Sediment Transport Equations Research Articles

A two‐dimensional finite volume morphodynamic model on unstructured triangular grids

AbstractWe discuss the application of a finite volume method to morphodynamic models on unstructured triangular meshes. The model is based on coupling the shallow water equations for the hydrodynamics with a sediment transport equation for the morphodynamics. The finite volume method is formulated for the quasi‐steady approach and the coupled approach. In the first approach, the steady hydrodynamic state is calculated first and the corresponding water velocity is used in the sediment transport equation to be solved subsequently. The second approach solves the coupled hydrodynamics and sediment transport system within the same time step. The gradient fluxes are discretized using a modified Roe's scheme incorporating the sign of the Jacobian matrix in the morphodynamic system. A well‐balanced discretization is used for the treatment of source terms. We also describe an adaptive procedure in the finite volume method by monitoring the bed–load in the computational domain during its transport process. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bed gradients that may form in the approximate solution. Numerical results are shown for a test problem in the evolution of an initially hump‐shaped bed in a squared channel. For the considered morphodynamical regimes, the obtained results point out that the coupled approach performs better than the quasi‐steady approach only when the bed–load rapidly interacts with the hydrodynamics. Copyright © 2009 John Wiley & Sons, Ltd.

Applicability of Sediment Transport Capacity Formulas to Dam-Break Flows over Movable Beds

In this paper, we investigate the extent to which well-known sediment transport capacity formulas can be used in one-dimensional (1D) numerical modeling of dam-break waves over movable beds. The 1D model considered here is a one-layer model based on the shallow-water equations, a bed update (Exner) equation, a space-lag equation for the nonequilibrium sediment transport and an empirical formula calculating the sediment transport capacity of the flow. The model incorporates a variety of sediment transport capacity formulas proposed by Meyer-Peter and Muller, Bagnold, Engelund and Hansen, Ackers and White, Smart and Jaeggi, van Rijn, Rickenmann, Cheng, Abrahams and Camenen, and Larson. We examine the performance of each formula by simulating four idealized laboratory cases on dam-break waves over sandy beds. Comparisons between numerical results and measurements show that for each case better predictions are obtained using a particular formula, but overall, formulas proposed by Meyer-Peter and Muller (with the factor 8 being replaced by 12), Smart and Jaggi, Cheng, Abrahams and Camenen, and Larson rank as the best predictors for the entire range of conditions studied here. Moreover, results show that in the cases where a bed step exists, implementing a mass failure mechanism in the numerical modeling plays an important role in reproducing the bed and water profiles.

Experimental Study and Numerical Simulation of Sediment Transport in a Shallow Reservoir

The prediction of sedimentation is an important aspect of reservoir planning and design. Such prediction can be supported by detailed analyses of flow patterns and sediment transport inside reservoirs, usually conducted through numerical simulation. This research compares laboratorial sedimentation experiments in a shallow reservoir and predictions using a 2D numerical model with depth-average Navier-Stokes equations and a sediment transport code. A number of sediment transport equations were tested, among which the Engelund and Fredsoe formulation better represented the measured data. Flows without sediment transport or without bed dunes could be simulated using Smagorinski’s turbulence model, while flows with sediment occurring over dunes needed the use of a constant turbulent viscosity. The similarity obtained between experimental data and numerical results, for both flow pattern and sediment deposition, confirms that the models and numerical codes used in this work are useful for the analysis and prediction of reservoir sedimentation.

