Numerical Simulation of Bed Load and Suspended Load Sediment Transport Using Well-Balanced Numerical Schemes

Sediment transport can be modelled using hydrodynamic models based on shallow water equations coupled with the sediment concentration conservation equation and the bed con-servation equation.The complete system of equations is made up of the energy balance law and the Exner equations.The numerical solution for this complete system is done in a seg-regated manner.First,the hyperbolic part of the system of balance laws is solved using a finite volume scheme.Three ways to compute the numerical flux have been considered,the Q-scheme of van Leer,the HLLCS approximate Riemann solver,and the last one takes into account the presence of non-conservative products in the model.The discretisation of the source terms is carried out according to the numerical flux chosen.In the second stage,the bed conservation equation is solved by using the approximation computed for the system of balance laws.The numerical schemes have been validated making comparisons between the obtained numerical results and the experimental data for some physical experiments.The numerical results show a good agreement with the experimental data.

Seasonal distribution and relationship of water mass and suspended load in North Yellow Sea

The concentration of suspended load can be determined by its linear relationship to turbidity. Our results present the basic distribution of suspended load in North Yellow Sea. In summer, the suspended load concentration is high along the coast and low in the center of the sea. There are four regions of high concentration in the surface layer： Penglai and Chengshantou along the north of the Shandong Peninsula, and the coastal areas of Ltishun and Changshan Islands. There is a 2 mg/L contour at 124°E that separates the North Yellow Sea from regions of lower concentrations in the open sea to the west. And there is a 2 mg/L contour at 124°E that separates the North Yellow Sea from regions of lower concentrations in the open sea to the west. The distribution features in the 10 m and bottom layer are similar to the surface layer, however, the suspended load concentration declines in the 10 m layer while it increases in the bottom layer. And in the bottom layer there is a low suspended load concentration water mass at the region south of 38°N and east of 123°E extending to the southeast. In general, the lowest suspended load concentration in a vertical profile is at a depth of 10 to 20 m, the highest suspended load concentration is in the bottom near Chengshantou area. In winter, the distribution of suspended load is similar to summer, but the average concentrations are three times higher. There are two tongue-shaped high suspended load concentration belt, one occurring from surface to seafloor, extends to the north near Chengshantou and the other invades north to south along the east margin of Dalian Bay. They separate the low suspended load concentration water masses in the center of North Yellow Sea into east and west parts, Vertical distribution is quite uniform in the whole North Yellow Sea because of the cooling effect and strong northeast winds. The distribution of suspended load has a very close relationship to the current circulation and wind-induced waves in the North Yellow Sea. Because of this, we have been able to show for the first time that the distribution of suspended load can be used to identify water masses.

Daily and Monthly Suspended Sediment Load Predictions Using Wavelet Based Artificial Intelligence Approaches

In the current study, the efficiency of Wavelet-based Least Square Support Vector Machine （WLSSVM） model was examined for prediction of daily and monthly Suspended Sediment Load （SSL） of the Mississippi River. For this purpose, in the first step, SSL was predicted via ad hoc LSSVM and Artificial Neural Network （ANN） models; then, streamflow and SSL data were decomposed into sub- signals via wavelet, and these decomposed sub-time series were imposed to LSSVM and ANN to simulate discharge-SSL relationship. Finally, the ability of WLSSVM was compared with other models in multi- step-ahead SSL predictions. The results showed that in daily SSL prediction, LSSVM has better outcomes with Determination Coefficient （DC）=o.92 than ad hoc ANN with DC=o.88. However unlike daily SSL, in monthly modeling, ANN has a bit accurate upshot. WLSSVM and wavelet-based ANN （WANN） models showed same consequences in daily and different in monthly SSL predictions, and adding wavelet led to more accuracy of LSSVM and ANN. Furthermore, conjunction of wavelet to LSSVM and ANN evaluated via multi-step-ahead SSL predictions and, e.g., DCLssVM=0.4 was increased to the DCwLsSVM=0.71 in 7- day ahead SSL prediction. In addition, WLSSVM outperformed WANN by increment of time horizon prediction.

