Testing bedload transport formulae using morphologic transport estimates and field data: lower Fraser River,British Columbia

Morphologic transport estimates available for a 65‐km stretch of Fraser River over the period 1952–1999 provide a unique opportunity to evaluate the performance of bedload transport formulae for a large river over decadal time scales. Formulae tested in this paper include the original and rational versions of the Bagnold formula, the Meyer‐Peter and Muller formula and a stream power correlation. The generalized approach adopted herein does not account for spatial variability in flow, bed structure and channel morphology. However, river managers and engineers, as well as those studying rivers within the context of long‐term landscape change, may find this approach satisfactory as it has minimal data requirements and provides a level of process specification that may be commensurable with longer time scales. Hydraulic geometry equations for width and depth are defined using morphologic maps based on aerial photography and bathymetric survey data. Comparison of transport predictions with bedload transport measurements completed at Mission indicates that the original Bagnold formula most closely approximates the main trends in the field data. Sensitivity analyses are conducted to evaluate the impact of inaccuracies in input variables width, depth, slope and grain size on transport predictions. The formulae differ in their sensitivity to input variables and between reaches. Average annual bedload transport predictions for the four formulae show that they vary between each other as well as from the morphologic transport estimates. The original Bagnold and Meyer‐Peter and Muller formulae provide the best transport predictions, although the former underestimates while the latter overestimates transport rates. Based on our findings, an error margin of up to an order of magnitude can be expected when adopting generalized approaches for the prediction of bedload transport. Copyright © 2005 John Wiley & Sons, Ltd.     

Bedload transport in two gravel-bedded streams

Bedload transport measurements in two upland streams are considered as a function of the excess stream power exerted on the bed by the flow. During low flows when the framework gravels remain undisturbed, fine sediments are winnowed from the bed-surface layer once a threshold of 3·4 W m^?2 is exceeded and the transport rate is strongly supply limited. However for stream powers in excess of 15 W m^?2 framework gravels are mobilized and the efficiency of the transport process approaches a local maximum of about 1 per cent for discharges up to 2/3 of bankfull. An inverse depth dependence in the efficiency of the transport process was noted but although bedload calibre increased as a function of discharge its influence on efficiency could not be demonstrated. However it was suspected that the size-sorting relationships of the bed-material in a number of rivers in relation to the transport efficiency might profitably be examined further.     

Parsimonious sediment transport equations based on Bagnold's stream power approach

It is increasingly recognized that effective river management requires a catchment scale approach. Sediment transport processes are relevant to a number of river functions but quantifying sediment fluxes at network scales is hampered by the difficulty of measuring the variables required for most sediment transport equations (e.g. shear stress, velocity, and flow depth). We develop new bedload and total load sediment transport equations based on specific stream power. These equations use data that are relatively easy to collect or estimate throughout stream networks using remote sensing and other available data: slope, discharge, channel width, and grain size. The new equations are parsimonious yet have similar accuracy to other, more established, alternatives. We further confirm previous findings that the dimensionless critical specific stream power for incipient particle motion is generally consistent across datasets, and that the uncertainty in this parameter has only a minor impact on calculated sediment transport rates. Finally, we test the new bedload transport equation by applying it in a simple channel incision model. Our model results are in close agreement to flume observations and can predict incision rates more accurately than a more complicated morphodynamic model. These new sediment transport equations are well suited for use at stream network scales, allowing quantification of this important process for river management applications. Copyright © 2017 John Wiley & Sons, Ltd.     