낙동강하구둑 상류 접근수로에서의 유사량 공식 및 유사 이송형태에 따른 하상변동 수치모의에 관한 연구

본 논문에서는 2차원 하상변동 수치모형인 CCHE2D 모형을이용하여 유사량 공식과 유사이송형태별 이류-확산 방정식의 선택이 하상변동 수치모의결과 값에 미치는 영향을 분석하고 실제 현장자료와 비교하였다. 또한 이러한 분석을 기초로 낙동강하구둑 상류 접근수로에서의 최적의 유사량 공식과 유사 이송형태별 이류-확산 방정식을 제안하였다. 낙동강하구둑 상류 접근수로에 대해 Ackers and White와 Engelund and Hansen의 유사량 공식과 소류사와 부유사 유사 이송형태에 따른 이류-확산 방정식을 각각 다르게 적용하여 모의한 결과, Engelund and Hansen 공식을 적용한 경우에는 Ackers and White 공식을 적용한 경우와 비교했을 때, 평수 및 홍수 조건에서 모두 하상변동량이 거의 없는 것으로 나타났다. 또한 Ackers and White 공식으로 2002년에 발생한 실제 수문사상을 적용하여 하상변동 모의한 결과, 소류사 이송형태의 이류-확산 방정식을 적용한 모의결과가 부유사 이송형태를 적용했을 경우 보다 실제 하상변동에 더 근접한 것으로 나타났다. The effects of the selection for sediment transport equations and advection-diffusion equations according to different sediment transport modes on the modeling results of bed changes were analyzed using the CCHE2D and compared with field data in this paper. The most suitable sediment transport equation and sediment transport mode for advection-diffusion equation were suggested for the upstream approached channel of the Nakdong River Estuary Barrage. The bed changes simulated by the Engelund and Hansen formula were very small in the modeling case for the low and high flow discharges compared with the case of the Ackers and White formula. Also, the numerical modeling with the actual hydraulic event in 2002 presents that the bed change result with the bed load transport type for advection-diffusion equation was close to the field measurement more than the suspended load type.

Numerical modelling of non-equilibrium graded sediment transport in a curved open channel

The computer code FAST3D has been developed to calculate flow and sediment transport in open channels. In the code, the flow field is calculated by solving the full Reynolds-averaged Navier–Stokes equations with k–ε turbulence model; the bed-load transport is simulated with a non-equilibrium model containing an important parameter, the so-called non-equilibrium adaptation length, which characterizes the distance for sediment to adjust from a non-equilibrium state to an equilibrium state; the bed deformation is obtained from an overall mass-balance equation for sediment transport. The governing equations are solved numerically with a finite volume method on an adaptive, non-staggered grid. The former model assumed uniform bed material. In order to take into account the influence of grain-size distribution of the bed-surface on the evolution of the bed topography and consequently also on the flow field, a sediment transport module has been presently developed by the authors at the Institute of Hydraulic and Water Resources Engineering, Technische Universität München, Germany, for fractional sediment transport using a multiple layer model. This paper presents the numerical results for sediment sorting and the bed deformation in a curved alluvial channel under unsteady-flow conditions according to Yen and Lee (1995). The calculations were compared with data from laboratory measurements. Further, the sensitivity of the simulated results to the non-equilibrium adaptation length is investigated.

A model for unsteady sediment transport in degrading alluvial channels

The collection of data for unsteady/non-uniform sediment transport rates in a river below a reservoir, which arrests sediment from upstream, is very difficult. The establishment of a model for the determination of these sediment transport rates is equally difficult but important for the safety of a structure below the reservoirs. An indirect technique based on continuity equation for sediment transport has been used to obtain such data for unsteady/non-uniform flow conditions. Based on these data and dimensional analysis, a relationship for determination of sediment transport rate below high capacity reservoirs under unsteady-non-uniform conditions has been proposed which gave very high efficiency when checked with the available data for such conditions. As a consequence, a relationship for extent of degradation has also been established.

Fine sediment carrying capacity of combined wave and current flows

Abstract The so-called fine sediment in many coastal areas and estuaries in China is mostly referred to the mixture of cohesive sediment and non-cohesive sediment. To predict the mixed type fine sediment transport, sediment carrying capacity formulae combined with the 2-D suspended sediment transport equation and morphologic equation have been widely used in China. In the present study, the sediment carrying capacity formula suggested by Dou et al. (1995) for wave conditions has been improved and implemented for the prediction of sediment transport in nearshore regions where wave activities are significant. The improvement is based on the wave energy dissipation principle inside and outside the surf zone. In the improved formula, sediment in suspension increases with the magnitude of the wave period and this feature complies with general observations. More than 300 laboratory and field measured data sets have been reviewed and 12 of them have been used to verify and determine the major coefficients in the improved formula. The application of the sediment carrying capacity model in combined wave and current situations shows that the model can faithfully reproduce the cross-shore sediment concentration distributions at the southwest coast of Bohai Bay.

