Bedload Transport Model Research Articles

Fluvial bedload transport modelling: advanced ensemble tree-based models or optimized deep learning algorithms?

The potential of advanced tree-based models and optimized deep learning algorithms to predict fluvial bedload transport was explored, identifying the most flexible and accurate algorithm, and the optimum set of readily available and reliable inputs. Using 926 datasets for 20 rivers, the performance of three groups of models was tested: (1) standalone tree-based models Alternating Model Tree (AMT) and Dual Perturb and Combine Tree (DPCT); (2) ensemble tree-based models Iterative Absolute Error Regression (IAER), ensembled with AMT and DPCT; and (3) optimized deep learning models Long Short-Term Memory (LSTM) and Recurrent Neural Network (RNN) ensembled with Grey Wolf Optimizer. Comparison of the predictive performance of the models with that of commonly used empirical equations and sensitivity analysis of the driving variables revealed that: (i) the coarse grain-size percentile D 90 was the most effective variable in bedload transport prediction (where D x is the xth percentile of the bed surface grain size distribution), followed by D 84, D 50, flow discharge, D 16, and channel slope and width; (ii) all tree-based models and optimized deep learning algorithms displayed ‘very good’ or ‘good’ performance, outperforming empirical equations; and (iii) all algorithms performed best when all input parameters were used. Thus, a range of different input variable combinations must be considered in the optimization of these models. Overall, ensemble algorithms provided more accurate predictions of bedload transport than their standalone counterpart. In particular, the ensemble tree-based model IAER-AMT performed most strongly, displaying great potential to produce robust predictions of bedload transport in coarse-grained rivers based on a few readily available flow and channel variables.

On the Effects of Turbulence Modulation Driven by Suspended Sediment Stratification in Emergent Rigid Canopies

AbstractAquatic vegetation has the potential to increase suspended sediment capture while also increasing sediment resuspension and bedload transport. Suspended sediment can induce density stratification, which modulates the turbulence in the water column. We derive a Rouse‐based formulation for suspended sediment concentration (SSC) including the effect of sediment‐induced density stratification. We perform Large Eddy Simulations of vegetated and non‐vegetated channels to explicitly highlight the effect of stratification on SSC profiles. We found that the impact of stratification is dominant in the near‐bed region within the bottom boundary layer, affecting both sediment resuspension and bedload transport. Stratification reduces the likelihood of both dominant sweep and ejection events in the near the bed region which may affect sediment entrainment and bedload transport. Modifications to existing models of sediment entrainment and bedload transport are suggested to account for the effects of sediment induced stratification in vegetated and non‐vegetated channels.

Non-Equilibrium Bedload Transport Model Applied to Erosive Overtopping Dambreach

Bedload sediment transport is an ubiquitous process in natural surface water flows (rivers, dams, coast, etc), but it also plays a key role in catastrophic events such as dyke erosion or dam breach collapse. The bedload transport mechanism can be under equilibrium state, where solid rate and flow carry capacity are balanced, or under non-equilibrium (non-capacity) conditions. Extremely transient surface flows, such as dam/dyke erosive collapses, are systems which always change in space and time, hence absolute equilibrium states in the coupled fluid/solid transport rarely exist. Intuitively, assuming non-equilibrium conditions in transient flows should allow to estimate correctly the bedload transport rates and the bed level evolution. To get insight into this topic, a 2D Finite Volume model for bedload transport based on the non-capacity approach is proposed in this work. This non-equilibrium model considers that the actual bedload sediment discharge can be delayed, spatial and temporally, from the instantaneous solid carry capacity of the flow. Furthermore, the actual solid rate and the adaptation length/time is governed by the temporal evolution of the bedload transport layer and the vertical exchange solid flux. The model is tested for the simulation of overtopping dyke erosion and dambreach opening cases. Numerical results seems to support that considering non-equilibrium conditions for the bedload transport improves the general agreement between the computed results and measured data in both benchmarking cases.

