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The effects of channel morphology on the mobility and dispersion of sediment in a small gravel-bed stream Papangelakis, Elli 2015

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The Effects of Channel Morphology on the Mobility and Dispersion of Sediment in a Small Gravel-bed Stream   by Elli Papangelakis B.Sc., The University of Toronto, 2013   A THESIS SUBMITTED IN PARTIAL FULFILMENT 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)  July, 2015  	  	   © Elli Papangelakis, 2015 ii 	  ABSTRACT The role of channel morphology in sediment transport is poorly understood due to the complexity of the interactions between morphology, sediment characteristics and flow. A better understanding of the ways in which channel morphology affects sediment transport at all scales and under varying flow conditions can improve predictions of channel behavior and provide insights for better stream restoration applications. This study aimed to capture the effects of morphology on bed mobility and sediment dispersion in a small gravel-bed stream through the use of a 10 year tracer dataset. The characterization of bed mobility and sediment dispersion conducted at three spatial scales (the reach, morphological unit and local scale), revealed the importance of scale when examining the role or morphology on sediment transport.   East Creek was found to be in conditions of marginal sediment transport, remaining near the critical conditions for sediment mobilization the majority of the time, and falling within a low sediment transport regime common in small gravel-bed streams. Both bed mobility and tracer travel distances increased with increasing flow conditions, and measures of cumulative flow energy had stronger relations to both variables than peak discharge. Grain size was not found to play no role in bed mobility or travel distance in East Creek. At the reach scale, morphology did not affect bed mobility, and influenced the travel distance of tracers only during high flows, or when averaged over long time periods. Although burial rates were high, burial depths were shallow, and burial showed no relation to flow or mobility. At the morphological unit scale, differences were observed in the rate of increase of bed area under mobility with increasing flow between reaches and between morphological units. Finally, at the local scale, bed mobility was highly localized and sporadic. Results of this study allow for the description of the role of morphology on bed mobility and sediment dispersion in a low sediment transport regime and throughout various spatial and temporal scales. Further research opportunities include the exploration of the role of morphology on bed mobility and sediment dispersion in a variety of morphological and sediment transport settings.       iii 	  PREFACE This thesis is based on field data collected between 2004 and 2014 as part of a long-term research project designed and led by M.A. Hassan in the Malcolm Knapp Research Forest (UBC). None of the text is taken directly from previously published collaborative articles.  The tracers used in this study were fabricated and seeded in 2004 by J. Caulkins. Data collection, including tracer recovery and bed surveys, has been led by J. Caulkins (2005-2008) and D. Reid. The ArcGIS algorithm for computing tracer travel distances was written by J. Caulkins. The critical discharge value was calculated using sediment trap data in the field by I. Klinghoffer. Modifications to FaSTMEC bed shear stress model were done by P. Cienciala.   Stream discharge data over the course of the study has been collected by a variety of stream gauging techniques. Pressure transducer flow gauges were set up in 2003 and 2004 within East Creek by J. Caulkins and A. Zimmerman, and the rating curve used was developed by J. Caulkins. The set-up of a weir within the Riffle-Pool-1 reach, and the development of a rating curve, was done in 2009 by T. Argast. Two water level recorders were set up, and the appropriate rating curve was developed, in 2012 by D. Reid. Gaps in the gauging data were filled with data from a weir in the upstream end of the study area, set up in 1971 by M. Feller. The rating curve for this weir was developed by M. Feller and J. Leach.       iv 	  TABLE OF CONTENTS ABSTRACT  ....................................................................................................................... ii PREFACE  ......................................................................................................................... iii TABLE OF CONTENTS  .................................................................................................. iv LIST OF TABLES  ............................................................................................................ vi LIST OF FIGURES  ......................................................................................................... vii ACKNOWLEDGEMENTS  .............................................................................................. ix 1. INTRODUCTION  ..........................................................................................................1     1.1 Background ................................................................................................................2     1.2 Research Objectives ...................................................................................................5 2. METHODS ......................................................................................................................6     2.1 Study Site ...................................................................................................................6     2.2 Study Design ..............................................................................................................8     2.3 Data Analysis ...........................................................................................................10          2.3.1 Hydrological analysis .......................................................................................10          2.3.2 Bed mobility.....................................................................................................12          2.3.3 Grain dispersion: travel distance and burial .....................................................13          2.3.4 Mobility maps ..................................................................................................15 3. RESULTS ......................................................................................................................18     3.1 Reach-scale Results .................................................................................................21          3.1.1 Mobility at the surface and subsurface ............................................................21          3.1.2 Relation of flow to mobility and travel distance ..............................................22          3.1.3 Mobility and travel distance by grain size .......................................................25          3.1.4 Mobility and travel distance by morphology ...................................................26          3.1.5 Travel distance distributions ............................................................................29          3.1.6 Tracer burial .....................................................................................................31     3.2 Within-reach Results ................................................................................................35          3.2.1 Mobility by bed area ........................................................................................40          3.2.2 Mobility and shear stress .................................................................................42          3.2.3 Mobility at the cell scale ..................................................................................44 v 	  4.DISCUSSION .................................................................................................................45     4.1 Characterization of Sediment Transport in East Creek ............................................45     4.2 Effects of Flow  ........................................................................................................47     4.3 Effects of Grain Size  ...............................................................................................49     4.4 Reach-scale Effects of Morphology .........................................................................51     4.5 Within-reach Effects of Morphology .......................................................................52 5. CONCLUSION  .............................................................................................................55 REFERENCES  .................................................................................................................57 APPENDIX A. PEAK RELATIONS TO MOBILITY AND TRAVEL DISTANCE ......62 APPENDIX B. MOBILITY AND TRAVEL DISTANCE BY SIZE ...............................63 APPENDIX C. TRAVEL DISTANCE DISTRIBUTIONS ..............................................65 APPENDIX D. BURIAL  ..................................................................................................68 APPENDIX E. MOBILITY MAPS ...................................................................................72 APPENDIX F. BED MOBILITY BY AREA ...................................................................76 APPENDIX G. SHEAR STRESS  ....................................................................................78 APPENDIX H. CORRELATION RESULTS ...................................................................82  	  	  	  	  	  	  	  	  vi 	  LIST OF TABLES Table 1. Summary of hydrological analysis and reach-scale tracer recoveries  ................19 Table 2. Proportion of mobile tracers from surface and subsurface  .................................22 Table 3. Proportion of mobile tracers from surface and subsurface  .................................67 Table 4. Tabulated results of spatial correlation between all seasons in RAP  .................82 Table 5. Tabulated results of spatial correlation between all seasons in RP1  ..................82 Table 6. Tabulated results of correlation between the average shear stress in each cell and mobility for both Qbf    and 0.5Qbf  shear stress values.  .........................................83 Table 7. Tabulated results of correlation between the maximum shear stress in each cell and mobility for both Qbf    and 0.5Qbf  shear stress values  ...................................83 Table 8. Tabulated results of correlation between the average ΔΕnet  in each cell and  mobility  ..............................................................................................................84 Table 9. Tabulated results of correlation between the average absolute elevation in each cell and mobility .................................................................................................84    	  	  	  	  	  	  	  	  	  vii 	  LIST OF FIGURES Figure 1. Map of the East Creek  study reaches ..................................................................7 Figure 2. Tracer and East Creek grain size distributions .....................................................9 Figure 3. Exceedance probability plots of Ω ......................................................................20 Figure 4. Total Fm and 𝐿 plotted against ΩT   ......................................................................24 Figure 5. Total Fm and 𝐿 plotted against grain size for a selection of seasons  .................26 Figure 6. Fraction of mobile tracers by morphology unit type ..........................................27 Figure 7. Average travel distance by morphology type over all seasons  ..........................28 Figure 8. Exceedance probability plots of travel distances with fitted Gamma and Weibull probability distributions  .......................................................................................30 Figure 9. Total Fb and 𝐵 plotted against grain size for a selection of seasons  .................32 Figure 10. Average burial depth by morphology type over all seasons  ............................33 Figure 11. Fraction of mobile tracers originating from three bed layers  ..........................34 Figure 12. Mobility maps of a subsection of each reach for a selection of seasons  .........36 Figure 13. Mobility maps of a subsection of each reach for a selection of seasons  .........37 Figure 14. Absolute elevation, ΔΕnet, modeled shear stress distribution and mobility map for a subsection of RP1 in 2012-13.  ....................................................................39 Figure 15. Stacked area plots of the fraction of bed area experiencing full, partial and no mobility against ΩT  in RP1  ..................................................................................41 Figure 16. Stacked bar plots of the fraction of cells under full, partial and no mobility in areas where the shear stress is equal to multiples of τcr  in for a selection of seasons  .................................................................................................................43 Figure 17. Total Fm  and average travel distances plotted against peak discharge  ............62 Figure 18. Fraction of mobile tracers by grain size for all seasons  ..................................63 Figure 19. Average tracer travel distance by grain size for all seasons  ............................64 Figure 20. Exceedance probability plots of tracer travel distances in RAP with fitted Pareto distributions to the distribution tails using Hill’s estimators .....................65 viii 	  Figure 21. Exceedance probability plots of tracer travel distances in RP1 with fitted Pareto distributions to the distribution tails using Hill’s estimators .....................66 Figure 22. Total Fb and 𝐵 plotted against QP  and ΩT  ........................................................68 Figure 23. Fraction of buried tracers by morphology type ................................................69 Figure 24. Fraction of buried tracers in RAP and RP1 by grain size for all seasons .........70 Figure 25. Average burial depth in RAP and RP1 by grain size for all seasons ...............71 Figure 26. Mobility maps of RAP for seasons from 2005 to 2010 ....................................72 Figure 27. Mobility maps of RAP for seasons from 2010 to 2014 ....................................73 Figure 28. Mobility maps of RP1 for seasons from 2005 to 2010 .....................................74 Figure 29. Mobility maps of RP1 for seasons from 2005 to 2010 .....................................75 Figure 30. Stacked area plots of the fraction of bed area experiencing full, partial and no mobility against ΩT  in different morphological units in RAP  ............................76 Figure 31. Stacked area plots of the fraction of bed area experiencing full, partial and no mobility against ΩT   in different morphological units in RP1  .............................77 Figure 32. Modeled Qbf    and 0.5Qbf  bed shear stress results for RAP  ..............................78 Figure 33. Modeled Qbf    and 0.5Qbf  bed shear stress results for RP1  ..............................79 Figure 34. Stacked bar plot of the fraction of cells in RAP under full, partial and no mobility in areas with shear stress equal to various multiples of τcr. ...................80 Figure 35. Stacked bar plot of the fraction of cells in RP1 under full, partial and no mobility in areas with shear stress equal to various multiples of τcr. ...................81 	  	  	      ix 	  ACKNOWLEDGEMENTS I would like to acknowledge the people who helped me both complete this thesis and grow throughout my time at UBC. First and foremost I thank my supervisor, Marwan Hassan, for helping me at every step of the way and for making me believe in myself. I am grateful for the financial support provided by NSERC and UBC that ultimately made this thesis possible. Carles Ferrer-Boix provided constructive comments and inspiration for solutions at the most important stages of this project. I would like to thank Shawn Chartrand for his advice, mentorship, and pushing me to do my best. I would also like to acknowledge David Reid for his incredible patience in answering all my questions, and Matteo Saletti for his long-distance support and incredible pasta dinners.  My parents have been role models in all my scientific endeavors, and I could not have succeeded without the unconditional love and support I receive from my family. I thank my father for teaching me to never stop asking questions, my mother for encouraging me to take life less seriously, and my brothers for never forgetting about their big sister even though she is half a continent away. I am grateful to the community at Green College for providing me with a home away from home and the opportunity to make beautiful friendships. My friends, near and far, new and old, have been central to my success through their constant encouragement, support and escape from my work. Finally, I owe much of this thesis to Sameer Shah, for his support, admirable patience, and for being by my side through the best and worst moments.    1  1. INTRODUCTION  Sediment transport in gravel-bed rivers is dominated by the transport of bed material and is a vital component in both understanding current river behavior, and predicting channel responses to environmental change. Therefore, understanding bedload transport is crucial for a variety of real world applications including riparian habitat maintenance, improved river restoration projects, and successful erosion management practices. Bedload transport studies have historically been dominated by attempts to empirically quantify bulk transport rates and correlate them to channel-averaged stream and sediment characteristics (Wong et al., 2007; Hassan et al., 2013). Since bulk bedload transport is the result of the cumulative movement of individual grains, an alternative approach is to study and characterize the behavior of individual grains (Church and Hassan, 1992; Hill et al., 2010; Hassan et al., 2013; Schneider et al., 2014). This approach provides unique insights that can lead to improvements in the estimation of bulk sediment transport rates, as well as improved predictions of morphologic responses in streams ( Hassan et al., 1991, 1992; Church and Hassan, 1992; Haschenburger and Church, 1998; Hassan and Ergenzinger, 2003; Wong et al., 2007). Marked tracer particles provide a direct method for studying the movement of individual grains and have been successfully applied in both field and flume experiments examining the effects of flow, sediment size, and bed texture on grain travel characteristics (Ferguson and Wathen, 1998). However, the majority of studies to date have been conducted in controlled flume experiments, or over limited temporal and spatial scales in the field, and therefore do not adequately capture the controls of sediment mobility over larger temporal and spatial scales (Ferguson et al., 2  2002; Haschenburger, 2013).  Results from such studies are difficult to place within the context of flow regime and channel morphology, highlighting a need for long-term studies exploring the relations between flow magnitude and duration, sediment mobility, and channel morphology. Recent advancements in particle tracing technologies has allowed for field tracer studies in the order of several years, capturing multiple and variable transport events, and allowing for closer study of sediment mobility and dispersion (e.g. Lamarre and Roy, 2008; Bradley and Tucker, 2012; Liébault et al., 2012; Phillips and Jerolmack, 2014; Schneider et al., 2014). Of note is the work of Haschenburger (2013), which analyzed tracer data collected in the field over a period of 17 years.   1.1 Background During low to medium flow events, bedload transport occurs in the form of partial mobility, where only a fraction of grains are mobile while the rest of the bed remains static (Wilcock and McArdell, 1993), and full mobility occurs only during the most extreme events ( Wilcock and McArdell, 1993; Haschenburger and Wilcock, 2003). Tracers allow for quantification of bed mobility through the measurement of the fraction of mobile grains on the bed. Research has shown that bed mobility increases with increasing flow conditions, and has been related to variables including shear stress (Ashworth and Ferguson, 1989; Wilcock and McArdell, 1997; Wong et al., 2007; Phillips and Jerolmack, 2014), maximum peak discharge (Haschenburger and Wilcock, 2003) and excess stream power (Hassan et al., 1992; Gintz et al., 1996; Lenzi, 2004).  It has also 3  been shown that for a given flow intensity, the fraction of mobile grains decreases with increasing grain size (Ashworth and Ferguson, 1989; Church and Hassan, 1992; 2002; Wilcock and McArdell, 1993; 1997; Haschenburger and Wilcock, 2003; Lenzi, 2004; Wong et al., 2007; MacVicar and Roy, 2011). Tracers also allow for the description of grain dispersion through the measurement of grain travel distances. Average travel distance scales as a power law to various flow metrics including shear stress (Wong et al., 2007), peak excess stream power (Schneider et al., 2014), cumulative excess stream power ( Hassan et al., 1992; Lenzi, 2004; Lamarre and Roy, 2008; Haschenburger, 2013; Schneider et al., 2014), and dimensionless impulse (Phillips et al., 2013; Phillips and Jerolmack, 2014). Average travel distance has also been demonstrated in numerous studies to scale negatively with grain size (Church and Hassan, 1992; Lenzi, 2004; MacVicar and Roy, 2011; Schneider et al., 2014).  Although it is established that flow and bed texture play an important role in bed mobility and sediment dispersion at the reach scale it has been observed that even within the same flow event, large spatial variability in mobility exists across the bed and can persist over time (Haschenburger and Wilcock, 2003). This suggests that sediment texture and flow characteristics are not the only controls on bed mobility, but that morphology may play an important role at the scale of the dominant channel morphology (Hassan, 1992). Although studies often note the importance of the channel morphology on grain displacement over longer timescales and large variability in flow conditions (Hassan et al., 1991; Hassan and Church, 1992; Sear, 1996; Habersack, 2001), few have explicitly attempted to describe and quantify this relation (Hassan, 1992). The notion that 4  morphology plays a role in grain mobility is intuitive; if bedforms are created and evolve through the processes of bedload transport then they must both influence and, in turn, depend on individual grain movements. In other words, grains must be displaced in patterns that lead to the development and maintenance of the bed morphology (Hassan, 1992; Pyrce and Ashmore, 2003a; Kasprak et al., 2015). Indeed, it has been observed that in cases where flow approaches or exceeds channel forming floods travel distances of grains are associated with the length scale of the dominant bed morphology (Church and Hassan, 1992; Pyrce and Ashmore, 2003a; 2003b; Lamarre and Roy, 2008; Bradley and Tucker, 2012; Kasprak et al., 2015).   Bed mobility and dispersion have been investigated in channels with riffle-pool morphology by measuring the differences in bed mobility and tracer travel distances between riffle and pool units, as well as within morphological units. When comparing mobility between riffles and pools, mobility has been hypothesized to be larger in riffles during low flows, but becomes larger in pools when approaching bankfull flow (Keller, 1971; Lisle, 1979; Sear, 1996; Thompson et al., 1999). This hypothesis has been termed ‘competence reversal’ and has been linked to the maintenance of pool-riffle morphologies (Keller, 1971; Thompson et al., 1999). When measuring tracer travel distances, Sear (1996) noted that at bankfull flow, travel distances are greater in pools than in riffles. Working in a meandering riffle-pool stream, Milan et al. (2002) observed that in low flows, tracers were transported within the same morphological unit and in medium flows from one unit to the immediate unit downstream. It was not until high flows (70 – 90% bankfull) that tracers were transported from one unit to the next (Milan 5  et al., 2002). This observation is similar to that measured in flume studies of bar formation in meandering streams (Pyrce and Ashmore, 2003a; 2005). At the within-unit scale MacVicar and Roy (2011) concluded that, in a forced riffle-pool reach, mobility occurred in the center and exit slope of the pool, while only partial mobility was observed in the entrance slope of the pool.   1.2 Research Objectives The role of channel morphology in sediment transport is difficult to quantify due to the complex interactions between bed morphology, sediment characteristics and flow. Although progress has been made in the past three decades on understanding dispersion of coarse bed material in gravel bed streams, research gaps persist. Such gaps include the investigation of the role of morphology over larger spatial and temporal scales. The objective of this study is to examine the temporal and spatial patterns of bedload mobility in a small gravel-bed stream by using a large-scale tracer study in diverse morphological settings. More specifically, this study aims to describe the role of channel morphology on sediment mobility through the characterization of bed mobility patterns, grain travel distances and grain burial. An attempt was made to link these spatial and temporal patterns of mobility to the spatial distribution of shear stress and bed topography changes in the channel. To reach these goals, a 10-year tracer dataset collected in two reaches with the same flow and sediment supply regimes, but distinct morphological settings, was analyzed.   6  2. METHODS  2.1. Study Site Data was collected in East Creek, a small gravel-bed stream located within the Malcolm Knapp Research Forest of UBC, northeast of Vancouver, BC, Canada. The stream has a drainage area of 1 km 2 and a bankfull discharge of Qbf  = 2 m3/s. The watershed is heavily forested and experiences a maritime climate, with the majority of precipitation falling as rainfall between October and April. Discharge measurements have been collected in 15-minute intervals in East Creek since the beginning of the study from a variety of techniques, including pressure transducer measurements (2004-09), weirs (2009-12), and two water level meters set up in 2012 (locations of measurements shown in Figure 1), which has been compiled into a single continuous time series. Tracer data was collected from two reaches: one rapid reach (RAP) and one riffle-pool reach (RP1) (Figure 1). The division between reaches is characterized by a downstream decrease in channel gradient, progressively finer bed texture and better-developed bed topography. Morphological units within the reaches were distinguished and classified using topographical bed surveys and low aerial photographs (taken from 9 m height) following the classifications outlined in Hassan et al. (2005).   7   RAP is a straight reach of 72 m length, a bankfull channel width of 2.3 m, and a reach-average slope of 0.02. The surface material is coarse, having a D50 and D84 of 55 and 105 mm respectively. At the upstream end, the reach has a 33.6 m long section with minimal bed development and a lack of clear morphological units, classified as ‘rapid’ morphology (Figure 1). Here, the term ‘rapid’ is used as suggested by Zimmerman and Church (2001) to describe featureless gravel channel units with moderate gradients. These units are the same as those described by Ikeda (1975) and Montgomery and Buffington (1997) as plane-bed morphologies. At the downstream end of RAP, there is a 38.8 m long sequence of pool-riffle units and alternate bars. Interspersed between pool and riffle units, there exist morphological units whose characteristics fall between those of the pool and riffle classifications, and have herein been classified as ‘runs’. RP1 is relatively straight, containing only few irregular bends (Figure 1). The reach is 117 m in length, has a bankfull channel width of 2.5 m, and a reach-averaged slope of 0.018. The surface material of RP1 is less coarse than that of RAP, having a D50 and D84 of 49 and 88 mm respectively.  