Local vs. cross station simulation of suspended sediment load in successive hydrometric stations: heuristic modeling approach

The present paper aims at modeling suspended sediment load(SSL) using heuristic data driven methodologies, e.g. Gene Expression Programming(GEP) and Support Vector Machine(SVM) in three successive hydrometric stations of Housatonic River in U.S. The simulations were carried out through local and cross-station data management scenarios to investigate the interrelations between the SSL values of upstream/downstream stations. The available scenarios were applied to predict SSL values using GEP to obtain the best models. Then, the best models were predicted by SVM approach and the obtained results were compared with those of GEP. The comparison of the results revealed that the SVM technique is more capable than the GEP for modeling the SSL through the both local and cross-station data management strategies. Besides, local application seems to be better than cross-station application for modeling SSL. Nevertheless, the cross-station application demonstrated to be a valid methodology for simulating SSL, which would be of interest for the stations with lack of observational data. Also, the prediction capability of conventional Sediment Rating Curve(SRC) method was compared with those of GEPand SVM techniques. The obtained results revealed the superiority of GEP and SVM-based models over the traditional SRC technique in the studied stations.

A DISCUSSION ON CURRENTS AND SUSPENDED LOAD TRANSPORT IN SURF ZONE

In this paper, the distribution characteristics of the breaking wave current and suspended load transport in the surf zone are discussed in main. Based on the measured data of the waves, the form of breaking wave, the breaking wave current and the sediment concentration of suspended load in the offshore surf zone near Nouakchott, the Islamic Republic of Mauritania, the author has analized the law governing the distribution of longshore current and sediment concentration of suspended load by means of statistical method, and presented a calculation method for the longshore sediment transport in offshore surf zone.

A 2D Mathematical Model for Sediment Transport by Waves and Tidal Currents

In this study, the combined actions of waves and tidal currents in estuarine and coastal areas are considered and a 2D mathematical model for sediment transport by waves and tidal currents has been established in orthogonal curvilinear coordinates. Non-equilibrium transport equations of suspended load and bed load are used in the model. The concept of background concentration is introduced, and the formula of sediment transport capacity of tidal currents for the Oujiang River estuary is obtained. The Dou Guoren formula is employed for the sediment transport capacity of waves. Sediment transport capacity in the form of mud and the intensity of back silting are calculated by use of Luo Zaosen＇ s formula. The calculated tidal stages are in good agreement with the field data, and the calculated velocities and flow directions of 46 vertical lines for 8 cross sections are also in good agreement with the measured data. On such a basis, simulations of back silting after excavation of the waterway with a sand bar under complicated boundary conditions in the navigation channel induced by suspended load, bed load and mud by waves and tidal currents are discussed.

Two-Dimensional Mathematical Model of Tidal Current and Sediment for Oujiang Estuary and Wenzhou Bay

A 2-D mathematical model of tidal current and sediment has been developed for the Oujiang Estuary and the Wenzhou Bay. This model accomodates complicated features including multiple islands, existence of turbidity, and significant differ-ence in size distribution of bed material. The governing equations for non-uniform suspended load and bed load transport are presented in a boundary-fitted orthogonal curvilinear coordinate system. The numerical solution procedures along with their initial conditions, boundary conditions, and movable boundary technique are presented. Strategies for computation of the critical condition of deposition or erosion, sediment transport capacity, non-uniform bed load discharge, etc. are suggested. The model verification computation shows that, the tidal levels computed from the model are in good agreement with the field data at the 18 tidal gauge stations. The computed velocities and flow directions also agree well with the values measured along the totally 52 synchronously observed verticals distributed over 8 cross sections. The coraputed tidal water throughputs through the Huangda'ao cross section are close to the measured data. And the computed values of bed deformation from Yangfushan to the estuary outfall and in the outer-sea area are in good agreement with the data observed from 1986 to 1992. The changes of tidal volumes through the estuary, velocities in different channels and the bed form due to the influence of the reclamation project on the Wenzhou shoal are predicted by means of this model.

