ISO/TR 11651:2015

Estimation of sediment deposition in reservoirs using one dimensional simulation models

ISO/TR 11651:2015 describes a method for estimation/prediction of sediment deposition within and upstream of a reservoir using numerical simulation techniques through one-dimensional flow and sediment transport equations. Numerical simulation models for predicting sediment distribution are applicable for reservoirs, where the length of the reservoir greatly exceeds the depth and width and the reservoir has a significant through flow. ISO/TR 11651:2015 includes the theoretical basis and fundamental assumptions of the technique and provides a summary of some numerical methods used to solve the unsteady flow and sediment transport equations. Also provided are details on the application of the model, including data requirements, procedures for model calibration, validation, testing, applications and identification of uncertainties associated with the method. This Technical Report does not provide sufficient information for the development of a computer program for solving the equations, but rather is based on the assumption that an adequately documented computer program is available.

Estimation du dépôt de sédiments dans le réservoir en utilisant des modèles de simulation à une dimension

General Information

• Status: Published
• Publication Date: 13-Aug-2015
• ICS: 17.120.20 - Flow in open channels
• Technical Committee: ISO/TC 113/SC 6 - Sediment transport
• Drafting Committee: ISO/TC 113/SC 6 - Sediment transport
• Current Stage: 6060 - International Standard published
• Start Date: 14-Aug-2015
• Completion Date: 13-Dec-2025

Overview

ISO/TR 11651:2015 provides guidance for the estimation and prediction of sediment deposition in reservoirs using one-dimensional numerical simulation models. The Technical Report describes the theoretical basis and fundamental assumptions for modelling sediment transport with one-dimensional flow and sediment-transport equations, summarizes common numerical solution methods, and details practical steps for model application - including data requirements, model calibration, validation, testing and treatment of uncertainties. It is intended for cases where the reservoir length greatly exceeds depth and width and there is significant through flow. Note: the report assumes an adequately documented computer program is already available and does not supply full software development details.

Key topics

• Scope & applicability: reservoirs suited to one-dimensional representation (length ≫ depth/width; through flow).
• Modelling approaches: comparison of quasi-unsteady and unsteady flow representations and their implications for sediment transport modelling.
• Governing concepts: conservation of mass and momentum for water and sediment; selection of sediment transport equations.
• Numerical methods overview: summaries of explicit/implicit finite-difference methods, finite element and finite volume approaches.
• Data requirements:
  • Cross-section geometry and bed material
  • Stage–discharge relationships and flow data
  • Velocity, discharge, lateral inflows/withdrawals
  • Suspended sediment and bedload characteristics (concentration, particle size distribution)
  • Manning’s n, movable bed/dredging data
• Model development workflow: formulation, computational grid/time-step choices, boundary/initial conditions, convergence testing.
• Calibration & validation: procedures for fitting and testing models against observations.
• Uncertainty analysis: sources from parameters, input data, governing equations and numerical approximations.

Applications

ISO/TR 11651:2015 supports practical tasks in reservoir sedimentation and water-resource management:

• Feasibility and design studies for new reservoirs (storage loss prediction, intake/outlet placement)
• Performance assessment and life‑cycle planning for existing dams
• Design of desilting basins, turbines and water conveyance systems affected by sediment
• Planning dredging, flushing and sediment management operations (sluicing, sediment routing)
• Flood risk assessment related to head-reach aggradation

Typical users include hydrologists, reservoir and sediment engineers, dam safety managers, environmental consultants, numerical modelers and regulatory agencies involved in water-resource planning.

Related standards

Normative and related ISO documents cited in the report include:

• ISO 748, ISO 772, ISO 1100-2
• ISO 4363, ISO 4364, ISO 4365
• ISO/TS 3716, ISO/TR 9212 These standards cover hydrometry measurements, sediment sampling and related measurement methods that feed into sedimentation modelling workflows.

Keywords: ISO/TR 11651:2015, sediment deposition, reservoir sedimentation, one-dimensional simulation models, sediment transport modelling, unsteady flow, quasi-unsteady, numerical simulation, model calibration, reservoir management.

