Channel flow competence and sediment transport in upland streams in southeast Australia

Bedload transport data from planebed and step‐pool reach types are used to determine grain size transport thresholds for selected upland streams in southeast Australia. Morphological differences between the reach types allow the effects of frictional losses from bedforms, microtopography and bed packing to be incorporated into the dimensionless critical shear stress value. Local sediment transport data are also included in a regime model and applied to mountain streams, to investigate whether empirical data improve the delineation of reach types on the basis of dimensionless discharge per unit width (q*) and dimensionless bedload transport (q_b*). Instrumented planebed and step‐pool sites are not competent to transport surface median grains (D_50s) at bankfull discharge (Q_bf). Application of a locally parametrized entrainment equation to the full range of reach types in the study area indicates that the majority of cascades, cascade‐pools, step‐pools and planebeds are also not competent at Q_bf and require a 10 year recurrence interval flood to mobilize their D_50s. Consequently, the hydraulic parameters of the regime diagram, which assume equilibrium conditions at bankfull, are ill suited to these streams and provide a poor basis of channel delineation. Modifying the diagram to better reflect the dominant transported bedload size (equivalent to the D₁₆ of surface sediment) made only slight improvements to reach delineation and had greatest effect on the morphologies with smaller surface grain sizes such as forced pool‐riffles and planebeds. Likewise, the Corey shape factor was incorporated into the regime diagram as an objective method for adjusting a base dimensionless critical shear stress (τ*_c50b) to account for lithologically controlled grain shape on bed packing and entrainment. However, it too provided only minor adjustments to reach type delineation. Copyright © 2007 John Wiley & Sons, Ltd.     

Quantifying the Morphological Print of Bedload Transport

Bedload and river morphology interact in a strong feedback manner. Bedload conditions the development of river morphology along different space and time scales; however, by concentrating the flow in preferential paths, a given morphology controls bedload for a given discharge. As bedload is a non‐linear response of shear stress, local morphology is likely to have a strong impact on bedload prediction when the shear stress is averaged over the section, as is usually done. This was investigated by comparing bedload measured in different bed morphologies (step‐pool, plane bed, riffle‐pool, braiding, and sand beds), with bedload measured in narrow flumes in the absence of any bed form, used here as a reference. The initial methodology consisted of fitting a bedload equation to the flume data. Secondly, the morphological signature of each river was studied as the distance to this referent equation. It was concluded that each morphology affects bedload in a different way. For a given average grain shear stress, the larger the river, the larger the deviation from the flume transport. Narrow streams are those morphologies that behave more like flumes; this is particularly true with flat beds, whereas results deviate from flumes to a greater extent in step‐pools. The riffle‐pool's morphology impacts bedload at different levels depending on the degree of bar development, considered here through the ratio D₈₄/D₅₀ which is used as a proxy for the local bed patchiness and morphology. In braiding rivers morphological effects are important but difficult to assess because width is dependent on transport rate. Bed morphology was found to have negligible effects in sand bed rivers where the Shields stress is usually sufficiently high to minimize the non‐linearity effects when hydraulics is averaged over the section. Copyright © 2015 John Wiley & Sons, Ltd.     

Reduced bed material stability and increased bedload transport caused by foraging fish: a flume study with juvenile Barbel (Barbus barbus)