Numerical Si mulation of Transportation of SPMfrom the Yellow River to the Bohai Sea

A 3D diagnostic model including a suspended sediment transport module, ECOMSED, driven by the monthly discharge and sediment load of the Yellow River in 1983 ～ 1984, was applied to the Bohai Sea. The simulation of the temporal-spatial variation of SPM （Suspended Particular Matter） concentration, sediment flux, and deposition rate was carfled out. It could be seen that, the SPM concentration exhibited distinct seasonal variation, and the variation characteristic was similar for two years. Some of the fine sediment of the Yellow River extended to the western bank of the Liaodong Bay, but most of the sediment deposited around the estuary of the Yellow River, the deposition flux rapidly decreasing with the increasing distance to the estuary. The deposition rate kept at 0.05 ～ 0.1 mm/a for most area, close to the insitu data. There were two areas of high SPM concentration in the Bohai Sea, one of which could be attributed to the Yellow River discharge, and another one, located at the seas with intensive resuspension power, to the tidal current energy. The sediment from the Yellow River was transported mainly along the track of the, Lagrangian residual cireulations. In one word, the suspended load transport was basically attributed to the wind-driven and tidal-induced Lagrangian residual circulations. The resuspenslon flux was related to the bottom currents： the larger the current speed, the more the sediment resuspended.

Equilibrium bed—concentration of nonuniform sediment

Knowledge of the equilibrium bed-concentration is vital to mathematic a l modeling of the river-bed deformation associated with suspended load but prev i ous investigations only dealt with the reference concentration of uniform sedime nt because of difficulties in observation of the bed-concentration. This work i s a first attempt to develop a theoretical formula for the equilibrium bed-conce n tration of any fraction of nonuniform sediment defined at the bed-surface. The f ormula is based on a stochastic-mechanistic model for the exchange of nonunifor m sediment near the bed, and described as a function of incipient motion probabil ity, non-ceasing probability, pick-up probability, and the ratio of the averag e single-step continuous motion time to static time. Comparison of bed-concentra ti on calculated from the proposed formula with the measured data showed satisfacto ry agreement, indicating the present formula can be used for solving the differe ntial equation governing the motion of suspended load.

Numrical Model of Total Sediment Transport in the Yangtze Estuary

Based on the non-equilibrium suspended load transport equation, bed load transport equation and sediment transport capacity formulas derived by Don et al. , a 2-D numerical model of total sediment transport in the Yangtze Estuary is presented. In the model, the actions of tidal currents and wind waves and the effect of salinity on sediment transport are considered. An automatically generated boundary-fitted grid is used to fit the boundaries of the estuary and the boundaries of engineering projects. The verification of calculations shows that the sediment concentration, the deformation of riverbed and siltation in the channels caused by typhoons can be successfully simulated.

Vertical distribution of sediment concentration

A simple formula is proposed to predict the vertical distribution of a suspended load concentration in a 2D steady turbulent flow. The proposed formula significantly improves the well-known Rouse formula where sediment concentration has an infinitely large value at the channel bottom and a zero value at the water surface. Based on this formula and the logarithmic ve- locity profile, a theoretical elementary function for the transport rate of a suspended load is developed. This equation improves the Einstein equation in which the unit-width suspended sediment discharge must be solved by numerical integration and a contra- diction between the lower limit of the integral and that of velocity distribution exists.

A method for simulating sediment incipient motion varying with time and space in an ocean model(FVCOM):development and validation

We modified the sediment incipient motion in a numerical model and evaluated the impact of this modification using a study case of the coastal area around Weihai, China. The modified and unmodified versions of the model were validated by comparing simulated and observed data of currents, waves, and suspended sediment concentrations(SSC) measured from July 25^(th) to July 26^(th), 2006. A fitted Shields diagram was introduced into the sediment model so that the critical erosional shear stress could vary with time. Thus, the simulated SSC patterns were improved to more closely reflect the observed values, so that the relative error of the variation range decreased by up to 34.5% and the relative error of simulated temporally averaged SSC decreased by up to 36%. In the modified model, the critical shear stress values of the simulated silt with a diameter of 0.035 mm and mud with a diameter of 0.004 mm varied from 0.05 to 0.13 N/m^2, and from 0.05 to 0.14 N/m^2, respectively, instead of remaining constant in the unmodified model. Besides, a method of applying spatially varying fractions of the mixed grain size sediment improved the simulated SSC distribution to fit better to the remote sensing map and reproduced the zonal area with high SSC between Heini Bay and the erosion groove in the modified model. The Relative Mean Absolute Error was reduced by between 6% and 79%, depending on the regional attributes when we used the modified method to simulate incipient sediment motion. But the modification achieved the higher accuracy in this study at a cost of computation speed decreasing by 1.52%.

