surface based transport model for mixed size sediment we present a transport model for mixed sand gravel sediments fractional transport rates are referenced to the size distribution of the bed surface rather than subsurface making the model completely explicit and capable of predicting transient conditions the model is developed using a new data set of 48 coupled observations of flow transport and bed surface grain size using five different sediments the model incorporates a hiding function that resolves discrepancies observed among earlier hiding functions the model uses the full size distribution of the bed surface including sand and incorporates a nonlinear effect of sand content on gravel transport rate not included in previous models the model shares some common elements with two previous surface based transport models but differs in using the full surface size distribution and in that it is directly developed from a relatively comprehensive data set with unambiguous measurement of surface grain size over a range of flow transport rate and sediments

normal and anomalous diffusion of gravel tracer particles in rivers received 12 december 2008 revised 16 november 2009 accepted 10 december 2009 published 4 may 2010 1 one way to study the mechanism of gravel bed load transport is to seed the bed with marked gravel tracer particles within a chosen patch and to follow the pattern of migration and dispersal of particles from this patch in this study we invoke the probabilistic exner equation for sediment conservation of bed gravel formulated in terms of the difference between the rate of entrainment of gravel into motion and the rate of deposition from motion assuming an active layer formulation stochasticity in particle motion is introduced by considering the step length distance traveled by a particle once entrained until it is deposited as a random variable for step lengths with a relatively thin e g exponential tail the above formulation leads to the standard advection diffusion equation for tracer dispersal however the complexity of rivers characterized by a broad distribution of particle sizes and extreme flood events can give rise to a heavy tailed distribution of step lengths this consideration leads to an anomalous advection diffusion equation involving fractional derivatives by identifying the probabilistic exner equation as a forward kolmogorov equation for the location of a randomly selected tracer particle a stochastic model describing the temporal evolution of the relative concentrations is developed the normal and anomalous advection diffusion equations are revealed as its long time asymptotic solution sample numerical results illustrate the large differences that can arise in predicted tracer concentrations under the normal and anomalous diffusion models they highlight the need for intensive data collection efforts to aid the selection of the appropriate model in real rivers

the cause of advective slowdown of tracer pebbles in rivers implementation of exner based master equation for coevolving streamwise and vertical dispersion tracer pebbles are often used to study bed load transport processes in gravel bed rivers models have been proposed for their downstream dispersion and also for vertical dispersion but not for the combined effects of downstream and vertical movement here we use the exner based master equation to characterize the transient coevolution of streamwise and vertical advection diffusion of tracer pebbles under equilibrium transport conditions no net aggradation or degradation the coevolution of streamwise and vertical dispersion gives rise to behavior that can differ markedly from that associated with purely streamwise processes with no vertical exchange one example is streamwise advective slowdown particles that are advected downward into zones where the probability of reentrainment becomes asymptotically small are essentially trapped and can no longer participate in streamwise advection as a result the mean streamwise velocity of the tracer plume declines in time qualitative and quantitative comparisons with two field experiments show encouraging agreement despite the simplified boundary conditions in the model

spatial variations of magnetic susceptibility of chinese loess for the last 600 kyr implications for monsoon evolution 1 we examine spatial variations in magnetic susceptibility ms over the loess plateau in china based on 50 sections in order to identify spatial changes in monsoon climate at key glacial interglacial and interstadial intervals for the last 600 kyr the results indicate strong coherence between ms variations during the interglacial periods and present day precipitation and temperature patterns this suggests that the strength of the summer monsoon had a dominant influence on the ms signals in soils through modulating pedogenic intensity the distribution of ms during glacial periods is characterized by weak s n gradients and rough w e zonal patterns indicating a negligible effect of the summer monsoon interstadial patterns are intermediate between the glacial and interglacial ones interglacial patterns for the last 600 kyr are essentially similar suggesting that the climate regime during these periods has not undergone significant changes and that the east asian summer monsoon has remained the main moisture carrier our estimates of the relative amplitudes of climate oscillations during these time slices are consistent with earlier paleoclimate studies these data associated with the available susceptibility based climofunctions may be used to estimate spatial changes of paleorainfall and paleotemperature for these key periods and hence to test climate models

probabilistic exner sediment continuity equation for mixtures with no active layer the exner equation of sediment continuity is the foundation of river morphodynamics generalization of this equation to mixtures of grain sizes has required the introduction of an active layer i e a buffer layer between the sediment moving in the water column and the immobile substrate below the active layer is defined to be a well mixed layer with no vertical structure that encompasses those grains available to exchange directly with the moving sediment the sediment in the substrate below exchanges with the active layer only as the bed aggrades or degrades the active layer concept is a useful one that has served the research community well for 3 decades however the division of the erodible bed into a discrete active layer and substrate must represent only an approximation of a more general formulation that contains no active layer and in which parameters pertaining to the entrainment from and deposition to the bed vary continuously with depth below the sediment water interface here the probability density function of bed elevation is used to derive a general exner equation of sediment continuity with no discrete layers the formulation is applicable to both sediment mixtures and tracers in uniform sediment although the treatment requires more information than that of the active layer approach it offers the prospect of a better understanding of how streams create a stratigraphic record of their activities through deposition

