Influence of bed clusters and size gradation on operational time distribution for non‐uniform bed‐load transport

The operational time distribution (OTD) defines the time for bed‐load sediment spent in motion, which is needed to characterize the random nature of sediment transport. This study explores the influence of bed clusters and size gradation on OTD for non‐uniform bed‐loads. First, both static and mobile bed armouring experiments were conducted in laboratorial flumes to monitor the transport of mixed sand/gravel sediments. Only in the mobile armouring experiment did apparent bed clusters develop, because of stable feeding and a longer transport period. Second, a generalized subordinated advection (GSA) model was applied to quantify the observed dynamics of tracer particles. Results show that for the static armour layer (without sediment feed), the best‐fit OTD assigns more weight to the large displacement of small particles, likely because of the size‐selective entrainment process. The capacity coefficient in the GSA model, which affects the width of the OTD, is space dependent only for small particles whose dynamics can be significantly affected by larger particles and whose distribution is more likely to be space dependent in a mixed sand and gravel system. However, the OTD for the mobile armour layer (with sediment recirculation) exhibited longer tails for larger particles. This is because the trailing edge of larger particles is more resistant to erosion, and their leading front may not be easily trapped by self‐organized bed clusters. The strong interaction between particle–bed may cause the capacity coefficient to be space‐dependent for bed‐load transport along mobile armour layers. Therefore, the combined laboratory experiments and stochastic model analysis show that the OTD may be affected more by particle–bed interactions (such as clusters) than by particle–particle interactions (e.g. hiding and exposing), and that the GSA model can quantify mixed‐size sand/gravel transport along river beds within either static or mobile armour layers. Copyright © 2016 John Wiley & Sons, Ltd.     

A bed‐load transport model for rough turbulent open‐channel flows on plane beds

Data from flume studies are used to develop a model for predicting bed‐load transport rates in rough turbulent two‐dimensional open‐channel flows moving well sorted non‐cohesive sediments over plane mobile beds. The object is not to predict transport rates in natural channel flows but rather to provide a standard against which measured bed‐load transport rates influenced by factors such as bed forms, bed armouring, or limited sediment availability may be compared in order to assess the impact of these factors on bed‐load transport rates. The model is based on a revised version of Bagnold's basic energy equation i_bs_b = e_bω, where i_b is the immersed bed‐load transport rate, ω is flow power per unit area, e_b is the efficiency coefficient, and s_b is the stress coefficient defined as the ratio of the tangential bed shear stress caused by grain collisions and fluid drag to the immersed weight of the bed load. Expressions are developed for s_b and e_b in terms of G, a normalized measure of sediment transport stage, and these expressions are substituted into the revised energy equation to obtain the bed‐load transport equation i_b = ω G ^3·4. This equation applies regardless of the mode of bed‐load transport (i.e. saltation or sheet flow) and reduces to i_b = ω where G approaches 1 in the sheet‐flow regime. That i_b = ω does not mean that all the available power is dissipated in transporting the bed load. Rather, it reflects the fact that i_b is a transport rate that must be multiplied by s_b to become a work rate before it can be compared with ω. It follows that the proportion of ω that is dissipated in the transport of bed load is i_bs_b/ω, which is approximately 0·6 when i_b = ω. It is suggested that this remarkably high transport efficiency is achieved in sheet flow (1) because the ratio of grain‐to‐grain to grain‐to‐bed collisions increases with bed shear stress, and (2) because on average much more momentum is lost in a grain‐to‐bed collision than in a grain‐to‐grain one. Copyright © 2006 John Wiley & Sons, Ltd.     

Transport and storage of bed material in a gravel‐bed channel during episodes of aggradation and degradation: a field and flume study

