Field application of close‐range digital photogrammetry (CRDP) for grain‐scale fluvial morphology studies

In situ measurement of grain‐scale fluvial morphology is important for studies on grain roughness, sediment transport and the interactions between animals and the geomorphology, topics relevant to many river practitioners. Close‐range digital photogrammetry (CRDP) and terrestrial laser scanning (TLS) are the two most common techniques to obtain high‐resolution digital elevation models (DEMs) from fluvial surfaces. However, field application of topography remote sensing at the grain scale is presently hindered mainly by the tedious workflow challenges that one needs to overcome to obtain high‐accuracy elevation data. A recommended approach for CRDP to collect high‐resolution and high‐accuracy DEMs has been developed for gravel‐bed flume studies. The present paper investigates the deployment of the laboratory technique on three exposed gravel bars in a natural river environment. In contrast to other approaches, having the calibration carried out in the laboratory removes the need for independently surveyed ground‐control targets, and makes for an efficient and effective data collection in the field. Optimization of the gravel‐bed imagery helps DEM collection, without being impacted by variable lighting conditions. The benefit of a light‐weight three‐dimensional printed gravel‐bed model for DEM quality assessment is shown, and confirms the reliability of grain roughness data measured with CRDP. Imagery and DEM analysis evidences sedimentological contrasts between gravel bars within the reach. The analysis of the surface elevations shows the effect variable grain‐size and sediment sorting have on the surface roughness. By plotting the two‐dimensional structure functions and surface slopes and aspects we identify different grain arrangements and surface structures. The calculation of the inclination index allows determining the surface‐forming flow direction(s). We show that progress in topography remote sensing is important to extend our knowledge on fluvial morphology processes at the grain scale, and how a technique customized for use by fluvial geomorphologists in the field benefits this progress. Copyright © 2016 John Wiley & Sons, Ltd.     

Network‐scale dynamics of grain‐size sorting: implications for downstream fining,stream‐profile concavity,and drainage basin morphology

We explore the link between channel‐bed texture and river basin concavity in equilibrium catchments using a numerical landscape evolution model. Theory from homogeneous sediment transport predicts that river basin concavity directly increases with bed sediment size. If the effective grain size on a river bed governs its concavity, then natural phenomena such as grain‐size sorting and channel armouring should be linked to concavity. We examine this hypothesis by allowing the bed sediment texture to evolve in a transport‐limited regime using a two grain‐size mixture of sand and gravel. Downstream ?ning through selective particle erosion is produced in equilibrium. As the channel‐bed texture adjusts downstream so does the local slope. Our model predicts that it is not the texture of the original sediment mixture that governs basin concavity. Rather, concavity is linked to the texture of the sorted surface layer. Two different textural regimes are produced in the experiments: a transitional regime where the mobility of sand and gravel changes with channel‐bed texture, and a sand‐dominated region where the mobility of sand and gravel is constant. The concavity of these regions varies depending on the median gravel‐ or sand‐grain size, erosion rate, and precipitation rate. The results highlight the importance of adjustments in both surface texture and slope in natural rivers in response to changes in ?uvial and sediment inputs throughout a drainage network. This adjustment can only be captured numerically using multiple grain sizes or empirical downstream ?ning rules. Copyright © 2004 John Wiley & Sons, Ltd.     

Visual characterization technique for gravel‐cobble river bed surface sediments; validation and environmental applications Contribution to the programme of CIRSA (Centre Interuniversitaire de Recherche sur le Saumon Atlantique)

This paper presents an evaluation of the feasibility and the reliability of a visual characterization technique for gravel–cobble river bed surface substrate. Based on principal axis regressions, using phi scale (ϕ), comparisons of visual estimation and grid sampling techniques show that useful predictive relations (R² = 0·78–0·88) exist between visual estimates of the surface d₁₆, d₅₀ and d₈₄ and estimates obtained for the same percentiles with the grid sampling technique. Comparisons of visual estimation and the surface‐bulk sampling technique also indicate a predictive relation (R² = 0·70) between the d₅₀ of the two methods. Trained operators can visually estimate gravel–cobble bed surface d₁₆ to uncertainties of 41 per cent, d₅₀ to 15 per cent and d₈₄ to 11 per cent (for example, there is a 5·5 mm error on a d₈₄ size of 50 mm). Furthermore, evidence shows that if operators are properly trained, a calibration relation for each percentile can be applied independently of operators. This visual characterization allows effective detailed mapping of spatial patterns in substrate size distribution along extensive reaches of gravel‐bed rivers. The technique can be very useful in creating terrain models for various geomorphological, hydrological and biological applications such as the determination of entrainment thresholds, hydraulic roughness and substrate suitability for benthic insects or salmonid habitat. Copyright © 2001 John Wiley & Sons, Ltd.     