Standards Content (Sample)

TECHNICAL ISO/TR
REPORT 11651
First edition
2015-08-15
Estimation of sediment deposition
in reservoir using one dimensional
simulation models
Estimation du dépôt de sédiments dans le réservoir en utilisant des
modèles de simulation à une dimension
Reference number
©
ISO 2015
© ISO 2015, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. [phone]
Fax [phone]
[e-mail]
www.iso.org
ii © ISO 2015 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Definitions . 2
4 Units of measurement . 2
5 Principles of quasi-unsteady sediment modelling . 2
6 Principles of unsteady flow models . 2
6.1 General . 2
6.2 Governing equations . 3
6.3 Numerical techniques for solution of governing equations . 6
6.3.1 Explicit finite-difference methods . 7
6.3.2 Implicit finite-difference methods . 7
6.3.3 Finite element methods . 7
6.3.4 Finite volume methods . 8
6.4 Sediment transport . 8
7 Data requirements .10
7.1 Selection of model boundaries .12
7.2 Cross-section data .12
7.2.1 General.12
7.2.2 Manning’s n values .13
7.2.3 Movable bed and dredging .13
7.3 Stage data.13
7.4 Velocity data .13
7.5 Discharge data .13
7.6 Lateral inflows and withdrawals .14
7.7 Sediment data . 14
8 Formulation, calibration, testing and validation of models .15
8.1 Formulation of numerical models .15
8.1.1 Hydrology .15
8.1.2 Geometry .16
8.1.3 Selection of transport equation .16
8.1.4 Bed mixing and armoring algorithm .16
8.2 Preliminary tests .16
8.3 Computational grid and time step.17
8.4 Convergence testing .18
8.5 Boundary and initial conditions .18
8.6 Calibration .18
8.7 Validation .19
8.8 Predictive simulation .20
8.9 Sensitivity testing .20
8.10 Specific models .20
9 Uncertainties .21
9.1 Model parameters .21
9.2 Data for model development, testing and application .21
9.3 Governing equations .22
9.4 Numerical approximations to governing equations .22
Annex A (normative) Models and case studies .24
Bibliography .25
Foreword
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bodies (ISO member bodies). The work of preparing International Standards is normally carried out
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committee has been established has the right to be represented on that committee. International
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electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
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Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 113, Hydrometry, Subcommittee SC 6,
Sediment transport.
iv © ISO 2015 – All rights reserved