A frictional–collisional model for bedload transport based on kinetic theory of granular flows: discrete and continuum approaches

In this work, the modelling of collisional bedload transport is investigated with a focus on the continuum modelling of the granular flow. For this purpose, a frictional–collisional approach, combining a Coulomb model with the kinetic theory of granular flows, is developed. The methodology is based on a comparison with coupled fluid–discrete simulations that the classical kinetic theory model fails to reproduce. This inaccuracy may be explained by the assumptions of negligible interparticle friction and the absence of a saltation model in the continuum approach. In order to provide guidelines for the modelling, the fluctuating energy balance is computed in the discrete simulations and systematically compared with the kinetic theory laws. Interparticle friction is shown to affect the radial distribution function and to increase the energy dissipation, in agreement with previous observations. In addition, a saltation regime is identified, leading to departure from the viscosity and pseudo-thermal diffusivity laws of the kinetic theory in the dilute regime. Based on these observations, modifications to account for interparticle friction are included in the two-fluid model, and the kinetic theory is coupled with a saltation model. The results show that for inelastic frictional particles, interparticle friction controls energy dissipation, and the macroscopic behaviour of the granular flow does not depend on the microscopic particle properties. The proposed model reproduces the$\mu (I)$rheology in the dense regime of the granular flow. Finally, the model is evaluated with experiments, showing significant improvements concerning the granular flow modelling.

Meta-analysis of a large bedload transport rate dataset

The estimation of bedload transport, a type of coarse fluvial sediment motion, is challenging because of higher-order, complex, and time-variable environmental processes. Still, models for calculating bedload transport mostly rely on semi-empirical formulae derived from time-averaged laboratory flume or field measurements and involve cross-section averaging of hydro-environmental parameters. Additionally, many models assume infinite, constant availability of sediment, which is unrealistic in natural environments. While most published models yield excellent results on the dataset they were trained on, they may be significantly inaccurate when applied to other cases. Also, more recent formulae relying on considerable amounts of data still lead to high calculation uncertainty. While the importance of short-term dynamics, for example, driven by turbulence, for bedload transport is well known, this study investigates the relevance of time-variable processes at monthly to seasonal scales. Our analysis of a large dataset and remote sensing data shows evidence for seasonal variability in measurements of bedload transport rates and challenges the validity of Gaussian statistics for interpolating bedload transport models. Measured bedload transport rates were smaller when snowmelt was taking place and when no glacier was present in the catchment, and were best represented by extreme value distributions. By controlling for biases from measurement devices, geomorphic patterns, and the presence of an upstream dam, we show that steady, constant at-a-station hydraulics only explain a limited share of the variance in the measurements. Ultimately, a model for estimating bedload transport rates should consider the temporal variability of processes across all scales, from turbulence to climate.

Quantifying nonlocal bedload transport: A regional-based nonlocal model for bedload transport from local to global scales

Recent studies have emphasized the importance of nonlocal models in characterizing bedload transport in natural rivers, particularly in mixed-size gravel beds or steep hillslopes. Nonlocality denotes that a quantity (flux) at a specific location x is dependent on the conditions in the surrounding area, as opposed to solely at the location itself. This concept applies in bedload transport even in planar flumes, where particles are entrained at an upstream position and travel a finite distance, ultimately contributing nonlocally to the sediment flux. However, existing bedload transport models, such as the advection–diffusion equation (ADE) or the fractional derivative equation (FDE) models, are inadequate in characterizing the nonlocal transport behavior of bedload at a regional scale. Large errors may arise from the lack of an accurate description of the nonlocal bedload transport processes at regional scales. This study proposes a regional-based nonlocal bedload transport model, which is conceptualized from the probabilistic Exner-based equations and the peridynamic (PD) differential operator. The PD model encapsulates the nonlocal motion of bedload sediments on the basis of the PD differential operator, by utilizing a pre-defined weight function and influence domain. Comparisons demonstrate that the PD model serves as a generalized tool connecting the local and the global models with different PD functions and influence domains. Its variability on kernel function and influence domain, enable it conveniently describe sub-, super-, and normal diffusion behaviors of bedload transport.