The spatial and temporal patterns of aggradation in a temperate,upland, gravel‐bed river

Intensive field monitoring of a reach of upland gravel‐bed river illustrates the temporal and spatial variability of in‐channel sedimentation. Over the six‐year monitoring period, the mean bed level in the channel has risen by 0·17 m with a maximum bed level rise of 0·5 m noted at one location over a five month winter period. These rapid levels of aggradation have a profound impact on the number and duration of overbank flows with flood frequency increasing on average 2·6 times and overbank flow time increasing by 12·8 hours. This work raises the profile of coarse sediment transfer in the design and operation of river management, specifically engineering schemes. It emphasizes the need for the implementation of strategic monitoring programmes before engineering work occurs to identify zones where aggradation is likely to be problematic. Exploration of the sediment supply and transfer system can explain patterns of channel sedimentation. The complex spatial, seasonal and annual variability in sediment supply and transfer raise uncertainties into the system's response to potential changes in climate and land‐use. Thus, there is a demand for schemes that monitor coarse sediment transfer and channel response. Copyright © 2009 John Wiley & Sons, Ltd.     

A hybrid method for size characterization of coarse subsurface fluvial sediments

This paper introduces and evaluates a novel method for ascertaining the grain‐size distribution of subsurface sediments that involves profoundly less sampling effort than standard methods. It is based on hybrid sampling principles previously applied to the construction of synthetic surface grain‐size distributions. The method is developed from an empirical demonstration of the approximate similarity of surface and subsurface grain‐size distributions when compared over a common range of sizes. Subsurface hybrid models are found to provide good facsimiles of grain‐size distributions de?ned using standard criteria and to yield distribution percentiles with millimetre accuracy. The technique is presented as an expedient alternative to standard methods for large, perennial gravel‐bed rivers. As this is a new technique, prudent application is advised in lieu of further investigation. Copyright © 2004 John Wiley & Sons, Ltd.     

The role of channel morphology on the mobility and dispersion of bed sediment in a small gravel‐bed stream

This study uses a unique 10‐year tracer dataset from a small gravel‐bed stream to examine bed mobility and sediment dispersion over long timescales and at a range of spatial scales. Seasonal tracer data that captured multiple mobilizing events was examined, while the effects of morphology on bed mobility and sediment dispersion were captured at three spatial scales: within morphological units (unit scale), between morphological units (reach scale) and between reaches with different channel morphologies (channel scale). This was achieved by analyzing both reach‐average mobility and travel distance data, as well as the development of ‘mobility maps’ that capture the spatial variability in tracer mobility within the channel. The tracer data suggest that sediment transport in East Creek remains near critical the majority of the time, with only rare large events resulting in high mobility rates and grain travel distances large enough to move sediment past dominant bedforms. While a variable capturing both the magnitude and frequency of flow events within a season yielded a better predictor to sediment mobility and dispersion than peak discharge alone, the distribution of events of different magnitude within the season played a large role in determining tracer mobility rates and travel distances. The effects of morphology differed depending on the analysis scale, demonstrating the importance of scale, and therefore study design, when examining the effect of morphology on sediment transport. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling the effects of pulsed versus chronic sand inputs on salmonid spawning habitat in a low‐gradient gravel‐bed river

It is widely recognized that high supplies of fine sediment, largely sand, can negatively impact the aquatic habitat quality of gravel‐bed rivers, but effects of the style of input (chronic vs. pulsed) have not been examined quantitatively. We hypothesize that a continuous (i.e. chronic) supply of sand will be more detrimental to the quality of aquatic habitat than an instantaneous sand pulse equal to the integrated volume of the chronic supply. We investigate this issue by applying a two‐dimensional numerical model to a 1 km long reach of prime salmonid spawning habitat in central Idaho. Results show that in both supply scenarios, sand moves through the study reach as bed load, and that both the movement and depth of sand on the streambed mirrors the hydrograph of this snowmelt‐dominated river. Predictions indicate greater and more persistent mortality of salmonid embryos under chronic supplies than pulse inputs, supporting our hypothesis. However, predicted mortality varies both with salmonid species and location of spawning. We found that the greatest impacts occur closer to the location of the sand input under both supply scenarios. Results also suggest that reach‐scale morphology may modulate the impact of sand loads, and that under conditions of high sand loading climate‐related increases in flow magnitude could increase embryo mortality through sand deposition, rather than streambed scour. Copyright © 2013 John Wiley & Sons, Ltd.     