Predicting sediment transport by interrill overland flow on rough surfaces

Modelling soil erosion requires an equation for predicting the sediment transport capacity by interrill overland flow on rough surfaces. The conventional practice of partitioning total shear stress into grain and form shear stress and predicting transport capacity using grain shear stress lacks rigour and is prone to underestimation. This study therefore explores the possibility that inasmuch as surface roughness affects flow hydraulic variables which, in turn, determine transport capacity, there may be one or more hydraulic variables which capture the effect of surface roughness on transport capacity suffciently well for good predictions of transport capacity to be achieved from data on these variables alone. To investigate this possibility, regression analyses were performed on data from 1506 flume experiments in which discharge, slope, water temperature, rainfall intensity, and roughness size, shape and concentration were varied. The analyses reveal that 89·8 per cent of the variance in transport capacity can be accounted for by excess flow power and flow depth. Including roughness size and concentration in the regression improves that explained variance by only 3·5 per cent. Evidently, flow depth, when used in combination with excess flow power, largely captures the effect of surface roughness on transport capacity. This finding promises to simplify greatly the task of developing a general sediment equation for interrill overland flow on rough surfaces. Copyright © 1998 John Wiley & Sons, Ltd.     

Sediment mobility and bedload transport conditions in an alpine stream

The mobility conditions of bedload transport in an alpine high‐gradient step–pool stream (Rio Cordon) are analysed. Since 1986, a device system at the downstream end section of the stream has been operating in order to monitor the water discharge, suspended sediment and bedload transport. Sediment distribution of bedload transported by various floods has been analysed, and equal‐mobility evidence is recognized only for the high‐magnitude flows ever recorded (RI > 50 years). The thresholds for size‐selective and equal‐mobility transport conditions are identified and quantified by using both data provided by the fractional transport rate and by length displacements of marked particles. Size‐selective bedload transport seems to dominate when the critical shear stress of the size fractions τ_ci considered is exceeded, whereas the equal‐mobility condition is approached as levels of excess shear stress become higher (τ_eqi = 1·45τ_ci). Copyright © 2006 John Wiley & Sons, Ltd.     

Dynamics of bedload transport in Turkey brook,a coarse-grained alluvial channel

Automatic and continuously recording samplers are deployed in a Hertfordshire gravel-bed stream to show that bedload transport is related to stream power. The pattern is similar to that already established for North American channels but, because the record is so detailed, it is possible to identify the cause of the considerable scatter that is normal in such relationships. A major factor is the occurrence of rhythmic pulses in bedload discharge that are not matched by similar fluctuations in hydraulic variables. It is suggested that these pulses reflect downstream differences in the concentration of mobile particles in a slow-moving traction carpet, and that they may be likened to kinematic waves. The record also reveals that the threshold of sediment transport—always presumed hithero to be associated with incipient motion—is related to the cessation of bedload transport in a river flood. Indeed, the mean value of stream power at the finish of bedload transport is only 20 percent of that prevailing at the moment of incipient sediment motion. Because of this, there is an inevitably poor correlation between actual bedload transport rates and those predicted by bedload equations which rely upon a single traction threshold. These new data show that the general inverse relationship between bedload discharge and water-depth : grain-size ratio proposed by Bagnold (1977, 1980) is not universal. Transport efficiency for this gravel-bed stream is typically 0.05 per cent of available stream power, which compares with 1.6 per cent for a river moving both gravel and sand, and 5 per cent for another channel where bedload is composed predominantly of sand-sized particles. It is argued that coarse and fine-grained alluvial channels may need to be considered separately. By allowing for differences in traction threshold at the beginning and end of bedload events, and by averaging bedload discharge flood by flood in order to smooth out the effect of pulses, it is possible to achieve a reasonably good prediction of average bedload transport rate in terms of stream power.     

Nondimensional sediment transport capacity of sand soils and its response to parameter in the Loess Plateau of China

