 1.28 13.19 29.94 - - - / 298 - - e02r02 - 1.98 - - - 0.15 15.16 30.14 - - - s 341 - - e02r03 - 1.93 - - - 0.17 15.11 30.83 - - - s 350 - - e02r04 - 1.57 - - - 0.29 14.34 30.14 - - - / 431 - - e02r05 - 1.40 - - - 0.41 18.14 31.99 - - - / 481 - - e02r06 - 1.22 - - - 0.92 15.28 30.75 - - - s 555 - - e03r01 5.64 2.21 0.78 12.20 1.14 0.86 12.55 27.00 0.053 0.059 0.014 s 306 473 5.27 e03r02 7.15 2.03 0.75 14.20 0.99 0.16 13.79 28.82 0.062 0.056 0.022 s 333 452 5.97 e03r03 8.13 1.95 0.74 15.55 1.02 0.17 17.70 30.67 0.053 0.055 0.019 / 346 546 6.93 e03r04 9.64 1.63 0.68 15.42 0.98 0.27 17.81 31.28 0.051 0.053 0.020 s 414 618 8.09 e03r05 10.89 1.48 0.66 15.79 1.01 0.51 17.37 31.35 0.053 0.054 0.021 1540 456 759 9.42 e03r06 12.59 1.19 0.60 14.66 1.01 0.52 15.95 31.28 0.053 0.049 0.024 1746 568 886 10.92 e03r07 12.98 1.35 0.63 17.15 0.96 0.16 18.14 31.87 0.057 0.049 0.026 2040 501 833 10.90 e03r08 13.15 1.22 0.60 15.69 0.94 0.05 19.20 32.47 0.050 0.047 0.024 s 554 812 10.90 e03r09 13.61 1.14 0.58 15.19 0.89 0.03 19.44 32.04 0.048 0.042 0.024 s 593 757 10.93 e04r01 10.55 1.44 0.65 14.94 1.05 8.11 12.53 23.43 0.042 0.051 0.001 s 467 808 9.47 e04r02 11.13 1.32 0.62 14.36 0.97 0.43 13.05 23.68 0.064 0.049 0.028 s 513 727 9.40 e04r03 10.91 1.27 0.61 13.61 1.00 0.22 13.60 22.95 0.059 0.049 0.027 242 530 756 9.41 26  e04r04 11.14 1.27 0.61 13.91 0.97 0.05 14.17 23.34 0.060 0.051 0.028 1714 530 725 9.40 e04r05 11.13 1.25 0.61 13.69 0.97 0.03 14.46 23.51 0.058 0.050 0.028 273 538 726 9.40 e04r06 11.09 1.23 0.61 13.41 0.97 0.01 15.05 23.71 0.055 0.049 0.027 s 547 732 9.40 e05r01 8.71 1.60 0.68 13.68 0.90 6.46 9.17 22.14 0.055 0.056 0.002 s 421 475 6.95 e05r02 7.99 1.59 0.68 12.49 1.04 0.36 10.73 23.00 0.067 0.053 0.026 s 423 564 6.94 e05r03 8.10 1.57 0.67 12.50 1.02 0.09 12.02 22.95 0.063 0.055 0.026 / 429 550 6.93 e05r04 8.36 1.52 0.66 12.46 0.97 0.04 12.27 23.09 0.062 0.053 0.026 / 444 516 6.93 e05r05 8.18 1.52 0.66 12.20 1.00 0.02 13.66 23.51 0.055 0.055 0.024 / 444 538 6.93 e05r06 8.29 1.51 0.66 12.27 0.98 0.01 14.57 23.89 0.052 0.054 0.022 / 447 525 6.93 e06r01 12.98 1.24 0.61 15.82 0.95 11.39 12.69 23.00 0.038 0.050 -0.002 488 543 834 10.90 e06r02 12.86 1.08 0.57 13.67 0.96 0.52 12.93 22.95 0.060 0.048 0.030 / 622 849 10.90 e06r03 13.09 0.97 0.55 12.51 0.94 0.20 14.71 23.58 0.050 0.042 0.027 476 693 819 10.90 e06r04 13.66 0.93 0.54 12.47 0.88 0.05 15.18 24.13 0.050 0.047 0.028 749 724 752 10.93 e06r05 13.43 0.91 0.53 11.98 0.90 0.03 15.37 24.01 0.048 0.046 0.027 1146 742 778 10.91 e06r06 13.53 0.88 0.52 11.64 0.89 0.01 15.31 24.25 0.047 0.043 0.028 1166 769 767 10.92 Notes:  1. Definitions of symbols are explained in the List of Symbols of this thesis. 2.  h (water depth) is not measured in e02, hence the data related to flow characteristics and critical shear stress are not available. The available data are calibrated based on Vanoni-Brooks sidewall correction. 3.  tc* (W-P) denotes the critical shear stress calculated by using Equation 3.1 based on Wong and Parker (2006). tc* (L) denotes the critical shear stress calculated based channel slope using Lamb et al. (2008). tc* (W-P-S0) is the critical shear stress calculated by using a combination of Equations 3.1-3.3, as an implementation of effective slope on Wong and Parker (2006). 27  4.  l r represents the measured rib wavelength in our experiments. l rA represents the wavelength lower limit estimated as ! = 0.15 !" in Allen (1983) where D and S denote grain size and channel slope, respectively. l rK represents the wavelength calculated as ! = #$%!&  (Kennedy, 1963) where U is the flow velocity calculated as water discharge divided by channel width and water depth ( '()). 5.  hb (the minimum barrier height for flow regime changes) is calculated as E-Emin, where ' = ℎ + *!#&+! and ',-. = **!&" , and q = Q/W as specific water discharge.  28    Figure 4.1 Grain mobility shown as the scaled fractional transport rates: (a) e02, (b) e03, and (c) the beginning (r01, after 15 mins) and end (r06, after 360 mins) of three constant flow experiments e04-06. The scaled fractional transport rate is calculated as Qspi/fi where Qs is the bedload transport rate, pi indicates the proportion of each grain size in the bedload material, and fi indicates the proportion of each grain size in the surface material.    