The causes of bedload pulses in a gravel channel: the implications of bedload grain‐size distributions

Unsteady bedload transport was measured in two c. 5 m wide anabranches of a gravel‐bed braided stream draining the Haut Glacier d'Arolla, Switzerland, during the 1998 and 1999 melt seasons. Bedload was directly sampled using 152 mm square Helley–Smith type samplers deployed from a portable measuring bridge, and independent transport rate estimates for the coarser size fractions were obtained from the dispersion of magnetically tagged tracer pebbles. Bedload transport time series show pulsing behaviour under both marginal (1998) and partial (1999) transport regimes. There are generally weak correlations between transport rates and shear stresses determined from velocity data recorded at the measuring bridge. Characteristic parameters of the bedload grain‐size distributions (D₅₀, D₈₄) are weakly correlated with transport rates. Analysis of full bedload grain‐size distributions reveals greater structure, with a tendency for transport to become less size selective at higher transport rates. The bedload time series show autoregressive behaviour but are dif?cult to distinguish by this method. State–space plots, and associated measures of time‐series separation, reveal the structure of the time series more clearly. The measured pulses have distinctly different time‐series characteristics from those modelled using a one‐dimensional sediment routing model in which bed shear stress and grain size are varied randomly. These results suggest a mechanism of pulse generation based on irregular low‐amplitude bedforms, that may be generated in‐channel or may represent the advection of material supplied by bank erosion events. Copyright © 2003 John Wiley & Sons, Ltd.     

Assessing the effect of vegetation‐related bank strength on channel morphology and stability in gravel‐bed streams using numerical models

Bank strength due to vegetation dominates the geometry of small stream channels, but has virtually no effect on the geometry of larger ones. The dependence of bank strength on channel scale affects the form of downstream hydraulic geometry relations and the meandering‐braiding threshold. It is also associated with a lateral migration threshold discharge, below which channels do not migrate appreciably across their floodplains. A rational regime model is used to explore these scale effects: it parameterizes vegetation‐related bank strength using a dimensionless effective cohesion, C_r*. The scale effects are explored primarily using an alluvial state space defined by the dimensionless formative discharge, Q*, and channel slope, S, which is analogous to the Q–S diagrams originally used to explore meandering‐braiding thresholds. The analyses show that the effect of vegetation on both downstream hydraulic geometry and the meandering‐braiding threshold is strongest for the smallest streams in a watershed, but that the effect disappears for Q* > 10⁶. The analysis of the migration threshold suggests that the critical discharge ranges from about 5 m³/s to 50 m³/s, depending on the characteristic rooting depth for the vegetation. The analysis also suggests that, where fires frequently affect riparian forests, channels may alternate between laterally stable gravel plane‐bed channels and laterally active riffle‐pool channels. These channels likely do not exhibit the classic dynamic equilibrium associated with alluvial streams, but instead exhibit a cyclical morphologic evolution, oscillating between laterally stable and laterally unstable end‐members with a frequency determined by the forest fire recurrence interval. Copyright © 2008 John Wiley & Sons, Ltd.     