The morphology of RP1 is more developed than that of RAP, and is RAP RP1 Figure 1. Map of the East Creek study reaches 8  characterized by alternating pool-riffle sequences interspersed by runs, and distinct side bars.   2.2 Study Design In the summer of 2004, 729 and 736 magnetic tracer stones were deployed in RAP and RP1 respectively, for a total of 1,465 tracers. Although magnetic tracers have limitations, deployment of the tracers used in this study was prior to the development of more advanced tracer technologies such as PIT tags. Regardless, recovery of the tracers was continued for the purpose of obtaining a long-term data set of tracer dispersion. The seeding site in RAP was within the upstream end of the rapid morphology, while the seeding site in RP1 was on the most upstream riffle unit (Figure 1). In both reaches, tracers were seeded on the surface in rows spanning the entire width of the channel.  Tracers were divided into eight half-phi size classes ranging from < 8 mm to < 90 mm. The proportion of tracer stones in each size class was chosen to match that found in the bed subsurface as closely as possible. The resulting grain size distribution of the tracers is shown in Figure 2, along with the surface and subsurface grain size distributions of RAP and RP1. Tracer stones in the < 16 mm size class and larger were made by drilling and inserting magnetic tags into randomly sampled grains from the bed.  Since stones in the < 8 and < 11 mm size classes were too small to drill and were  fabricated using casting 9  resin and lead shots to obtain the correct stone density. A detailed description of tracer fabrication can be found in Hassan et al. (1999).   The close succession of floods made it difficult to recover tracers after each mobilizing event, so tracers were recovered once a year during the low flow season (May - July) from 2005 to 2014. There was no recovery in 2009 because no mobilizing flows were recorded in the 2008-09 season. With each recovery, the position and depth of each tracer was recorded before being placed back into the channel in the same location. Due to the use of magnetic tracers, buried tracers were dug from the bed during recovery. Although this disturbs the bed and affects the mobility of the tracers (Hassan and Ergenzinger, 2003), the effects are estimated to be small due to the occurrence of several small flow events preceding large floods each season, resulting in a smoothing of the bed prior to major mobilizing events. From the recovery surveys, ArcGIS was used to map the 020406080100Grain Size (mm)Percent Finer Than (%)0.01 0.1 1 10 100 1000TracersRAP SubsurfaceRAP SurfaceRP1 SubsurfaceRP1 SurfaceFigure 2. Size distribution of the tracers plotted with the surface and subsurface grain size distributions of the RAP and RP1 study reaches. 10  locations of the recovered tracers and calculate their yearly travel distance along the thalweg. The threshold for tracer movement was set to 0.5 m as a conservative estimate of recovery accuracy accounting for both survey instrument and human error in recovering and replacing the tracing stones.   2.3 Data Analysis The characterization of the temporal and spatial patterns of bed mobility and grain dispersion in East Creek is divided into three scales. The first is the reach scale, in which the role of flow, grain size and morphology are explored within the reach and compared between reaches by considering reach-averaged measurements. The second is the morphological unit scale, which captures spatial variability in mobility within and between the morphological units.  The final scale is the local scale, corresponding to small patches, herein referred to as ‘cells’, in which temporal and spatial patterns of mobility are mapped and correlated to flow conditions and changes in bed surface elevation.  To avoid the influence of seeding on tracer dispersion (Hassan et al., 1991), results from the first year of study, were excluded from the analysis.   2.3.1 Hydrological analysis To link tracer mobility and dispersion to reach-scale flow characteristics, the discharge data was used to calculate a number of metrics describing the hydrological conditions of each season. Mobilizing flows are considered as events during which discharge reaches 11  above the estimated critical discharge value of Qc  = 0.5 m3/s. This value represents the discharge at which sediment mobility is initiated for the median bed grain size, and was estimated using sediment transport rates calculated from sediment trap data.   To capture the intensity of flow events, the number of mobilizing events that occurred in each season, along with the peak discharges of the smallest and largest mobilizing events, was recorded. The largest discharge measured in each season is hereafter termed the maximum peak discharge (QP). According to Hassan et al. (1992), since the majority of sediment transport occurs during the largest events, it can be assumed that QP is a dominant control on bed mobility and grain dispersion. However, if the hydrograph has multiple peaks, and it is assumed that sediment transport occurs for all flows above Qc, then a measure capturing both the magnitude and duration of competent flow in the form of excess energy is most appropriate. To this end, the discharge data was used to calculate the total excess flow energy expenditure of each season following Haschenburger (2013):                                             𝛺𝑇 =  𝜌𝑔𝑆 ∫ (𝑡𝑟+1𝑡𝑟𝑄 − 𝑄𝑐) 𝑑𝑡                                            (1) where ΩT = total excess flow energy expended over the season (J/m),  ρ = the density of water (1,000 kg/m3), g = the acceleration due to gravity (9.81 m/s2), and S = the reach-average slope.  This represents the area under the specific stream power curve for the time that Q > Qc  from the time of tracer recovery, tr, to the following recovery, tr+1. The area under the curve was calculated using trapezoidal numerical integration with a spacing value of 15 minutes to match the resolution of the discharge data. Exceedance 12  probabilities, P(X > x), for the excess energy expenditure (Ω) were calculated to provide a more detailed picture of the hydrograph by capturing information on the distribution of flows larger than Qc  within each season.   2.3.2 Bed mobility  To explore sediment mobility at the reach scale, the total fraction of mobile tracers was calculated for both reaches and related to flow characteristics obtained from the hydrological analysis. The fraction of mobile tracers (Fm) was calculated as the ratio between number of tracers that moved (Nm) and the total number of tracers that were recovered (Nr):                             𝐹𝑚 = 𝑁𝑚𝑁𝑟                                                                (2)  Tracers that were not recovered are excluded from the calculation. A linear relation was fit between the reach Fm, and both QP  and ΩT. The contribution of mobile tracers from the surface and subsurface was measured by considering whether the initial locations of the mobile tracers were on the surface or subsurface (i.e. whether or not they were buried during the last recovery). Additionally, reach-scale patterns between mobility and morphology were investigated by calculating the Fm of tracers with initial positions in each morphology unit type, while the Fm of each size class was calculated to explore the influence of grain size on tracer mobility.  13  2.3.3 Grain dispersion: travel distance and burial To measure tracer dispersion at the reach scale, the average travel distance (?̅?) of the recovered tracers in each reach was calculated for each season and related to flow characteristics. Following results from other studies (e.g. Church and Hassan, 1992; Lamarre and Roy, 2008; Haschenburger, 2013; Schneider et al., 2014), a power relation was fit between ?̅? , and both QP and ΩT. To explore the relation between grain size and tracer dispersion, the ?̅? of reach size class was also calculated. The effect of morphology on tracer travel distances over long timescales was investigated by calculating the average travel distance of tracers entrained from each morphology unit type for all seasons combined.   Tracer dispersion was examined more closely by calculating the exceedance probabilities, P(X > x), of tracer travel distances, which were then fitted with the Gamma probability distribution following results from other studies (e.g. Hassan et al., 1991; Bradley and Tucker, 2012; Liébault et al., 2012). Exceedance probability distributions were also fitted with a Weibull probability distribution; a special case of the Generalized Extreme Value distribution. The Kolmogorov-Smirnov (K-S) test was used to assess the goodness-of-fit of the two probability distributions. To better examine the variation in the tails of the distributions, two methods were used to test if they were thin- or heavy-tailed.  The first was fitting a power law to the tail of the distribution using a power regression, and exploring the fitted power value. This represents the slope of the straight line slope fitted to the tail of the distribution in log-log space. If the slope α > −2, then the 14  distribution is heavy-tailed. Although this method is known to be imprecise, it allows for the calculation of a goodness-of-fit statistic and the significance of the regression (Hassan et al., 2013). The second method is using Hill’s estimators (Hill, 1975); Maximum Likelihood Estimators (MLEs) for the power and slope in the Pareto distribution P(X  > x) =  Cx-α fitted to the tail of sample data:                                     𝛼𝐻 =  𝑟 [∑ (ln 𝑋𝑖 − ln𝑋(𝑟+1))𝑟𝑖=1 ]−1                                                 (3)                                                         𝐶𝐻 = 𝑟𝑛 (𝑋(𝑟+1))𝛼𝐻                                                          (4)   where Xi are order statistics such that X1 ≥ X2  ≥…≥  Xn and r is the rank of the smallest data point in the tail of the distribution. Following Hassan et al. (2013), distributions with tails having a power 𝛼𝐻< 2 are considered heavy-tailed, while those with 𝛼𝐻 ≥ 2 are considered thin-tailed. Hill’s estimators do not allow for an evaluation of the goodness-of-fit statistic. The largest limitations with both methods is the fact that the identification of the “tail” of the distribution is subjective, and the use of a limited number of data points that constitute the tail (Hassan et al., 2013).   Patterns of tracer burial at the reach scale were captured through the calculation of the fraction of tracers recovered buried (Fb) and the average tracer burial depth (?̅?) for each reach, by morphology unit type and for each grain size class. Fb  was calculated as the ratio between tracers that were recovered from a buried position and the total number of tracers recovered. Tracers that were not recovered are ignored form the calculations. Burial was linked to mobility by calculating the fraction of mobile tracers entrained from 15  three depth layers of the bed corresponding to multiples of the surface D50. Three layers were chosen based on the availability of data; an insufficient number of tracers were located in layers ≥ 3D50  to obtain meaningful results.  2.3.4 Mobility maps To closely investigate the spatial patterns of mobility at the local scale, mobility maps were created for each season using ArcMap 10.1 (ESRI). The locations of tracer stones, along with a 0.1 by 0.1 m grid were overlaid onto a morphological map of the channel, and the fraction of mobile tracers in each cell was calculated. Cells were assigned “Full mobility” (Fm  > 0.9), “Partial mobility” (0.1 < Fm < 0.9), or “No mobility”  (Fm < 0.1) following the categories outlined by Wilcock and McArdell (1997). To explore spatial patterns of mobility at the morphological unit scale, the proportion of the bed area experiencing full, partial and no mobility was calculated by dividing the area of the bed under each type of mobility by the total area of the bed for which there is data.  Maps of bed shear stress were modeled for Qbf  using FaSTMECH; a two-dimensional hydrodynamic model integrated with a MD_WSMS interface (Nelson et al., 2003; McDonald et al., 2005). Although not all mobilizing flows reach Qbf, modeled shear stress results of bankfull flow can be used to explore the spatial patterns of shear stress. Inputs to the model include bed topography from bed surveys, a bed roughness parameter, discharge, downstream water surface elevation, and a lateral eddy viscosity (LEV).  The model solves vertically- and Reynolds- averaged Navier-Stokes equations 16  cast in a channel-fitted curvilinear coordinate system to output velocity, depth, water surface elevation, and shear stress values at each computational cell. Since this study is focused on grain entrainment and transport, the model output was used to analyze the hydraulic forces represented by the “grain” component of bed shear stress, τo’. This shear stress corresponds to the force exerted on sediment particles and is responsible for entrainment. A more detailed explanation of the model inputs and their calculation, as well as model performance evaluation can be found in Cienciala and Hassan (2013). Elevation maps (DEMs) were created for each season by interpolating the topographical survey points using a triangulated irregular network algorithm followed by a conversion to raster format. The net change in elevation (ΔΕnet) between consecutive surveys was calculated as a DoD (DEM of difference) by subtracting successive DEMs. More detailed information about the DEMs and DoDs, including a discussion on uncertainty can be found in Cienciala and Hassan (2013).   The relation between mobility and shear stress was explored at the morphological unit scale by looking at the fraction of the cells experiencing full, partial and no mobility corresponding to cells with shear stress equal to various multiples of the critical shear stress (τcr): < 0.5 τcr, 0.5 – 1 τcr, 1 – 2 τcr, and > 2 τcr. Here, the critical shear stress, represents the shear stress (in units of Pa) required to initiate bedload transport of the median surface grain size, and is estimated from the Shields parameter as follows:                                                   𝜏𝑐𝑟 = 𝜏∗[(𝜌𝑠 −  𝜌)𝑔𝐷50]                                                    (5) 17  where ρs = the density of the sediment (here assumed to be the density of quartz, 2650 kg/m3), and τ* = the Shields parameter, assumed to be the commonly accepted value of 0.045 (Buffington and Montgomery, 1997). This was calculated to be 20.0 Pa in RAP and 17.8 Pa in RP1.   