Modeling sediment transport beneath skewed asymmetric waves above a plane bed

A one‐dimensional model solving the Reynolds‐averaged Navier‐Stokes and advection‐diffusion equations in conjunction with a k − ε model for turbulence closure is used to systematically explore net sediment transport rates beneath skewed asymmetric waves under sheet flow conditions. The model, which reproduces net rates obtained in U tube experiments under purely skewed and asymmetric oscillatory flow well, is forced with an analytical expression of free stream oscillatory flow in which we varied the degree of skewness versus asymmetry, the magnitude of the total wave nonlinearity, the oscillatory flow amplitude, and the wave period. We find that for a wide range of conditions sediment entrained into the flow during a particular wave half‐cycle has not completely settled before flow reversal and tends to be transported during the next half‐cycle. Consistent with earlier work, these phase‐lag effects reduce transport rates under oscillatory flow dominated by velocity skewness, while they enhance net transport rates under oscillatory flow dominated by velocity asymmetry. Phase‐lag effects are particularly important in fine‐medium sands (<≈250 μm). For a given grain size phase‐lag effects become more pronounced with an increase in wave nonlinearity and in velocity amplitude, and with a decrease (increase) in wave period under skewed (asymmetric) oscillatory flow. When phase‐lag effects are negligible, transport rates are largest under skewed oscillatory flow containing some asymmetry; otherwise, they are largest under asymmetric flow. Our work implies that nearshore sediment transport equations based on the instantaneous bed shear stress may be restricted in applicability to situations when the grain size exceeds ≈250 μm.

Modeling of Hillslope Runoff and Soil Erosion at Rainfall Events Using Cellular Automata Approach

A novel quantitative cellular automata (CA) model that simulates and predicts hillslope runoff and soil erosion caused by rainfall events was developed by integrating the local interaction rules and the hillslope surface hydraulic processes. In this CA model, the hillslope surface was subdivided into a series of discrete spatial cells with the same geometric features. At each time step, water and sediment were transported between two adjacent spatial cells. The flow direction was determined by a combination of water surface slope and stochastic assignment. The amounts of interchanged water and sediment were computed using the Chezy-Manning formula and the empirical sediment transport equation. The water and sediment discharged from the open boundary cells were considered as the runoff and the sediment yields over the entire hillslope surface. Two hillslope soil erosion experiments under simulated rainfall events were carried out. Cumulative runoff and sediment yields were measured, respectively. Then, the CA model was applied to simulate the water and soil erosion for these two experiments. Analysis of simulation results indicated that the size of the spatial cell, hydraulic parameters, and the setting of time step and iteration times had a large impact on the model accuracy. The comparison of the simulated and measured data suggested that the CA model was an applicable alternate for simulating the hillslope water flow and soil erosion.

Computational simulations of blown sand fluxes over the surfaces of complex microtopography

Studies of sand saltation are currently concentrating on wind tunnel experiments, theoretical analyses and numerical simulations under ideal as well as controllable conditions. These theoretical analyses and numerical simulations cannot accurately predict sand movements in field environments. In this paper, we simulate wind field patterns for two different surfaces of complex microtopography using the computational fluid dynamic model, FLUENT. To demonstrate that the model can successfully reproduce wind patterns in complex microtopography, we first simulate a well-studied mesquite bush and coppice dune field from the Chihuahuan Desert. This is then followed by an analysis of the wind field pattern around a large barchan dune that is complex in shape. For this case, the wind pattern was linked with a sediment transport equation to estimate sediment flux and transport. Finally, as shown by the simulation results, the sand flux, from the right horn to the left horn of the dune, first increased then decreased after reaching its maximum at the intersection of the brink and the longitudinal centreline of the dune.

Review of Hydrodynamics and Water Quality: Modeling Rivers, Lakes, and Estuaries by Zhen-Gang JiHydrodynamics and Water Quality: Modeling Rivers, Lakes, and EstuariesWiley Interscience, John Wiley & Sons, Inc.978-0-470-13543-3