Particle path length distributions in meandering gravel‐bed streams: results from physical models

In gravel‐bed rivers with well‐de?ned pool–bar morphology, the path length of transported bed particles must be, at least during ‘channel‐forming’ ?ows, equal to the length scale of the morphology. This is the basis for some methods for estimating bed material transport rates. However, previous data, especially from ?eld tests, are often strongly positively skewed with mean much shorter than the pool–bar spacing. One possible explanation is that positively skewed distributions occur only in channels lacking distinct pool–bar topography or only at lower discharges in pool–bar channels. A series of ?ume experiments using ?uorescent tracers was used to measure path length distributions in low‐sinuosity meandering channels to assess the relation with channel morphology and ?ow conditions. At channel‐forming ?ows, 55 to 75 per cent of the tracer grains were deposited on the ?rst point bar downstream of the point of tracer input, with 15 per cent passing beyond the ?rst bar. Path length distributions are symmetrical with mean equal to the pool–bar spacing and can be described with a Cauchy distribution. In some cases there was a secondary mode close to the point of tracer introduction; this bimodal distribution ?ts a combined gamma–Cauchy distribution. Only when discharge was reduced below the channel‐forming ?ow were frequency distributions unimodal and positively skewed with no relation to the pool–bar spacing. Thus, path length distributions become more symmetrical, and mean path length increases to coincide with pool–bar spacing, as ?ow approaches channel‐forming conditions. This is a substantial modi?cation of existing models of particle transfer in gravel‐bed rivers. Copyright © 2003 John Wiley & Sons, Ltd.     

Benefits of design modifications to the Birkbeck bedload sampler illustrated by flash‐floods in an ephemeral gravel‐bed channel

The benefits of three simple modifications to the design of a Birkbeck bedload slot‐sampling system that has been continuously operating in Nahal Eshtemoa, Israel, since the early 1990s are demonstrated. The modifications include the deployment of a removable slot cover which delays the accumulation of sediment, so allowing sampling at late stages of a flood and, in conjunction with other samplers, extending the period of sampling during a flood wave; inclusion of a slot the size of which is adjustable so that that the probability of sampling the largest clast sizes in transit as bedload can be increased post‐installation, once knowledge is gained about the bedload grain‐size distribution; and a sampler side‐wall door that allows stratification and textural changes within the accumulated bedload to be identified, so promoting intelligent sampling of the deposit for grain‐size determination. Results from seven flash‐floods are presented and discussed, with recommendations for bedload monitoring, particularly in rivers where sediment flux is high and dynamic sediment records are inevitably short because of instrumental limitations. Copyright © 2006 John Wiley & Sons, Ltd.     

Effect of changes in fine‐grained matrix on bedload sediment transport in a gravel‐bed river

While clay and silt matrices of gravel‐bed rivers have received attention from ecologists concerned variously with the deteriorating environments of benthic and hyporheic organisms, their impact on sediment entrainment and transport has been explored less. A recent increase of such a matrix in the bed of Nahal Eshtemoa, an ephemeral river of the northern Negev, has more than doubled the boundary shear stress needed to initiate bedload, from 7 N m^‐2 (τ^* = 0.027) during the flash floods of 1991–2001 to 15 N m^‐2 (τ^* = 0.059) during those of 2008–2009. The relation between bedload flux and boundary shear stress continues to be well‐defined, but it is displaced. The matrix now contains a significant amount of silt and clay size material. The reasons for the increased entrainment threshold of bedload are explored. Large‐scale laser scanning of the dry bed reveals a reduction in grain‐scale morphological roughness, while artificial in situ tests of matrix integrity indicate considerable cohesion. The implications for adopting bed material sampling strategies that account for matrix development are assessed. Copyright © 2012 John Wiley & Sons, Ltd.     

Persistence of the surface texture of a gravel‐bed river during a large flood

We present herein clear field evidence for the persistence of a coarse surface layer in a gravel‐bed river during flows capable of transporting all grain sizes present on the channel bed. Detailed field measurements of channel topography and bed surface grain size were made in a gravel‐bed reach of the Colorado River prior to a flood in 2003. Runoff produced during the 2003 snowmelt was far above average, resulting in a sustained period of high flow with a peak discharge of 27 m³/s (170% of normal peak flow); all available grain sizes within the study reach were mobilized in this period of time. During the 2003 peak flow, the river avulsed immediately upstream of the study reach, thereby abandoning approximately one half kilometer of the former channel. The abandonment was rapid (probably within a few hours), leaving the bed texture essentially frozen in place at the peak of the flood. All locations sampled prior to the flood were resampled following the stream abandonment. In response to the high flow, the surface median grain size (D_50s) coarsened slightly in the outer part of the bend while remaining nearly constant along the inner part of the bend, resulting in an overall increase from 18 to 21 mm for the study reach. Thus, the coarse bed surface texture persisted despite shear stresses throughout the bend that were well above the critical entrainment value. This may be explained because the response of the bed texture to increases in flow strength depends primarily upon the continued availability of the various grain size percentiles in the supply, which in this case was essentially unlimited for all sizes present in the channel. Copyright © 2007 John Wiley & Sons, Ltd.     