Finally, to link spatial patterns of mobility at the cell scale to local flow conditions and to changes in bed elevation, the bed mobility maps were spatially correlated to bed shear stress, absolute elevation, and change in elevation maps on a cell-to-cell basis. Since the grid cell size of the resulting shear stress and DoD maps is smaller than that of the mobility maps, partial mobility in each cell was spatially correlated to both the average and maximum of the bed shear stress values within each mobility cell, and to the average elevation and net change in elevation values within each mobility cell. Furthermore, mobility in each season were correlated cell-by-cell to each other in order to explore whether there are areas of high and low mobility that persist in the bed at this scale.       18  3. RESULTS The recovery rates of tracers were high, with total recovery rates ranging from 77 to 88% (Table 1).  Recovery rates generally increased with tracer size within each recovery, ranging from an average of around 60% for the smallest size class, to near 100% for the largest size classes. Table 1 outlines the results from the hydrological analysis and reach-scale calculations. A total of 64 mobilizing events occurred between 2005 and 2014, with maximum peak discharges ranging between QP = 0.4Qbf  in 2011-12, and QP = 2.4Qbf  in 2006-07. The majority of peak discharges remain below 0.5Qbf.                            19   Table 1. Summary of results from the hydrological analysis and reach-scale results of tracer recoveries.                                                       Hydrology Season Number of Events Q > Qc Minimum Peak (m3/s) Maximum Peak, QP  (m3/s) Total Time  Q > Qc (hours) Total Excess Flow Energy Expenditure, ΩT  (J/m) 2005-06 8 0.57 1.06 68 9,387 8,448 2006-07 10 0.63 4.73 173.5 83,203 74,882 2007-08 4 0.62 1.99 91.25 20,034 18,031 2008-10 6 0.51 1.61 90.25 27,662 24,896 2010-11 6 0.51 1.33 45.25 7,865 7,079 2011-12 8 0.51 0.89 47.75 4,461 4,015 2012-13 12 0.53 2.94 169.75 57,186 51,468 2013-14 10 0.52 3.13 118.75 27,164 24,448                                                 Tracer Recovery  Recovery (%) Total Fraction of Mobile Tracers, Fm Average Tracer Travel Distance, ?̅? (m) Total Fraction of Buried Tracers, Fb Average Burial Depth, ?̅? (cm) Season RAP RP1 RAP RP1 RAP RP1 RAP RP1 2005-06 82 0.32 0.46 1.77 3.49 0.58 0.49 3.79 2.76 2006-07 88 0.93 0.82 27.15 35.74 1.00 1.00 7.86 7.95 2007-08 83 0.20 0.22 1.89 1.86 0.78 0.71 6.45 5.19 2008-10 77 0.34 0.25 1.96 1.70 0.71 0.65 5.29 5.02 2010-11 83 0.36 0.34 2.32 1.57 0.69 0.61 5.25 4.65 2011-12 81 0.09 0.10 0.27 0.25 0.63 0.56 5.64 3.85 2012-13 81 0.48 0.66 3.16 9.01 0.65 0.60 5.03 4.08 2013-14 78 0.21 0.25 1.08 3.20 0.71 0.70 5.23 3.91 20  The exceedance probabilities of excess energy expenditure provide more detailed insight into the hydrological conditions of each season. Three types of distribution shapes are seen (Figure 3). The first type collapses quickly (2011-12, 2005-06, 2010-11 and 2008-10) and correspond to seasons where the majority of mobilizing events are small, only slightly above Qc, and multiple moderate events between 0.5Qbf  and Qbf  occur. Only 2011-12 had all peaks < 0.5Qbf. The second type has two parts to the distribution: a wide upper part, and lower part that collapses quickly (2007-08 and 2013-14). These distributions correspond to seasons that have a number of small events near Qc, and only a single large event above Qbf. The final type of distribution is wide, with large values of Ω  (2012-13 and 2006-07), corresponding to seasons with few moderate events (0.5Qbf  - Qbf), and multiple very large events much greater than Qbf.5000 10000 20000 50000log[W S]log[P(X > x)]0.0020.020.212005−062006−072007−082008−102010−112011−122012−132013−14Figure 3. Exceedance probability plots of the cumulative excess energy expenditure for flows where Q > Qc. 21  3.1 Reach-scale results 3.1.1 Mobility at the surface and subsurface The fraction of mobile tracers originating from the surface and subsurface calculated for both reaches (Table 2) show both temporal and flow dependences in surface and subsurface mobility. In 2005-06, the majority of mobile tracers originate from the surface, as little vertical mixing has had time to occur since the seeding time, while in the following season (2006-07), approximately half the tracers originate from the subsurface in both reaches. This season reached the highest peak discharge (QP = 2.4Qbf) and buried all tracers, explaining why all mobile tracers in 2007-08 originated in the subsurface. In RAP, during the subsequent two seasons (2008-10 and 2010-11), the majority of the tracers continue to be mobilized from the subsurface but approach values of equal contribution from the surface and subsurface. In RP1, these seasons display equal contributions from the surface and subsurface. During the lowest flow season of 2011-12 (QP = 0.4Qbf), the majority tracers were mobilized from the surface, before an equal contribution from the surface and subsurface is achieved again the final two study seasons. An equal contribution of mobile tracers from the surface and subsurface appears to be a dominant condition in East Creek with the exception of the season following the seeding time, and seasons with exceptionally high or low flows.     22  Table 2. Fraction of mobile tracers originating from the surface and subsurface.                RAP                   RP1 Season Surface Subsurface Surface Subsurface 2005-06 0.73 0.27 0.84 0.16 2006-07 0.44 0.56 0.53 0.47 2007-08 0.00 1.00 0.00 1.00 2008-10 0.24 0.76 0.45 0.55 2010-11 0.42 0.58 0.50 0.50 2011-12 0.56 0.44 0.64 0.36 2012-13 0.49 0.51 0.48 0.52 2013-14 0.58 0.42 0.63 0.37   3.1.2 Relation of flow to mobility and travel distance The total fraction of mobile tracers across the entire reach ranged between 0.09 and 0.93 in RAP, and between 0.10 and 0.82 in RP1 (Table 1). The linear fit between Fm  and the flow variables yielded a stronger relation to ΩT  (RAP: R2 = 0.78; RP1: R2 = 0.72) than to QP (RAP: R2 = 0.61; RP1: R2 = 0.52). The result that considering both the magnitude and duration of all mobilizing events yields a better predictor of bed mobility suggests that all mobilizing events contribute to bed mobilization. The slopes of the linear fit between Fm  and ΩT in the two reaches (Figure 4A) are nearly identical (0.15 and 0.14 in RAP and RP1 respectively), suggesting there is no significant difference in the relation between Fm  and flow between the two reaches.  Close examination of Figure 4A reveals further effects of flow on mobility. Here, two seasons around 5,000 - 7,000 ΩT (corresponding to 2005-06 and 2010-11) have higher mobility values than those around 20,000 - 30,000 ΩT (corresponding to 2007-08, 2013-23  14 and 2008-10). When comparing these results to Figure 3, the seasons whose exceedance probability distributions of Ω collapse quickly (2005-06 and 2010-11) have higher total reach Fm than those with the distributions with two parts (2013-14 and 2007-08). This suggests that a large number of small peaks and multiple moderate peaks (even if < Qbf) result in higher values of Fm than multiple small peaks and only one large event (> Qbf), supporting the conclusion that all mobilizing events contribute to bed mobilization.   Reach total ?̅? values range between 0.25 and 35.74 m in RAP, and between 0.27 and 27.15 m in RP1, and remain < 10 m for all seasons but 2006-07. Results from the power fit between the reach total ?̅? and the flow variables also yield a stronger relation to ΩT  (RAP: R2 = 0.60; RP1: R2 = 0.75) than to QP  (RAP: R2 = 0.54; RP1: R2 = 0.70). Furthermore, the coefficients and powers of the two regressions are different by an order of magnitude, with ?̅? increasing more rapidly with increasing ΩT in RP1 than in RAP (Figure 4B). However, despite the strong relation between ?̅? and ΩT, the powers of the relation are close to zero (in the order of 10-5 in RAP and 10-4 in RP1) suggesting a lack of a true relation between ?̅? and ΩT. Examining Figure 4B shows that aside from the lowest and highest ΩT values, no relation exists between ?̅? and ΩT. When comparing with Figure 3, a similar result to what was observed with Fm values is seen: seasons whose exceedance probability distributions of Ω collapse quickly (2005-06 and 2010-11) have higher total reach ?̅? than those with the distributions with two parts (2013-14 and 2007-08). This indicates that tracers are mobilized during all mobilizing flows, but that travel 24  distances remain small and of similar magnitude for all flows except those which are exceptionally high or low. The regression results of Fm  and ?̅? with QP  can be found in Appendix A.   0 20000 40000 60000 800000.00.20.40.60.81.0WT (J/m)FmA) 5000 10000 20000 500000.10.52.05.020.0WT (J/m)L (m)00RAPRP1Regression RAPRegression RP1B) Figure 4. A: Total fraction of mobile tracers (Fm) plotted against the total excess flow energy expenditure (ΩT), with the results of the linear regression; and B: the average tracer travel distance (?̅?) plotted against ΩT with the results of the power regression.  25  3.1.3 Mobility and travel distance by grain size Grain size was not observed to have a large effect on mobility. Figure 5A illustrates this by showing the Fm of each tracer size class for a selection of transport seasons with varying QP values in RAP and RP1. In both reaches, Fm increases with increasing flow, but all size classes appear to have similar levels of mobility within each season. All seasons, even those where QP < 0.5Qbf ,  were able to mobilize tracers larger than the surface D50 in both reaches. In both RAP and RP1, there is a notable decline in Fm in the 11 mm size class (Figure 5A).   There also appears to be no clear relationship between grain size and travel distance in either reach, although some weak trends emerge. Figure 5B shows the ?̅? of tracers in each size class for a selection of seasons. In RAP, ?̅? appears to be equal across grain sizes in all seasons but 2006-07, in which there is a small increase in ?̅? with size. Of note is the dip in ?̅? of the 11 mm size class tracers. In RP1, ?̅? has a stronger trend with grain size, particularly for the seasons with higher flow conditions where ?̅? dips for tracers in the 11 mm size class, and then peaks again for tracers in the 22 – 45 mm size classes. The dip in ?̅? of the 11 mm size class is similar to the dip seen in Fm, suggesting these tracers not only move less frequently, but also move shorter distances once they are mobilized.  Figures of the fraction of mobile tracers and the ?̅? of tracers in each size class for all seasons can be found in Appendix B.  26   3.1.4 Mobility and travel distance by morphology  In both reaches, the Fm of tracers entrained in each morphology unit type is highly variable (Figure 6), although some trends appear in the RP1 (Figure 6B). Here, in seasons after 2005-06, bars and runs have consistently high Fm values. In the 2007-08, 2008-10, 2011-12 and 2013-14 seasons, during which the total Fm  ≤ 0.25, riffles had higher Fm  values than pools. Conversely, in the 2010-11 and 2012-13 seasons, which had total Fm A) B) RP1Grian Size (mm)8 11 16 22 32 45 64 90RAPFm00.20.40.60.81Grian Size (mm)L (m)8 11 16 22 32 45 64 9001020304050002006−072008−102011−122012−13Figure 5. A: Fm and B: ࡸ̅ in plotted against grain size for seasons with QP equal to: 2.4Qbf (2006-07), 1.5Qbf (2012-13), 0.8Qbf (2008-10), and 0.4Qbf (2011-12).  27  values equal to 0.34 and 0.66 respectively, pools had higher mobility rates than riffles. These observations suggest a weak pattern in RP1 where during low flow seasons riffles experience higher mobility than pools, while the opposite is true during moderate to high flow seasons.   Figure 6. Fraction of mobile tracers by morphology unit type.  0.00.10.20.30.40.50.60.70.80.91.02005-06 2006-07 2007-08 2008-10 2010-11 2011-12 2012-13 2013-14Fm Rapid Pools Riffles Bars RunsRAP 0.00.10.20.30.40.50.60.70.80.91.02005-06 2006-07 2007-08 2008-10 2010-11 2011-12 2012-13 2013-14Fm RP1 28  The ?̅? of tracers entrained from each morphology unit type calculated over all seasons show a significant difference in the ?̅? of tracers entrained in different morphologies in RAP (F4 = 32.43, p < 0.001), with ?̅? of tracers entrained in the rapid section being significantly higher than those in other morphologies (p < 0.001) (Figure 7). Tracers entrained in pools and runs had the lowest average travel distances. Similarly, in RP1, there was a significant difference in the ?̅? of tracers entrained in different morphologies (F4 = 23.52, p < 0.001) with the ?̅? in riffles being significantly higher than those in other morphologies (p < 0.001), while the ?̅? of tracers entrained in pools, bars and runs were comparable.   Figure 7. Average travel distance by morphology type over all seasons.    012345678910RAP RP1Average Travel Distance (m) Rapid Pools Riffles Bars Runs29  3.3.5 Travel distance distributions Travel distance distributions varied substantially between seasons, but low to moderate flow seasons resulted in almost identical distributions between the two reaches that differ only in the tail (Figure 8). Here, RP1 had larger extreme values than RAP for all seasons but 2011-12. Only the three highest flow seasons (2006-07, 2012-13 and 2013-14) display different distributions between the reaches, with RP1 displaying much wider distributions than RAP. The Gamma and Weibull probability distributions are visually a good fit to most seasons (particularly the upper part of the distributions), but fail the K-S goodness-of-fit test in all seasons but 2008-10. This may be due to the divergence of the exceedance probabilities in the tail of the distribution from the fitted distributions. The tests to determine if distributions are thin- versus heavy-tailed yielded only two cases in RAP: 2011-12 (α = −1.67; 𝛼𝐻= 1.55) and 2011-12 (α = −1.94; 𝛼𝐻 = 1.60). Only 2008-10 was heavy-tailed in RP1 (𝛼 = −1.54; 𝛼𝐻 = 1.28) to be heavy-tailed, but there appears to be no systematic pattern in the occurrence of heavy-tailed distributions in either reach.  