Management of surface water systems, including rivers, reservoirs, lakes, wetlands, and estuaries, requires technical tools that must be based on physical, chemical, biological, and social sciences. Some of these tools entail numerical hydrodynamic and water quality models, made possible these days by everincreasing computing prowess. This book attempts to describe physical, chemical, and biological concepts underlying these models. To that end, the book aims at providing an integrated treatment of hydrodynamics, sediment transport and processes, toxic fate and transport, water quality, and eutrophication in surface water systems. The emphasis in the book is on principles, basic processes, mathematical descriptions, and practical applications via case studies. Justifiably, it avoids long mathematical derivations. The book also presents case studies to illustrate the implementation of basic concepts and theories and technical approaches based thereon into mathematical models, as well as application of these models to address practical environmental and water resources problems. The subject matter of the book is logically divided into 10 chapters and three appendices. Chapter 1 provides an overview and develops the context for the material to be described in the book. Chapter 2 provides basic concepts and principles of hydrodynamics. Starting with a description of hydrodynamic processes, it goes on to discuss governing equations and their approximations in one-dimensional, two-dimensional and three-dimensional Cartesian coordinates. Equations in curvilinear coordinates are presented next, followed by a discussion of initial and boundary conditions. Then temperature and heat fluxes are presented. This discussion is integrated in the following section on hydrodynamic modeling, with case studies of Lake Ockeechobee and the St. Lucie Estuary and Indian River Lagoon. These case studies are very helpful to understand hydrodynamics and its practical application. Sediment transport is discussed in Chapter 3. Providing an overview, including sediment properties, problems associated with sediment, and sediment processes, it discusses sediment transport equations for both cohesive and noncohesive sediments, as well as wind waves and their impact on sediment transport. The chapter presents two case studies one on wind wave modeling and the other on sediment transport modeling in Lake Ockeechobee. The third case study is on sediment transport modeling for Blackstone River. These case studies clearly show how to set up a model, define initial and boundary conditions, prepare data

Formation of evenly spaced ridges and valleys

Seen from above, it's clear that in many hilly landscapes the ridges and valleys appear uniformly spaced. Current physically based models of landscape evolution produce realistic looking topography, but cannot predict the 'wavelength' typical of evenly spaced ridges and valleys in natural landscapes. Taylor Perron and colleagues use equations of mass conservation and sediment transport to derive a characteristic length scale that is directly proportional to the ridge–valley wavelength in models of landform evolution and at five field study sites across the United States, including Nappa Valley in California and Point of the Mountain in Utah. The findings provide a quantitative explanation for one of the most widely observed characteristics of landscapes and suggest that valley spacing records the effects of material properties and climate on erosional processes. Ridges and valleys in many landscapes are uniformly spaced, but no theory has predicted this fundamental topographic wavelength. A characteristic length scale is now derived from equations of mass conservation and sediment transport; it is found to be directly proportional to the valley spacing in models of landform evolution, and to the measured valley spacing at five study sites in the USA. One of the most striking examples of self-organization in landscapes is the emergence of evenly spaced ridges and valleys1,2,3,4,5,6. Despite the prevalence of uniform valley spacing, no theory has been shown to predict this fundamental topographic wavelength. Models of long-term landscape evolution can produce landforms that look realistic7,8,9, but few metrics exist to assess the similarity between models and natural landscapes. Here we show that the ridge–valley wavelength can be predicted from erosional mechanics. From equations of mass conservation and sediment transport, we derive a characteristic length scale at which the timescales for erosion by diffusive soil creep and advective stream incision are equal. This length scale is directly proportional to the valley spacing that emerges in a numerical model of landform evolution, and to the measured valley spacing at five field sites. Our results provide a quantitative explanation for one of the most widely observed characteristics of landscapes. The findings also imply that valley spacing is a fundamental topographic signature that records how material properties and climate regulate erosional processes.

Landscape texture set to scale

Why, in many landscapes, does ridge–valley spacing show such regularity? The combination of high-resolution data and an elegant model offers a solution to this long-standing puzzle, for some cases at least. Seen from above, it's clear that in many hilly landscapes the ridges and valleys appear uniformly spaced. Current physically based models of landscape evolution produce realistic looking topography, but cannot predict the 'wavelength' typical of evenly spaced ridges and valleys in natural landscapes. Taylor Perron and colleagues use equations of mass conservation and sediment transport to derive a characteristic length scale that is directly proportional to the ridge–valley wavelength in models of landform evolution and at five field study sites across the United States, including Nappa Valley in California and Point of the Mountain in Utah. The findings provide a quantitative explanation for one of the most widely observed characteristics of landscapes and suggest that valley spacing records the effects of material properties and climate on erosional processes.