Dynamics of Dual‐Mode Bedload Transport With Three‐Dimensional Alternate Bars Migration in Subcritical Flow: Experiments and Model Analysis

AbstractBedload transport often exhibits dual‐mode behavior due to interactions of spatiotemporal controlling factors with the migrating three‐dimensional bedforms (characterized by the fully developed patterns in the bed, such as alternate bars, pools, and clusters). This study explores dual‐mode bedload transport based on experimental measurements and develops Einstein's exponential‐based model to characterize large fluctuations of bedload sediment discharge. The particle waiting time, particle flux, and bed elevation are measured in a series of well‐controlled laboratory experiments. Flume experiments show that the waiting time distribution of sediments gives a bimodal characteristic, two distinct modes can be identified from the measured data. This study encapsulates this dual‐mode bedload transport behavior in a hyperexponential distribution of sediment resting times and introduces it into the continuous time random walk (CTRW) framework. Considering the scaling limit of the thin/heavy‐tailed CTRW processes, a single‐rate mass transfer (SRMT) and fractional‐derivative SRMT (F‐SRMT) models are obtained, and the model parameters are determined from the hyperexponential distribution. Further analyses reveal that the dual‐mode bedload transport behavior is controlled by mass exchange between the mobile and immobile zones, and a dimensionless index η can quantify the intensity of dual‐mode behavior. Applications show that the dual‐mode bedload transport models are much more accurate in characterizing bedload transport in a mixed‐size gravel bed than the traditional exponential‐based model, and the nonlocal movement of bedload sediments is significant in the mixed‐size gravel bed. Further investigations will focus on the applicability test of the dual‐mode models to other flow regimes and conditions.

MacCormack method for solving one-dimensional bed-load sediment transport model

In this work, we investigate the numerical solution of one-dimensional bed-load sediment transport model using two steps finite difference method which so-called MacCormack method. Bed-load sediment transport model is composed by the shallow water equation and Exner equation. The Meyer-Peter and Muller (MPM) formula and Wu formula will be used to determine the Grass factor of the bed-load sediment transport. These governing equations will be discretized into predictor and corrector steps of the MacCormack method. The numerical results of the MacCormack method will be validated with an analytical solution of the bed-load sediment transport model. In addition, the MacCormack solution will also be compared with experimental solutions and another numerical method solutions that have existed previously. The numerical results based on MacCormack method give excellent results in which the numerical and the analytical results are hardly differentiated with RMSE of around 00042 or 4,2 .

How Does Precipitation Variability Control Bedload Response Across a Mountainous Channel Network in a Maritime Climate?

AbstractModeled stream discharge is often used to drive sediment transport models across channel networks. Because sediment transport varies non‐linearly with flow rates, discharge modeled from daily total precipitation distributed evenly over 24‐hr may significantly underestimate actual bedload transport capacity. In this study, we assume bedload transport capacity determined from a hydrograph resulting from the use of hourly (1‐hr) precipitation is a close approximation of actual transport capacity and quantify the error introduced into a network‐scale bedload transport model driven by daily precipitation at channel network locations varying from lowland pool‐riffle channels to upland colluvial channels in a watershed where snow accumulation and melt can affect runoff processes. Transport capacity is determined using effective stresses and the Wilcock and Crowe (2003) equations and expressed in terms of transport capacity normalized by the bankfull value. We find that, depending on channel network location, cumulative error can range from 10% to more than two orders of magnitude. Surprisingly, variation in flow rates due to differences in hillslope and channel runoff do not seem to dictate the network locations where the largest errors in predicted bedload transport capacity occur. Rather, spatial variability of the magnitude of the effective‐bankfull‐excess shear stress and changes in runoff due to snow accumulation and melt exert the greatest influence. These findings have implications for flood‐hazard and aquatic habitat models that rely on modeled sediment transport driven by coarse‐temporal‐resolution climate data.

A semi-implicit approach for sediment transport models with gravitational effects

In this work efficient semi-implicit methods for sediment bedload transport models with gravitational effects under subcritical regimes is proposed. Several families of models with gravitational effects are presented and rewritten under a general formulation that allows us to apply the semi-implicit method. In the numerical tests we focus on the application of a generalization of the Ashida-Michiue model, which includes the gradient of both the bedload and the fluid surface. Analytical steady states solutions (both lake at rest and non vanishing velocity) are deduced an approximated with the proposed scheme. In all the presented tests, the computational efforts are notably reduced thanks to the proposed method without losing the accuracy in the results.