The plants and animals that inhabit river channels may act as zoogeomorphic agents affecting the nature and rates of sediment recruitment, transport and deposition. The impact of benthic‐feeding fish, which disturb bed material sediments during their search for food, has received very little attention, even though benthic feeding species are widespread in rivers and may collectively expend significant amounts of energy foraging across the bed. An ex situ experiment was conducted to investigate the impact of a benthic feeding fish (Barbel Barbus barbus) on particle displacements, bed sediment structures, gravel entrainment and transport fluxes. In a laboratory flume changes in bed surface topography were measured and grain displacements examined when an imbricated, water‐worked bed of 5.6 to 16 mm gravels was exposed to feeding juvenile Barbel (on average, 0.195 m in length). Grain entrainment rates and bedload fluxes were measured under a moderate transport regime for substrates that had been exposed to feeding fish and control substrates which had not. On average, approximately 37% of the substrate, by area, was modified by foraging fish during a four‐hour treatment period, resulting in increased microtopographic roughness and reduced particle imbrication. Structural changes by fish corresponded with an average increase in bedload flux of 60% under entrainment flows, whilst on average the total number of grains transported during the entrainment phase was 82% higher from substrates that had been disturbed by Barbel. Together, these results indicate that by increasing surface microtopography and undoing the naturally stable structures produced by water working, foraging can increase the mobility of gravel‐bed materials. An interesting implication of this result is that by increasing the quantity of available, transportable sediment and lowering entrainment thresholds, benthic feeding might affect bedload fluxes in gravel‐bed rivers. The evidence presented here is sufficient to suggest that further investigation of this possibility is warranted. Copyright © 2014 John Wiley & Sons, Ltd.     

Increase in coarse sediment transport associated with disturbance of gravel river beds by signal crayfish (Pacifastacus leniusculus)

There is growing acknowledgement of the interaction between animals and the river bed on which they live and the implications of biological activity for geomorphic processes. It has been observed that signal crayfish (Pacifastacus leniusculus) disturb gravel substrates, potentially promoting sediment transport and impacting ecological communities. However, the mechanisms involved and the extent of their impact remain poorly understood, especially in relation to other processes that affect grain mobility in gravel‐bed rivers. A series of flume experiments, using loose and water‐worked gravel beds of narrowly graded grain sizes that were exposed to 6 h of crayfish activity under low‐velocity flows, showed a substantial increase in the number of grains entrained by subsequent higher‐velocity flows when compared with control runs in which crayfish were never introduced. Crayfish alter the topography of their substrate by constructing pits and mounds, which affect grain protrusion. When walking and foraging, they also alter gravel fabric by reorienting and changing the friction angle of surface grains. In water‐worked surfaces, this fabric rearrangement is shown to lead to a statistically significant, partial reversal of the structuring that had been achieved by antecedent flow. For these previously water‐worked surfaces, the increase in entrainment arising from disturbance by crayfish was statistically significant, with grain transport nearly twice as great. This suggests that signal crayfish, an increasingly widespread invasive species in temperate latitudes beyond their native NW North America, have the potential to enhance coarse‐grained bedload flux by altering the surface structure of gravel river beds and reducing the stability of surface grains. This study illustrates further the importance of acknowledging the impact of mobile organisms in conditioning the river bed when assessing sediment entrainment mechanics in the context of predicting bedload flux. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of bedload transport characteristics of Idaho streams and rivers

Field data are essential in evaluating the adequacy of predictive equations for sediment transport. Each dataset based on the sediment transport rates and other relevant information gives an increased understanding and improved quantification of different factors influencing the sediment transport regime in the specific environment. Data collected for 33 sites on 31 mountain streams and rivers in Central Idaho have enabled the analysis of sediment transport characteristics in streams and rivers with different geological, topographic, morphological, hydrological, hydraulic, and sedimentological characteristics. All of these streams and rivers have armored, poorly sorted bed material with the median particle size of surface layer coarser than the subsurface layer. The fact that the largest particles in the bedload samples did not exceed the median particle size of the bed surface material indicates that the armor layer is stable for the observed flow discharges (generally bankfull or less, and in some cases two times higher than bankfull discharge). The bedload transport is size‐selective. The transport rates are generally low, since sediment supply is less than the ability of flow to move the sediment for one range of flow discharges, or, the hydraulic ability of the stream is insufficient for entrainment of the coarse bed material. Detailed analyses of bedload transport rates, bedload and bed material characteristics were performed for each site. The obtained results and conclusions are used to identify different influences on bedload transport rates in analyzed gravel‐bed rivers. Copyright © 2008 John Wiley & Sons, Ltd.     