The two methods for testing between thin- and heavy-tailed distributions agree, and the power fit to the tail yielded R2 values above 0.80 in all seasons. Tracer travel distance distributions with fitted Hill’s estimators, along with a table of the results from both methods can be found in Appendix C.   30                 Figure 8. Exceedance probability plots of travel distances with fitted Gamma and Weibull probability distributions. log[L]log[P(X > x)]0.05 0.2 0.5 2 5 20 50 2000.0020.050.21B) 2006−07log[L]log[P(X > x)]0.05 0.2 0.5 2 5 20 50 2000.0020.050.21D) 2008−10log[L]log[P(X > x)]0.05 0.2 0.5 2 5 20 50 2000.0020.050.21A) 2005−06RAPRP1Gamma RAPGamma RP1Weibull RAPWeibull RP1log[L]log[P(X > x)]0.05 0.2 0.5 2 5 20 50 2000.0020.050.21C) 2007−08log[L]log[P(X > x)]0.05 0.2 0.5 2 5 20 50 2000.0020.050.21F) 2011−12log[L]log[P(X > x)]0.05 0.2 0.5 2 5 20 50 2000.0020.050.21H) 2013−14log[L]log[P(X > x)]0.05 0.2 0.5 2 5 20 50 2000.0020.050.21E) 2010−11log[L]log[P(X > x)]0.05 0.2 0.5 2 5 20 50 2000.0020.050.21G) 2012−1331  3.3.6 Tracer burial Burial rates are high, with Fb > 0.5 in all seasons, while ?̅? values are within the surface D50 of each reach for most seasons, and are well below the surface D84 in all seasons (Table 1). Both Fb and ?̅? were found to have no relation to QP or ΩT in either reaches, suggesting flow does not play a dominant role in tracer burial in East Creek. RAP has higher Fb and ?̅? than in RP1 for all seasons but the highest flow season of 2006-07 (Table 1).   Figure 9 shows Fb and ?̅? plotted against grain size for five seasons with different flow characteristics and at different times within the study. In both reaches, Fb and ?̅? are lowest for 2005-06 (Figure 9), which is expected, as it is early in the study and the bed had less time for vertical mixing since seeding. On the other end, Fb and ?̅? are highest for the highest flow season of 2006-07 (QP = 2.4Qbf). There is no consistent pattern between Fb or ?̅? and flow in the remaining three seasons plotted, suggesting that once a certain level of vertical mixing has occurred, flow conditions do not play a dominant role on Fb and ?̅? except during exceptionally high flow seasons. However, Fb and ?̅? had a strong inverse relationship with tracer size, except for 2006-07, during which all recovered tracers were buried (Figure 9). Both Fb and ?̅? peak for tracers in the 11 mm size class in RP1, while only Fb  appears to peak slightly for the 11 mm size class in RAP .   32       A) B) RP1Grain Size (mm)8 11 16 22 32 45 64 90RAPFb00.20.40.60.81Grain Size (mm)B (cm)8 11 16 22 32 45 64 90024681012002005−062006−072008−102011−122012−13Figure 9. A: Fb and B: ?̅? in plotted against grain size for seasons with maximum peak discharge of: 2.4Qbf (2006-07), 1.5Qbf (2012-13), 0.8Qbf (2008-10), and 0.4Qbf (2011-12). The year 2005-06 (QP = 1.06Qbf) is plotted to show the temporal variability in Fm and 𝐵.   33  No consistent patterns were observed in the burial fraction by morphology unit type in either reach. When investigating the average burial depth of tracers recovered in each morphology type for all over all seasons (Figure 10), there was a significant difference in the average burial depth in different morphologies in RAP (F4 = 17.09, p < 0.001), with the average burial depth in bars being significantly lower than in other morphologies (p < 0.001). In RP1, there was also a significant difference in the average travel distance in different morphologies (F4 = 17.97, p < 0.001). Here, tracers recovered in pools and rifles had almost identical average burial depths, while tracers recovered in bars and runs had comparable average burial depths and were significantly lower than those in pools and riffles (p < 0.001) (Figure 10). Additional tracer burial plots, including Fb and ?̅? plotted against grain size for all study years, as well as the fraction of buried tracers by morphology unit type can be found in Appendix D.    Figure 10. Average burial depth by morphology type for all years in RAP and RP1.   01234567RAP RP1Average Burial Depth (cm) Rapid Pools Riffles Bars Runs34  Figure 11 shows the fraction of mobile tracers of mobile tracers entrained from three vertical layers of the bed corresponding to various multiples of the surface D50. In both reaches, most seasons exhibit nearly equal tracer mobility in each layer, while some seasons experience a slight decrease in mobility with increasing depth.  This suggests that areas that experience mobility do so throughout the vertical profile of the bed. Of interest is also the differences seen between reaches. In RAP, mobility values remain low and remain around similar values for most seasons but the high flow seasons, while in RP1, mobility values experience a larger spread between seasons.       RP1Tracer Depth< D501−2 D50>2 D500.00.20.40.60.81.0RAPTracer DepthFraction of Tracers Mobile< D501−2 D50>2 D50Figure 11. Fraction of mobile tracers originating from different depths. 002013−142012−132011−122010−112008−102007−082006−072005−0635  3.2 Within-reach results Mobility patterns both between and within morphological units were explored through the creation of mobility maps. Figure 12 and Figure 13 show examples of these maps for a subsection of RAP and RP1 respectively for three seasons with different flow conditions that exemplify the temporal and spatial patterns of observed mobility. Although the increase in total bed mobility with increasing flow conditions can be seen clearly, spatial patterns of mobility are less obvious. Areas of the bed exist where cells of full, partial and no mobility neighbor, suggesting that mobility is extremely localized and stochastic. Despite this, examination of the maps suggests that patterns exist in the location of fully mobile cells, particularly in RP1. During the low flow season of 2011-12, mobility is very sporadic, with only few fully mobile cells spread across the bed (Figure 13A). In the moderate flow season (2010-11), fully mobile cells continue to be sporadic across the upstream riffle and the downstream bar and run, but are concentrated along the center of the channel from the upstream bar and through the pool (Figure 13B). Finally, in the high flow season (2012-13), fully mobile cells appear to be concentrated along the center of the channel from the upstream riffle through to the tail of the pool, downstream of which they span the entirety of the bed (Figure 12C). In summary, RP1 displays areas where full mobility is concentrated along a longitudinal path. Such ‘mobility paths’ are more distinguishable during high flows and are common down the center of pools, but extend to other areas of the bed with increasing flow conditions. Such patterns are not observed in RAP, where cells of full mobility are dispersed sporadically across the bed in all during all seasons (Figure 12). Mobility maps of the entire reaches for all seasons can be found in Appendix E.36  0 2 41 mFigure 12. Bed mobility maps for a subsection of RAP for seasons with varying maximum peak discharge values. The subsection is of the downstream riffle-pool section of the reach. Maps exemplify the increase in total mobility with increasing flow conditions and the sporadic nature of bed mobility.  Bed MobilityNo tracersNo mobilityPartial mobilityFull mobilityTracer LocationsDid not moveMovedNot recoveredChannel MorphologyWoodPoolRiffleBarRunVegetationFlow Direction A) 2011-12; QP = 0.4Qbf B) 2010-11; QP = 0.7Qbf C) 2012-13; QP = 1.5Qbf 37   0 2 41 mFigure 13. Bed mobility maps for a subsection of RP1 for seasons with varying maximum peak discharge values. The subsection is immediately downstream of the seeding riffle. Maps exemplify the increase in total mobility with increasing flow conditions, the sporadic nature of bed mobility, and the presence of mobility paths.  Bed MobilityNo tracersNo mobilityPartial mobilityFull mobilityTracer LocationsDid not moveMovedNot recoveredChannel MorphologyWoodPoolRiffleBarRunVegetationFlow Direction B) 2010-11; QP = 0.7Qbf C) 2012-13; QP = 1.5Qbf A) 2010-11; QP = 0.7Qbf 38  The relationships between mobility, changes in bed topography and shear stress are illustrated in Figure 14, which shows the absolute bed elevation, the ΔΕnet, bankfull bed shear stress, and mobility map for the 2012 -13 season. Here, the sporadic nature of both scour and fill, and the bed mobility are visible. The maps suggests that there is a relationship between bed mobility and shear stress, but not between mobility and absolute elevation or ΔΕnet. A clear example is seen in the pool, where cells of full mobility are concentrated down the center and exit of the pool, which also correspond to a lane of increased bed shear stress. Although the ΔΕnet   map suggests that scour is concentrated in areas corresponding to full mobility in the pool, this trend is not present in other areas of the bed in all seasons, suggesting a more complex relationship between mobility and ΔΕnet39      Figure 13. A: Absolute elevation, B: ΔΕnet, C: modeled bankfull bed shear stress distribution and D: mobility map for a subsection of RP1 in 2012-13. Shear stress is binned as multiples of the critical shear stress: < 0.5τcr, 0.5 – 1τcr, 1 – 2τcr, and > 2τcr.   Flow Direction A) 0 2 41 mChange in Elevation(m)-0.75- -0.26-0.26- -0.041-0.041- 0.0270.027 - 0.0990.099 - 0.48BarRunChannel MorphologyPoolRiffleBed MobilityNo tracersNo mobilityPartial mobilityFul  mobilityB) 0 2 41 mElevation(m a.s.l.)135.45 - 135.94135.94 - 136.18136.18 - 136.45136.45 - 136.86136.86 - 137.58Bed Shear Stress(Pa)0 - 9.139.13 - 27.4027.40 - 39.8039.80 - 52.1952.19 - 165.72BarRunChannel M rphologyPoolRi flBed MobilityNo tracersNo mobilityPartial mobilityFull mobilityC) 0 2 41 mElevation(m a.s.l.)135.45 - 135.94135.94 - 136.18136.18 - 136.45136.45 - 136.86136.86 - 137.58BarRunChannel MorphologyoolRiffleBed MobilityNo tracersNo mobilityPartial mobilityFull mobilityD) 0 2 41 mElevation(m a.s.l.)5.45 - 5.945.94 - .18.18 - 6.45136.45 - 136.86136.86 - 137.58BarRunChannel MorphologyPoolRiffleBed M bilityo tracersNo mobilityParti l mobilityFull mobilityA) Flow Direction 40  3.2.1 Mobility by bed area The proportion of bed area under full mobility increased with increasing ΩT   in both reaches and for all morphology unit types. However, differences in the rate of increase are observed, which is demonstrated in Figure 15. Herein, the total bed area of RAP under full mobility increases more rapidly with increasing ΩT , and reaches a higher maximum value, than in RP1 (Figure 15A). Within-reach differences are also observed between morphology unit types. In RP1, the total riffle, bar and run bed areas increase in a similar pattern to the total reach bed area. These experience a gradual increase in the proportion of bed area under full mobility with increasing ΩT, reaching a maximum between 0.82 and 0.89, a pattern exemplified in the total RP1 bed area (Figure 15A), and the RP1 riffle area (Figure 15B). In contrast, pools display a steeper increase in the proportion of pool area under full mobility than the other morphology units until ΩT   ~ 50,000 J/m after which it plateaus around 0.7 (Figure 15B). Riffles also have a larger proportion of the bed area under partial mobility than all other morphology units. The sharp peak in the proportion of bed area under full mobility ΩT   ~ 9,000 J/m corresponds to 2005-06, and can be explained by its proximity to the seeding time and thus higher proportion of tracers on the surface resulting in an overrepresentation of the bed area under mobility. Similar results were observed in RAP, although more subtle.  Figures of the fraction of the area under no, partial and full mobility for RAP and for the surface and subsurface of both reaches can be found in Appendix F.    41         Figure 15. Stacked area plots of the fraction of bed area experiencing full, partial and no mobility against ΩT  for: A: total RAP and total RP1 bed area; B: total pool and total riffle bed area in RP1. A) B) ΩT (J/m) ΩT (J/m) 42  3.2.2 Mobility and shear stress  When looking at the fraction of cells under each type of mobility in areas where the bankfull bed shear stress is equal to various multiples of τcr, patterns emerge. These patterns are exemplified in Figure 16, where results from a subset of seasons are shown. An increase in the fraction of cells under full mobility is seen between seasons with increasing flow conditions, but does not surpass 0.5 except in 2006-07 (Figure 16D).  In most seasons, the fraction of cells under full mobility increases with increasing shear stress, a trend that was observed in 4 seasons in RAP and in 5 seasons in RP1. This can be seen in both reaches in 2010-11 (Figure 16B) and in RP1 in 2011-12 (Figure 16A). In the remainder of the seasons, although the fraction of cells under full mobility increases up to 1-2τcr, the areas of the bed with shear stress > 2τcr had an equal or lower fraction of cells under full mobility. This is the case in RAP in 2011-12 (Figure 16A), and in both reaches in 2012-13 (figure 16C). Maps of the modeled bed shear stress, as well as figures of the fraction of the bed under no, partial, and full mobility with increasing multiples of τcr  for all seasons can be found in Appendix G.        43      Figure 16. Stacked bar plots of the fraction of cells under no, partial and full mobility in areas where the shear stress is equal to multiples of τcr for seasons with QP equal to: A: 0.4Qbf (2011-12); B: 0.7Qbf (2010-11); C: 1.5Qbf (2012-13); D: 2.4Qbf (2006-07).  A) B) C) D) RAP RP1 Multiples of τcr Multiples of τcr 44  3.2.3 Mobility at the cell scale Results of the spatial correlation of mobility values between seasons performed on a cell-to-cell basis yielded negligible positive (0 < r < 0.2) or weak positive (0.2 < r < 0.3) relationships. This indicates that there are no consistent spatial patterns of mobility at this scale, confirming the highly localized and sporadic nature of mobility. The spatial correlation between bankfull shear stress model results and mobility on a cell-to-cell basis also yielded negligible or weak positive relationships when correlating mobility to both the average and maximum shear stress in each mobility cell. The results suggest that there is no relationship between the bed shear stress distribution and bed mobility at the cell scale, which may be a result of the localized and stochastic nature of mobility.   