100 101 102Grain size ner than (mm)10-210-1100101102103104Scaled fractional transport rates (kg/hr)(a)e0224.0 L/s30.0 L/s37.9 L/s47.4 L/s59.2 L/s100 101 102Grain size ner than (mm)10-210-1100101102103104(b)e0324.0 L/s30.0 L/s37.9 L/s47.4 L/s59.2 L/s rst hour59.2 L/s fourth hour100 101 102Grain size ner than (mm)10-210-1100101102103104(c)constantowexperiments47.4 L/s 15 mins47.4 L/s 360 mins30.0 L/s 15 mins30.0 L/s 360 mins59.2 L/s 15 mins59.2 L/s 360 mins29   Figure 4.2 Longitudinal profiles and temporal development of bedforms according to Fourier transform: (a) Longitudinal profiles of e03 showing progressive development of longitudinal profiles during r01 to r06 and upstream bedform migration during the flow extension period (r06-r09). (b) Longitudinal profiles of e06 showing that bedforms were quickly established during the first flow (r01) and only small changes occur afterwards. (c) Temporal development of bedforms according to Fourier transform. Generally, no regular bedforms were detected within the first four hours (up to r03) in stepped hydrograph experiments, and after two hours in e04, in which the flow was constantly 47.4 L/s.  During the flow extension period in e03 (r07-09, another 3 hours of 59.2 L/s flow), the rate of overall sediment transport (Table 4.1) was greatly reduced and the degree of partial transport was slightly enhanced compared to r06, the first hour of 59.2 L/s (Figure 4.1b). Visually, upstream migration of bedforms was notable during the flow extension period (Figure 4.2a, from r06 to r09), and, according to the spectral analysis, the bedform regularity was only slightly weakened (Figure 4.2c).  1000 2000 3000 4000Distance from the outlet (mm)160200240280Elevation (mm)160200240280Elevation (mm)r01r05r061000 2000 3000 4000Distance from the outlet (mm) Time (min)0 120 240 360 48024681012(a) Longitudinal profile in e03(b) Longitudinal profile in e06(c)r01r05r06e04e05e06e02e03e04e05e06120 240Time (min)Amplitude (mm)24681012 (c) Temporal development of bedformsr04r09r0430   Near-critical flow and supercritical flow (Table 4.1) was also observed throughout three experimental sets with constant flow magnitude (e04 with 47.4 L/s, e05 with 30 L/s, e06 with 59.2 L/s). The first period of flow caused more degradation compared to that used in the stepped hydrograph experiments even though the flow was run for only 15 minutes, as shown by the values of Qs and S in Table 4.1. Bedforms were instantly established during the first flow (Figures 4.2b, 4.3b, 4.3c), despite their relatively low regularity, compared to the bedforms observed in the highest flow in e02 and e03 (Figures 4.2c).   The rest part of the constant flow experiments experienced greatly reduced sediment transport rates (Table 4.1) and enhanced partial sediment transport mode (Figure 4.1c). Consistent with the lowered sediment transport, longitudinal profiles did not show noticeable degradation other than local scours (Figures 4.2b, 4.3b, and 4.3c). The regularity of the bedforms considerably decayed within the first 2 hours in the high flow experiments (Figure 4.2c); bedforms in e04 (with 47.4 L/s) could no longer be found after 2 hours, and the signal of the bedforms in e06 (with 59.2 L/s) was significantly weakened. However, Figure 4.2c also shows that less developed but persistent bedforms were found throughout the entire low flow experiment (e05 with 30.0 L/s). 31   Figure 4.3 Longitudinal profiles of experiments additional to those displayed in Figure 4.2: (a) longitudinal profiles of e02, (b) longitudinal profiles of e04, and (c) longitudinal profiles in e05.  4.2 Longitudinal coarse grain segregation and sediment texture Figure 4.4a confirms spatial grain segregation as, throughout the experiments, the bed surface with relatively high elevation consistently had larger coarse particle density than the relatively low areas. During the stepped hydrograph experiments (e02 and e03), for both relatively high and low areas, the coarse particle density increased except in r04 (37.9 L/s) wherein the coarse particle density in the low areas was reduced. During the flow extension period in e03 (r07-09, another 3 hours of 59.2 L/s flow), the grain size segregation also did not change much, similar to the small changes in bedforms mentioned in Section 4.1. The constant flow experiments show that different flows contributed to different degrees of coarse particle segregation on the longitudinal profiles (Figure 4.4a). Despite the common phenomenon that the surface with high 1000 2000 3000 4000Distance from the outlet (mm)160180200220240260280300Elevation (mm)(a) Longitudinal