Soil erosion is a major contributor to land degradation in the Loess Plateau in China. To clarify the sediment transport capacity of overland flow influenced by hydraulic parameters, such as shear stress, sand shear stress (hydraulic gradient partition method and hydraulic radius partition method), mean flow velocity, Froude number, stream power, and unit stream power, indoor experiments with eight-unit-width flow discharges from 0.0667 × 10⁻³ to 0.3333 × 10⁻³ m²·s⁻¹, six slope gradients from 3.49 to 20.79%, and two kinds of sand soils (d₅₀ = 0.17 and 0.53 mm) were systematically investigated. A nondimensional method was adopted in data processing. Results showed that there was a partition phenomenon of relation curves because of the different median grain diameters. The correlation between the nondimensional stream power and nondimensional sediment transport capacity was the highest, followed by the correlation between the nondimensional unit stream power and nondimensional sediment transport capacity. However, there was a poor correlation between the flow intensity indices of velocity category and nondimensional sediment transport capacity. Nondimensional stream power, nondimensional unit stream power, and nondimensional shear stress could predict sediment transport capacity well. Ignoring the partition phenomenon of the relation curves, stream power could be used to predict sediment transport capacity, with a coefficient of determination of .85. Furthermore, a general flow intensity index was obtained to predict sediment transport capacity of overland flow. Finally, an empirical formula for predicting sediment transport capacity with a coefficient of determination of .90 was established by multiple regression analyses based on the general flow intensity index. During the analysis between measured sediment transport capacities in present study and predicted values based on Zhang model, Mahmoodabadi model, and Wu model, it was found that these three models could not accurately predict sediment transport capacities of this study because different models are estimated on the basis of different experimental conditions.     

Evolution of grain size distributions and bed mobility during hydrographs in gravel-bed braided rivers

Evolution of bed material mobility and bedload grain size distributions under a range of discharges is rarely observed in braiding gravel-bed rivers. Yet, the changing of bedload grain size distributions with discharge is expected to be different from laterally-stable, threshold, channels on which most gravel bedload theory and observation are based. Here, simultaneous observations of flow, bedload transport rate, and morphological change were made in a physical model of a gravel-bed braided river to document the evolution of grain size distributions and bed mobility over three experimental event hydrographs. Bedload transport rate and grain size distributions were measured from bedload samples collected in sediment baskets. Morphological change was mapped with high-resolution (~1 mm precision) digital elevation models generated from close-range digital photogrammetry. Bedload transport rates were extremely low below a discharge equivalent to ~50% of the channel-forming discharge (dimensionless stream power ~70). Fractional transport rates and plots of grain size distributions indicate that the bed experienced partial mobility at low discharge when the coarsest grains on the bed were immobile, weak selective mobility at higher discharge, and occasionally near-equal mobility at peak channel-forming discharge. The transition to selective mobility and increased bedload transport rates coincided with the lower threshold for morphological change measured by the morphological active depth and active width. Below this threshold discharge, active depths were of the order of D₉₀ and active widths were narrow (< 3% of wetted width). Above this discharge, both increased so that at channel-forming discharge, the active depth had a local maximum of 9D₉₀ while active width was up to 20% of wetted width. The modelled rivers approached equal mobility when rates of morphological change were greatest. Therefore, changes in the morphological active layer with discharge are directly connected to the conditions of bed mobility, and strongly correlated with bedload transport rate. © 2018 John Wiley & Sons, Ltd.     

Bedload transport measurements at the Erlenbach stream with geophones and automated basket samplers

In the Erlenbach stream, a pre‐alpine steep channel in Switzerland, sediment transport has been monitored for more than 25 years. Near the confluence with the main valley river, stream flow is monitored and sediment is collected in a retention basin with a capacity of about 2000 m³. The basin is surveyed at regular intervals and after large flood events. In addition, sediment transport has been continuously monitored with piezoelectric bedload impact and geophone sensors since 1986. In 2008–2009, the measuring system in the Erlenbach stream was enhanced by installing an automatic system to obtain bedload samples. Movable metal baskets are mounted on a rail at the downstream wall of the large check dam above the retention basin, and they can be moved automatically into the flow to take bedload transport samples. The wire mesh of the baskets has a spacing of 10 mm to sample all sediment particles coarser than this size (which is about the limiting grain size detected by the geophones). The upgraded measuring system permits to obtain bedload samples over short sampling periods and to measure the grain size distribution of the transported material and its variation over time and with discharge. The analysis of calibration relationships for the geophone measuring system confirms findings from very similar measurements which were performed until 1999 with piezoelectric bedload impact sensors; there is a linear relationship between impulse counts and bedload mass passing over the sensors. Findings from flume experiments are used to discuss the most important factors which affect the calibration of the geophone signal. The bedload transport rates as measured by the moving baskets are among the highest measured in natural streams, with values of the order of several kilograms per meter per second. Copyright © 2012 John Wiley & Sons, Ltd.     