The spatial correlation between mobility and ΔΕnet  on a cell-to-cell basis yielded negligible negative (0 > r > −0.2) or weak negative (−0.2 > r > −0.3) relationships for most seasons. Only three seasons in RP1 and one season in RAP yielded moderate negative relationships between the variables (−0.3 > r > −0.4). Correlation between surface and subsurface partial mobility and ΔΕnet also yielded negligible or weak negative relationships in most seasons. The few seasons with moderate negative relationships also had moderate negative relationships with surface mobility, but no correlation with subsurface mobility. Correlations between absolute bed elevation and ΔΕnet, as well as between absolute elevation and mobility yielded no significant correlation between these variables, suggesting absolute elevation is not a determinant of bed mobility or bed scour. Tabulated results of all correlation results can be found in Appendix H. 45  4. DISCUSSION 4.1 Characterization of sediment transport in East Creek This study used a unique10-year dataset to examine the temporal and spatial patterns of bed mobility in a small gravel-bed stream. Analysis of the tracer data can be used to characterize the temporal and spatial patterns of sediment mobility and dispersion in East Creek. Reach total Fm was low except for one season with exceptionally high flow conditions (2006-07; QP = 2.4Qbf) that reached an Fm  of 93% in RAP and 82% in RP1. Even the 2012-13 seasons, which had QP =1.5Qbf, only reached Fm values of 48 and 66% in RAP and RP1 respectively. Close examination of the spatial patterns of bed mobility revealed that mobility is highly localized and sporadic, displaying large spatial and temporal variability across the bed, confirming a stochastic nature of sediment transport. Furthermore, mobility in East Creek appears to occur in sporadic patches of full mobility, rather than partial mobility occurring over the entire bed area, meaning that an increase in mobility is due to an increase in the contributing mobile area. The lack of relation between burial and mobility indicate that in areas where the bed is mobile, it is mobile throughout the vertical profile. This is also confirmed by the sporadic nature of scour and fill patterns in the channel, as well as the tendency for equal contribution of surface and subsurface tracers in the total mobility. This may be an effect of the shallow active layer in the channel, indicated by the shallow tracer burial depths measured; the majority of tracers were buried within a depth equal to 2D50 of the surface material, which is shallower than the commonly assumed depth of the active layer equal to ~2D90 of the surface (Wilcock and McArdell, 1997).  46   ?̅? values are also low in East Creek compared to other streams, staying below 3.5 m with the exception of two, high flow seasons. Even in the highest flow season of 2006-07, ?̅? values only reached ~30 m. In comparison, average travel distances in other gravel-bed streams have been recorded in the order of 101 m during most seasons, while maximum average travel distances of 102 m are reported for flows of similar ratio to critical flow as this study (e.g. Bradley and Tucker, 2012; Liébault et al., 2012; Haschenburger, 2013; Schneider et al., 2014). In East Creek, riffle spacing is equal to 7.5 m and 18.5 m in RAP and RP1 respectively, indicating that the majority of grains travel within the same bedform most of the time, and require either multiple seasons or exceptionally high flow conditions to travel past dominant bedforms. The combination of the mobility and dispersion characteristics outlined above indicate that East Creek experiences a low sediment transport rate that promotes the maintenance of bedforms and contributes to the high stability of the channel.  The low sediment transport rate in East Creek may be explained by the nature of its hydrology. Although the time spent where Q > Qc is large (ranging between 45.3 and 173.5 hours each season), the majority of flows are low, remaining near Qc, which is also evident from the exceedance probabilities of Ω values. This suggests that the majority of the time, East Creek remains near the critical conditions for sediment transport, explaining the low mobility and dispersion rates, and highly sporadic sediment movement measured. Furthermore, the grain size distributions of the surface and subsurface material 47  in East Creek suggest that the bed is armored, a feature that reduces bed mobility (Brayshaw, 1985; Wilcock and McArdell, 1997; Church et al., 1998). These flow and bed packing characteristics have been observed in many gravel-bed streams with low sediment transport rates and stable morphology (Parker, 1978; Church et al., 1998), and have been defined as distinct regime of sediment transport (Church and Hassan, 2005).   4.2 Effects of flow  The increase in Fm with increasing flow observed in East Creek agrees with results from other studies (e.g. Wilcock and McArdell, 1993; Wilcock, 1997; Haschenburger and Wilcock, 2003), as does the power law fit between ?̅? and metrics of cumulative flow energy (e.g. Hassan et al., 1992; Lamarre and Roy, 2008; Haschenburger, 2013; Schneider et al., 2014). Both variables however show a weak relationship with ΩT, and further examination of the hydrology of East Creek reveals that the distribution of mobilizing events plays an important role in mobilizing sediment in East Creek. As expected, the season that experienced all mobilizing events < 0.5 Qbf, (2011-12) had the lowest Fm and ?̅? values in the study, while 2006-07 and 2012-13, which experienced multiple large events > Qbf, had the highest. Of interest is the seasons in between; seasons with most events near Qc, and multiple moderate events < Qbf, resulted in higher Fm values than seasons with many events near Qc  and a single large event >Qbf. This leads to the conclusion that sediment mobilization occurs during all flows in East Creek.  48  Hassan et al. (1992) conclude that the majority of sediment transport occurs during flows near the peak discharge, and that therefore, the peak discharge is the dominant flow variable controlling sediment mobility. Data from East Creek show that QP  relates to both Fm and ?̅?, supporting that the peak flow is important in mobilizing sediment. However, ΩT   has a stronger relation to both Fm and ?̅? than QP, which may be an effect of differences in the study streams; Hassan et al. (1992) focused on flashy, desert streams in which sediment transport occurs only during large floods with long periods of no sediment mobilization in between. In contrast, East Creek experiences multiple mobilizing events each season, and results show that sediment is mobile during all these events.   Although ?̅? also showed a stronger relation to ΩT than QP, the fitted powers are ~ 0, suggesting no true relation between the variables. Only the seasons with exceptionally low (2011-12) and high (2006-07) flows have significantly lower and higher ?̅? than the remaining seasons, respectively. The low values of ?̅? measured in this study suggest that regardless of flow, sediment moves within the same morphological unit, only travelling farther during very high flows able to transport grains past these bedforms. This result is similar to other streams (e.g. Milan et al., 2002), and can be linked to the stability of the bedforms, since very few events are able to move sediment in ways that can contribute to bed evolution (Pyrce and Ashmore, 2005; Milan, 2013). Flow also has no relation to burial in East Creek, where data suggest that grain size is the largest controls on burial, while flow plays a secondary role during high flow seasons. 49  4.3 Effects of grain size No clear relation was found between Fm or ?̅? and grain size in this study, although it is commonly reported in other gravel-bed streams that there is a decrease with increasing grain size in both mobility (e.g. Ashworth and Ferguson, 1989; Wilcock and McArdell, 1993; 1997; Wilcock, 1997; Ferguson and Wathen, 1998; Church and Hassan, 2002; Haschenburger and Wilcock, 2003) and grain travel distances (e.g. Church and Hassan, 1992; Ferguson and Wathen, 1998; Habersack, 2001; Ferguson et al., 2002; MacVicar and Roy, 2011; Liébault et al., 2012; Schneider et al., 2014). More specifically, bed mobility and grain travel distances have been shown to decrease only slightly for size classes < D50, and decrease rapidly for larger grain sizes (Church and Hassan, 1992; Wilcock and McArdell, 1993; Wilcock, 1997; Ferguson and Wathen, 1998). Then, it is possible then that the size distribution of tracers in this study is too limited to capture the expected decrease in mobility and travel distance with size, as even tracers in the largest size classes experience high mobility.  Despite the large body of evidence suggesting travel distance decreases with grain size, the lack of relation between travel distance and size measured in East Creek is not unique. No or weak relations between travel distance and grain size have been reported in other gravel-bed streams (Andrews, 1983; Schneider et al., 2014), while positive relations between travel distance and size have also been documented in steep natural streams (Brummer and Montgomery, 2003), as well as in flume experiments (e.g. Solari and Parker, 2000; Wong et al., 2007; Hill et al., 2010;). A proposed explanation for this 50  phenomenon is the effect of competing controls on grain mobilization: small particles have lower masses, but may experience larger hiding effects than large particle, which have larger masses, but are more exposed to the flow (Paintal, 1971; Laronne and Carson, 1976; Andrews, 1983; Kirchner et al., 1990; Church and Hassan, 1992). Therefore, bed structuring and packing in East Creek, including the observed bed armoring, may promote the equal mobilization of all grain sizes (Laronne and Carson, 1976; Andrews, 1983; Brayshaw, 1985; Kirchner et al., 1990; Church et al., 1998). Furthermore, although burial rates were high, burial depths remain within the surface D50, suggesting a limited scour depth, and promoting mobility across all grain sizes.   Contrary to mobility and travel distance, Fb and ?̅? both had strong inverse relationships with grain size. Of interesting note is the unusually low mobility and travel distances of the 11 mm size class, which is explained by preferential trapping higher burial probability. When looking onto the burial fractions of tracers, this size class showed higher Fb and larger ?̅? values than all other size classes. This may be due to the size of these tracers compared to the surface material of the bed, or it may be due to positioning during seeding.   51  4.4 Reach-scale effects of morphology   When comparing RAP and RP1, no significant difference is seen in the relation between the Fm and flow between the two reaches, suggesting that at the reach scale, morphology plays no significant role in the mobility of tracers in East Creek. In contrast ?̅? increases more rapidly with increasing flow in RP1 than in RAP, which may be explained by a larger difference in the ability of the tracers to travel between low and high flows in more developed morphological settings. In low flows, the travel distances are constrained within morphological units, while during high flows, the travel distances may increase rapidly as flow becomes large enough to allow for tracers to travel past the first morphological feature. This is captured clearly in East Creek in the tracer travel distributions of the two reaches; tracer travel distributions showed differences between RP1 than in RAP only during high flows. During low to moderate flow seasons, tracer travel distributions in the two reaches differed only in the tail, with the distributions in RP1 reaching higher extreme values than RAP in all seasons but the lowest flow seasons of 2011-12. These extreme values in the distribution may correspond to tracers that are able to be transported past the first morphological unit, and may be absent in 2011-12 due to inability of any tracers to do so. In high flow seasons, RP1 yielded much wider distributions than RAP in seasons with high QP value as tracers can travel past morphological unit. The difference in the changes in the travel distance distributions with increasing flow conditions between reaches can be linked to the bed morphology as feedback process where the presence of more defined bedforms may both drive the greater shifts seen in RP1, and also contribute to their maintenance and evolution (Pyrce and Ashmore, 2005).  52   The lack of strong patterns in mobility between morphology unit types at the reach scale can also be linked to bedform maintenance, as alternating morphological units in the reaches experience high mobility from season to season. The weak trend observed in RP1 that riffles have higher mobility than pools during low flows but that this is reversed during high flows, supports observations from other studies (Keller, 1971; Lisle, 1979; Sear, 1996) that propose this phenomenon as the mechanism for pool-riffle maintenance. The influence of morphology on ?̅? at the reach scale is only clear when averaged over long timescales. The greater travel distances in riffles measured in RP1 is contrary to results by Sear et al. (1996), who reported lower travel distances in riffles than in pools. The tracers in the rapid section of the RAP reach have the highest average travel distance of all tracers in the study, which can be attributed to the lack of large morphological units to trap tracers.   4.5 Within-reach effects of morphology Within the reaches, mobility is highly localized and stochastic, and even when the reach-total Fm is high, there continue to be areas of the bed experiencing no or low mobility.  The mobility maps created in this study demonstrate how areas of full, partial and no mobility neighbor. This observation is consistent with Haschenburger and Wilcock (2003), who also found large spatial variability in the mobility of tracer stones a similar study in Carnation Creek, a gravel-bed stream on Vancouver Island, BC. At the morphological unit scale, there appear to be ‘mobility paths’ in RP1, which are absent in 53  RAP. This is also demonstrated by the more rapid increase in the total bed area under full mobility in RAP than in RP1, showing that the bed area under full mobility is more spread across the bed, rather than concentrated in certain areas. This can explain the lack of prominent bedforms in RAP: the mobility of tracers is more evenly distributed across the bed, lacking patterns that allow for the evolution and maintenance of bed morphology.  