profile in e02 r01r04r05r061000 2000 3000 4000Distance from the outlet (mm)160180200220240260280300(b) Longitudinal profile in e04 r01r04r05r061000 2000 3000 4000Distance from the outlet (mm)160180200220240260280300(c) Longitudinal profile in e05 r01r04r05r0632  elevation contained a denser collection of coarse particles during the experiments, the high flow experiments (e04 and e06) had more complex trends of grain segregation, whereas the degree of coarse grain segregation was enhanced in e05, the experiment using the lowest flow (30 L/s) among the constant flow experiments. Figures 4.4b and 4.4c show that the first flow (r01) greatly coarsened the bed surface. For both stepped hydrograph (e02 and e03) and constant flow (e04-06) experiments, the D50 and D84 of the bed surface were significantly coarser compared to the initial bed made of well-mixed material. However, the overall bed surface texture did not change noticeably in terms of D50 and D84 after the first flow (Figures 4.4b and 4.4c), which is in contrast to the active evolution of coarse particle segregation as shown in Figure 4.4a.  The constant flow experiments also showed that surface grain size is to some degree independent of the flow magnitude as e04-06 yielded similar D50 and D84 (Figures 4.4b and 4.4c) despite the different magnitude of the first flow in these experiments. In addition, e02 and e03, two experiments in which the first flow was smaller but longer (19.4 L/s for one hour), yielded coarser D84 compared to the constant flow experiments (e04-06, in which the first flow was larger but lasted for only 15 minutes). Additionally, Figures 4.4b and 4.4c show that stepped hydrograph and constant flow experiments have different temporal patterns of bedload texture. For stepped hydrographs (e02 and e03), bedload material was initially fine and coarsened when the flow was large enough. During the two highest flows (47.4 L/s in r05 and 59.2 L/s in r06), the bedload material was similar to the bulk material. In contrast, in constant flow experiments (e04-06), the bedload material was initially coarse and finer afterwards. This fining trend was also seen during the flow extension part of e03 (r07-09, an additional three hours of the highest flow). 33    Figure 4.4 Temporal evolution of (a) coarse particle density (number/area) on the bed surface with relatively high and low elevation (HB and LB) showing the longitudinal segregation of coarse particles, and (b) D50 and (c) D84 of the surface and bedload material (s and l). No significant bed coarsening was observed after the first flow whereas the longitudinal coarse particle segregation had an ongoing active adjustment throughout the experiments.   34  4.3 Development of bed structures Bed structures reproduced in the experiments were identified by the semi-automated method (Figures 4.5-4.9) and the changes of the numbers and coverages (Figure 4.10) of these structures were recorded systematically. Different bed structures coexisted throughout the experiments, and no particular bed structures can be exclusively linked to certain flow regimes. Based on the numbers and coverages of different structures (e.g., Figure 4.10), stone clusters were the most prominent bed structure throughout the experiment; stone cells were the second most notable bed structure. Transverse ribs are a relatively small population but can occupy relatively large areas when there are more than three ribs (e.g., Figures 4.7, 4.9, and 4.10). Partial ribs occurred rarely and covered only a small area. Figure 4.5 shows the dynamic temporal evolution of bed structures in e03. Structures frequently formed, transformed into other structures, and disappeared. For example, an individual rib was formed instantly after the first flow (r01). However, during the next run (r02) the rib did not persist; it transformed into a partial transverse rib and some clusters via the dislodging of coarse particles of the rib. This phenomenon, related to particle dislodgement, was very prevalent in the experiment: For example, the destruction of a rib formed in r03 led to the formation of a stone cell and several clusters. Figure 4.5 also shows that transverse ribs were formed from previous smaller structures such as partial ribs (e.g., r07), stone clusters (e.g., r05), and stone cells (e.g. r04 and r08) via entrapping more coarse particles. Dynamic evolution can also be seen in smaller bed structures (partial ribs, clusters, and stone cells) throughout the experiment (Figure 4.5). Similar processes were observed in other experiments (Figures 4.6-4.9). For example, Figures 4.7 and 4.9 demonstrate that the constant flow experiments with relatively high flows (e04 with 47.4 L/s and e06 with 59.2 L/s) were similar to the flow extension part of 35  e03 (Figure 4.5) in that transverse ribs could either persist in high flows with some morphologic adjustments or become remnant stone cells with relatively high stability when rib destruction happened.  