Introduction
Storage reservoirs built across rivers or streams lose their capacity on account of deposition of sediment.
Surveys indicate that world-wide reservoirs are losing their storage capacity, at an annual rate of about
one percent, due to accumulation of sediments. The impacts of sedimentation on the performance of the
reservoir project are manifold. Some of the important aspects are the following:
a) reduction in live storage capacity of the reservoir;
b) accumulation of sediment at or near the dam may interfere with the functioning of water intakes
and hence is an important parameter in deciding the location and level of various outlets;
c) increased inflow of sediment into the water conveyance systems and hence to be considered in the
design of water conductor systems, desilting basins, turbines, etc;
d) sediment deposition in the head reaches may cause rise in flood levels;
e) the location and quantity of sediment deposition affects the performance of the sediment sluicing
and flushing measures used to restore the storage capacity.
Hence, prediction of sediment distribution in reservoirs is essential in the following:
a) feasibility studies during planning and design of various components of new projects;
b) performance assessment of existing projects.
The most simple and earliest models to predict the sedimentation processes in reservoirs are the
empirical ones. The trap-efficiency curves derived from records of existing reservoirs are among the
most commonly used empirical methods. Recently, due to better understanding of the fundamentals
of reservoir hydraulics and morphology, along with the rapid growth of computational facilities,
development and application of mathematical models have become a normal practice.
Compared to empirical methods, the mathematical approach of the sediment distribution enables more
time and space dependent and more accurate modelling. A large number of mathematical models have
been developed during the past few decades. Flow in the reservoir can be represented by the basic
equations for conservation of momentum and mass of water and sediment.
TECHNICAL REPORT ISO/TR 11651:2015(E)
Estimation of sediment deposition in reservoir using one
dimensional simulation models
1 Scope
This Technical Report describes a method for estimation/prediction of sediment deposition within
and upstream of a reservoir using numerical simulation techniques through one-dimensional flow and
sediment transport equations.
Numerical simulation models for predicting sediment distribution are applicable for reservoirs, where
the length of the reservoir greatly exceeds the depth and width and the reservoir has a significant
through flow.
This Technical Report includes the theoretical basis and fundamental assumptions of the technique and
provides a summary of some numerical methods used to solve the unsteady flow and sediment transport
equations. Also provided are details on the application of the model, including data requirements,
procedures for model calibration, validation, testing, applications and identification of uncertainties
associated with the method. This Technical Report does not provide sufficient information for the
development of a computer program for solving the equations, but rather is based on the assumption
that an adequately documented computer program is available.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 748, Hydrometry — Measurement of liquid flow in open channels using current-meters or floats
ISO 772, Hydrometry — Vocabulary and symbols
ISO 1100-2, Hydrometry — Measurement of liquid flow in open channels — Part 2: Determination of the
stage-discharge relationship
ISO 2425, Hydrometry — Measurement of liquid flow in open channels under tidal conditions
ISO 2537, Hydrometry — Rotating-element current-meters
ISO 3454, Hydrometry — Direct depth sounding and suspension equipment
ISO 4363, Measurement of liquid flow in open channels — Methods for measurement of characteristics of
suspended sediment
ISO 4364, Measurement of liquid flow in open channels — Bed material sampling
ISO 4365, Liquid flow in open channels — Sediment in streams and canals — Determination of concentration,
particle size distribution and relative density
ISO 4373, Hydrometry — Water level measuring devices
ISO 6416, Hydrometry — Measurement of discharge by the ultrasonic (acoustic) method
ISO 18365, Hydrometry — Selection, establishment and operation of a gauging station
ISO/TS 3716, Hydrometry — Functional requirements and characteristics of suspended-sediment samplers
ISO/TR 9212, Methods of measurement of bedload discharge
3 Definitions
For the purposes of this document, the terms and definitions given in ISO 772 apply.
4 Units of measurement
The units of measurement used in this Technical Report are SI units.
5 Principles of quasi-unsteady sediment modelling
Many early and contemporary sediment models simplify hydrodynamics of sediment transport models
by invoking a “quasi-unsteady” flow assumption. Instead of solving the Saint-Venant equations explicitly
or implicitly, the hydrodynamics are represented by a series of steady flow backwater computations
and associated with temporal durations. Most generalized sediment transport models still utilize
this approach. Because sediment transport and hydraulic processes respond on different time and
distance scales and because of the inherent uncertainties associated with sediment simulations, the
simplification provided by this approximation often justify the error introduced. However, because the
quasi-unsteady approach does not route water, it can be difficult to implement for reservoir modelling.
Quasi-unsteady models have been used successfully to model reservoir sedimentation but they require
external hydrologic routing computations to define reservoir stage. This process often has to be
iterative because the hydrologic routing parameters change in time as the capacity of the reservoir
changes with sediment deposition. Therefore, an unsteady approach can be advantageous.
6 Principles of unsteady flow models
6.1 General
Numerical models are used to solve sedimentation problems in river engineering, especially for long-
term simulation of long river reaches. The modelling cycle is schematically represented in Figure 1. The
prototype is the reality to be studied and is defined by data and by knowledge. The data represents
boundary conditions, such as bathymetry, water discharges, sediment particle size distributions,
vegetation types, etc. The knowledge contains the physical processes that are known to determine the
system’s behaviour, such as flow turbulence, sediment transport mechanisms and mixing processes.
Understanding the prototype and data constitute the first step of the cycle.
Mathematical
Solution
model
Interpretation
Numerical
Prototype
model
Interpretation
Results of
Solution
modeling
Figure 1 — Modelling cycle
In the first interpretation step, all the relevant physical processes that were identified in the prototype
are translated into governing equations that are compiled into the mathematical model.
2 © ISO 2015 – All rights reserved