The dynamics of sediment transport capacity in gravel‐bed rivers is critical to understanding the formation and preservation of fluvial landforms and formulating sediment‐routing models in drainage systems. We examine transport‐storage relations during cycles of aggradation and degradation by augmenting observations of three events of channel aggradation and degradation in Cuneo Creek, a steep (3%) gravel‐bed channel in northern California, with measurements from a series of flume runs modeling those events. An armored, single‐thread channel was formed before feed rates were increased in each aggradation run. Output rates increased as the channel became finer and later widened, steepened, and braided. After feed rates were cut, output rates remained high or increased in early stages of degradation as the incising channel remained fine‐grained, and later decreased as armoring intensified. If equilibrium was not reached before sediment feed rate was cut, then a rapid transition from a braided channel to a single‐thread channel caused output rates for a given storage volume to be higher during degradation than during aggradation. Variations in channel morphology, and surface bed texture during runs that modeled the three cycles of aggradation and degradation were similar to those observed in Cuneo Creek and provide confidence in interpretations of the history of change: Cuneo Creek aggraded rapidly as it widened, shallowed, and braided, then degraded rapidly before armoring stabilized the channel. Such morphology‐driven changes in transport capacity may explain the formation of flood terraces in proximal channels. Transport‐storage relations can be expected to vary between aggradation and degradation and be influenced by channel conditions at the onset of changes in sediment supply. Published in 2011. This article is a US Government work and is in the public domain in the USA.     

Neural network prediction of bed material load transport

Abstract

Bed material load, which comprises bed load and suspended load, has been extensively studied in the past few decades and many equations have been developed, but they differ from each other in derivation and form. If a process can be related to various flow conditions on a general basis, a proper understanding of bed material load movement can be ascertained. As the process is extremely complex, obtaining a deterministic or analytical form of it is too difficult. Neural network modelling, which is particularly useful in modelling processes about which knowledge of the physics is limited, is presented here as a complimentary tool for modelling bed material load transport. The developed model demonstrated a superior performance compared to other traditional methods based on different statistical criteria, such as the coefficient of determination, Nash-Sutcliffe coefficient and discrepancy ratio. The significance of the different input parameters has been analysed in the present work to understand the influence of these parameters on the transport process.

Editor D. Koutsoyiannis

Citation Kumar, B., 2012. Neural network prediction of bed material load transport. Hydrological Sciences Journal, 57 (5), 956–966.     

On evolution of bed material waves in alluvial rivers

Field and laboratory measurements have shown distinct characteristics of bed sediment waves under differing conditions, whilst their theoretical interpretation has emerged to be equivocal. This note aims to clarify the interpretation of evolution of bed material waves. The complete set of governing equations for the flow–sediment–morphology system is deduced to demonstrate its universally hyperbolic nature, irrespective of the sediment transport functions implemented to close the equations. The hyperbolic nature can admit not only attenuating bed material waves, but also shock‐like waves that are not unusual in the real world. It is suggested that the theory of dispersion/diffusion is not universally appropriate for evolution of bed material waves. Copyright © 2003 John Wiley & Sons, Ltd.     

Resistance to overland flow due to bed‐load transport on plane mobile beds

During bed‐load transport by overland ?ow, momentum is transferred from the ?ow to the bed via grain collisions, resulting in a decrease in ?ow velocity and an increase in ?ow resistance, herein termed bed‐load transport resistance. In overland ?ow on mobile plane beds, total ?ow resistance f consists of grain resistance f_g and bed‐load transport resistance f_bt. In order to identify and evaluate the relative importance of the factors controlling f_bt, 38 ?ume experiments were performed on slopes of 2·7 and 5·5° using sediment with median diameters of 0·74 and 1·16 mm. All ?ows were supercritical and turbulent. This study is an extension of a recent study by Gao and Abrahams (Earth Surface Processes and Landforms 2004, vol. 29, pp. 423–435). These authors found that f_bt is controlled by three factors: sediment concentration C, dimensionless sediment diameter D_*, and relative submergence h/D, where h is ?ow depth, D is median sediment diameter. However, a new dimensional analysis identi?es two additional factors: Froude number F and slope S. Multiple regression analyses reveal (1) that these ?ve factors together explain 97 per cent of the variance of f_bt, and (2) that S controls f_bt entirely through C. The variable C is therefore redundant, and a new functional equation relating f_bt to D_*, h/D, S and F is developed. This equation may be used to predict f_bt. An advantage of this equation is that it may be used to predict f_bt without measuring bed‐load transport rate. Copyright © 2004 John Wiley & Sons, Ltd.     