real and apparent changes in sediment deposition rates through time 1 field measurements show that estimated sediment deposition rate decreases as a power law function of the measurement interval this apparent decrease in sediment deposition has been attributed to completeness of the sedimentary record the effect arises because of incorporation of longer hiatuses in deposition as averaging time is increased we demonstrate that a heavy tailed distribution of periods of nondeposition hiatuses produces this phenomenon and that observed accumulation rate decreases as t 1 over multiple orders of magnitude where 0 1 is the parameter describing the tail of the distribution of quiescent period length by using continuous time random walks and limit theory we can estimate the actual average deposition rate from observations of the surface location over time if geologic and geometric constraints place an upper limit on the length of hiatuses then average accumulation rates approach a constant value at very long times our model suggests an alternative explanation for the apparent increase in global sediment accumulation rates over the last 5 million years

distance of movement of coarse particles in gravel bed streams distributions of distance of bedload particle movement were examined in two gravel bed streams using several hundred magnetically tagged cobbles and pebbles the compound poisson model of einstein hubbell sayre and a simple gamma function model were compared with observed distributions of moved particles and of all particles both models fit the data reasonably well for small mean displacements but notable misfits occurred in an event with large mean displacement when mean particle travel distance approaches the scale of bar spacing trapping in the bars interrupts particle progress and the dispersion process the data remain very noisy so definitive discrimination of suitable models will require trials with more than 103 particles

sediment pulses in mountain rivers 2 comparison between experiments and numerical predictions 1 mountain rivers in particular are prone to sediment input in the form of pulses rather than a more continuous supply these pulses often enter in the form of landslides from adjacent hillslopes or debris flows from steeper tributaries the activities of humans such as timber harvesting road building and urban development can increase the frequency of sediment pulses the question as to how mountain rivers accommodate pulses of sediment thus becomes of practical as well as academic significance in part 1 cui et al 2003 the results of three laboratory experiments on sediment pulses are reported it was found there that the pulses were eliminated from the flume predominantly by dispersion of the topographic high significant translation was observed only when the pulse material was substantially finer than the ambient load in the river here the laboratory data are used to test a numerical model originally devised for predicting the evolution of sediment pulses in field scale gravel bed streams the model successfully reproduces the predominantly dispersive deformation of the experimental pulses rates of dispersion are generally underestimated largely because bed load transport rates are underestimated by the transport equation used in the model the model reproduces the experimental data best when the pulse is significantly coarser than the ambient sediment in this case the model successfully predicts the formation and downstream progradation of a delta that formed in the backwater zone of the pulse in run 3 the performance of the model is less successful when the pulse is composed primarily of sand this is likely because the bed load equation used in the study is specifically designed for gravel when the model is adapted to conditions characteristic of large sand bed rivers with low froude numbers it predicts substantial translation of pulses as well as dispersion

sedimentary bed evolution as a mean reverting random walk implications for tracer statistics sediment tracers are increasingly employed to estimate bed load transport and landscape evolution rates tracer trajectories are dominated by periods of immobility waiting times as they are buried and reexcavated in the stochastically evolving river bed here we model bed evolution as a random walk with mean reverting tendency ornstein uhlenbeck process originating from the restoring effect of erosion and deposition the ornstein uhlenbeck model contains two parameters a and b related to the particle feed rate and range of bed elevation fluctuations respectively observations of bed evolution in flume experiments agree with model predictions in particular the model reproduces the asymptotic t 1 tail in the tracer waiting time exceedance probability distribution this waiting time distribution is similar to that inferred for tracers in natural gravel streams and avalanching rice piles indicating applicability of the ornstein uhlenbeck mean reverting model to many disordered transport systems with tracer burial and excavation

numerical simulation of downstream fining by selective transport in gravel bed rivers model development and illustration a numerical model has been developed for the routing of gravel sized sediment along a river channel which is free to adjust both its long profile and surface texture hydraulic calculations use a step backwater approach and sediment transport is predicted with the method of parker 1990a which uses a low degree of size selectivity exchange of sediment between the surface and subsurface is described using the modified exner equation of parker and sutherland 1990 the model is applied to an idealized channel based on the highly concave allt dubhaig scotland in which fining by particle wear is minor the rapid downstream fining observed in this river is closely matched by model predictions after a time equivalent to 102 years under the present flow regime of the river the evolution of the fining pattern during the model run and associated changes in sediment transport and bed aggradation are described it is concluded that strong profile concavity can force rapid downstream fining even though bed load transport is only slightly size selective this run of the model serves as a basis for testing of the sensitivity of downstream fining to alternative choices of parameter values and boundary conditions which are summarized here and will be described in a subsequent paper

revisiting the linear theory of sand dune formation a linear stability theory for dune and antidune formation is presented that implements a rotational two dimensional flow model as in previous linear theories the phase lag between sediment transport and bed elevation remains the main mechanism driving instability however it is shown that this phase lag varies significantly in a neighbourhood of the bed moreover since the layer in which sediments are moving has a finite though small thickness it is assumed that the perturbations of the fluid stress driving bedload transport should be evaluated at the top of the layer itself it is shown that such an apparently minor modification of the classical approach alters remarkably the balance between stabilizing and destabilizing effects that drives the instability process this also allows a clarification of the debated role of bedslope on the formation of dunes and antidunes following the above ideas antidunes are shown to form in the absence of suspended sediment load and without any effect associated with sediment inertia the present analysis ultimately allows a successful unification of the theories of dune and antidune formation

finite amplitude river dunes the linear and weakly nonlinear stability of a uniform flow in an infinitely wide open channel with erodible bottom is studied under suitable conditions the flow is found to be unstable leading to the formation of dunes and antidunes at a linear level the corresponding regions of existence are presented and compared with experimental data a weakly nonlinear analysis is then performed in a neighbourhood of the critical conditions for dune and antidune formation the analysis shows that for values of the ratio of the shear velocity to the depth averaged velocity of practical interest dune bifurcation is supercritical whereas antidune bifurcation is subcritical the latter result suggests a possible interpretation of the plane antidune transition where plane bed and antidune configurations are observed to coexist for the same values of the flow and the sediment parameters the supercritical behaviour of the dune bifurcation allows for the prediction of an equilibrium amplitude that successfully compares with the amplitudes measured in laboratory experiments