A two‐dimensional morphodynamic model of gravel‐bed river with floodplain vegetation

Artificially straight river channels tend to be unstable, and ultimately develop into river meanders through bank erosion and point‐bar deposition. In this paper account is taken of the effects of riparian and floodplain vegetation on bank strength, floodplain flow resistance, shear stress partitioning, and bedload transport. This is incorporated into an existing 2D hydrodynamic‐morphological model. By applying the new model to an initially straight and single‐threaded channel, the way that its planform and cross‐sectional geometry evolve for different hydraulic and floodplain vegetation conditions is demonstrated. The results show the formation and upstream migration of gravel bars, confluence scouring and the development of meandering and braiding channel patterns. In cases where the channel becomes unstable, the instability grows out of bar formation. The resulting braiding patterns are similar to analytical results. The formation of a transition configuration requires a strong influence from vegetation. Copyright © 2010 John Wiley & Sons, Ltd.     

High‐frequency streamflow acquisition and bed level/flow angle estimates in a mountainous river using shallow‐water acoustic tomography

The acquisition of reliable discharge estimates is crucial in hydrological studies. This study demonstrates a promising acoustic method for measuring streamflow at high sampling rate for a long period using the fluvial acoustic tomography system (FATS). The FATS recently emerged as an innovative technique for continuous measurements of streamflow. In contrast to the traditional point/transect measurements of discharge, the FATS enables the depth‐averaged and range‐averaged flow velocity along the ray path to be measured in a fraction of a second. The field test was conducted in a shallow gravel‐bed river (0.9 m deep under low‐flow conditions, 115 m wide) for 1 month. The parameters (stream direction and bottom elevation) required for calculating the streamflow were deduced by a nonlinear regression to the discharge data from the well‐established rating curve. The cross‐sectional average velocities were automatically calculated from the acoustic data, which were collected on both riverbanks every 30 s. The FATS was connected to the internet so that the real‐time flow data could be obtained. The FATS captured discharge variations at a cut‐off frequency of approximately 70 day^?1. The stream exhibited temporal discharge changes at multiple time scales ranging from a few tens of minutes to days. Copyright © 2016 John Wiley & Sons, Ltd.     

Flow resistance in gravel‐bed channels with large‐scale roughness

A previously published mixing length (ML) model for evaluating the Darcy–Weisbach friction factor for a large‐scale roughness condition (depth to sediment height ratio ranging from 1 to 4) is brie?y reviewed and modi?ed (MML). Then the MML model and a modi?ed drag (MD) model are experimentally tested using laboratory measurements carried out for gravel‐bed channels and large‐scale roughness condition. This analysis showed that the MML gives accurate estimates of the Darcy–Weisbach coef?cient and for Froude number values greater than 0·5 the MML model coincides with the ML one. Testing of the MD model shows limited accuracy in estimating ?ow resistance. Finally, the MML and MD models are compared with the performance of a quasi‐theoretical (QT) model deduced applying the P‐theorem of the dimensional analysis and the incomplete self‐similarity condition for the depth/sediment ratio and the Froude number. Using the experimental gravel‐bed data to calibrate the QT model, a constant value of the exponent of the Froude number is determined while two relationships are proposed for estimating the scale factor and the exponent of the depth/sediment ratio. This indirect estimate procedure of the coef?cients (b₀, b₁ and b₂) of the QT model can produce a negligible overestimation or underestimation of the friction factor. Copyright © 2003 John Wiley & Sons, Ltd.     