Channel morphology and bedload pulses in braided rivers: a laboratory study

Bedload pulses in gravel-bed rivers have been widely reported in recent years and attempts have been made to relate them to channel morphology. Bedload transport and channel morphology were measured in a small-scale generic model of braided gravel-bed streams. Two experiments are described in which braided channels developed in a 14 m × 3 m sand tray. Total bedload output from the tray was weighed every 15 minutes. Stream bed geometry was surveyed every four hours. Pulses were observed in the bedload output time series, and were qualitatively related to the channel morphology immediately upstream of the measuring section. The Bagnold (1980) bedload equation generally overpredicts measured bedload transport rates when applied to channels that were in equilibrium or aggrading. Underprediction occurred when applied to degrading channels. Aggradation was associated with channel multiplication and bar deposition. Channel pattern simplification occurred when degradation took place, and bars emerged from the water flow. Development of phases of aggradation and degradation is dependent upon the three-dimensional geometry of the stream beds. Spatial and temporal feedback loops can be identified, enabling links between channel morphology and bedload transport rate to be directly identified.     

Effect of particle density and inflow concentration of suspended sediment on bedload transport in rill flow

Laboratory flume experiments were carried out to evaluate the effect of particle density on bedload transport of sand‐sized particles and the effect of a suspended load of clay particles (kaolinite) on bedload transport of sand‐sized particles in rill flow conditions. Three materials in the range 400–600 µm were selected to simulate bedload transport of primary particles and aggregates: sand (2650 kg/m³), crushed brick (2450 kg/m³) and anthracite (1300–1700 kg/m³). In the two first experiments, two different methods were applied to determine bedload transport capacity of coarse particles for various conditions of flow discharge (from 2 to 15 L/min) and slope (2.2, 3 and 4%). In the third experiment, clear water was replaced with kaolinite–water mixture and bedload transport capacity of crushed brick particles was determined for a 4% slope and different concentrations of kaolinite (0, 7, 41 and 84 g/L). The results showed that bedload transport increased significantly with the decrease in particle density but the effect of particle density on transport rates was much less important than flow discharge. Velocity measurements of clear flow, flow mixed with coarse particles and coarse particles confirmed the existence of a differentiation between suspended load and bedload. In these experimental conditions, suspended load of kaolinite did not affect bedload rates of crushed brick particles. Three transport capacity formulae were tested against observed bedload rates. A calibration of the Foster formula revealed that the shear stress exponent should be greater than 1.5. The Low and the Govers unit stream power (USP) equations were then evaluated. The Low equation was preferred for the prediction of bedload rates of primary particles but it was not recommended in the case of aggregates of low density because of the limited experimental conditions applied to derive this equation. Copyright © 2008 John Wiley & Sons, Ltd.     

Lithology‐controlled evolution of stream bed sediment and basin‐scale sediment yields in adjacent mountain watersheds,Idaho, USA

The composition, grain‐size, and flux of stream sediment evolve downstream in response to variations in basin‐scale sediment delivery, channel network structure, and diminution during transport. Here, we document downstream changes in lithology and grain size within two adjacent ~300 km² catchments in the northern Rocky Mountains, USA, which drain differing mixtures of soft and resistant rock types, and where measured sediment yields differ two‐fold. We use a simple erosion–abrasion mass balance model to predict the downstream evolution of sediment flux and composition using a Monte Carlo approach constrained by measured sediment flux. Results show that the downstream evolution of the bed sediment composition is predictably related to changes in underlying geology, influencing the proportion of sediment carried as bedload or suspended load. In the Big Wood basin, particle abrasion reduces the proportion of fine‐grained sedimentary and volcanic rocks, depressing bedload in favor of suspended load. Reduced bedload transport leads to stronger bed armoring, and coarse granitic rocks are concentrated in the stream bed. By contrast, in the North Fork Big Lost basin, bedload yields are three times higher, the stream bed is less armored, and bed sediment becomes dominated by durable quartzitic sandstones. For both basins, the geology‐based mass balance model can reproduce within ~5% root‐mean‐square error the composition of the bed substrate using realistic erosion and abrasion parameters. As bed sediment evolves downstream, bedload fluxes increase and decrease as a function of the abrasion parameter and the frequency and size of tributary junctions, while suspended load increases steadily. Variable erosion and abrasion rates produce conditions of variable bed‐material transport rates that are sensitive to the distribution of lithologies and channel network structure, and, provided sufficient diversity in bedrock geology, measurements of bed sediment composition allow for an assessment of sediment source areas and yield using a simple modeling approach. Copyright © 2016 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.     