Figure 4.5 Temporal evolution of bed structures identified in e03, consisting of the stepped hydrograph part (r01-r06) and the flow extension period (r07-r09).  500 1000 1500 2000 2500 3000 3500 4000 4500Distance from the outlet (mm)Transverse rib Partial rib Cluster Stone Cell(a) e03r01(b) e03r02(c) e03r03(d) e03r04(e) e03r05(f) e03r06(g) e03r07(h) e03r08(i) e03r0936   Figure 4.6 Temporal evolution of bed structures identified in e02.   (a) e02r01(b) e02r02(c) e02r03(d) e02r04(e) e02r05(f) e02r06500 1000 1500 2000 2500 3000 3500 4000 4500Distance from the outlet (mm)Transverse rib Partial rib Cluster Stone Cell(c) e03r03(d) e03r04(e) e03r05(f) e03r06(g) e03r07(h) e03r08(i) e03r0937   Figure 4.7 Temporal evolution of bed structures identified in e04. (a) e04r01(b) e04r02(c) e04r03(d) e04r04(e) e04r05(f) e04r06500 1000 1500 2000 2500 3000 3500 4000 4500Distance from the outlet (mm)Transverse rib Partial rib Cluster Stone Cell(c) e03r03(d) e03r04(e) e03r05(f) e03r06(g) e03r07(h) e03r08(i) e03r0938   Figure 4.8 Temporal evolution of bed structures identified in e05. (a) e05r01(b) e05r02(c) e05r03(d) e05r04(e) e05r05(f) e05r06500 1000 1500 2000 2500 3000 3500 4000 4500Distance from the outlet (mm)Transverse rib Partial rib Cluster Stone Cell(c) e03r03(d) e03r04(e) e03r05(f) e03r06(g) e03r07(h) e03r08(i) e03r0939   Figure 4.9 Temporal evolution of bed structures identified in e06. (a) e06r01(b) e06r02(c) e06r03(d) e06r04(e) e06r05(f) e06r06500 1000 1500 2000 2500 3000 3500 4000 4500Distance from the outlet (mm)Transverse rib Partial rib Cluster Stone Cell(c) e03r03(d) e03r04(e) e03r05(f) e03r06(g) e03r07(h) e03r08(i) e03r0940   Figure 4.10 Temporal changes in the numbers and areal coverage of each type of bed structure during the experiments.  In contrast to the temporal evolution of bed surface texture (Figures 4.4b and 4.4c), the development of bed structures remained active when the bed surface was not significantly coarsened after the first flow (e.g., Figures 4.5 and 4.10). Figure 4.10 shows that the development of bed structures in e02 and e03, two experiments with the same conditions (regarding flow regimes and the initial bulk material) and similar evolution of bedforms (Figure 4.2c) and surface grain size (Figures 4.4b and 4.4c), were different in terms of the number and coverage of the various structures. However, the total coverage of bed structures is around 15-20% most of the time (Figure 4.10), despite the active evolution of individual bed structures shown in Figures 4.5-4.9. 010203001020300102030010203030 60 120 180 240 300 360 420 480 5400102030010%20%010%20%010%20%010%20%30 60 120 180 240 300 360 420 480 540010%20%Transverse rib Partial rib Cluster Stone cell TotalStructure numberStructural coverageTime (min) Time (min)(a) e02(b) e03(c) e04(d) e05(e) e06(f) e02(g) e03(h) e04(i) e05(j) e0641   4.4 Threshold of particle mobility The change of critical shear stress (tc*) was calculated as an indicator of the change of bed surface stability influenced by the formation of bed structures by using Equation 3.1 (Figure 4.11a). Similar to the changes in bed structures, the critical shear stress changed throughout the experiments. The value of tc* collected in the stepped hydrograph (e03r01-r06) was constantly higher than 0.0495, the value proposed by Wong and Parker (2006). For the constant flow experiments (e04-06) and the flow extension period in e03 (r07-r09), tc* increased first then decreased, and its temporal evolution also contrasts with the constant value proposed in Wong and Parker (2006). In addition, the dynamic change of tc* is different from the trend of bed surface texture (Figures 4.4b and 4.4c) and is difficult to estimate based on channel slope (Figure 4.12). Figure 4.11b shows tc* estimated by the partition method based on the effective slope for sediment transport by using a combination of Equations 3.1-3.3. The implementation of the effective slope reduces the