Bedload transport measurements with impact plate geophones: comparison of sensor calibration in different gravel‐bed streams

Indirect bedload transport measurements have been made with the Swiss plate geophone system in five gravel‐bed mountain streams. These geophone sensors record the motion of bedload particles transported over a steel plate mounted flush with the channel bed. To calibrate the geophone system, direct bedload transport measurements were undertaken simultaneously. At the Erlenbach in Switzerland, a moving‐basket sampler was used. At the Fischbach and Ruetz streams in Austria, a Helley–Smith type bedload sampler provided the calibration measurements. A Bunte‐type bedload trap was used at the Rofenache stream in Austria. At the Nahal Eshtemoa in Israel, Reid‐type slot bedload samplers were used. To characterize the response of the geophone signal to bedload particles impacting on the plate, geophone summary values were calculated from the raw signal and stored at one second intervals. The number of impulses, i.e. the number of peaks above a pre‐defined threshold value of the geophone output signal, correlated well with field measured gravel transport loads and was found to be a robust parameter. The relations of impulses to gravel transport loads were generally near‐linear, but the steepness of the calibration relations differed from site to site. By comparing the calibration measurements from the different field sites and utilizing insights gained during preliminary flume experiments, it has been possible to identify the main factors that are responsible for site specific differences in the calibration coefficient. The analysis of these calibration measurements indicates that the geophone signal also contains some information about the grain size distribution of bedload. Copyright © 2013 John Wiley & Sons, Ltd.     

Bedload: a granular phenomenon

Bedload, the transport of sediment remaining in contact with the stream bed, has mainly been studied from the perspective of the correlation between fluid driving forces and the responding sediment flux. Yet grain–grain interactions are important and bedload should also be considered as a granular phenomenon. We review progress made recently in the study of granular flows, especially on segregation and rheology, that better illuminates the nature of bedload. Granular flows may exhibit gas‐like or fluid‐like flow, or quasi‐solid deformation. All three conditions might be duplicated in bedload. Understanding of intense bedload transport occurring continuously in a layer several grains deep – typical of sand beds – might greatly benefit from results in granular physics, as illustrated by grain‐inspired bedload results. However, processes restricted to the surface of the bed, when particles move intermittently and the bed becomes structured, while characteristic in gravel‐bed channels, are not well addressed in granular physics. Mutual study of these phenomena may benefit both physics and fluvial geomorphology. We intend, therefore, to contribute to an enhanced dialogue between granular physics and bedload science communities. Copyright © 2010 John Wiley & Sons, Ltd.     

The concept of travelling bedload and its consequences for bedload computation in mountain streams

In bedload transport modelling, it is usually presumed that transported material is fed by the bed itself. This may not be true in some mountain streams where the bed can be very coarse and immobile for the majority of common floods, whereas a finer material, supplied by bed‐external sources, is efficiently transported during floods, with marginal morphological activities. This transport mode was introduced in an earlier paper as ‘travelling bedload’. It could be considered an extension of the washload concept of suspension, applied to bedload transport in high‐energy, heavily armoured streams. Since this fine material is poorly represented in the bed surface, standard surface‐based approaches are likely to strongly underestimate the true transport in such streams. This paper proposes a simple method to account for travelling bedload in bedload transport estimations. The method is tested on published datasets and on a typical Alpine stream, the Roize (Voreppe, France). The results, particularly on active streams that experience greater transport than expected from the grain sizes of their bed material, reinforce the necessity of accounting for the ‘travelling bedload concept’ in bedload computation. The method relevance is discussed regarding varying flood magnitudes, geomorphic responses and eventual anthropic origin of the ‘travelling bedload’ phenomena. To conclude, this paper considers how to compute bedload transport for a wide range of situations, ranging from sediment‐starved cases to the general mobile bed alluvial case, including the intermediate situation of external source supply on armoured bed. Copyright © 2017 John Wiley & Sons, Ltd.     