bedload entrainment travel lengths step lengths rest periods studied with passive iron magnetic and active radio tracer techniques this paper reports results from bedload transport investigations with active radio and passive iron magnetic tracers in the lainbach a step pool mountain river in bavaria southern germany the spatial distributions of the iron tracers after flood events can be best described by exponential or gamma distributions there is some indication of a tendency of size selective transport of the iron tracers but there is also a considerable amount of scatter in the correlations between weight size and travel length owing to the masking influence of other variables such as the shape of the particles and different positions in the river bed the experiments with artificial magnetic tracers showed that elongated pebbles rods had the longest mean transport distance platy ones discs remained relatively close to the starting points the particles from the pool showed the greatest transport lengths and a 100 per cent chance of being eroded the pebble transmitter system petsy consists of transmitters implanted into individual pebbles a computerized receiver a stationary antenna system with an antenna switchboard and a data logging system the particles do not move continuously but in a series of transport steps and non movement intervals a single value for a given size class is not adequate to describe the critical conditions of entrainment under natural circumstances a probability approach is much more suitable the critical unit discharges total discharge divided by active channel width along the measuring reach are dependent on river bed morphology in the steps bedload needs higher unit discharges to be entrained once entrained the transport of bedload is stochastic in nature and the single particle transport is controlled by the step lengths and the duration of rest periods the distributions of both parameters can be approximated by exponential functions applying the stochastic concept proposed by einstein the mean values of the random variables step length and duration of rest period measured with the petsy technique were used for the simulation of spatial distributions of bedload particles from point sources more field and laboratory data are needed to include varying flow and roughness conditions with tracers representing different particle characteristics

modeling of riverbed evolution for bedload sediment mixtures a new computational methodology for fully coupled simulation of unsteady water and sediment movement in mobile bed alluvial rivers has been developed and tested the one dimensional approach treats bedload transport of nonuniform sediment mixtures with sorting and armoring effects considered spatial lag effects in nonequilibrium bedload transport are taken into account through innovative use of the recently developed notion of a loading law the new system of equations for water and sediment movement is solved in a fully coupled implicit manner using the preissmann finite difference scheme implemented to allow for either upstream or downstream induced mobile bed perturbations formal analysis of the coupled system sheds new light on boundary condition requirements for the multiple size class problem the fully coupled implicit solution has proven to be robust and stable and it respects the underlying volumetric conservation laws remarkably well as demonstrated in continuity analyses of computed bed e

radio tracking gravel particles in a large braided river in new zealand a field test of the stochastic theory of bed load transport proposed by einstein hans a einstein initiated a probabilistic approach to modelling sediment transport in rivers his formulae were based on theory and were stimulated by laboratory investigations the theory assumes that bed load movement occurs in individual steps of rolling sliding or saltation and rest periods so far very few attempts have been made to measure stochastic elements in nature for the first time this paper presents results of radio tracing the travel path of individual particles in a large braided gravel bed river the waimakariri river of new zealand as proposed by einstein it was found that rest periods can be modelled by an exponential distribution but particle step lengths are better represented by a gamma distribution einstein assumed an average travel distance of 100 grain diameters for any bed load particle between consecutive points of deposition but larger values of 6 7 m or 150 grain diameters and 6 1 m or 120 grain diameters were measured for two test particle sizes together with other available large scale field data a dependence of the mean step length on particle diameter relative to the d50 of the bed surface was found during small floods the time used for movement represents only 2 7 of the total time from erosion to deposition the increase in percentage of time being used for transport means that it then has to be regarded in stochastic transport models tracing the flow path of bed load particles between erosion and deposition sites is a step towards explaining the interactions between sediment transport and river morphology copyright 2001 john wiley sons ltd

tracing river gravels insights into dispersion from a long term field experiment abstract sediment dispersion is a fundamental component of the sediment transfer process in gravel bed rivers modeling this process requires an understanding of the collective movement of mixed size clasts this study explores the temporal evolution of gravel dispersion to underscore the importance of field observation in informing modeling efforts magnetically tagged gravels deployed in carnation creek have been monitored repeatedly over 17 years four metrics used to describe the extent of dispersion document that the overall shape in the spatial distribution of grain location changes over time the general trends mask the complexity of the dispersion process expressed by channel sections where tracers are concentrated regardless of grain size the distribution of total grain displacement responsible for dispersion evolves as tracers become well mixed results demonstrate that observations from the field are crucial to the understanding and modeling of sediment dispersion because they provide key insights into the dispersion process that must be known a priori for mathematical modeling and similar observations cannot be collected using laboratory flumes

reconstructing a sediment pulse modeling the effect of placer mining on fraser river canada gold mining along 525 km of the fraser river between 1858 and 1909 added an estimated 1 1 108 t of tailings half gravel and the rest finer to the river s natural sediment load we simulate the response using a 1 d multigrain size morphodynamic model since premining conditions are unknown and modern data are insufficient for tuning the process representation we devised a novel modeling strategy which may be useful in other data poor applications we start the model from a smoothed version of the modern longitudinal profile with bed grain size distributions optimized to match alternative assumptions about natural sediment supply and compare runs that include mining with control runs that can be used to quantify the effects of deficiencies in process representation and initialization simulations with an appropriate choice of natural supply rate closely match the best available test data which consist of a detailed 1952 1999 gravel budget for the distal part of the model domain the simulations suggest that the main response to mining was rapid bed fining which allowed a major increase in bed load transport rate with only slight 0 1 m mean aggradation within the mining region and most of the excess sediment exported well beyond the mountain front within the mining period or soon afterward we compare this pattern of response by a large powerful river with previous case studies of river adjustment to sediment supply change