A rational sediment transport scaling relation based on dimensionless stream power

The concept of stream channel grade – according to which a stream channel reach will adjust its gradient, S, in order to transport the imposed sediment load having magnitude Q_b and characteristic grain size D_b, with the available discharge Q (Mackin, 1948 , Geological Society of America Bulletin 59 : 463–512; Lane, 1955 , American Society of Civil Engineers, Proceedings 81 : 1–17) is one of the most influential ideas in fluvial geomorphology. Herein, we derive a scaling relation that describes how externally imposed changes in either Q_b or Q can be accommodated by changes in the channel configuration, described by the energy gradient, mean flow depth, characteristic grain size and a parameter describing the effect of bed surface structures on grain entrainment. One version of this scaling relation is based on the dimensionless bed material transport parameter (W*) presented by Parker and Klingeman ( 1982 , Water Resources Research 18 : 1409–1423). An equivalent version is based on a new dimensionless transport parameter (E*) using dimensionless unit stream power. This version is nearly identical to the relation based on W*, except that it is independent of flow resistance. Both versions of the scaling relation are directly comparable to Lane's original relation. In order to generate this stream power‐based scaling relation, we derived an empirical transport function relation relating E* to dimensionless stream power using data from a wide range of stable, bed load‐dominated channels: the form of that transport function is based on the understanding that, while grain entrainment is related to the forces acting on the bed (described by dimensionless shear stress), sediment transport rate is related to the transfer of momentum from the fluid to the bed material (described by dimensionless stream power). Copyright © 2010 John Wiley & Sons, Ltd.     

Back‐calculation of bedload transport in steep channels with a numerical model

In August 2005 severe flood events occurred in the Alps. A sediment routing model for steep torrent channel networks called SETRAC has been applied to six well‐documented case study streams with substantial sediment transport in Austria and Switzerland. For these streams information on the sediment budget along the main channel is available. Flood hydrographs were reconstructed based on precipitation data and stream gauges in neighbouring catchments. Different scenarios are modelled and discussed regarding sediment availability and the effect of armouring and macro‐roughness on sediment transport calculations. The simulation results show the importance of considering increased flow resistance for small relative flow depth when modelling bedload transport during high‐intensity flood events in torrents and mountain rivers. Without any correction of increased flow resistance using a reduced energy slope, the predicted bedload volumes are about a factor of 10 higher on average than the observed values. Simulation results were also used for a back‐calculation of macro‐roughness effects from bedload transport data, and compared with an independent estimate of flow resistance partitioning based on flow resistance data. Copyright © 2010 John Wiley & Sons, Ltd.     

Relation between flow,surface‐layer armoring and sediment transport in gravel‐bed rivers

This study investigates trends in bed surface and substrate grain sizes in relation to reach‐scale hydraulics using data from more than 100 gravel‐bed stream reaches in Colorado and Utah. Collocated measurements of surface and substrate sediment, bankfull channel geometry and channel slope are used to examine relations between reach‐average shear stress and bed sediment grain size. Slopes at the study sites range from 0·0003 to 0·07; bankfull depths range from 0·2 to 5 m and bankfull widths range from 2 to 200 m. The data show that there is much less variation in the median grain size of the substrate, D_50s, than there is in the median grain size of the surface, D₅₀; the ratio of D₅₀ to D_50s thus decreases from about four in headwater reaches with high shear stress to less than two in downstream reaches with low shear stress. Similar trends are observed in an independent data set obtained from measurements in gravel‐bed streams in Idaho. A conceptual quantitative model is developed on the basis of these observations to track differences in bed load transport through an idealized stream system. The results of the transport model suggest that downstream trends in total bed load flux may vary appreciably, depending on the assumed relation between surface and substrate grain sizes. Copyright © 2007 John Wiley & Sons, Ltd.     