Particle clusters in gravel‐bed rivers: an experimental morphological approach to bed material transport and stability concepts

Structured gravel river beds clearly exert a major influence on bed stability. Indexing structural stability by field measurements of bed strength neglects the processes operating to entrain and transport bed material in different parts of each structure. This study takes a morphological approach to interpreting the critical processes, using particle tracing to determine the movement of individual cluster particles over a range of flood event magnitudes and durations. The experiment was carried out on the River South Tyne, UK; it uses flow hydrographs measured nearby and also benefits from previous studies of historical development, channel morphology and sediment transport at the same site. More than 30 clusters were monitored over a seven‐month period during which clusters occupied 7–16 per cent of the bed. Threshold flows delimiting three apparently contrasting bed sediment process regimes for cluster particles are tentatively set at 100 m³ s^?1 and 183 m³ s^?1; durations of flow at these levels are critical for cluster development, rather than flow peak values. Wake particles are transported most easily. Flow straightening in the wandering channel planform reduces the stability of clusters, since mechanical strength is markedly reduced by this change of direction. The overall area covered by clusters between significant transport events varies little, implying a dynamic equilibrium condition. Copyright © 2005 John Wiley & Sons, Ltd.     

Rill flow resistance law under equilibrium bed‐load transport conditions

In this paper, a recently deduced flow resistance equation for open channel flow was tested under equilibrium bed‐load transport conditions in a rill. First, the flow resistance equation was deduced applying dimensional analysis and the incomplete self‐similarity condition for the flow velocity distribution. Then, the following steps were carried out for developing the analysis: (a) a relationship (Equation  13 ) between the Γ function of the velocity profile, the rill slope, and the Froude number was calibrated by the available measurements by Jiang et al.; (b) a relationship (Equation  17 ) between the Γ function, the rill slope, the Shields number, and the Froude number was calibrated by the same measurements; and (c) the Darcy–Weisbach friction factor values measured by Jiang et al. were compared with those calculated by the rill flow resistance equation with Γ estimated by Equations  13 and 17 . This last comparison demonstrated that the rill flow resistance equation, in which slope and Shields number, representative of sediment transport effects, are introduced, is characterized by the lowest values of the estimate errors.     

Coarse bed load transport in an alluvial gravel bed stream,Dupuyer Creek,Montana

Coarse bed load was sampled in a gravel/cobble bed stream during two major floods in the snowmelt runoff season. The channel is characterized by high rates of bank erosion and, therefore, high rates of sediment supply and bed load flux. Peak discharge reached four times bank‐full, and bed load was sampled at flows 0·7–1·7 times bank‐full. A large aperture bed load sampler (1 m by 0·45 m) captured the largest particles in motion, and specifically targeted the coarse bed load size distribution by using a relatively large mesh (32 mm or D₂₅ of streambed surface size distribution). Bed load flux was highly variable, with a peak value of 0·85 kg/s/m for the coarse fraction above 38 mm. Bed load size distribution and maximum particle size was related to flow strength. Entrainment was size selective for particles D₇₀ and larger (88–155 mm), while particles in the range D₃₀–D₇₀ (35–88 mm) ceased to move at essentially the same flow. Bed load flux was size selective in that coarse fractions of the streambed surface were under‐represented in or absent from the bed load. Painted tracer particles revealed that the streambed surface in the riffles could remain stable even during high rates of bed load transport. These observations suggest that a large proportion of bed load sediments was sourced from outside the riffles. Repeat surveys confirmed major scour and fill in pools (up to 0·75 m), and bank erosion (>2 m), which together contributed large volumes of sediment to the bed load. Copyright © 2007 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.     

Implications of climate change in the twenty‐first century for simulated magnitude and frequency of bed‐material transport in tributaries of the Saint‐Lawrence River

More frequent extreme flood events are likely to occur in many areas in the twenty‐first century due to climate change. The impacts of these changes on sediment transport are examined at the event scale using a 1D morphodynamic model (SEDROUT4‐M) for three tributaries of the Saint‐Lawrence River (Québec, Canada) using daily discharge series generated with a hydrological model (HSAMI) from three global climate models (GCMs). For all tributaries, larger flood events occur in all future scenarios, leading to increases in bed‐material transport rates, number of transport events and number of days in the year where sediment transport occurs. The effective and half‐load discharges increase under all GCM simulations. Differences in flood timing within the tributaries, with a shift of peak annual discharge from the spring towards the winter, compared to the hydrograph of the Saint‐Lawrence River, generate higher sediment transport rates because of increased water surface slope and stream power. Previous research had shown that channel erosion is expected under all GCMs' discharge scenarios. This study shows that, despite lower bed elevations, flood risk is likely to increase as a result of higher flood magnitude, even with falling base level in the Saint‐Lawrence River. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of incoming sediment on the transport rate of bed load in mountain streams