the relation between particle path length distributions and channel morphology in gravel bed streams a synthesis abstract the path length downstream displacement over a given time period of individual bed particles in gravel bed rivers is central to morphological methods for measuring bed load transport rate and is also fundamental to understanding the bed load transport process and the development of channel morphology previous studies of particle movement using tracers report predominantly strongly positively skewed frequency distributions of path length with modes close to the point of entrainment however gravel bed rivers often have regularly spaced erosion scour pools and deposition channel bars sites that are several channel widths apart and it is reasonable to expect that particle path length would reflect this morphological scale at least during flows large enough to create and modify the morphology here we synthesize and re analyze results from published bed load tracing experiments in gravel bed rivers to identify the variety of possible path length distributions for differing channel morphology channel dimensions bed particle size and particle mobility i e flow magnitude and to look for occurrences of path length coinciding with the length scale of the morphology the results show that path length distributions may be positively skewed symmetrical and uni bi or multi modal and may include modes that coincide with known or expected pool bar spacing primary path length modes equivalent to possible pool bar spacing are more probable at higher non dimensional bed shear stress from which it is inferred that both particle mobility and channel morphology exert an influence on particle path lengths and that particle movement is unlikely to be stochastic except at relatively low particle mobility existing data are inadequate for more than a preliminary analysis of this problem consequently there is a need for new data collected explicitly and systematically to confirm these preliminary results isolate the effect of the several variables that influence the characteristics of path length frequency distributions and identify the conditions under which path length coincides with the length scale of the dominant morphology

ripple and dune formation in rivers a linear stability analysis for dune and ripple formation is presented that implements a rotational two dimensional flow model valid in the smooth as well as in the transitional and rough flow regimes sediment is assumed to be transported as bedload disregarding the role of suspension therefore the main mechanism driving instability for both ripples and dunes is the phase lag between bed shear stress and bed elevation ripples are shown to be confined to relatively low values of the shields parameter and of the particle reynolds number for higher values of the shields parameter and of the particle reynolds number and thus of the froude number and of the roughness reynolds number ripples are replaced by dunes the present analysis ultimately allows for a successful unification of the theories of dune and ripple formation and for a clarification of the debated role of ripples on the formation of dunes a good agreement between predicted and observed wavelengths for both ripples and dunes is found

vertical sorting in bed forms flume experiments with a natural and a trimodal sediment mixture two sets of flume experiments were conducted to examine grain size selective transport and vertical sorting in conditions with migrating bed forms and bed load transport in the two sets of experiments we used a sediment mixture from the river rhine and a trimodal mixture respectively the vertical sorting profiles showed a downward coarsening trend within the bed forms and in some experiments an essentially immobile coarse bed layer formed underneath the migrating bed forms three mechanisms contribute to the formation of such a coarse bed layer 1 the avalanching process at the lee face 2 conditions of partial transport in which a relatively large amount of coarse material does not participate in the transport process and 3 the winnowing of fines from the trough surface and subsurface the experiments show that vertical sorting fluxes not only occur through net degradation or aggradation but also through the migration of bed forms and through the variability in trough elevations this is contradictory to the way vertical sorting processes are modeled in most existing sediment continuity models for nonuniform sediment the present study is therefore also a plea for modifying existing sediment continuity models to account for vertical sorting processes other than through net aggradation or degradation

sediment feed and recirculating flumes fundamental difference two standard modes of laboratory sediment transport flume operation are sediment feed and recirculating in the case of uniform sediment the final equilibriums achieved in the two modes are equivalent and independent of initial conditions even though the specified flow and sediment constraints differ when the sediment consists of a mixture of sizes however this symmetry breaks down in a sediment feed flume both the feed rate and size distribution are specified by the user and must be identical to those of the bed load at final equilibrium the final state thus becomes independent of initial conditions in a recirculating flume however the equilibrium size distribution of neither the bed load nor the bed surface material can be specified in advance as a result the final state depends on the initial conditions and can include the possibility of partial transport the equilibriums themselves are equivalent in that they obey the same laws of flow and sediment transport their ia priori n predictability however differs due to the difference in governing constraints when fractional transport is scaled by the bulk size distribution the two flume modes may produce very different transport relations even for the same sediment a consistent approach requires that the transport be scaled by the size distribution of the bed surface

different approaches to handling vertical and streamwise sorting in modeling river morphodynamics this paper presents an assessment of the strengths and weaknesses of four sediment continuity models for nonuniform sediment by applying these models to an aggradational flume experiment that is dominated by nonuniform sediment and dunes the author makes simulations of the flume experiment using four numerical morphodynamic model systems to which the following sediment continuity models are applied the commonly applied active layer model a a two layer model b a sorting evolution model while assuming bed form size to be regular c1 and a sorting evolution model while taking into account the variability in bed form geometry c2 the model systems that incorporate the variability of bed form geometry i e the two layer model and the sorting evolution model with irregular dunes show an improved prediction of the adaptation timescale of the composition of both the bed surface and the transported sediment as well as the vertical sorting profile this is because including the variability of bed form geometry enables the model system to account for sediment being stored temporarily at elevations that are exposed to the flow less frequently future application of both models to field cases is difficult however as the two layer model is not sufficiently generic and may lead to ellipticity of its set of equations whereas the sorting evolution model requires a very small numerical time step