variation for constant flow experiments, as e04 and e06, two experiments with relatively high discharge, now have the almost identical temporal evolution of tc*. However, e05 (in which the discharge was the lowest) still preserves the increase-decrease pattern observed in Figure 4.11a, whereas the decrease in tc* is no longer notable in e04 and e06. After shear stress partitioning, the value of tc* is shown to be very small during the first period of flow during the constant flow experiments, consistent with the high sediment mobility (Qs in Table 4.1). Interestingly, Figure 4.11b shows that tc* was overall increasing as the flow increased for e03 after the slope partition (consistent with the increasing water discharge), a different trend 42  compared to Figure 4.11a. Nonetheless, the contrast between the trend of bed coarsening and tc* still persists (compare Figure 4.11b to Figures 4.4b and 4.4c).   Figure 4.11 Temporal evolution of critical shear stress: (a) Critical shear stress estimated by Wong and Parker (2006). The dashed line represents tc* = 0.0495. (b) Critical shear stress calculated by using Wong and Parker (2006) with the implementation of effective slope (Chiari and Rickenmann, 2011). Note the combination of implementing effective slope and large bedload transport causes a negative value of tc* during the first period of e06, indicating the sediment mobility was remarkably high. (a) (b)00.01-0.010.020.030.040.050.060.070 120 300180 480420 54036024060Time (min)120 300180 480420 54036024060Time (min)0e03e04e05e06 c*43   Figure 4.12 A comparison between the critical shear stress estimated by Wong and Parker (2006) using Equation 3.1 and the critical shear stress estimated by channel slope based on Lamb et al. (2008). 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07*c estimated by Lamb et al. (2008)0.030.0350.040.0450.050.0550.060.0650.07* cestimated by Wong and Parker (2006)e03 hydrographe04e05e06e03 flow extension1:1 line44  Chapter 5: Discussion  5.1 Bed surface adjustment during degradation The bed surface adjustment during sediment starvation consisted of overall coarsened surface grain size, bedform development, and bed structuring. The experimental results of this thesis are consistent with previous research (e.g., Harrison, 1950; Gessler, 1970; Little and Mayer, 1972) in that a coarsened bed surface was formed and reduced further bed degradation. However, the limit of bed coarsening was reached very quickly in this study (Figures 4.4b and 4.4c), and the additional bed stability can be attributed to bedform development (Figure 4.2) and bed structuring (e.g., Figures 4.5 and 4.10), a phenomenon also reported by Church et al. (1998), Hassan and Church (2000), Chen et al. (2017), and Hassan et al. (2020a, 2020b). The additional bed stability can be ascribed to the relatively small value of S0 compared to S (Table 4.1), indicating that only a fraction of the shear stress was used for sediment transport (similar phenomenon also reported by Mao et al. (2020). This research also suggests that the bed coarsening can be more related to flow duration than magnitude. According to Figure 4.4c, three constant flow experiments, with three different flow rates (ranging from 30 to 59.2 L/s) but the same duration (15 minutes), yielded similar bed surface D84. Additionally, the two stepped hydrograph experiments (e02 and e03), with much lower flow (19.2 L/s) but longer duration (1 hour), produced coarser bed surface texture. This may indicate that longer duration with moderate discharge can coarsen a bed surface more effectively (compared to high and flashy flows) and, once a bed is coarsened to a certain degree, it is difficult to further increase the overall bed surface texture. 45  An interesting disparity can be found from comparing the temporal development of bed surface coarsening with grain sorting in Figure 6. Surfacing coarsening (Figures 4.4b and 4.4c) is severe only during the first flow of the experiments, while spatial sorting of grains (Figure 4.4a) is a continuing process throughout the experiments. A similar contrast can be found between surface coarsening and bed structuring, as the development of bed structures (e.g., Figures 4.5 and 4.10) also exhibit an ongoing stochastic process related to the continuous sediment transport for the duration of the experiments.  