Integrated Two-Dimensional Surface and Three-Dimensional Subsurface Contaminant Transport Model Considering Soil Erosion and Sorption

To investigate the complex hydrological, morphodynamic, and environmental processes in watersheds, a physically-based integrated two-dimensional (2D) surface and three-dimensional (3D) subsurface model for flow, soil erosion and transport, and contaminant transport in the surface-subsurface system is presented in this paper. The model simulates the rainfall-induced surface flow by solving the depth-averaged 2D diffusion wave equation and the variably-saturated subsurface flow by solving the 3D mixed-form Richards equation. The surface and subsurface flow equations are coupled using the continuity conditions of pressure and exchange flux at the ground surface. The model uses the concept of nonequilibrium in the depth-averaged 2D simulation of nonuniform total-load sediment transport in upland fields, considering detachments by rainsplash and hydraulic erosion driven by surface flow. The integrated 2D surface and 3D subsurface contaminant transport model takes into account the contaminant changes due to sediment sorption and desorption, as well as exchanges between surface and subsurface domains due to infiltration, diffusion, and bed change. The model applies the same set of surface equations of flow, sediment, and contaminant transport for describing both upland areas and streams, so that no special treatments are required at their interface. The established model has been evaluated by comparisons with published experimental, numerical, and analytical data and then applied in an agricultural watershed. The model is suitable for wetland areas and agricultural watersheds in which streams are not very narrow and deep, and meanwhile a relatively fine mesh that can distinguish the streams is preferred.

Modelling evolution of bed profile and grain size distribution in unsurveyed rivers

The water flow and sediment transport equations have been linearized and analytically solved under the hypothesis of quasi-equilibrium conditions. This solution permits to reconstruct the river bathymetry from planimetric data, the only ones available from satellite images for most of the large rivers of the world. The linearized quasi-equilibrium solution provides a criterion to evaluate the accuracy of the approximate (uniform-flow) model, compared to the regular (steady-flow) model. For non-equilibrium conditions, a further constraint on time resolution should be added, which is however generally satisfied for long-term morphological simulations. The uniform-flow solution presents many advantages which become crucial for long-term numerical computations at watershed scale. The article provides a detailed numerical comparison of the accuracy and resolution of both steady- and uniform-flow models, with an application to the evolution of the lower Zambezi River, which confirms the theoretical criterion. The accuracy of the uniform-flow solution appears to improve when the river is schematized with a coarse computational grid although, of course, with a corresponding loss of spatial resolution.

Modeling overland flow and soil erosion on nonuniform hillslopes: A finite volume scheme

This paper presents a finite volume scheme for coupling the Saint‐Venant equations with the multiparticle size class Hairsine‐Rose soil erosion model. A well‐balanced monotone upstream‐centered schemes for conservation laws‐Hancock (MUSCL‐Hancock) method is proposed to minimize spurious waves in the solution arising from an imbalance between the flux gradient and the source terms in the momentum equation. Additional criteria for numerical stability when dealing with very shallow flows and wet/dry fronts are highlighted. Numerical tests show that the scheme performs well in terms of accuracy and robustness for both the water and sediment transport equations. The proposed scheme facilitates the application of the Hairsine‐Rose model to complex scenarios of soil erosion with concurrent interacting erosion processes over a nonuniform topography.

Aggregate Stability and Erosion Response to Antecedent Water Content of a Loess Soil

Soil erosion processes are affected by the erodibility of the soil and by the erosivity of the rain. The effects of rain characteristics and invariant soil properties such as texture and organic matter content on soil erosion processes are well documented. The effect of antecedent soil water content (θa) on aggregate breakdown, seal formation, and subsequent soil erosion is much more disputable, however, as opposing effects have been reported. We conducted lab experiments with a rainfall simulator on a Belgian silt loam soil. The objectives were to determine the effect of θa on seal formation, runoff, and soil loss and to evaluate its effect on an empirical sediment transport equation. Air‐dried soil aggregates were subjected to θa of 0.04 (air‐dry aggregates), 0.12, and 0.19 m3 m−3 No runoff occurred on the soils with the highest θa, highest total runoff values were observed for intermediate θa, while intermediate amounts of total runoff were observed for the air‐dry aggregates. Soil loss, however, showed a different trend: highest values were found for the lowest θa, intermediate values for the intermediate θa, and no soil loss for the highest θa We further observed that θa had no influence on the final runoff rates and on the final infiltration rate through the soil surface. In using a water discharge and stream power equation to predict sediment transport, the intercept and exponent of the regression equations were found to be lower for θa of 0.19 than 0.12 m3 m−3, indicating decreasing erodibility with increasing θa We therefore suggest including θa as an additional variable to assess soil erodibility in deterministic event‐based water erosion models.