Accuracy of bed-load transport models in eddy-resolving simulations

This work investigates the accuracy of commonly used bed-load transport models when applied in combination with high-resolution Navier-Stokes solvers. Empirical bed-load models predict the transport rate of sediments based on the average bottom shear-stress, while eddy-resolving approaches allow for a space- and time-dependent description of the bottom shear-stress distribution. We discuss the effect that a fine-graining of the stress distribution provided by the flow solver has on the transport model prediction, and we examine the space and time scales at which the averaged values of the transport rate, obtained using the local stress distribution, converge to the transport rate predicted using the average stress. To this aim, we performed Direct Numerical Simulation of a channel flow and used the resulting database to mimic Wall-Resolved and Wall-Modelled Large-Eddy Simulations. We compared the prediction of several bed-load transport models to experimental measurements in order to identify and highlight the limitations that stem from the coupling of these models with eddy-resolving techniques. We find that for small values of the Shields parameter (ratio of viscous and gravitational forces) the fine spatial and temporal resolution of wall-resolved simulations can yield overestimation of the bed-load transport rate; whereas more coarse-grained methods, such as wall-modelled Large Eddy Simulation, result in improved predictions. We also show that a short-time averaging of the force exerted by the fluid on the sediments, which we tested in three different configurations (channel flow with smooth and rough walls and flow over an idealized two-dimensional river dune), improves the accuracy of the bed-load transport predictions, thus providing indications about the flow scales that control the transport process.

Mechanism of collision model for bedload transport

The current study introduces a new particle–particle collision model as well as a classical particle–wall collision model to simulate the process of bedload transport. Large eddy simulation and two-way coupling Lagrangian point–particle models also are applied. Flow conditions for all simulations are done based on previous experiments and four comparison cases are studied. The bedload function result obtained using this model agrees with the previous studies, which proves that the model is reasonable and effective in dealing with bedload transport in turbulent flow. Otherwise, failure to consider the particle–particle collision, Basset force, or Saffman lift force in the model lead to underestimating the bedload transport rate.

Validation of an Experimental Procedure to Determine Bedload Transport Rates in Steep Channels with Coarse Sediment

The current study presents an experimental procedure used to determine bedload sediment transport rates in channels with high gradients and coarse sediment. With the aim to validate the procedure for further investigations, laboratory experiments were performed to calculate bedload transport rates. The experiments were performed in a laboratory tilting flume with slopes ranging from 3% to 5%. The sediment particles were uniform in shape (spheres). The experiments were divided into four cases based on sediment size. Three cases of uniform sizes of 10 mm, 15 mm and 25 mm and a case with a grain size distribution formed with the uniform particle sizes were considered. From the experimental results a mathematical bedload transport model was obtained through multiple linear regression. The experimental model was compared with equations presented in the literature obtained for gravel bed rivers. The experimental results agree with some of the models presented in the literature. The closest agreement was seen with models developed for steep slopes especially for the highest slopes considered in the present study. Therefore, it can be concluded that the methodology used can be replicated for the study of bedload transport rates of channels with high gradients and coarse sediment particles to study more general cases of this process such as sediments with non-uniform shapes and sizes. However, a simplified model is proposed to estimate bedload transport rates for slopes up to 5%.

Bedload transport in rivers, size matters but so does shape

Bedload transport modelling in rivers takes into account the size and density of pebbles to estimate particle mobility, but does not formally consider particle shape. To address this issue and to compare the relative roles of the density and shape of particles, we performed original sediment transport experiments in an annular flume using molded artificial pebbles equipped with a radio frequency identification tracking system. The particles were designed with four distinct shapes and four different densities while having the same volume, and their speeds and distances traveled under constant hydraulic conditions were analyzed. The results show that particle shape has more influence than particle density on the resting time between particle displacement and the mean traveling distance. For all densities investigated, the particle shape systematically induced differences in travel distance that were strongly correlated (R2 = 0.94) with the Sneed and Folks shape index. Such shape influences, although often mentioned, are here quantified for the first time, demonstrating why and how they can be included in bedload transport models.