A clear increase the fraction of bed area under full mobility was measured with increasing ΩT, a result consistent with results from Carnation Creek (Haschenburger and Wilcock, 2003). In East Creek, differences were seen between morphological units, with pools experiencing a faster increase in the bed area under full mobility with increasing ΩT   than the other morphology units. The observation that mobility increases more rapidly in pools than riffles is consistent with the reach scale results in RP1, and with hypotheses on pool-riffle maintenance (Keller, 1971; Lisle, 1979; Sear, 1996). The more subtle differences between morphological units in RAP is expected due to the poorer development of RAP compared to RP1.   At the local scale, there appears to be no correlation between mobility, shear stress, or changes in bed topography. The lack of correlation in mobility between seasons shows no consistent spatial patterns of mobility. However, along with the lack of correlation between shear stress and bed mobility at the cell-to-cell scale, this may be attributed to the localized nature of tracer displacement even under high transport conditions. Indeed, 54  when looking at the morphological unit scale, a general increase in the fraction of cells with full mobility can be seen in areas with increasing shear stress. This trend however does not hold for all years, pointing to changing areas of high mobility from season to season. This, along with the lack of spatial correlation in mobility between seasons at the cell scale, fits with observations of East Creek reported in Cienciala and Hassan (2013), who observed that areas of bed experience alternating high and low mobility from season to season. This was related this to alternating patterns of scour and fill, and ultimately to the maintenance of the bed morphology (Cienciala and Hassan, 2013). Alternating patterns of scour and fill is further supported in this study by the presence of moderate relationships between mobility and ΔΕnet  in only a subset of seasons.              55  5. CONCLUSION A 10-year dataset of tracers from a small gravel-bed stream was used to examine the temporal and spatial patterns of bed mobility and sediment dispersion in different morphological settings. Bed mobility and grain dispersion were characterized at the reach, morphological unit, and local (0.1 by 0.1 m cell) scales in an attempt to capture the full range of effects morphology has on sediment mobility and dispersion. The following were found: 1. Sediment transport in East Creek remains near critical the majority of the time, and the stream experiences low bed mobility rates and small grain travel distances. This places East Creek within a low sediment transport regime, and explains the stability of the stream.  2. Although burial rates were high (> 50%), burial depths were shallow, staying within 2D50 of the surface. Areas that experience mobility do so throughout the vertical profile of the bed, leading to localized patches of scour and fill.  3. All flows in East Creek contribute to bed mobilization. The distribution of flow magnitudes within a season is a key to control bed mobility and grain dispersion at the reach scale.  4. Grain size was not a control on bed mobility or tracer travel distances, but was the key control on both tracer burial rates and depth. 5. Morphology had no effect on bed mobility at the reach scale, and only had an effect on tracer travel distances during high flows, or when averaged over long timescales.  56  6. At the morphological unit scale, differences were measured in the rate of increase of bed area under full mobility with increasing flow between the two reaches and between morphological unit types. Pools experienced a more rapid increase in bed mobility with increasing flow than other morphology types. An increase in the fraction of the bed under full mobility was observed with increasing shear stress for most seasons, but not all. This observation, along with the localized nature of scour and fill, was linked to the maintenance of the dominant morphology.   7. Finally, at the local scale, bed mobility is highly sporadic and localized, so that even under high overall transport conditions, areas of the bed remain under no or low mobility conditions. Bed mobility does not exhibit spatial patterns at this scale between seasons, and does not correlate to shear stress or changes in elevation.   The effects of morphology on bed mobility and grain dispersion were captured in a small gravel-bed stream at different scales, and over a wide range of flow conditions. Results demonstrate the unique sediment transport regime of stable gravel-bed streams, and highlight the importance of scale in describing the effect of morphology on sediment transport. Due to the complex nature of the interactions between sediment transport and bed morphology, continued research is needed in a wide range of environments and morphological settings to fully understand these processes.   57  REFERENCES Andrews ED. 1983. Entrainment of gravel from naturally sorted riverbed material. Geological Society of America Bulletin 94(10): 1225–1231.  Ashworth PJ, Ferguson RI. 1989. Size-selective entrainment of bed load in gravel bed streams. Water Resources Research 25(4): 627–634.  Bradley D, Tucker GE. 2012. Measuring gravel transport and dispersion in a mountain river using passive radio tracers. Earth Surface Processes and Landforms 37(10): 1034–1045.  Brayshaw AC. 1985. Bed microtopography and entrainment thresholds in gravel-bed rivers. Geological Society of America Bulletin 96(2): 218–223.  Brummer CJ, Montgomery DR. 2003. Downstream coarsening in headwater channels. Water Resources Research 39(10): 1294–1308.  Buffington JM, Montgomery DR. 1997. A systematic analysis of eight decades of incipient motion studies, with special reference to gravel-bedded rivers. Water Resources Research 33(8): 1993–2029.  Church M, Hassan MA. 1992. Size and distance of travel of unconstrained clasts on a streambed. Water Resources Research 28(1): 299–303.  Church M, Hassan MA. 2002. Mobility of bed material in Harris Creek. Water Resources Research 38(11): 1237–1248. Church M, Hassan MA. 2005. Upland gravel-bed rivers with low sediment transport. Developments in Earth Surface Processes 7: 141–168.  Church M, Hassan MA, Wolcott JF. 1998. Stabilizing self-organized structures in gravel-bed stream channels: Field and experimental observations. Water Resources Research 34(11): 3169–3179.  Cienciala P, Hassan MA. 2013. Linking spatial patterns of bed surface texture, bed mobility, and channel hydraulics in a mountain stream to potential spawning substrate for small resident trout. Geomorphology 197: 96–107.  Ferguson RI, Bloomer DJ, Hoey TB, Werritty A. 2002. Mobility of river tracer pebbles over different timescales. Water Resources Research 38(5): 1045–1055.  Ferguson RI, Wathen SJ. 1998. Tracer-pebble movement along a concave river profile: Virtual velocity in relation to grain size and shear stress. Water Resources Research 34(8): 2031–2038.  Gintz D, Hassan MA, Schmidt KH. 1996. Frequency and Magnitude of bedload transport 58  in a mountain river. Earth Surface Processes and Landforms 21(5): 433–445.  Habersack HM. 2001. Radio-tracking gravel particles in a large braided river in New Zealand: a field test of the stochastic theory of bed load transport proposed by Einstein. Hydrological Processes 15(3): 377–391.  Haschenburger JK. 2013. Tracing river gravels: Insights into dispersion from a long-term field experiment. Geomorphology 200: 121–131.  Haschenburger JK, Church M. 1998. Bed material transport estimated from the virtual velocity of sediment. Earth Surface Processes and Landforms 23(9): 791–808.  Haschenburger JK, Wilcock PR. 2003. Partial transport in a natural gravel bed channel. Water Resources Research 39(1): 1020–1029.  Hassan M, Voepel H, Schumer R, Parker G, Fraccarollo L. 2013. Displacement characteristics of coarse fluvial bed sediment. Journal of Geophysical Research: Earth Surface 118(1): 155–165.  Hassan MA. 1992. Structural controls of the mobility of coarse material in gravel-bed channels. Israel journal of earth-sciences 41(2–4): 105–122. Hassan MA, Church M. 1992. The Movement of Individual Grains on the Streambed. In Dynamics of Gravel-bed Rivers, Billy P, Hey RD, and Thorne CR (eds). John Wiley & Sons Ltd, Chichester, UK; 1–17. Hassan MA, Church M, Ashworth PJ. 1992. Virtual rate and mean distance of travel of individual clasts in gravel-bed channels. Earth Surface Processes and Landforms 17(6): 617–627.  Hassan MA, Church M, Lisle TE, Brardinoni F, Benda L,Grand GE. 2005. Sediment transport and channel morphology of small, forested streams. Journal of the American Water Resources Association 41(4): 853–876. Hassan MA, Church M, Schick AP. 1991. Distance of movement of coarse particles in gravel bed streams. Water Resources Research 27(4): 503–511.  Hassan MA, Ergenzinger P. 2003. Use of Tracers in Fluvial Geomorphology. In Tools in Fluvial Geomorphology, Piégay H and Kondolf GM (eds). John Wiley & Sons, Ltd: Chichester, UK. Hassan MA, Schick AP, Shaw PA. 1999. The transport of gravel in an ephemeral sanded river. Earth Surface Processes and Landforms 24(7): 623–640. Hill BM. 1975. A Simple General Approach to Inference About the Tail of a Distribution. The annals of statistics 3(5): 1163–1174.   59  Hill KM, DellAngelo L, Meerschaert MM. 2010. Heavy-tailed travel distance in gravel bed transport: An exploratory enquiry. Journal of Geophysical Research 115: F00A14.  Ikeda H. 1975. On the bed configuration in alluvial channels: their types and condition of formation with references to bars. Geographical Review of Japan 48(10): 712–730.  Kasprak A, Wheaton JM, Ashmore PE, Hensleigh JW, Peirce S. 2015. The relationship between particle travel distance and channel morphology: Results from physical models of braided rivers. Journal of Geophysical Research: Earth Surface 120(1): 55–74.  Keller EA. 1971. Areal Sorting of Bed-Load Material: The Hypothesis of Velocity Reversal. Geological Society of America Bulletin 82(3): 753–756.  Kirchner JW, Dietrich WE, Iseya F, Ikeda H. 1990. The variability of critical shear stress, friction angle, and grain protrusion in water-worked sediments. Sedimentology 37(4): 647–672.  Lamarre H, Roy AG. 2008. The role of morphology on the displacement of particles in a step–pool river system. Geomorphology 99(1–4): 270–279.  Laronne JB, Carson MA. 1976. Interrelationships between bed morphology and bed‐material transport for a small, gravel-bed channel. Sedimentology 23(1): 67–85.  Lenzi MA. 2004. Displacement and transport of marked pebbles, cobbles and boulders during floods in a steep mountain stream. Hydrological Processes 18(10): 1899–1914.  Liébault F, Bellot H, Chapuis M, Klotz S, Deschâtres M. 2012. Bedload tracing in a high-sediment-load mountain stream. Earth Surface Processes and Landforms 37(4): 385–399.  Lisle T. 1979. A Sorting Mechanism for a Riffle-Pool Sequence. Geological Society of America Bulletin, Part I, 90: 616–617.  MacVicar BJ, Roy AG. 2011. Sediment mobility in a forced riffle-pool. Geomorphology 125(3): 445–456.  McDonald RR, Nelson JM, Bennett JP. 2005. Multidimensional Surface Water Modeling System User's Guide: US Geological Survey Techniques and Methods. Book 6  Milan DJ. 2013. Sediment routing hypothesis for pool-riffle maintenance. Earth Surface Processes and Landforms 38(14): 1623–1641.  Milan DJ, Heritage GL, Large ARG. 2002. Tracer pebble entrainment and deposition loci: influence of flow character and implications for riffle-pool maintenance. Geological Society, London, Special Publications 191(1): 133–148.  60  Montgomery DR, Buffington JM. 1997. Channel-reach morphology in mountain drainage basins. Geological Society of America Bulletin 109(5): 596–611. Nelson JM, Bennett JP, Wiele SM. 2003. Flow and sediment-transport modeling. In Tools in Fluvial Geomorphology, Piégay H and Kondolf GM (eds). John Wiley & Sons, Ltd: Chichester, UK. Paintal AS. 1971. A stochastic model of bed load transport. Journal of Hydraulic Research 9(4): 527–554. Parker G. 1978. Self-formed straight rivers with equilibrium banks and mobile bed. Part 2. The gravel river. Journal of Fluid Mechanics 89(1): 127–146.  Phillips CB, Jerolmack DJ. 2014. Dynamics and mechanics of tracer particles. Earth Surface Dynamics Discussions 2(1): 429–476. Phillips CB, Martin RL, Jerolmack DJ. 2013. Impulse framework for unsteady flows reveals superdiffusive bed load transport. Geophysical Research Letters 40(7): 1328–1333.  Pyrce RS, Ashmore PE. 2003a. Particle path length distributions in meandering gravel-bed streams: results from physical models. Earth Surface Processes and Landforms 28(9): 951–966.  Pyrce RS, Ashmore PE. 2003b. The relation between particle path length distributions and channel morphology in gravel-bed streams: a synthesis. Geomorphology 56(1–2): 167–187.  Pyrce RS, Ashmore PE. 2005. Bedload path length and point bar development in gravel-bed river models. Sedimentology 52(4): 839–857.  Schneider JM, Turowski JM, Rickenmann D, Hegglin R, Arrigo S, Mao L, Kirchner JW. 2014. Scaling relationships between bed load volumes, transport distances, and stream power in steep mountain channels. Journal of Geophysical Research: Earth Surface 119(3): 533–549.  Sear DA. 1996. Sediment transport processes in pool-riffle sequences. Earth Surface Processes and Landforms 21(3): 241–262.  Solari L, Parker G. 2000. The curious case of mobility reversal in sediment mixtures. Journal of Hydraulic Engineering 126(3): 185–197. Thompson DM, Wohl EE, Jarrett RD. 1999. Velocity reversals and sediment sorting in pools and riffles controlled by channel constrictions. Geomorphology 27(3–4): 229–241.  Wilcock PR. 1997. Entrainment, displacement and transport of tracer gravels. Earth Surface Processes and Landforms 22(12): 1125–1138. 61  Wilcock PR, McArdell BW. 1993. Surface-based fractional transport rates: Mobilization thresholds and partial transport of a sand-gravel sediment. Water Resources Research 29(4): 1297–1312. Wilcock PR, McArdell BW. 1997. Partial transport of a sand/gravel sediment. Water Resources Research 33(1): 235–245.  