Field experiments were conducted on bed load transport in the Diaoga River, a mountain stream in southwest China, to study the variation of bed load transport with varying sediment supply. The rate of bed load transport is greatly affected by incoming sediment （load and size）. Under the same flow conditions, bed load transport rates may differ by three orders of magnitude depending on whether measurements were taken before or after the first flood of the year. The relation of the ＂bed load transport rate versus flow intensity＂ appears to have similar characteristics as a clockwise looped-rating curve. Experiments also were conducted during the non-flood season to study bed load transport processes with different incoming load from an upstream section. Bed load with different sizes can be grouped into two types： traveling bed load and structural bed load. Traveling bed load is composed of sediment finer than a critical size, De, and its transport rate depends mainly on the incoming sediment rate. The incoming sediment rate can alter the rate of bed load transport by three orders of magnitude. Structural bed load is composed of coarser sediment and its transport rate closely relies on the flow intensity.     

Further perspectives on the evolution of bed material waves in alluvial rivers

In one‐dimensional mathematical models of ?uvial ?ow, sediment transport and morphological evolution, the governing equations based on mass and momentum conservation laws constitute a hyperbolic system. Succinctly, the hyperbolic nature excludes dispersion or diffusion operators, which is well known in the context of differential equations. There is no doubt that the so‐called ‘dispersion’ argument for bed material wave evolution is questionable, as we have explicitly asserted. Surprisingly, in a recent communication, the authors of the ‘dispersion’ argument suggest that dispersion is not precluded in hyperbolic systems. We provide herein further perspectives to help explain that the dispersion argument is neither appropriate nor necessary for interpreting bed material wave evolution. Also the continuity equations involved are addressed to prompt wider understanding of their signi?cance. In particular, the continuity equation of the water–sediment mixture proposed by the authors of the ‘dispersion’ argument is proved to be incorrect, and inevitably their reasoning based on it is problematic. Copyright © 2005 John Wiley & Sons, Ltd.     

Patterns of grain‐size dependent sediment transport in low‐ordered,ephemeral channels

Sediment data were analyzed to determine grain‐size dependant factors affecting sediment transport in a low‐ordered, ephemeral watershed. Sediment and flow samples were collected during 22 flow events at the outlet of a 4·53 ha sub‐watershed within the Walnut Gulch Experimental Watershed in south‐eastern Arizona. Measured concentrations ranged from 4191 to 115 045 mg l^?1 and included grain sizes up to 8·0 mm in diameter. Two grain‐size dependent transport patterns were observed, that of the finer grain‐size fraction (approximately < 0·25 mm) and that of a coarser grain‐size fraction (approximately ≥ 0·25 mm). The concentration of the fine fraction decreased with flow duration, peaking near the beginning of a flow event and declining thereafter. The concentration of the fine fraction showed slight trends with season and recovery period. The concentration of the coarse fraction displayed a slight negative trend with instantaneous discharge and was not correlated with event duration. These patterns typically produced a condition where the majority of the fine fraction of the sediment yield was evacuated out of the watershed before the hydrograph peak while the majority of the coarser sediment was evacuated during the falling limb of the hydrograph. Each grain‐size dependent transport pattern was likely influenced by the source of the associated sediment. At the flow event time scale, the fines were primarily wash load, supplied from the hillslopes and the coarser grains were entrained from the channel bed. Because transport patterns differ based on grain size, attempts to define the total sediment concentration and sediment yield by the behavior of a single grain‐size fraction may lead to erroneous results, especially when a large range of sediment grain sizes are present. Copyright © 2010 John Wiley & Sons, Ltd.     