Smartrock Transport in a Mountain Stream: Bedload Hysteresis and Changing Thresholds of Motion

AbstractBedload movement is fundamentally probabilistic. Our quantitative understanding of gravel transport is particularly limited when flow conditions just exceed thresholds of motion, in part because of difficulties in measuring transport statistics during natural floods. We used accelerometer‐embedded tracer clasts to precisely measure the timing of grain motions and rests during snowmelt floods in Halfmoon Creek, a gravel‐bed mountain stream in Colorado, USA. These new data let us explore how probabilities of tracer movement varied as functions of discharge and time. Bedload hysteresis occurred over both daily and seasonal timescales and included clockwise, counterclockwise, and figure‐eight patterns. We empirically explain the hysteresis by modifying a bedload transport model to have an evolving threshold of motion parameter. We calculate how the thresholds of motion progressively evolved through time over 22 days during the 2015 snowmelt flood. Our results quantitatively show that thresholds of motion are functions of both (a) cumulative shear stress and (b) temporal changes in shear stress during floods.

The influence of channel morphology on bedload path lengths: Insights from a survival process model

SummaryTracer studies are a commonly used tool to develop and test Einstein‐type stochastic bedload transport models. The movements of these tracers are controlled by many factors including grain characteristics, hydrologic forcing, and channel morphology. Although the influence of these sediment storage zones related to morphological features (e.g., bars, pools, riffles) have long been observed to “trap” bedload particles in transport, this influence has not been adequately quantified. In this paper we explore the influence of channel morphology on particle travel distances through the development of a Bayesian survival process model. This model simulates particle path length distributions using a location‐specific “trapping probability” parameter (pi), which is estimated using the starting and ending locations of bedload tracers. We test this model using a field tracer study from Halfmoon Creek, Colorado. We find that (1) the model is able to adequately recreate the observed multi‐modal path length distributions, (2) particles tend to accumulate in trapping zones, especially during large floods, and (3) particles entrained near a trapping zone will travel a shorter distance than one that is further away. Particle starting positions can affect path lengths by as much as a factor of two, which we confirm by modelling “starting‐location‐specific” path length probability distributions. This study highlights the importance of considering both tracer locations and channel topography in examinations of field tracer studies. © 2020 John Wiley & Sons, Ltd.

Measuring and Modeling Gravel Transport at Caspar Creek, CA, to Detect Changes in Sediment Supply, Storage, and Transport Efficiency

AbstractWe developed a technique for reconstructing annual gravel yields and generated a 55‐year record of gravel transport for the North Fork catchment of the Caspar Creek Experimental Watersheds in Northern California. The technique relies on field data collection including annual surveys of weir pond volumes and suspended sediment measurements, as well as an accounting for settling of suspended sediment and organic matter in the pond. We compared these annual yields to gravel yields predicted by the Wilcock two‐fraction bed load transport model, which we calibrated from measured values at Caspar Creek. We considered three velocity‐discharge relationships and found that values of hydraulic variables measured during storms produced the best fit between reconstructed and predicted annual gravel yields when years with large disturbances were excluded. We also compared predicted gravel transport rates to bed load transport rates measured from 1988 to 1995 with bed load pit samplers. We found that the calibrated model predictions agreed well with the field‐measured bed load transport rates. To investigate the role of supply and storage on gravel transport, we compared the reconstructed gravel yields to predicted gravel yields and found that increased occurrence of landslides and headcut erosion in the 1990s and early 2000s did not lead to an increase in gravel yields. Instead, input of large downed wood in the 1990s created storage space and decreased bed load delivery to the weir pond.