Wong M, Parker G, DeVries P, Brown TM, Burges SJ. 2007. Experiments on dispersion of tracer stones under lower-regime plane-bed equilibrium bed load transport. Water Resources Research 43(3): W03440.  Zimmerman A, Church M. 2001. Channel morphology, gradient profiles and bed stresses during spring runoff in a step-pool channel. Geomorphology 40(3): 311–328.                              62 APPENDIX A: PEAK RELATIONS TO MOBILITY AND TRAVEL DISTANCE           Figure 17. A: Total fraction of mobile tracers, Fm plotted against peak discharge, QP, and the results of the linear regression; and B: the average tracer travel distance, ?̅?  plotted against peak discharge, QP, and the results of the power regression.     1 2 3 40.20.40.60.8QP (m3s)Fm1 2 3 4 50.10.52.05.020.0QP (m3s)L (m)A) B) 00RAPRP1Regression RAPRegression RP1 63 APPENDIX B: MOBILITY AND TRAVEL DISTANCE BY SIZE    Figure 18. Fraction of mobile tracers in RAP and RP1 by grain size for all seasons.    Grain Size (mm)Fm0.00.20.40.60.81.02005−068 11 16 22 32 45 64 90Grain Size (mm)Fm0.00.20.40.60.81.02006−078 11 16 22 32 45 64 90Grain Size (mm)Fm0.00.20.40.60.81.02007−088 11 16 22 32 45 64 90Grain Size (mm)Fm0.00.20.40.60.81.02008−108 11 16 22 32 45 64 90Grain Size (mm)Fm0.00.20.40.60.81.02010−118 11 16 22 32 45 64 90Grain Size (mm)Fm0.00.20.40.60.81.02011−128 11 16 22 32 45 64 90Grain Size (mm)Fm0.00.20.40.60.81.02012−138 11 16 22 32 45 64 90Grain Size (mm)Fm0.00.20.40.60.81.02013−148 11 16 22 32 45 64 9000RAPRP1 64   Figure 19. Average tracer travel distance in RAP and RP1 by grain size for all seasons.     Grain Size (mm)L (m)010203040502005−068 11 16 22 32 45 64 90Grain Size (mm)L (m)010203040502006−078 11 16 22 32 45 64 90Grain Size (mm)L (m)010203040502007−088 11 16 22 32 45 64 90Grain Size (mm)L (m)010203040502008−108 11 16 22 32 45 64 90Grain Size (mm)L (m)010203040502010−118 11 16 22 32 45 64 90Grain Size (mm)L (m)010203040502011−128 11 16 22 32 45 64 90Grain Size (mm)L (m)010203040502012−138 11 16 22 32 45 64 90Grain Size (mm)L (m)010203040502013−148 11 16 22 32 45 64 9000RAPRP1 65 APPENDIX C: TRAVEL DISTANCE DISTRIBUTIONS    Figure 20. Exceedance probability plots of tracer travel distances in RAP with fitted Pareto distributions to the distribution tails using the Hill’s estimator method.    log[L]log[P(X > x)]2005−060.05 0.2 0.5 2 5 20 500.0020.020.21log[L]log[P(X > x)]2006−070.05 0.2 0.5 2 5 20 500.0020.020.21log[L]log[P(X > x)]2007−080.05 0.2 0.5 2 5 20 500.0020.020.21log[L]log[P(X > x)]2008−100.05 0.2 .5 2 5 20 500.0050.020.21log[L]log[P(X > x)]2010−110.05 0.2 0.5 2 5 20 500.0020.020.21log[L]log[P(X > x)]2011−1205 0.2 0.5 2 50.0020.020.21log[L]log[P(X > x)]2011−120. 5 0.2 0.5 2 50.0020.020.21log[L]log[P(X > x)]2013−140.0 0. 0. 2 5 20 500.0050.020.21 66   Figure 21. Exceedance probability plots of tracer travel distances in RP1 with fitted Pareto distributions to the distribution tails using the Hill’s estimator method. log[L]log[P(X > x)]2005−060.05 0.2 0.5 2 5 20 500.0020.020.21log[L]log[P(X > x)]2006−070.05 0.2 0.5 2 5 2 50 2000.0020.020.21log[L]log[P(X > x)]2007−080.05 0.2 0.5 2 5 500.0020.020.21log[L]log[P(X > x)]2008−100.05 0.2 0.5 2 5 20 500.0020.020.21log[L]log[P(X > x)]2010−110.05 0.2 0.5 2 5 20 500.0020.020.21log[L]log[P(X > x)]2011−1205 0.2 0. 2 50.0020.020.21log[L]log[P(X > x)]2012−130.05 0.2 0.5 2 20 500.0020.020.21log[L]log[P(X > x)]2013−14.05 0.2 0.5 2 5 20 500.0020.020.21 67       Table 4. Summary of the  power law and Hill’s estimator method for testing if travel distance distributions are thin- or heavy-tailed. 9alues with ‘’ indicate that the distribution is heavy-tailed.   RAP RP1 Season Points in Tail α R2 𝛼𝐻 Points in Tail α R2 𝛼𝐻 13-14 3 -2.99 1 2.81 6 -3.69 0.93 3.37 12-13 5 -1.94* 0.91 1.55* 10 -2.64 0.99 2.87 11-12 7 -1.67* 0.99 1.60* 4 -3.31 0.79 2.70 10-11 7 -3.87 0.94 4.83 5 -2.72 0.82 2.93 08-10 6 -3.61 0.86 3.13 6 -1.54* 0.96 1.28* 07-08 3 -10.38 0.95 13.90 4 -2.79 0.96 2.12 06-07 11 -24.09 0.94 29.94 14 -4.82 0.97 5.33 05-06 9 -2.622 0.92 2.16 4 -2.75 0.96 3.00              68 APPENDIX D: BURIAL                   0 20000 40000 60000 800000.00.20.40.60.81.0WT (J/m)Fb0 20000 40000 60000 8000045678WT (J/m)B (cm)0 1 2 3 4 50.00.20.40.60.81.0QP (m3s)Fb0 1 2 3 4 545678QP (m3s)B (cm)A) B) Figure 22. A)  Total burial fraction, Fb and B)  average burial depth, ?̅?  plotted against maximum peak discharge, QP and the excess flow energy expenditure, ΩT. 00RAPRP1 69   Figure 23. Fraction of buried tracers by morphology type.      0.00.10.20.30.40.50.60.70.80.91.02005-06 2006-07 2007-08 2008-10 2010-11 2011-12 2012-13 2013-14Fraction of Tracers Buried Rapid Pools Riffles Bars RunsRAP 0.00.10.20.30.40.50.60.70.80.91.02005-06 2006-07 2007-08 2008-10 2010-11 2011-12 2012-13 2013-14Fraction of Tracers Buried  RP1  70       Figure 24. Fraction of buried tracers in RAP and RP1 by grain size for all seasons.     Grain Size (mm)Fb0.00.20.40.60.81.02005−068 11 16 22 32 45 64 90Grain Size (mm) (mm)Fb0.00.20.40.60.81.02006−078 11 16 22 32 45 64 90Grain Size (mm)Fb0.00.20.40.60.81.02007−088 11 16 22 32 45 64 90Grain Size (mm)Fb0.00.20.40.60.81.02008−108 11 16 22 32 45 64 90Grain Size (mm)Fb0.00.20.40.60.81.02010−118 11 16 22 32 45 64 90Grain Size (mm)Fb0.00.20.40.60.81.02011−128 11 16 22 32 45 64 90Grain Size (mm)Fb0.00.20.40.60.81.02012−138 11 16 22 32 45 64 90Grain Size (mm)Fb0.00.20.40.60.81.02013−148 11 16 22 32 45 64 9000RAPRP1 71     Figure 25. Average burial depth in RAP and RP1 by grain size for all seasons.   Grain Size (mm)B (cm)0246810122005−068 11 16 22 32 45 64 90Grain Size (mm)B (cm)0246810122006−078 11 16 22 32 45 64 90Grain Size (mm)B (cm)0246810122007−088 11 16 22 32 45 64 90Grain Size (mm)B (cm)0246810122008−108 11 16 22 32 45 64 90Grain Size (mm)B (cm)0246810122010−118 11 16 22 32 45 64 90Grain Size (mm)B (cm)0246810122011−128 11 16 22 32 45 64 90Grain Size (mm)B (cm)0246810122012−138 11 16 22 32 45 64 90Grain Size (mm)B (cm)0246810122013−148 11 16 22 32 45 64 9000RAPRP1 72  2005-062006-072007-082008-100 4 82 mChannel MorphologyWoodRapidPoolRiffleBarRunVegetationChannel MorphologyWoodRapidPoolRiffleBarRunVegetationBed MobilityNo tracersNo mobilityPartial mobilityFull mobilityFigure 26. Mobility maps of RAP for seasons from 2005 to 2010.  APPENDIX E: MOBILITY MAPS   Flow Direction  73  2010-112011-122012-132013-140 4 82 mFigure 27. Mobility maps of RAP for seasons from 2010 to 2014.  Channel MorphologyWoodRapidPoolRiffleBarRunVegetationChannel MorphologyWoodRapidPoolRiffleBarRunVegetationBed MobilityNo tracersNo mobilityPartial mobilityFull mobilityFlow Direction  74  0 5 102.5 m2005-062006-072007-082008-10Figure 28. Mobility maps of RAP for seasons from 2005 to 2010.  Channel MorphologyWoodRapidPoolRiffleBarRunVegetationChannel MorphologyWoodRapidPoolRiffleBarRunVegetationBed MobilityNo tracersNo mobilityPartial mobilityFull mobilityFlow Direction  75  Figure 29. Mobility maps of RP1 for seasons from 2010 to 2014.   0 5 102.5 m2010-112011-122012-132013-14Channel MorphologyWoodRapidPoolRiffleBarRunVegetationChannel MorphologyWoodRapidPoolRiffleBarRunVegetationBed MobilityNo tracersNo mobilityPartial mobilityFull mobilityFlow Direction  76 APPENDIX  F: BED MOBILITY BY AREA   Figure 30. Stacked area plots of the fraction of bed area experiencing full, partial and no mobility against ŸT  in different morphological units in RAP   77    Figure 31. Stacked area plots of the fraction of bed area experiencing full, partial and no mobility against ŸT  in different morphological units in RAP  78 APPENDIX G: SHEAR STRESS                  Figure 32. Modeled A)  Qbf and B)  0.5Qbf. bed shear stress results for RAP.A) B) Bed Shear Stress(Pa)< 20.020.0 - 40.140.1 - 80.1> 80.1Channel MorphologyWoodPoolRiffleBarRunVegetation0 4 82 mA) B) Channel MorphologyWoodRapidPoolRiffleBarRunVegetationBed Shear Stress(Pa)< 20.020.0 - 40.140.1 - 80.1> 80.1Channel MorphologyWoodPoolRiffleBarRunVegetation0 4 82 m 79  Figure 33. Modeled A)  Qbf and B)  0.5Qbf. bed shear stress results for RP1. Channel MorphologyWoodPoolRiffleBarRunVegetationBed Shear Stress(Pa)< 17.817.8 - 35.735.7 - 71.4>71.40 5 102.5 mChannel MorphologyWoodPoolRiffleBarRunVegetationBed Shear Stress(Pa)< 17.817.8 - 35.735.7 - 71.4>71.40 5 102.5 mA) B)  80                  Figure 34. Stacked bar plot of the fraction of map cells in RAP under full, partial and no mobility corresponding to areas with shear stress equal to various multiples of τc. 2005-06 2006-07 2007-08 2008-10 2010-11 2011-12 2012-13 2013-14 Multiples of τcr Multiples of τcr  81                  Figure 35. Stacked bar plot of the fraction of map cells in RP1 under full, partial and no mobility corresponding to areas with shear stress equal to various multiples of τc.2005-06 2006-07 2007-08 2008-10 2010-11 2011-12 2012-13 2013-14 Multiples of τcr Multiples of τcr  82  APPENDIX H. CORRELATION RESULTS  Table 4. Tabulated results of spatial correlation between all seasons in R$P. Pearson’s r values and associated p-values in brackets are shown. Correlations with * are significant at the 0.05 significance level, and ** are significant at the 0.01 significance level.  2005-06             2006-07 0.18 * (0.03) 2006-07           2007-08 0.18  (0.15) 0.01 (0.93) 2007-08         2008-10 0.18 (0.14) -0.01 (0.94) 0.14 (0.06) 2008-10       2010-11 0.10 (0.40) 0.05 (0.68) 0.03 (0.72) 0.06 (0.46) 2010-11     2011-12 0.16 (0.21) 0.10 (0.43) 0.10 (0.24) 0.15 (0.08) 0.20** (0.009) 2011-12   2012-13 0.34** (0.008) 0.13 (0.33) 0.08 (0.34) 0.15 (0.10) 0.001 (0.98) -0.01 (0.88) 2012-13 2013-14 0.09 (0.50) 0.14 (0.32) 0.05 (0.57) -0.05 (0.58) 0.05 (0.59) 0.13 (0.13) 0.23** (0.01)  Table 5. Tabulated results of spatial correlation between all seasons in RP1. Pearson’s r values and associated p-values in brackets are shown. Correlations with * are significant at the 0.05 significance level, and ** are significant at the 0.01 level.  2005-06             2006-07 0.13 (0.15) 2006-07           2007-08 0.41**  (< 0.001) 0.09 (0.33) 2007-08         2008-10 -0.04 (0.72) 0.08 (0.43) 0.07 (0.28) 2008-10       2010-11 0.08 (0.45) 0.21* (0.03) -0.03 (0.59) 0.13* (0.04) 2010-11     2011-12 0.18 (0.08) 0.16 (0.11) 0.01 (0.84) 0.23** (<0.001) 0.12* (0.03) 2011-12   2012-13 -0.08 (0..044) 0.04 (0.73) -0.01 (0.14) 0.02 (0.47) -0.05 (0.39) -0.02 (0.66) 2012-13 2013-14 0.20 (0.06) 0.05 (0.60) 0.05 (0.49) -0.02 (0.75) 0.06 (0.35) 0.05 (0.46) 0.10 (0.14)  Table 6. Tabulated results of correlation between the average shear stress in each cell and partial mobility for both Qbf and 0.5Qbf  shear stress values. Pearson’s r values and  83 associated p-values in brackets are shown. Correlations with * are significant at the 0.05 significance level, and ** are significant at the 0.01 level.  Qbf 0.5Qbf Season RAP RP1 RAP RP1 2005-06 0.18** (0.01) 0.03 (0.69) 0.18** (0.01) -0.19** (0.01) 2006-07 0.24**   (< 0.001) 0.11 (0.13) 0.21** (0.003) 0.19** (0.01) 2007-08 0.09 (0.14) 0.14** (0.007) 0.08 (0.22) 0.04 (0.47) 2008-10 0.21**   (< 0.001) 0.11* (0.03) 0.25**   (< 0.001) 0.18**    (< 0.001) 2010-11 0.23**   (< 0.001) 0.13** (0.01) 0.20** (0.002) 0.14** (0.007) 2011-12 0.08 (0.20) 0.13** (0.01) 0.078 (0.22) 0.14** (0.006) 2012-13 0.13* (0.05) 0.12* (0.02) 0.11 (0.08) 0.15** (0.005) 2013-14 0.07 (0.30) 0.02 (0.70) 0.08 (0.24) 0.03 (0.56)  Table 7. Tabulated results of correlation between the maximum shear stress in each cell and partial mobility for both Qbf and 0.5Qbf shear stress values. Pearson’s r values and associated p-values in brackets are shown. Correlations with * are significant at the 0.05 significance level, and ** are significant at the 0.01 level.  Qbf 0.5Qbf Season RAP RP1 RAP RP1 2005-06 0.18** (0.01) 0.06 (0.40) 0.18** (0.01) -0.12 (0.10) 2006-07 0.25**   (< 0.001) 0.02 (0.77) 0.23** (0.001) 0.11 (0.13) 2007-08 0.06 (0.36) 0.17** (0.02) 0.03 (0.58) 0.06 (0.22) 2008-10 0.22**   (< 0.001) 0.09 (0.09) 0.28**   (< 0.001) 0.18**    (< 0.001) 2010-11 0.17** (0.007) 0.10* (0.04) 0.17** (0.01) 0.13** (0.01) 2011-12 0.03 (0.63) 0.10 (0.06) 0.03 (0.59) 0.16** (0.002) 2012-13 0.07 (0.27) 0.07 (0.15) 0.05 (0.44) 0.07 (0.18) 2013-14 0.02 (0.78) 0.04 (0.43) 0.04 (0.52) 0.05 (0.33) Table 8. Tabulated results of correlation between the average net change in elevation in each cell and partial mobility. Pearson’s r values and associated p-values in brackets are  84 shown. Correlations with * are significant at the 0.05 significance level, and ** are significant at the 0.01 level.   Total Surface Subsurface Season RAP RP1 RAP RP1 RAP RP1 2005-06 -0.32**  (< 0.001) -0.41** (< 0.001) -0.28** (0.001) -0.36** (< 0.001) -0.39** (< 0.001) -0.37** (0.001) 2006-07 -0.21**  (0.002) -0.18* (0.04) -0.18 (0.08) -0.14 (0.15) -0.09 (0.22) -0.21* (0.02) 2007-08 -0.023 (0.69) -0.20** (< 0.001) n/a n/a -0.03 (0.67) -0.19** (< 0.001) 2008-10 -0.26**  (< 0.001) -0.32** (< 0.001) -0.28* (0.02) -0.28** (0.002) -0.25** (< 0.001) -0.31** (< 0.001) 2010-11 -0.17** (0.009) -0.03 (0.58) -0.24* (0.02) -0.11 (0.13) -0.11 (0.10) -0.05 (0.44) 2011-12 -0.15** (0.01) 0.07 (0.22) -0.13 (0.16) 0.04 (0.56) -0.13 (0.06) 0.06 (0.39) 2012-13 -0.07 (0.26) -0.38** (< 0.001) -0.02 (0.81) -0.38** (< 0.001) -0.09 (0.15) -0.39** (< 0.001) 2013-14 -0.02 (0.72) -0.15** (0.004) -0.005 (0.96) -0.13 (0.06) -0.11 (0.13) -0.14* (0.03)  Table 9. Tabulated results of correlation between the average absolute elevation in each cell and partial mobility. Pearson’s r values and associated p-values in brackets are shown. Correlations with * are significant at the 0.05 significance level, and ** are significant at the 0.01 level.   Total Surface Subsurface Season RAP RP1 RAP RP1 RAP RP1 2005-06 -0.19** (0.009) -0.26** (< 0.001) -0.21** (0.01) -0.26** (0.002) 0.005 (0.96) -0.27* (0.02) 2006-07 -0.16* (0.03) -0.26** (< 0.001) -0.26** (0.01) 0.15 (0.06) -0.15* (0.05) 0.15 (0.06) 2007-08 -0.18** (0.002) -0.14** (0.004) n/a n/a -0.18** (0.002) -0.10* (0.03) 2008-10 -0.12 (0.07) -0.20** (0.0001) -0.09 (0.46) -0.26** (0.01) -0.03 (0.66) -0.25** (< 0.001) 2010-11 -0.12 (0.07) 0.01 (0.84) -0.18 (0.07) -0.02 (0.81) -0.11 (0.11) 0.006 (0.19) 2011-12 -0.10 (0.09) -0.12* (0.02) -0.14 (0.15) -0.07 (0.30) -0.10 (0.17) -0.17** (0.004) 2012-13 -0.12 (0.06) -0.04 (0.42) -0.13 (0.17) 0.002 (0.97) -0.08 (0.20) -0.03 (0.46) 2013-14 -0.22** (0.001) -0.16** (< 0.001) -0.20* (0.03) -0.12 (0.07) -0.15* (0.04) -0.20** (< 0.001)  

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