Riffle‐pool morphometry and stage‐dependant morphodynamics of a large floodplain river (Vereinigte Mulde,Sachsen‐Anhalt,Germany)

Riffle‐pool sequences are a common feature of gravel‐bed rivers. However, mechanisms of their generation and maintenance are still not fully understood. In this study a monitoring approach is employed that focuses on analysing cross‐sectional and longitudinal channel geometry of a large floodplain river (Vereinigte Mulde, Sachsen‐Anhalt, Germany) with a high temporal and spatial resolution, in order to conclude from stage‐dependant morphometric changes to riffle and pool maintaining processes. In accordance with previous authors, pool cross‐sections of the Mulde River are narrow and riffle cross‐sections are wide suggesting that they should rather be addressed as two general types of channel cross‐sections than solely as bedforms. At high flows, riffles and pools in the study reaches changed in length and height but not in position. Pools were scoured and riffles aggraded, a development which was reversed during receding flows below the threshold of 0·4Q_bf (40% bankfull discharge). An index for the longitudinal amplitude of riffle‐pool sequences, the bed undulation intensity or bedform amplitude, is introduced and proved to be highly significant as a form parameter, its first derivative as a process parameter. The process of pool scour and riffle fill is addressed as bedform maintenance or bedform accentuation. It is indicated by increasing longitudinal bed amplitudes. According to the observed dynamics of bed amplitudes, maintenance of riffle‐pool sequences lags behind discharge peaks. Maximum bed amplitudes may be reached with a delay of several days after peak discharges. Increasing bed undulation intensity is interpreted to indicate bed mobility. Post‐flood decrease of the bed undulation intensity indicates a retrograde phase when transport from pools to riffles has ceased and bed mobility is restricted to riffle tails and heads of pools. This type of transport behaviour is referred to as disconnected mobility. The comparison of two river reaches, one with undisturbed sediment supply, the other with sediment deficit, suggests that high bed undulation intensity values at low flows indicate sediment deficit and potentially channel degrading conditions. It is more generally hypothesized that channel bed undulations constitute a major component of form roughness and that increased bed amplitudes are an important feature of channel bed adjustment to sediment deficit be it temporally during late floods or permanently due to a supply limitation of bedload. Copyright © 2011 John Wiley & Sons, Ltd.     

Comparison of hydraulic geometry between sand‐ and gravel‐bed rivers in relation to channel pattern discrimination

A comparison has been made between the hydraulic geometry of sand‐ and gravel‐bed rivers, based on data from alluvial rivers around the world. The results indicate a signi?cant difference in hydraulic geometry among sand‐ and gravel‐bed rivers with different channel patterns. On this basis, some diagrams for discrimination of meandering and braided channel patterns have been established. The relationships between channel width and water discharge, between channel depth and water discharge, between width–depth ratio and water discharge and between channel slope and water discharge can all be used for channel pattern discrimination. The relationship between channel width and channel depth can also be used for channel pattern discrimination. However, the accuracy of these relationships for channel pattern discrimination varies, and the depth–discharge relationship is a better discriminator of pattern type than the classic slope–discharge function. The cause for this difference has been explained qualitatively. To predict the development of channel patterns under different natural conditions, the pattern discriminator should be searched on the basis of independent or at least semi‐independent variables. The relationship between stream power and bed material grain size can be used to discriminate channel patterns, which shows a better result than the discriminator using the slope–discharge relationship. Copyright © 2004 John Wiley & Sons, Ltd.     

Effects of helical flow in one‐dimensional modelling of sediment distribution at river bifurcations

Complex flow processes at river bifurcations and the influence of the layout of a bifurcation make it difficult to predict sediment distribution over the downstream branches in case bedload transport dominates. In one‐dimensional models we need a nodal point relationship that prescribes the distribution of sediment over the downstream branches. We have identified which factors need to be included in such a relationship for the division of bedload transport at bifurcations. Next, irrotational flow theory for idealized geometries has been used to derive a simple physics‐based nodal point relationship that accounts for the effects of helical flow in the situation that a channel takes off under an angle from a straight main channel. This first step towards a complete nodal point relationship is applicable to bedload transport situations if the flow is clearly curved and if there is no pronounced bed topography. The relationship has been tested against data from a unique set of laboratory measurements, numerical data and data from a scale model of the Rhine bifurcation at Pannerden in the Netherlands. We find that the derived model yields a reasonable prediction of the sediment division over the downstream branches, and yields better predictions than the Wang et al. model for the situation considered. Considering the relative complexity and limited accuracy of the nodal point relationship for the effect of helical flow alone, however, we conclude thatderiving a practical physics‐based 1‐D relationship including all relevant processes is not feasible. We therefore recommend 2‐D or 3‐D modelling for all cases in general where morphological evolution depends on the division of bedload transport at bifurcations. Copyright © 2012 John Wiley & Sons, Ltd.