vertical sorting and the morphodynamics of bed form dominated rivers a modeling framework uncertainties and errors in predictions by morphodynamic models of rivers with nonuniform sediment are usually attributed to shortcomings pertaining to the submodel of sediment transport this mistakenly neglects shortcomings in the submodel of sediment continuity which describes the vertical sorting and the bed surface composition whereas the latter is one of the main input parameters for calculating sediment transport and thus morphological changes hirano 1971 1972 was the first to develop a sediment continuity model for nonuniform sediment since this commonly used hirano active layer model and its variants suffer from a number of shortcomings the authors have developed a new type of sediment continuity model that describes the bed composition and vertical sorting fluxes without distinguishing discrete bed layers this continuum sorting model is aimed at conditions dominated by bed forms and bed load transport it is based on 1 the parker paola leclair framework for sediment continuity 2 the einstein step length formulation 3 a newly developed lee sorting function and 4 a newly developed method to account for the variability in bed form trough elevations the resulting model is deterministic in the computation of the vertical sorting profile and is probabilistic in terms of the riverbed surface due to the presence of dunes

vertical sorting and the morphodynamics of bed form dominated rivers an equilibrium sorting model a modeling framework is developed for taking into account the effects of sediment sorting in the morphodynamic modeling of bed form dominated rivers for the case of equilibrium or stationary conditions dominated by bed load transport to this end the blom and parker 2004 framework for sediment continuity is reduced to an equilibrium sorting model the predicted equilibrium sorting profile is mainly determined by the probability density function pdf of bed form trough elevations and by a lee sorting function the pdf of trough elevations needs to be known from either model predictions or measurements a simple formulation for the lee sorting function is suggested yet data on the avalanche mechanism down lee faces of dunes is required so as to improve the function and make it generic the equilibrium sorting model is calibrated and verified using data from flume experiments the agreement between the predicted and measured equilibrium sorting profiles is reasonable although the model does not reproduce an observed coarse top layer in a hydraulic morphodynamic model this equilibrium sorting model may be applied instantaneously if the timescale of large scale morphological changes is much larger than the ones of changes in vertical sorting and dune dimensions

routing graded sediments in streams formulations a one dimensional numerical model is developed for simulating the movement of well graded sediments through a stream network the model is based on the physical processes governing the mechanics of sediment movement in alluvial channels it incorporates the effect of sediment gradation on the stream s potential transport capacity it also accounts for the effect of particle exchange between the sediment load and the bed while simulating aggradation degradation and armoring of the bed the applicability of the model is restricted to noncohesive materials and relatively stable channel geometries any valid water routing algorithm can be used in simulating the movement of water

depth averaged two dimensional numerical modeling of unsteady flow and nonuniform sediment transport in open channels a depth averaged two dimensional 2d numerical model for unsteady flow and nonuniform sediment transport in open channels is established using the finite volume method on a nonstaggered curvilinear grid the 2d shallow water equations are solved by the isimple c n algorithms with the rhie and chow s momentum interpolation technique the proposed sediment transport model adopts a nonequilibrium approach for nonuniform total load sediment transport the bed load and suspended load are calculated separately or jointly according to sediment transport mode the sediment transport capacity is determined by four formulas which are capable of accounting for the hiding and exposure effects among different size classes an empirical formula is proposed to consider the effects of the gravity on the sediment transport capacity and the bed load movement direction in channels with steep slopes flow and sediment transport are simulated in a decoupled manner but the sediment module adopts a coupling procedure for the computations of sediment transport bed change and bed material sorting the model has been tested against several experimental and field cases showing good agreement between the simulated results and measured data

entrainment and motion of coarse particles in a shallow water stream down a steep slope we investigate the entrainment deposition and motion of coarse spherical particles within a turbulent shallow water stream down a steep slope this is an idealization of bed load transport in mountain streams earlier investigations have described this kind of sediment transport using empirical correlations or concepts borrowed from continuum mechanics the intermittent character of particle transport at low water discharges led us to consider it as a random process sediment transport in this regime results from the imbalance between entrainment and deposition of particles rather than from momentum balance between water and particles we develop a birth death immigration emigration markov process to describe the particle exchanges between the bed and the water stream a key feature of the model is its long autocorrelation times and wide frequent fluctuations in the solid discharge a phenomenon never previously explained despite its ubiquity in both nature and laboratory experiments we present experimental data obtained using a nearly two dimensional channel and glass beads as a substitute for sediment entrainment trajectories and deposition were monitored using a high speed digital camera the empirical probability distributions of the solid discharge and deposition frequency were properly described by the theoretical model experiments confirmed the existence of wide and frequent fluctuations of the solid discharge and revealed the existence of long autocorrelation time but theory overestimates the autocorrelation times by a factor of around three particle velocity was weakly dependent on the fluid velocity contrary to the predictions of the theoretical model which performs well when a single particle is moving for our experiments the dependence of the solid discharge on the fluid velocity is entirely controlled by the number of moving particles rather than by their velocity we also noted significant changes in the behaviour of particle transport when the bed slope or the water discharge was increased the more vigorous the stream was the more continuous the solid discharge became moreover although 90 of the energy supplied by gravity to the stream is dissipated by turbulence for slopes lower than 10 particles dissipate more and more energy when the bed slope is increased but surprisingly the dissipation rate is nearly independent of fluid velocity a movie is available with the online version of the paper