Coarse sediment transport in mountain streams in Colorado and Wyoming,USA

Since the early 1990s, US Forest Service researchers have made thousands of bedload measurements in steep, coarse‐grained channels in Colorado and Wyoming, USA. In this paper we use data from 19 of those sites to characterize patterns and rates of coarse sediment transport for a range of channel types and sizes, including step–pool, plane‐bed, pool–riffle, and near‐braided channels. This effort builds upon previous work where we applied a piecewise regression model to (1) relate flow to rates of bedload transport and (2) define phases of transport in coarse‐grained channels. Earlier, the model was tested using bedload data from eight sites on the Fraser Experimental Forest near Fraser, Colorado. The analysis showed good application to those data and to data from four supplementary channels to which the procedure was applied. The earlier results were, however, derived from data collected at sites that, for the most part, have quite similar geology and runoff regimes. In this paper we evaluate further the application of piecewise regression to data from channels with a wider range of geomorphic conditions. The results corroborate with those from the earlier work in that there is a relatively narrow range of discharges at which a substantial change in the nature of bedload transport occurs. The transition from primarily low rates of sand transport (phase I) to higher rates of sand and coarse gravel transport (phase II) occurs, on average, at about 80 per cent of the bankfull (1·5‐year return interval) discharge. A comparison of grain sizes moved during the two phases showed that coarse gravel is rarely trapped in the samplers during phase I transport. Moreover, the movement and capture of the D₁₆ to D₂₅ grain size of the bed surface seems to correspond with the onset of phase II transport, particularly in systems with largely static channel surfaces. However, while there were many similarities in observed patterns of bedload transport at the 19 studied sites, each had its own ‘bedload signal’ in that the rate and size of materials transported largely reflected the nature of flow and sediment particular to that system. Published in 2005 by John Wiley & Sons, Ltd.     

How does the bed surface impact low-magnitude bedload transport rates over gravel-bed rivers?

Bedload transport is a complex phenomenon that is not well understood, especially for poorly sorted sediment and low transport rates, which is what is typically found in alpine gravel-bed rivers. In this paper, the interaction between bedload rate, bed stability and flow is investigated using flume experiments. Significant differences in bedload rates were observed for experiments conducted on beds formed with the same gravel material but presenting diverse arrangements and bedforms. Tests were performed under regimes of low transport rate, which are mainly controlled by gravel-bed roughness. Different scales of roughness were identified using the statistical characteristics of detailed bed elevation measurements: grain, structure and large bedform scales. The role played by these different roughness scales in bedload dynamics was examined. For quasi-flat beds, bed stability was quantified using a combination of bed surface criteria describing grain and structure scales. It was found that bed stability affects the bedload rate directly and not only through its influence on the flow or on the incipient motion. For beds with large bedforms, the analysis of bedload dynamics also showed the importance of accounting for effective bed shear stress distributions. An empirical bedload model for low transport regimes was suggested. Compared with previous formulae developed for alpine rivers, this model accounts for bed stability and distribution of effective bed shear stress. It significantly improves the understanding of gravel dynamics over complex beds such as arranged beds or those with large bedforms. However, further tests are needed to use the model outside the range of conditions of this study. © 2019 John Wiley & Sons, Ltd.     

The effects of kinetic sorting on sediment mobility on steep slopes

In poorly mobile static armour, sorting is usually considered the result of hiding/exposure effects. We called this effect ‘static sorting’ in opposition to very efficient grain‐to‐grain mechanisms produced by a mobile mixture, called ‘kinetic sorting’. We hypothesized that kinetic sorting can be an important contributor to the morphodynamics of mountain streams and attempted to demonstrate this with new flume experiments. Two long runs were produced with natural poorly sorted sediments, and with transport stages of the coarse fraction (defined by the ratio between the shear stress and the critical shear stress for transport), smaller and higher than 1, respectively. Both runs produced an efficient transfer downstream of the injected material, but with a major difference: the first run (no kinetic sorting) produced permanent armour figuring clusters, akin to what has already been observed in similar experiments; the second run (with kinetic sorting) also produced bed armouring, but this armour was periodically totally destroyed, leading to substantial bed erosion. This phenomenon was explained by kinetic sorting, the effects of which are to produce an efficient downward migration of fine materials and bed surface armouring. The consequence is that fine materials are hidden to the flow during aggradation, allowing the slope to attain values much steeper than would have been expected at equilibrium for the mixture. However, whereas the surface armouring tends to stabilize the bed, construction of a layer of fine sediments at the subsurface also contributes to making it very unstable. These two contradictory effects explain the complex bed behaviours and the existence of very large bedload and slope fluctuations. Copyright © 2014 John Wiley & Sons, Ltd.     