Comparisons between unsteady sediment-transport modeling

The comparative study between unsteady flow models in alluvial streams shows a chaotic residue as for the choices of a forecasting model. The difficulty resides in the choice of the expressions of friction resistance and sediment transport. Three types of mathematical models were selected. Models of type one and two are fairly general, but require a considerable number of boundary conditions, which related to each size range of sediments. It can be a handicap during rivers studies which are not very well followed in terms of experimental measurements. Also, the use of complex models is not always founded. But then, the model of type three requires a limited number of boundary conditions and solves only a system of three equations at each time step. It allows a considerable saving in calculating times.

Contrasting lipid biomarkers in mountain rivers in the Nepal Himalayas: Organic matter characteristics and contribution to the fluvial carbon pool

The Nepal Himalayas is the source of many glacial and spring-fed river systems crisscrossing the mountainous terrain.There is an increasing recognition of small mountain rivers(SMRs)to have a significant combined export of dissolved and particulate organic carbon to the global carbon flux.We analyzed fluvial sediments from two SMRs and compared the results with two large mountain rivers(LMRs)in Nepal.We investigated the organic matter(OM),its compositional variability,and seasonal export using a suite of lipid biomarkers,namely n-alkanes,n-alkanoic acids,n-alkanols,and sterols.The SMRs indicated a similarity in lipid distribution and were affected by a strong seasonal variability.The LMRs showed a distinct contrast in the distribution of lipids in suspended sediments.Bedload sediments in SMRs were derived from diverse sources with weak terrigenous dominance all-year-round compared to the suspended load.Functional lipids(n-alkanoic acids and n-alkanols)were the major constituents in SMR sediments,indicating better preservation.In contrast,n-alkane concentration dominated over other fractions in suspended sediments retrieved from LMRs.The biomarker trends differentiate SMRs from LMRs with lower transformed/degraded OM in SMRs.A common observation was the strong presence of even carbon compounds in short-chain n-alkanes in SMR bedload sediments and their predominance in suspended sediments in LMRs.Such an unusual trend is attributed to specific biomarker sources from the catchment and ongoing processes in fluvial systems.Topsoil colonized by fungal species under moist acidic conditions and autochthonous bacteria contributes to the organic matter pool in shallow SMRs.In LMRs,the contribution from thermally mature sedimentary hydrocarbons and the diagenetic reduction of nalkanoic acids to n-alkanes are additional contributors to the allochthonous carbon pool.The differences in lipid concentrations,their distribution,seasonality,and the size of rivers suggest differential preservation/degradation of the organic matter pool and their importance in contributing to the carbon budget.

Numerical Analysis of Adaptation-to-capacity Length for Fluvial Sediment Transport

Over the last several decades,various sediment transport capacity formulations have been used by geomorphologists and engineers to calculate fluvial morphological changes.However,it remains poorly understood if the adaptation to capacity could be fulfilled instantly in response to differing inflow discharges and sediment supplies,and thus if the calculation of morphological changes in rivers based on the assumed capacity status is fully justified.Here we present a numerical investigation on this issue.The distance required for sediment transport to adapt to capacity(i.e.,adaptation-to-capacity length) of both bed load and suspended sediment transport is computationally studied using a coupled shallow water hydrodynamic model,in line with varied inlet sediment concentrations.It is found that the adaptation-to-capacity length generally decreases as the Rouse number increases,irrespective of whether the inlet sediment concentration increases or reduces.For cases with vanishing inlet sediment concentration a unified relationship is found between the adaptation-to-capacity length and the Rouse number.Quantitatively,the adaptation-to-capacity length of bed load sediment is limited to tens of times of the flow depth,whilst that of suspended sediment increases substantially with decreasing Rouse number and can be up to hundreds of times of the flow depth.The present finding concurs that bed load sediment transport can adapt to capacity much more rapidly than suspended sediment transport,and it facilitates a quantitative criterion on which the applicability of bed load or suspended sediment transport capacity for natural rivers can be readily assessed.