vertical mixing of coarse particles in gravel bed rivers a kinematic model burial of transported material in gravel bed rivers was examined using several hundred magnetically tagged particles burial depth of individual particles varies with no simple relation to particle size distributions of burial depth of particles were examined by considering observed burial depth of individual size groups of all mobile particles and of all tagged particles including static ones simple single peak flow events yielded exponential distributions of burial depth of mobile particles distributions with secondary peaks were obtained from large and multipeak events season long results were skew peaked with a tendency toward uniformity an m layer model is developed to account for the variation of frequency of burial depth of particles based on the assumptions that the burial depth of particles in a simple event is exponentially distributed and the proportion of particles which change vertical position from a given layer is constant from event to event the model is elaborated for varying mixing rates varying scour depths and variable behavior of different size classes after many events the material is uniformly distributed throughout all layers in conformity with field experience

bifurcation modelling in a meandering gravel sand bed river the rhine bifurcation at pannerden forms the major distribution point for water supply in the netherlands distributing not only water and sediment but also flooding risks and navigability its morphological stability has been a concern for centuries we present experiences from more than two decades of numerical morphological modelling of this bifurcation with a gravel sand bed and a meandering planform successive computations have shown the importance of upstream approach conditions the necessity to include physical mechanisms for grain sorting and alluvial roughness and the need to assume a thicker active layer of the river bed than is suggested by laboratory flume experiments using a constant discharge the active layer must be thicker in the model to account for river bed variations due to higher frequency discharge variations that are filtered out in morphological modelling we discuss limitations in calibration and verification but argue that notwithstanding these limitations 2d and 3d morphological models are valuable tools not only for pragmatic applications to engineering problems but also for revealing the limitations of established knowledge and understanding of the relevant physical processes the application of numerical models to the pannerden bifurcation appeared to reveal shortcomings in established model formulations that do not pose particular problems in other cases this application is therefore particularly useful for setting the agenda for further research copyright 2012 john wiley sons ltd

mobility of river tracer pebbles over different timescales 1 tracer pebbles are widely used to learn about gravel transport along rivers movement over short times and distances is dominated by factors controlling entrainment relative particle size and shear stress movement at longer scales also involves depositional factors burial and reexposure and exchange between channels bars and other depositional environments we mapped mixed size tracers in six reaches of a small scottish river after 2 and 8 years to investigate differences in relative and absolute mobility and infer the importance of burial and exchange patterns of relative mobility according to size and shear stress both within and between reaches did not change significantly some local bunching of tracers was apparent in both surveys with redistribution from pools into riffles and bars the main change was that virtual velocities were 50 lower and estimated gravel fluxes were also lower in the longer term this slowdown is attributed to vertical mixing giving decreased mobility as surface seeded tracers become buried long term storage in bars and other less active parts of the system and in this channel advection of tracers downstream onto a finer bed giving higher relative size

local high slope effects on sediment transport and fluvial bed form dynamics 1 we investigate the morphodynamic evolution of an arbitrarily tilted coarse mobile bed under the action of a free surface water flow the analysis is based on the experimental observations of the evolution of a mobile bed from its initial laterally tilted configuration to the final laterally flat state due to the presence of a lateral component of bed load transport measurements of the bed topography at different times allow one to reconstruct the flattening process the experimental observations are interpreted by means of a three dimensional numerical hydromorphodynamic model employing different relationships linear and nonlinear to evaluate bed load intensity and direction the analysis shows that the inclusion of nonlinear gravitational effects in the description of the bed load leads to a more satisfactory description of the bed evolution this finding opens important issues on how the inclusion of the nonlinear gravitational effects on the bed load can affect the morphodynamic evolution of complex bed topography occurring in natural rivers to investigate this point an application to the evolution of river bars is presented

the transport of gravel in an ephemeral sandbed river the channel dynamics of an ephemeral sandbed river the metsemotlhaba in southeast botswana were studied over a five year period using tagged magnetic particles of pebble and cobble size scour chains and topographic cross sections with particular emphasis on the three dimensional dispersal of gravels patterns of scour and fill and depth of active layer two major flow events of equivalent magnitude occurred moving the tagged particles in december 1987 a mean distance of 837 m at a mean burial depth of 0 40 m and in march 1991 a mean distance of 263 m at a mean burial depth of 0 39 m the volume of mobile sediment based on scour depth and distance of travel was 2 7 times greater in the december 1987 event in which the mean scour depth was almost twice the mean burial depth of the tagged particles the distribution of distance of movement was asymmetrical in this first flood when the tracer started from a surface location but was monotonic thereafter intervening small to medium events yielded limited tracer movement with a mean burial depth equivalent to depth of scour the tracer moved in the low and transitional flow regimes burial depth distribution followed the gamma model field data confirm that longitudinal transport is independent of particle size and shape and strongly skewed with respect to distance whilst depths of scour in excess of 1 m for high magnitude events suggest that scour values predicted from the empirical equation of leopold et al underestimate by an order of magnitude copyright 1999 john wiley sons ltd

stochastic theory of particle trajectories through alluvial valley floors abstract temporary storage of sediment within alluvial valley floors modulates the long term transport of sediment through landscapes the fate of weathering minerals or sediment bound constituents in fluvial environments depends on the relative time scales of constituent degradation and particle residence time within valleys particles follow a set of trajectories through valley floors some particles pass directly through the channel reaching the basin outlet rapidly after being introduced to the fluvial system others remain for long periods in deposits such as flood plains traditional sediment routing theory based on the principle of sediment mass conservation along reaches of channel does not account for exchanges of sediment with temporary sediment storage reservoirs outside the channel such as flood plains deltas and alluvial fans this article formalizes a theory that incorporates the role of such exchanges in the migration of sediment through river systems by computing the probabilistic s