Width control on event-scale deposition and evacuation of sediment in bedrock-confined channels

In mixed bedrock–alluvial rivers, the response of the system to a flood event can be affected by a number of factors, including coarse sediment availability in the channel, sediment supply from the hillslopes and upstream, flood sequencing and coarse sediment grain size distribution. However, the impact of along-stream changes in channel width on bedload transport dynamics remains largely unexplored. We combine field data, theory and numerical modelling to address this gap. First, we present observations from the Daan River gorge in western Taiwan, where the river flows through a 1 km long 20–50 m wide bedrock gorge bounded upstream and downstream by wide braidplains. We documented two flood events during which coarse sediment evacuation and redeposition appear to cause changes of up to several metres in channel bed elevation. Motivated by this case study, we examined the relationships between discharge, channel width and bedload transport capacity, and show that for a given slope narrow channels transport bedload more efficiently than wide ones at low discharges, whereas wider channels are more efficient at high discharges. We used the model sedFlow to explore this effect, running a random sequence of floods through a channel with a narrow gorge section bounded upstream and downstream by wider reaches. Channel response to imposed floods is complex, as high and low discharges drive different spatial patterns of erosion and deposition, and the channel may experience both of these regimes during the peak and recession periods of each flood. Our modelling suggests that width differences alone can drive substantial variations in sediment flux and bed response, without the need for variations in sediment supply or mobility. The fluctuations in sediment transport rates that result from width variations can lead to intermittent bed exposure, driving incision in different segments of the channel during different portions of the hydrograph. © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd     

The impact of inter-flood duration on non-cohesive sediment bed stability

Limited field and flume data suggests that both uniform and graded beds appear to progressively stabilize when subjected to inter-flood flows as characterized by the absence of active bedload transport. Previous work has shown that the degree of bed stabilization scales with duration of inter-flood flow, however, the sensitivity of this response to bed surface grain size distribution has not been explored. This article presents the first detailed comparison of the dependence of graded bed stability on inter-flood flow duration. Sixty discrete experiments, including repetitions, were undertaken using three grain size distributions of identical D₅₀ (4.8 mm); near-uniform (σ_g = 1.13), unimodal (σ_g = 1.63) and bimodal (σ_g = 2.08). Each bed was conditioned for between 0 (benchmark) and 960 minutes by an antecedent shear stress below the entrainment threshold of the bed (τ*_c50). The degree of bed stabilization was determined by measuring changes to critical entrainment thresholds and bedload flux characteristics. Results show that (i) increasing inter-flood duration from 0 to 960 minutes increases the average threshold shear stress of the D₅₀ by up to 18%; (ii) bedload transport rates were reduced by up to 90% as inter-flood duration increased from 0 to 960 minutes; (iii) the rate of response to changes in inter-flood duration in both critical shear stress and bedload transport rate is non-linear and is inversely proportional to antecedent duration; (iv) there is a grade dependent response to changes in critical shear stress where the magnitude of response in uniform beds is up to twice that of the graded beds; and (v) there is a grade dependent response to changes in bedload transport rate where the bimodal bed is most responsive in terms of the magnitude of change. These advances underpin the development of more accurate predictions of both entrainment thresholds and bedload flux timing and magnitude, as well as having implications for the management of environmental flow design. © 2019 John Wiley & Sons, Ltd. © 2019 John Wiley & Sons, Ltd.     