Evaluation of suspended load transport rate using transport formulas and arti- ficial neural network models (Case study: Chelchay Catchment)

Accurate estimation of sediment load or transport rate is very important to a wide range of water resources projects. This study was undertaken to determine the most appropriate model to predict suspended load in the Chelehay Watershed, northeast of Iran. In total, 59 data series were collected from four gravel bed-rivers and a sand bed river and two depth integrating suspended load samplers to evaluate nine suspended load formulas and feed forward backpropagation Artificial Neural Network （ANN） structures. Although the Chang formula with higher correlation coefficient （r = 0.69） and lower Root Mean Square Error （RMSE = 0.013） is the best suspended load predictor among the nine studied formulas, the ANN models significantly outperform traditional suspended load formulas and show their superior performance for all statistical parameters. Among different ANN structures two models inclu- ding 4 inputs, 4 hidden and one output neurons, and 4 inputs, 4 and one hidden and one output neurons provide the best simulation with the RMSE values of 0.0009 and 0.001, respectively.

Application of 2-D sediment model to fluctuating backwater area of Yangtze River

Based on the characteristics of backflow, a two-dimensional mathematical model of sediment movement was established. The complexity of the watercourse boundary at the confluence of the main stream and the tributary was dealt with using a boundary-fitting orthogonal coordinate system. The basic equation of the two-dimensional total sediment load model, the numerical calculation format, and key problems associated with using the orthogonal curvilinear coordinate system were discussed. Water and sediment flow in the Chongqing reach of the Yangtze River were simulated. The calculated water level, flow velocity distribution, amount of silting and scouring, and alluvial distribution are found to be in agreement with the measured data, which indicates that the numerical model and calculation method are reasonable. The model can be used for calculation of flow in a relatively complicated river network.

RESEARCHES ON THE TRANSVERSE DISTRIBUTION OF SUSPENDED LOAD CONCENTRATION

In the paper the simplified three-dimensional turbulent diffusion equation ofthe suspended load is deduced by the power series method. The formula on the transversedistribution of the suspended load concentration is obtained, which is tested by a few field data onYangtze River. The simulation results indicate that the calculated data are in primary agreementwith the field data within the allowable error. It is certain value in theory and practice.

Impact of the Iron Gates on the Sediments with an Emphasis on the Area of the Future Belene Nuclear Power Plant

The present investigation has been fulfilled with a view to the future nuclear power station constriction near the Belene Island.Sediment loads and sediment transportation are important factors for the technical water supply of the nuclear station Belene.The paper deals with change of suspended sediment load at Bulgarian part of the Danube River downstream of the Iron Gates.Recent data on suspended sediment loads for the hydrometric gauge station at Svishtov have been collected,computed and presented.The results obtained discover the time variability of the sediment loads,climate change and the anthropogenic impact on the suspended sediments.The tendency of alteration and inter-annual variability of the suspended sediments are investigated and characteristics of average annual,monthly and maximal values are shown.In the material archive granulometric data are presented for this part of the Bulgarian stretch before the Iron Gates construction in the conditions of the natural sediment regime.There are statistical parameters of the studied characteristics of the river turbidity and discharge before and after the anthropogenic impact.The increase of the absolute minimal turbidity has been determined after the Iron Gate I as a result of activation of the bed processes and hydro-morphological changes.

MATHEMATICAL MODELLING OF DEGRADATION AND FLUVIAL PROCESS DOWNSTREAM RESERVOIRS

To research into the problem of degradation and fluvial process downstream reservoirs and its influence on flood control and navigation, a 1-D mathematical model of degradation and fluvial process downstream the reservoir was established in this paper. The non-equilibrium transport of non-uniform suspended load, the non-uniform bedload transport and bed material sorting were considered in the model. Some techniques were suggested for some problems in calculation, such as the effective suspended load carrying capacity of the different reaches of bed materials, the coefficient of suspended load carrying capacity, the recovering coefficient of carrying capacity, the mixed layer thickness, the bedload transport width, bifurcation and confluence of main and branch channel, and the distribution of deposition and erosion along the cross section, etc. The model was tested by the data of degradation downstream the Danjiangkou reservoir on the Hanjiang River and the data of degradation downstream the Gezhouba Project on the Yangtze River.