simulation of bed armoring in alluvial channels a numerical procedure for simulating the temporal variation of sediment transport rate and corresponding variation of bed material composition in a straight alluvial channel has been developed the procedure is based on a simple model for the exchange of grain sizes between a surface and a subsurface layer of bed sediment together with a standard bed load function verification was made with laboratory data the procedure should be a useful tool for estimates of the effect of alternative flow regulation measures on a channel bed s long term stability

vertical sorting and the morphodynamics of bed form dominated rivers a sorting evolution model existing sediment continuity models for nonuniform sediment suffer from a number of shortcomings as they fail to describe vertical sorting fluxes other than through net aggradation or degradation of the bed and are based on a discrete representation of the bed material interacting with the flow we present a new type of sediment continuity model that is based on a stochastic description of the bed surface rather than discrete bed layers the model is aimed at conditions dominated by bed load transport wherein the river bed is fully covered by river dunes application of the model should be limited to spatial scales covering a significant number of bed forms the resulting model i e the sorting evolution model is suitable for unsteady conditions as it takes into account the time evolution of for instance vertical sorting in modeling net aggradation or degradation of the river bed the present paper lists the various submodels of a morphodynamic model system to which the sorting evolution model is applied we compare the results of the morphodynamic model system to measured data from two flume experiments the new model shows reasonable results for the predicted time evolution of the vertical sorting profile as well as the time evolution of the grain size distribution of the bed load transport yet the model does not properly include sorting mechanisms associated with partial transport and the winnowing of fines from the trough surface and subsurface the model serves as a basis for a future simplification of the model into a new stochastics based bed layer type sediment continuity model in which vertical sediment fluxes are included in a parameterized way

sediment transport part i bed load transport a method is presented which enables the computation of the bed load transport as the product of the saltation height the particle velocity and the bed load concentration the equations of motions for a solitary particle are solved numerically to determine the saltation height and particle velocity experiments with gravel particles transported as bed load are selected to calibrate the mathematical model using the lift coefficient as a free parameter the model is used to compute the saltation heights and lengths for a range of flow conditions the computational results are used to determine simple relationships for the saltation characteristics measured transport rates of the bed load are used to compute the sediment concentration in the bed load layer a simple expression specifying the bed load concentration as a function of the flow and sediment conditions is proposed a verification analysis using about 600 alternative data shows that about 77 of the predicted bed load transport rates are within 0 5 and 2 times the observed values

a generalized exner equation for sediment mass balance 1 the advance of morphodynamics research into new areas has led to a proliferation of forms of sediment mass balance equation without a general equation it is often difficult to know what these problem specific versions of sediment mass balance leave out to address this we derive a general form of the standard exner equation for sediment mass balance that includes effects of tectonic uplift and subsidence soil formation and creep compaction and chemical precipitation and dissolution the complete equation 17 allows for independent evolution of two critical interfaces that between bedrock and sediment or soil and that between sediment and flow by eliminating terms from the general equation it is straightforward to derive mass balance equations applicable to a wide range of problems such as short term bed evolution basin evolution bedrock uplift and soil formation and carbonate precipitation and transport dropping terms makes explicit what is not being considered in a given problem and can be done by inspection or by a formal scaling analysis of the terms scaling analysis leads directly to dimensionless numbers that measure the relative importance of terms in the equation for example the relative influence of spatial versus temporal changes in sediment load on bed evolution combining scaling analysis with time averaging shows how the relative importance of terms in the equation can change with timescale for example the term representing bed evolution due to temporal change in sediment load tends to zero as timescale increases

a well posed alternative to the hirano active layer model for rivers with mixed size sediment the active layer model hirano 1971 is frequently used for modeling mixed size sediment river morphodynamic processes it assumes that all the dynamics of the bed surface are captured by a homogeneous top layer that interacts with the flow although successful in reproducing a wide range of phenomena it has two problems 1 it may become mathematically ill posed which causes the model to lose its predictive capabilities and 2 it does not capture dispersion of tracer sediment we extend the active layer model by accounting for conservation of the sediment in transport and obtain a new model that overcomes the two problems we analytically assess the model properties and discover an instability mechanism associated with the formation of waves under conditions in which the active layer model is ill posed numerical simulations using the new model show that it is capable of reproducing two laboratory experiments conducted under conditions in which the active layer model is ill posed the new model captures the formation of waves and mixing due to an increase in active layer thickness simulations of tracer dispersion show that the model reproduces reasonably well a laboratory experiment under conditions in which the effect of temporary burial of sediment due to bedforms is negligible simulations of a field experiment illustrate that the model does not capture the effect of temporary burial of sediment by bedforms