Bedload transport and temporal variation of non-uniform sediment in a seepage-affected alluvial channel

Understanding bedload transport fluctuations in rivers is crucial for complementing the existing knowledge on sediment transport theory. In this contribution, we use a natural-scale laboratory flume to analyse bedload transport fluctuations in non-uniform sand under normal flow conditions. Based on the significance of downward seepage, we incorporate the seepage effect on bedload transport over a non-uniform sand bed channel. The weight of the dry material was measured, and the volumetric transport rate per unit width (bedload transport rate) was estimated. An important observation is that the bedload transport rate initially rapidly increases with time and reaches a maximum value. Based on experimental data, we propose an empirical expression to estimate temporal bedload transport. In addition, an empirical model for bedload transport is proposed by incorporating downward seepage among other variables. The performance of several existing bedload transport formulae was also taken into account by the experimental datasets.     

The active layer in gravel-bed rivers: An empirical appraisal

The vertical position of the streambed–water boundary fluctuates during the course of sediment transport episodes, due to particle entrainment/deposition and bedform migration, amongst other hydraulic and bedload mechanisms. These vertical oscillations define a topmost stratum of the streambed (i.e. the ‘active layer or active depth’), which usually represents the main source of particles entrained during long and high-magnitude bedload transport episodes. The vertical extent of this layer is hence a capital parameter for the quantification of bedload volumes and a major driver of stream ecology in gravel-bed rivers. However, knowledge on how the active depth scales to flow strength and the nature of the different controls on the relation between the flow strength and the active depth is still scarce. In this paper we present a meta-analysis over active depth data coming from ~130 transport episodes extracted from a series of published field studies. We also incorporate our own field data for the rivers Ebro and Muga (unpublished), both in the Iberian Peninsula. We explore the database searching for the influence of flow strength, grain size, streambed mobility and channel morphology on the vertical extent of the active layer. A multivariate statistical analysis (stepwise multiple regression) confirms that the set of selected variables explains a significant amount of variance in the compiled variables. The analysis shows a positive scaling between active depth and flow strength. We have also identified some links between the active depth and particle travel distances. However, these relations are also largely modulated by other fluvial drivers, such as the grain size of the bed surface and the dominant channel macro-bedforms, with remarkable differences between plane-bed, step-pool and riffle-pool channels. © 2020 John Wiley & Sons, Ltd.     

Defining phases of bedload transport using piecewise regression

Differences in the transport rate and size of bedload exist for varying levels of flow in coarse‐grained channels. For gravel‐bed rivers, at least two phases of bedload transport, with notably differing qualities, have been described in the literature. Phase I consists primarily of sand and small gravel moving at relatively low rates over a stable channel surface. Transport rates during Phase II are considerably greater than Phase I and more coarse grains are moved, including material from both the channel surface and subsurface. Transition from Phase I to Phase II indicates initiation and transport of grains comprising the coarse surface layer common in steep mountain channels. While the existence of different phases of transport is generally acknowledged, the threshold between them is often poorly defined. We present the results of the application of a piecewise regression analysis to data on bedload transport collected at 12 gravel‐bed channels in Colorado and Wyoming, USA. The piecewise regression recognizes the existence of different linear relationships over different ranges of discharge. The inflection, where the fitted functions intersect, is interpreted as the point of transition from Phase I to Phase II transport; this is termed breakpoint. A comparison of grain sizes moved during the two phases shows that coarse gravel is rarely trapped in the samplers during Phase I transport, indicating negligible movement of grains in this size range. Gravel larger than about D₁₆ of the channel surface is more consistently trapped during Phase II transport. The persistence of coarse gravel in bedload samples provides good evidence that conditions suitable for coarse grain transport have been reached, even though the size of the sediment approaches the size limits of the sampler (76 mm in all cases). A relative breakpoint (R_br) was defined by the ratio between the discharge at the breakpoint and the 1·5‐year flow (a surrogate for bankfull discharge) expressed as a percentage. The median value of R_br was about 80 percent, suggesting that Phase II begins at about 80 percent of the bankfull discharge, though the observed values of R_br ranged from about 60 to 100 percent. Variation in this value appears to be independent of drainage area, median grain size, sorting of bed materials, and channel gradient, at least for the range of parameters measured in 12 gravel‐bed channels. Published in 2002 by John Wiley & Sons, Ltd.     