One‐dimensional numerical modeling of sediment transport and bed deformation in open channels

A one‐dimensional numerical model for simulating unsteady flow and sediment transport in open channels is presented and tested. The flow hydrodynamics is represented by the shallow water equations, and the bed morphodynamics is represented by the Exner equation and an additional equation describing the nonequilibrium sediment transport. Sediment size distribution is represented by the median grain diameter and the standard deviation, instead of the usual modeling with multiple particle size classes. Various methods for computing bed elevation changes at a cross section due to erosion or deposition of sediment are proposed and tested, including an innovative approach that relates the spatial pattern of erosion and deposition rates to boundary shear stress distribution, which is calculated by the Merged Perpendicular Method. An explicit finite difference scheme is employed for solving the water and sediment governing equations. The pertinence of the model is examined for two hypothetical cases. The model is then tested on one set of laboratory experiments on bed degradation under steady flow, showing excellent model data fit, and indicating that incorporating a nonequilibrium sediment transport equation into the model structure is an important element in reproducing the bed degradation process. Finally, the model is applied to simulate the morphological changes taking place in the Ha!Ha! River (Quebec) after the failure of the Ha!Ha! Dyke on July 1996. Relevant results can be obtained in terms of changes in longitudinal bed profile and cross‐sectional geometry as well as water levels, although some discrepancies are obtained between the simulated and surveyed cross‐sectional geometries, mainly because bank failure and channel widening are not modeled.

Development of an empirical model for calculating sediment-transport capacity in shallow overland flows: Model calibration

Previous research has demonstrated the poor performance of fluvial sediment transport equations when applied to overland flow. An empirical sediment-transport capacity model, specifically designed for overland flow, has been developed and calibrated. The model separates the portion of the transport capacity due to flowing water from that due to rainfall impact. Model development has been described by Guy et al. (2009a). This paper outlines model calibration results and model interpretation. Tests of the model are presented in Guy et al. (2009b). Model calibration data were obtained in a 1.50 m long by 0.253 m wide flume, with rainfall supplied by a single-nozzle rainfall simulator, and flow provided by a constant head tank. Sediment was injected into steady flow over an impermeable, roughened bed, at a rate that balanced the outflow. Transport capacity and hydraulic measurements were obtained at five gradients between 1 and 12%, with four test materials covering a range of size and density, four simulated rainfall intensities, and a range of base flow rates. Hydraulic measurements obtained with flows with Reynolds numbers in the laminar flow regime indicated that the depth of zero velocity was raised into the moving sediment layer, such that it exceeded the predictions of the velocity profile model. Surface velocities matched model predictions, such that flow resistance did not need explicit consideration in developing a transport model. The transport component due to flow processes depends on discharge, slope, and material properties, and is similar to the Schoklitsch equation. The significance of bed slope and discharge is between that required by stream power per unit bed area and shear stress. The component due to rainfall impact depends on rainfall intensity, discharge, slope, and relative particle density. Particle size was statistically insignificant but this may be due to the relatively small size range examined. The portion of the transport capacity due to rainfall impact varied from 100% at the lower limit of the study data (at flows less than the fluvial transport thresholds) to approximately 50% at the upper limit. The results suggested that sediment transport can be classified into three types: in shallow flow sediment transport (investigated in this study), the rainfall-impact component of transport capacity increases with discharge, although its relative significance decreases. In intermediate flow sediment transport, the rainfall-impact component decreases to insignificance. In deep flow sediment transport, rainfall does not contribute to the transport capacity.

Well-balanced high-order centred schemes for non-conservative hyperbolic systems. Applications to shallow water equations with fixed and mobile bed

This paper concerns the development of high-order accurate centred schemes for the numerical solution of one-dimensional hyperbolic systems containing non-conservative products and source terms. Combining the PRICE-T method developed in [Toro E, Siviglia A. PRICE: primitive centred schemes for hyperbolic system of equations. Int J Numer Methods Fluids 2003;42:1263–91] with the theoretical insights gained by the recently developed path-conservative schemes [Castro M, Gallardo J, Parés C. High-order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products applications to shallow-water systems. Math Comput 2006;75:1103–34; Parés C. Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J Numer Anal 2006;44:300–21], we propose the new PRICE-C scheme that automatically reduces to a modified conservative FORCE scheme if the underlying PDE system is a conservation law. The resulting first-order accurate centred method is then extended to high order of accuracy in space and time via the ADER approach together with a WENO reconstruction technique. The well-balanced properties of the PRICE-C method are investigated for the shallow water equations. Finally, we apply the new scheme to the shallow water equations with fix bottom topography and with variable bottom solving an additional sediment transport equation.