The combination of in-phase waves (Figure 3.1a), near-critical or supercritical flows throughout all the experiments (Fr in Table 4.1), and upstream-migrating bedforms (Figure 4.2a) suggests that the bedforms during the highest discharge (59.2 L/s) certainly are antidunes. Coexistence between grain sorting and antidunes was reported in early gravel antidune research (e.g., Shaw and Kellerhals, 1977; Alexander and Fielding, 1997) but it is still an ongoing question (Recking et al., 2009; Núñez-González, 2012). Many previous researchers (e.g., Whittaker and Jaeggi, 1982; Ashida et al., 1984; Grant and Mizuyama, 1991; Hasegawa, 2005) have attributed the formation of steps to the spatial sorting of grains on antidunes. This effect might also be used to explain other bed structures resting on antidunes.  5.2 Conditions and possible processes for bed surface structures In the experiments of this research, various bed structures (transverse ribs, stone cells, stone clusters) were formed by the occurrence of a combination of relatively steep channel gradient, a wide range of grain size, and relatively high flow discharge that can mobilize particles of all sizes while remaining in the domain of partial transport, and sediment starvation. These findings are to a certain degree similar to step formation conditions summarized in previous research 46  (e.g., Chartrand and Whiting, 2000; Hasegawa, 2005; Church and Zimmermann, 2007; Saletti and Hassan, 2020). However, the experimental setup in this study, consisting of fixed channel width and relatively mobile coarse particles (around one-tenth of channel width), shows that the formative conditions of these bed structures in this study are different from step formation conditions such as strong jamming effect (Zimmermann et al., 2010; Saletti and Hassan, 2020) and reduced shear stress caused by channel widening (Golly et al., 2019; Saletti and Hassan, 2020). No bed structure types are fully dependent on flow regimes as the coexistence among diverse bed structures was observed, regardless of the flow magnitude and duration. Instead, the formation and development of bed surface structures are notably controlled by the interactions among coarse particles (e.g., Figure 4.5) according to this research. Generally, bed structures are formed by coarse particles moving from positions with less stability to positions with more stability due to particle interactions (also described in Church et al. 1998). This process also integrates smaller bed structures (e.g., clusters, partial ribs, cells) into larger structures (e.g., transverse ribs) via entrapping additional coarse particles. When the stabilizing effect of existent structures is surpassed by the shear stress, the coarse stones of the structures can either be released downstream, or stay in place as part of the structure remnant, triggering subsequent grain interactions (also reported in Hassan et al., 2020a). This observation is consistent with previous experiments (e.g., Church et al., 1998; Hassan et al., 2020a) and numerical simulations emphasizing particle kinematics and interactions (Tribe and Church, 1999; Malmaeus and Hassan, 2002). Therefore, a hypothesis that the formation of bed structures entails a combination of hydraulic controls and grain interactions is proposed. In this study, the combination of hydraulic 47  controls and grain interactions manifested as antidune bedforms along with spatial sorting of grains. The antidunes influence the reach-scale flow pattern, and spatial sorting on antidunes is the product of grain interactions and a smaller scale of resistance effects related to bed structures. Grain sorting may also promote grain interactions by increasing the density of coarse particles and trigger the transition from smaller structures to larger structures (e.g., Figure 4.5), and therefore alter the local flow resistance via the change of structure coverage (Figure 4.10) and local critical shear stress (Figure 4.11).  