Observations of bedload transport in a gravel bed river during high flow using fiber‐optic DTS methods

The question: ‘how does a streambed change over a minor flood?’ does not have a clear answer due to lack of measurement methods during high flows. We investigate bedload transport and disentrainment during a 1.5‐year flood by linking field measurements using fiber optic distributed temperature sensing (DTS) cable with sediment transport theory and an existing explicit analytical solution to predict depth of sediment deposition from amplitude and phase changes of the diurnal near‐bed pore‐water temperature. The method facilitates the study of gravel transport by using near‐bed temperature time series to estimate rates of sediment deposition continuously over the duration of a high flow event coinciding with bar formation. The observations indicate that all gravel and cobble particles present were transported along the riffle at a relatively low Shields Number for the median particle size, and were re‐deposited on the lee side of the bar at rates that varied over time during a constant flow. Approximately 1–6% of the bed was predicted to be mobile during the 1.5‐year flood, indicating that large inactive regions of the bed, particularly between riffles, persist between years despite field observations of narrow zones of local transport and bar growth on the order ~3–5 times the median particle size. In contrast, during a seven‐year flood approximately 8–55% of the bed was predicted to become mobile, indicating that the continuous along‐stream mobility required to mobilize coarse gravel through long pools and downstream to the next riffle is infrequent. Copyright © 2017 John Wiley & Sons, Ltd.     

Re‐examination of Bagnold's empirical bedload ­formulae

Bagnold developed his formula for bedload transport over several decades, with the final form of the relation given in his 1980 paper. In this formula, bedload transport rate is a function of stream power above some threshold value, depth and grain size. In 1986, he presented a graph which illustrated the strength of his relation. A double‐log graph of bedload transport rate, adjusted for depth and grain size, versus excess stream power was shown to collapse along a line having a slope of 1·5. However, Bagnold based his analyses on limited data. In this paper, the formula is re‐examined using a large data set in order to define the most consistent empirical representation, and dimensional analysis is performed to seek a rationalization of the formula. Functional analysis is performed for the final version of the equation defined by Bagnold to determine if the slope of 1·5 is preserved and to assess the strength of the relation. Finally, relations between excess stream power and bedload transport are examined for a fixed slope of 1·5 to assess the performance of various depth and grain size adjustment factors. The rational scaling is found to provide the best result. Copyright © 2000 John Wiley & Sons, Ltd.     

Linkages between bedload displacements and topographic change

Changes in bed topography that build and maintain channel morphology are driven by the displacements of individual particles, either though their entrainment or deposition. However, the linkages between these topographic changes and individual grain displacements have not been comprehensively addressed, as many historical tracer studies have not included coincident topographic data. In this study, we compare the movements of bedload tracers to the differences in repeat topographic surveys across four gravel-bed river reaches. To do this, we apply a 1-D Bayesian survival process model to the starting and ending locations of tracers. This model estimates downstream trapping probabilities, which represent the likelihood that a given segment of channel will “trap” an entrained particle. We then adapt this model to estimate downstream trapping probabilities using digital elevation models of difference and compare the results. The estimates from the tracer and topographic trapping models showed general alignment, meaning that tracers were preferentially trapped in segments that experienced deposition along the channel. Thus, tracers in this study were able to identify downstream differences in bedload transport. The comparison also highlighted that tracer-estimated trapping probabilities were larger than topographically estimated ones. This supports previous observations that sediment travel distances estimated using tracers are shorter than those estimated using morphological methods. We find that the differences between these two estimates vary systematically across study environments. These variations are attributable to either study design (i.e., tracers being larger than the median size of the sediment that deforms the bed) or differences in compensating scour and fill. We explore potential causes for differences in compensating scour and fill, including hydrograph shape, sediment delivery regime, channel deformation style, and channel width, highlighting that morphodynamics needs to be considered in designing bedload tracer studies.