bedload transport of fine gravel observed by motion picture photography motion pictures taken at duck creek a clear stream 6 5 m wide and 35 cm deep near pinedale wyoming provide detailed quantitative information on both the modes of motion of individual bedload particles and the collective motions of large numbers of them bed shear stress was approximately 6 pa 60 dynes cm 2 which was about twice the threshold for movement of the 4 mm median diameter fine gravel bed material and transport was almost entirely as bedload the displacements of individual particles occurred mainly by rolling of the majority of the particles and saltation of the smallest ones and rarely by brief sliding of large angular ones entrainment was principally by rollover of the larger particles and liftoff of the smaller ones and infrequently by ejection caused by impacts whereas distrainment was primarily by diminution of fluid forces in the case of rolling particles and by collisions with larger bed particles in the case of saltating ones the displacement times averaged about 0 2 0 4 s and generally were much shorter than the intervening repose times the collective motions of the particles were characterized by frequent brief localized random sweep transport events of very high rates of entrainment and transport which in the aggregate transported approximately 70 of the total load moved these events occurred 9 of the time at any particular point of the bed lasted 1 2 s affected areas typically 20 50 cm long by 10 20 cm wide and involved bedload concentrations approximately 10 times greater than background the distances travelled during displacements averaged about 15 times the particle diameter despite the differences in their dominant modes of movement the 8 16 mm particles typically travelled only about 30 slower during displacement than the 2 4 mm ones whose speeds averaged 21 cm s 1 particles starting from the same point not only moved intermittently downstream but also dispersed both longitudinally and transversely with diffusivities of 4 6 and 0 26 cm 2 s 1 respectively the bedload transport rates measured from the films were consistent with those determined conventionally with a bedload sampler the 2 4 mm particles were entrained 6 times faster on finer areas of the bed where 8 16 mm particles covered 6 of the surface area than on coarser ones where they covered 12 even though 2 4 and 4 8 mm particles covered practically the same percentage areas in both cases the 4 8 and 8 16 mm particles in contrast were entrained at the same rates in both cases to within the statistical uncertainty the rates of distrainment balanced the rates of entrainment for all three sizes and were approximately proportional to the corresponding concentrations of bedload

measuring gravel transport and dispersion in a mountain river using passive radio tracers random walk models of fluvial sediment transport recognize that grains move intermittently with short duration steps separated by rests that are comparatively long these models are built upon the probability distributions of the step length and the resting time motivated by these models tracer experiments have attempted to measure directly the steps and rests of sediment grains in natural streams this paper describes results from a large tracer experiment designed to test stochastic transport models we used passive integrated transponder pit tags to label 893 coarse gravel clasts and placed them in halfmoon creek a small alpine stream near leadville colorado usa the pit tags allow us to locate and identify tracers without picking them up or digging them out of the streambed they also enable us to find a very high percentage of our rocks 98 after three years and 96 after the fourth year we use the annual tracer displacement to test two stochastic transport models the einstein hubbell sayre ehs model and the yang sayre gamma exponential model gem we find that the gem is a better fit to the observations particularly for slower moving tracers and suggest that the strength of the gem is that the gamma distribution of step lengths approximates a compound poisson distribution published in 2012 this article is a us government work and is in the public domain in the usa

the rate of fluvial gravel dispersion 1 sediment dispersion is a fundamental process embedded in the bedload of rivers but the rate at which it occurs is poorly known this study quantifies the streamwise and vertical dispersion rates of gravels over a long flood sequence by using magnetically tagged clasts both grain virtual velocity and grain burial rate decline rapidly as a function of expended flow energy and attain limiting values that are a small proportion of initial rates differences between grain sizes lessen over time as equilibrium rates of dispersion are achieved relative rates demonstrate that streamwise dispersion dominates over vertical dispersion although the latter persists as an essential part of the dispersion process

bed load transport i mechanical characteristics this paper deals with the mechanical characteristics of saltation of bed load transport in flowing water experiments have been carried out by means of high speed photography and advanced data processing techniques taking saltation as the mode of bed load transport systematic analysis has been made with regard to the forces acting on grains and the variation of their magnitudes along the saltation trajectories to obtain the kinematic and dynamic properties of these grains moveover the relations between magnitudes of saltation parameters and flow intensity are attained from the measured data some parameters in bagnold s theory of bed load transport are also discussed

mathematical analysis of the saint venant hirano model for mixed sediment morphodynamics sediment of different size are transported in rivers under the action of flow the first and still most popular sediment continuity model able to deal with mixed sediment is the so called active layer model proposed by hirano 1971 1972 in this paper we consider the one dimensional hydromorphodynamic model given by the saint venant equations for free surface flow coupled with the active layer model we perform a mathematical analysis of this model extending the previous analysis by ribberink 1987 including full unsteadiness and grainsize selectivity of the transported load by explicitly considering multiple sediment fractions the presence of multiple fractions gives rise to distinct waves traveling in the downstream direction for which we provide an analytical approximation of propagation velocity under any froude regime we finally investigate the role of different waves in advecting morphodynamic changes through the domain to this aim we implement an analytical linearized solver to analyze the propagation of small amplitude perturbations of the bed elevation and grainsize distribution of the active layer as described by the system of governing equations we find that initial gradients in the grainsize distribution of the active layer are able to trigger significant bed variations which propagate in the downstream direction at faster pace than the bed wave arising from the unisize sediment saint venant exner model we also verify that multiple sorting waves carry multiple associated bed perturbations traveling at different speeds

bed load at low shields stress on arbitrarily sloping beds failure of the bagnold hypothesis 1 the bagnold hypothesis has been a major tool in the development of mechanistic models of bed load transport according to the hypothesis a necessary constraint for the maintenance of equilibrium bed load transport is that the fluid shear stress at the bed must be reduced to the critical or threshold value associated with incipient motion of grains the constraint determines a functional form for the areal concentration of bed load grains as a function of flow parameters it is shown here however that the bagnold hypothesis breaks down when applied to equilibrium bed load transport on beds with transverse slopes above a relatively modest value that is well below the angle of repose in particular under such conditions it is shown that no areal concentration no matter how large is sufficient to reduce the fluid shear stress at the bed to the critical value this failure motivates the abandonment of the bagnold constraint even for nearly horizontal beds the framework presented here however provides a natural basis for an entrainment based model of sediment transport that neither satisfies nor suffers from the drawbacks of the bagnold constraint