Finally, this study advances the importance of grain interactions for the formation of transverse ribs. Previous theories of rib formation include upstream-migrating hydraulic jumps (McDonald and Day, 1978), cascades of hydraulic jumps (Allen, 1983), antidune remnants (Gustavson, 1974; Boothroyd and Ashley, 1975; Koster, 1978). However, no hydraulic jumps were observed in this study and the barrier height required to change flows from supercritical to subcritical (or vice versa) is much larger (5-10 cm) based on the specific energy in open channel flow (hb in Table 1) than the c-axis of the coarsest stone (22.5 mm, estimated as half of the b-axis length). Additionally, comparison between the measured rib wavelength, noted as lr, and wavelength estimated by the hydraulic jump cascade model proposed by Allen (1983), noted as lrA, shows that the hydraulic cascade model cannot reproduce the wavelength distribution observed in this research and cannot explain the existence of individual ribs, which occurred more frequently than rib sequences (lr and lrA in Table 4.1). Similarly, despite a potential association between transverse ribs and the growth of antidunes, rib sequences usually being found on antidune crests (e.g., Figures 4.2a and 4.5), the comparison between measured rib wavelength (lr) and rib wavelength estimated using antidune remanent hypothesis (lrK) in Table 4.1 shows that the Kennedy equation is unable to explain the wavelength of rib sequences (also 48  mentioned in Allen, 1983) and neither can it explain the existence of individual ribs. This study suggests that previous theories of rib formation are inadequate to explain rib formation because they consider only flow hydraulics and ignore particle interactions, an important variable for the formation of ribs and other bed surface structures.  5.3 Implication of bed structures for channel stability In the experiments of this study, the bed surface achieved stability via the development of continuous bedforms with a coarsened surface and the formation of discrete bed structures. Many bed structures persisted in later runs, despite the relatively high mobility of individual particles (e.g., Figure 4.5). The coexistence of bedforms and bed structures is not restricted to experiments with fixed width. For example, Hasegawa (2005) formed a combination of a meandering channel and steps on a stream table, which suggests that discrete structures can be formed that enhance channel stability even when channels are free to adjust their width. This research shows that the evolution of individual bed structures can be very active (Figures 4.5-4.9) while the total coverage of the bed structures (Figure 4.10) is usually around 15-20% (consistent with Rouse, 1965 and Hassan et al., 2020a). This finding is compatible with studies on the relation between the distribution of large elements on the bed surface and flow resistance. Previous research has pointed out the optimum coverage (Rouse, 1965; Nowell and Church, 1979; Hassan et al., 2020a) and alignment (Canovaro et al., 2007) of resistance-enhancing elements. The results of optimum coverage and alignment of coarse particles might be fundamentally linked to the hydraulic control theory of different bed structures (e.g., Allen, 1983; Abrahams et al., 1995; Chartrand and Whiting, 2000). And the results on the total 49  coverage of bed structures (Figure 4.10) along with the aforementioned studies suggest that bed structures should be an important component of channel stability. This thesis shows that using reach-average variables such as representative grain size (compare Figure 4.11 to Figures 4.4b and 4.4c) and channel slope (compare Figure 4.11 to Figure 4.12) is incapable of capturing the dynamic temporal changes in particle mobility (indicated by tc*) due to the presence of bed structures and bedforms, a result compatible with previous research (e.g., Hassan et al., 2020b).  Furthermore, the difference between Figures 4.11a and 4.11b is related to the implementation of effective slope, a method used to account for the flow resistance caused by macro-roughness (e.g., Chiari and Rickenmann, 2011; Mao et al., 2020). After adopting the effective slope, the temporal evolution of bed mobility in e04 and e06 seems identical while the critical shear stress in e05 is constantly smaller (Figure 9b). This discrepancy might be explained by the relatively rare occurrence of transverse ribs in e05 compared to e04 and e06 (Figures 4.10 and 4.7-4.9). The results of this study demonstrate that bed structures can influence the overall channel stability and support the suggestion proposed in previous research (e.g., Gomez and Church, 1989; Church, 2006; Johnson, 2016) that the incorporation of bed state (including bed structures) could improve the performance of sediment transport models.  