Field Application and Validation of a Seismic Bedload Transport Model

AbstractBedload transport drives morphological changes in gravel‐bed streams and sediment transfer in catchments. The large impact forces associated with bedload motion and its highly dynamic spatiotemporal nature make it difficult to monitor bedload transport in the field. In this study, we revise a physically‐based model of bedload‐induced seismic ground motion proposed by Tsai et al. (2012) and apply it to invert bedload flux from seismic measurements alongside an Alpine stream. First, we constrain the seismic response of a braided river reach with a simple active experiment using a series of large‐rock impacts. This allows the characterization of surface wave propagation and attenuation with distance from the impact source. Second, we distinguish bedload‐generated ground vibrations from those caused by turbulent flow using frequency‐based scaling relationships between seismic power and discharge. Finally, absolute bedload transport rates are quantified from seismic measurements using inverse modeling based on a simplified formulation of bedload particle motion. The results are verified with a large data set of bedload samples (between 0.01 and 1 kg/m/s), demonstrating that seismic measurements can provide an indirect measure for bedload flux with an uncertainty of less than one order of magnitude. Larger deviations may be due to the contribution of turbulent flow effects and remaining uncertainties in particle impact mechanics (elasticity and velocity). When constraining these uncertainties, seismic monitoring may provide an accurate and continuous means to investigate bedload dynamics in gravel‐bed streams.

Joint Stochastic Bedload Transport and Bed Elevation Model: Variance Regulation and Power Law Rests

We describe the joint dynamics of bedload transport and bed elevation changes with a stochastic population model, and we analyze (1) the dependence of bedload flux statistics on local bed elevations and (2) resting time distributions for sediment undergoing burial in the fluctuating sedimentary bed. The model involves entrainment and deposition in a control volume characterized by elevation‐dependent rates, and it exhibits a statistical regulation effect, whereby bed aggradation suppresses the variance of the bedload flux while degradation enhances it. This variance regulation effect is contingent on collective entrainment, whereby moving grains destabilize stationary grains in a positive feedback. When collective entrainment is turned off,bedload transport fluctuations become independent of the bed elevation. Return times from above in the bed elevation time series provide heavy‐tailed power law distributions of resting times with tail behavior characterized by the mean erosion rate and the active layer depth. These results imply bedload statistics measurements on relatively short timescales can be strongly biased by bed elevation changes when collective entrainment occurs, and they support the growing consensus that sediment burial generates heavy‐tailed sediment resting times that ultimately generate anomalous bedload diffusion.

Bedload transport rate prediction: Application of novel hybrid data mining techniques

The accurate prediction of bedload transport in gravel-bed rivers remains a significant challenge in river science. However the potential for data mining algorithms to provide models of bedload transport have yet to be explored. This study provides the first quantification of the predictive power of a range of standalone and hybrid data mining models. Using bedload transport data collected in laboratory flume experiments, the performance of four types of recently developed standalone data mining techniques - the M5P, random tree (RT), random forest (RF) and the reduced error pruning tree (REPT) - are assessed, along with four types of hybrid algorithms trained with a Bagging (BA) data mining algorithm (BA-M5P, BA-RF, BA-RT and BA-REPT). The main findings are four-fold. First, the BA-M5P model had the highest prediction power (R2 = 0.943; RMSE = 0.061 kg m−1 s−1; MAE = 0.040 kg m−1 s−1; NSE = 0.945; PBIAS = −1.60) followed by M5P, BA-RT, RT, BA-RF, RF, BA-REPT, and REPT. All models displayed ‘very good’ performance except the BA-REPT and REPT model, which were ‘satisfactory’. Second, the M5P, BA-RT, and RT models underestimated, and the BA-M5P, BA-RF, RF, BA-REPT and REPT models overestimated, bedload transport rates. Third, flow velocity had the most significant impact on bedload transport rate (PCC = 0.760) followed by shear stress (PCC = 0.709), discharge (PCC = 0.668), bed shear velocity (PCC = 0.663), bed slope (PCC = 0.490), flow depth (PCC = 0.303), median sediment diameter (PCC = 0.247), and relative roughness (PCC = 0.003). Fourth, the maximum depth of tree was the most sensitive operator in decision tree-based algorithms, and batch size, number of execution slots and number of decimal places did not have any impact on model’ prediction power. Overall the results revealed that hybrid data mining techniques provide more accurate predictions of bedload transport rate than standalone data mining models. In particular, M5P models, trained with a Bagging data mining algorithm, have great potential to produce robust predictions of bedload transport in gravel-bed rivers.