Sediment transport in Swiss torrents

Sediment loads have been measured in six Swiss mountain torrents over several decades. Most of these torrent catchments are situated in the prealpine belt. They have catchment areas of between 0·5 and 1·7 km². Bedslopes at the measuring sites vary between 5 and 17 per cent, and peak discharges up to 12 m³ s⁻¹ have been recorded. Geophone sensors installed in the Erlenbach stream allow bedload transport activity to be monitored and sediment volumes associated with each flood event to be determined. A detailed analysis of the measurements in this stream results in an empirical equation in which the sediment load per flood event is expressed as a function of the effective runoff volume (discharges above the threshold for bedload motion) and of the normalized peak discharge. For the total of 143 investigated flood events in the Erlenbach stream, the deviation of the predicted from the measured value is within a factor of two for more than two-thirds of all events. A distinction can be made between summer and winter events in analysing the bedload transport events. The summer events, mainly caused by thunderstorms, transport comparatively larger sediment loads than the winter events. For the other investigated streams, the periods of the deposited sediment volume surveys cover in general several flood events. An analysis is performed analogous to that for the Erlenbach stream. The sediment loads show a similar dependency on the two factors effective runoff volume and normalized peak discharge. However, the exponents of these factors in the power law expressions differ from stream to stream. A comparison of the investigated stream shows that some of the variation can be explained by considering the bedslope above the measuring site. The inclusion of a bedslope factor is in agreement with laboratory investigations on bedload transport. © 1997 John Wiley & Sons, Ltd.     

‘Bedload’ dynamics: Grain-grain interactions in water flows

Owing to experimental difficulties, the transport stage at which collisions between moving ‘bedload’ grains might become significant has never been investigated, yet the existence or otherwise of such collisions is of some importance in the understanding of the mechanics of sediment transport, in particular the theory developed by Bagnold. Application of the basic principles of gaseous kinetic theory to ‘bedload’ grains moving in saltant trajectories and the adoption of a ‘characteristic’ saltation path leads to the prediction that grain-grain collisions should dominate in the transport of coarse sands over plane beds in water flows above a transport stage of about 2, i.e. when the mean boundary fluid shear stress exceeds the critical boundary shear stress for grain motion by about 4 times. Above this stage interrupted saltations should always occur, with the ‘bedload’ grains held above the stationary bed by a combination of fluid and solid momentum transfer mechanisms. A classification of the types of grain motions is given and evidence is presented for the existence of an upward decrease in grain collision frequency and of grain concentration at the top of the ‘bedload’ zone.     

Temporal variations in bedload transport rates: The effect of progressive bed armouring

The quantitative bedload transport data that are presently available confirm that the generalized bedload transport rate-stream power relationship is applicable to natural streams. However, the bedload transport rate is not solely dependent upon hydraulic parameters, but also upon the inter-relationship between bed material characteristics and flow properties. Segregation of the surficial bed material, as expressed through the development of an armour coat, limits the availability of transportable material. Under such circumstances observed bedload transport rates are less than the predicted values. The effect which the development of an armoured surface has upon the bedload transport rate is described with reference to bedload and bed material sampling in the Borgne d'Arolla, Valais, Switzerland. The data refer to two periods when the resumption of baseflow conditions following flood events which were of a sufficient magnitude to transport all but the coarsest (0·3–0·5 m) particles on the streambed, provided the opportunity for the bed to adjust to a comparatively stable flow regime. Observed and predicted bedload transport rate-stream power relationships are compared. The theoretical relationship does not adequately describe conditions in some gravel-bed channels, since it fails to take into account the effect which armouring may have upon the supply of transportable material.     

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.