Channel response to an extreme flood and sediment pulse in a mixed bedrock and gravel‐bed river

We exploit a natural experiment caused by an extreme flood (~500 year recurrence interval) and sediment pulse derived from more than 2500 concurrent landslides to explore the influence of valley‐scale geomorphic controls on sediment slug evolution and the impact of sediment pulse passage and slug deposition and dispersion on channel stability and channel form. Sediment slug movement is a crucial process that shapes gravel‐bed rivers and alluvial valleys and is an important mechanism of downstream bed material transport. Further, increased bed material transport rates during slug deposition can trigger channel responses including increases in lateral mobility, channel width, and alluvial bar dominance. Pre‐ and post‐flood LiDAR and aerial photographs bracketing the 2007 flood on the Chehalis River in south‐western Washington State, USA, document the channel response with high spatial and temporal definition. The sediment slug behaved as a Gilbert Wave, with both channel aggradation and sequestration of large volumes of material in floodplains of headwaters' reaches and reaches where confined valleys enter into broad alluvial valleys. Differences between the valley form of two separate sub‐basins impacted by the pulse highlight the important role channel and channel‐floodplain connectivity play in governing downstream movement of sediment slug material. Finally, channel response to the extreme flood and sediment pulse illustrate the connection between bed material transport and channel form. Specifically, the channel widened, lateral channel mobility increased, and the proportion of the active channel covered by bars increased in all reaches in the study area. The response scaled tightly with the relative amount of bed material sediment transport through individual reaches, indicating that the amount of morphological change caused by the flood was conditioned by the simultaneous introduction of a sediment pulse to the channel network. Copyright © 2015 John Wiley & Sons, Ltd.     

Effects of sediment pulses on bed relief in bar‐pool channels

To further develop prediction of the range of morphological adjustments associated with sediment pulses in bar‐pool channels, we analyze channel bed topographic data collected prior to and following the removal of two dams in Oregon: Marmot Dam on the Sandy River and Brownsville Dam on the Calapooia River. We hypothesize that, in gravel‐bed, bar‐pool channels, the response of bed relief to sand and gravel sediment pulses is a function of initial relief and pulse magnitude. Modest increases in sediment supply to initially low‐relief, sediment‐poor cross‐sections will increase bed relief and variance of bed relief via bar deposition. Modest increases in sediment supply to initially high‐relief cross‐sections, characteristic of alternate bar morphology, will result in decreased bed relief and variance of relief via deposition in bar‐adjacent pools. These hypothesized adjustments are measured in terms of bed relief, which we define as the difference in elevation between the pool‐bottom and bar‐top. We evaluate how relief varies with sediment thickness, where both relief and mean sediment thickness at a cross‐section are normalized by the 90th percentile of observed relief values within a reach prior to a sediment pulse. Field measurements generally supported the stated hypotheses, demonstrating how introduction of a sediment pulse to low‐relief reaches can increase mean and variance of relief, while introduction to high‐relief reaches can decrease the mean and variance of bed relief, at least temporarily. In general, at both sites, the degree of impact increased with the thickness of sediment delivered to the cross‐section. Results thus suggest that the analysis is a useful step for understanding the morphological effects of sediment pulses introduced to gravel‐bed, bar‐pool channels. Copyright © 2015 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.     

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.     

Hyporheic and total transient storage in small,sand‐bed streams

Key processes in stream ecosystems are linked to hydraulic retention, which is the departure of stream flow from ideal ‘plug flow’, and reflects fluid movement through surface and hyporheic storage zones. Most existing information about hyporheic exchange is based on flume studies or field measurements in relatively steep streams with beds coarser than sand. Stream tracer studies may be used to quantify overall hydraulic retention, but disaggregation of surface and hyporheic retention remains difficult. A stream tracer approach was used to compute the rates at which stream water is exchanged with water in storage zones (total storage) in short reaches of two small, sand‐bed streams under free and obstructed flow conditions. Tracer curves were fit to the one‐dimensional transport with inflow storage model OTIS‐P. Networks of piezometers were used to measure specific discharge between the stream and the groundwater. In the sand‐bed streams studied, parameters describing total retention were in the upper 50% of data compiled from the literature, most of which represented streams with beds coarser than sand. However, hyporheic storage was an insignificant component of total hydraulic retention, representing only 0·01–0·49% of total exchange, and this fraction did not increase after installation of flow obstructions. Total retention did not vary systematically with bed material size, but increased 50–100% following flow obstruction. Removal of roughness elements, such as large wood and debris dams, is detrimental to processes dependent upon transient storage in small, sand‐bed streams. Copyright © 2007 John Wiley & Sons, Ltd.