5.4 Limitations and future work The results of flume experiments (Figures 5.1a and 5.1b) were compared to field observation (e.g., Figures 1.1a and 5.1c). Both flume experiments (Figures 5.1a and 5.1b) and field observation (e.g. Figure 5.1c) show an armoured bed surface, and coarse particles are spatially organized into diverse and complex bed structures such as transverse ribs and stone 50  cells. The transverse ribs reproduced in this research (Figure 5.1b) and the ribs found in the field (Figures 1.1c and 5.1d) are similar in appearance. However, field cases, especially Harris Creek (Figure 1.1a), contain more developed ribs. The difference between the experimental results and field observation can be ascribed to the variables, including the relatively short flow duration and simple history of flow and sediment supply regimes in flume experiments. For example, stone clusters and stone cells might eventually evolve into channel-spanning ribs after several long periods of low sediment transport events.   Figure 5.1 Comparison between bed structures reproduced in the study and structures found in the field: (a) Orthogonal bed surface photo combined with the identification result after e03r06. (b) Close-up photo of a transverse rib found after e03r06 with relatively low flow. (c) Bed structures in East Creek.  More investigations are needed into this topic, especially regarding  (a) exploring bed structure formation and evolution under different conditions, such as sediment supply, channel slope, and flow history (as a constant flume gradient and no sediment supply were utilized in this study);  500 1000 1500 2000 2500 3000 3500 4000 4500Distance from the outlet (mm)Transverse rib Partial rib Cluster Stone Cell(a) e03r00(b) e03r01(c) e03r02(d) e03r03(e) e03r04(f) e03r05(g) e03r06(h) e03r07(i)  e03r08500 1000 1500 2000 2500 3000 3500 4000 4500Distance from the outlet (mm)Transverse rib Partial rib Cluster Stone Cell(a) e03r00(b) e03r01(c) e03r02(d) e03r03(e) e03r04(f) e03r05(g) e03r06(h) e03r07(i)  e03r08(a)(b)(c)b51  (b) further investigating the development of an armoured bed surface in relation to bed structuring and bedform development, and linking surface condition to the prediction of sediment transport, channel morphology, and channel morphodynamics; and  (c) numerically modelling the hydraulic conditions caused by bed structures and bedforms (as this research shows that reach-scale parameters cannot capture dynamic sediment transport processes).  52  Chapter 6: Conclusion  In flume experiments, the self-formation of various bed structures (including transverse ribs, stone cells, and clusters) was reproduced as a means of increasing channel bed stability along with bed coarsening and bedform development. A semi-automated method was also developed to record the evolution of these bed surface structures. Based on the hydraulic, bed surface, and sediment transport data, the whole thesis is concluded by answering the research questions proposed in Chapter 1: 1. Bed surface structures (transverse ribs, stone cells, stone clusters) are formed by a combination of relatively steep channel gradient, a wide range of grain size, flows that can mobilize the large particles on the surface in a partial transport manner, and sediment starvation. Various types of bed structures can develop and coexist throughout the experiment, regardless of the changing flow regimes. Grain interactions lead to the dynamic formation, transformation, and disappearance of bed structures, and grain sorting on bedforms. The incorporation of grain interactions is considered critical when explaining the formation of bed structures, (especially transverse ribs). 2. Bed structures, once formed, are relatively more stable than individual particles, especially during higher flows. The dynamic development of a wide variety of bed structures can contribute to the variation of bed stability, which is difficult to explain using reach-average variables such as grain size and slope. Despite the dynamic behaviour of individual structures most of the time, the overall bed structure coverage was around 15-20%, which can indicate an optimum range of structure coverage to enhance bed stability. Because of the variation 53  introduced by bed structures, investigating bed structuring is necessary for understanding sediment transport, channel morphology, and channel morphodynamics. 54  References Abrahams, A.D., Li, G., Atkinson, J.F., 1995. Step-pool streams: Adjustment to maximum flow resistance. Water Resour. Res. 31, 2593–2602. https://doi.org/10.1029/95WR01957 Alexander, J., Fielding, C., 1997. 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