A mathematical model therefore constitutes the first approximation to the problem. It is the prerequisite
for a numerical model. At this time, many simplifying approximations are made, such as steady versus
unsteady and one- versus two- versus three-dimensional formulations, simplifying descriptions of
turbulence, etc. In water resources, one usually (but not always) arrives to the set-up of a boundary
value problem whose governing equations contain partial differential equations and nonlinear terms.
Next, a solution step is required to solve the mathematical model. The numerical model embodies the
numerical techniques used to solve the set of governing equations that forms the mathematical model.
In this step, one chooses, for example, finite difference versus finite element versus finite volume
discretization techniques and selects the approach to deal with the nonlinear terms. This is a further
approximating step because the partial differential equations are transformed into algebraic equations,
which are approximate but not equivalent to the former.
Another solution step involves the solution of the numerical model in a computer and provides the
results of modelling. This step embodies further approximations and simplifications, such as those
associated with unknown boundary conditions, imprecise bathymetry, unknown water and or sediment
discharges and friction factors.
Finally, the data needs to be interpreted and placed in the appropriate prototype context. This last
step closes the modelling cycle and ultimately provides the answer to the problem that drives the
modelling efforts.
The choice of model for each specific problem should take into account the requirements of the problem,
the knowledge of the system, and the available data. On one hand, the model must take into account all
the significant phenomena that are known to occur in the system and that will influence the aspects
that are being studied. On the other hand, model complexity is limited by the available data. There is
no universal model that can be applied to every problem. The specific requirements of each problem
should be analysed and the model chosen should reflect this analysis in its features and complexity.
6.2 Governing equations
The governing equations are the one-dimensional, cross-sectionally averaged expressions for (1)
the conservation of mass (or equation of continuity), (2) conservation of linear momentum and (3)
continuity of the bed material.
The following one-dimensional flow equations are solved to get the hydraulic parameters such as
energy slope, velocity and depth of flow at each cross-section at each time step. The sediment transport
capacities at each cross-section are then computed and compared with the sediment inflow. The scour
or deposition at each section is computed using sediment continuity equation and new cross-section
bed levels are determined accordingly. The computations then proceed to the next time step and the
cycle is repeated with the updated geometry.
Conservation of mass (or equation of continuity),
∂A ∂Q
+ = q (1)
∂t ∂x
Conservation of linear momentum
 2
∂Q ∂ Q  ∂y



+ β + gA +−gA()SS = qu' (2)


 f 0

∂tx∂ A  ∂x


 
Equation of Continuity of the Bed Material
∂G ∂G
∂ ∂
bs
+ + CA +ρ Bz =0 (3)
() ()
sd∗
∂x ∂xt∂ ∂t
where
A is the cross-sectional area of the channel, and varies with x, t, and z;
t is the time;
Q is the discharge, and varies with x and t;
u’ is longitudinal component of the lateral inflow velocity and varies with x and t;
x is the longitudinal position along the channel axis;
y is the depth of flow, and varies with x and t;
g is the acceleration of gravity;
β is the momentum coefficient and varies with x, z, and t;
q is the lateral inflow per unit length of channel, and varies with x and t;
S is the bed slope, and varies with x;
S is the friction slope, and varies with x, t and z;
f
G is the bed load;
b
G is the suspended load;
s
C is the average spatial sediment concentration in the cross-section;
s
ρ is the density of sediment in the bed;
*
B is the deformable bed width and varies with t;
d
z is the bed elevation and varies with t.
4 © ISO 2015 – All rights reserved

The momentum coefficient may be computed using Formula (4):
udA
β = (4)
∫
UA
where
u is the velocity in some elemental area dA;
U is the mean velocity in the same cross-section having a total area A.
The friction slope, S , accounts for the resistance due to external boundary stresses. The friction slope
f
is generally represented by Chezy or Manning’s equations.
For the Chezy equation, the bed resistance term in the momentum formula is described as:
gQ Q
S (5)
f
CAR
where
Q is the discharge;
A is the flow area;
R is the resistance or hydraulic radius.
For the Manning description, the term is:
gQ Q
S = (6)
f
24/3
MAR
The Manning number, M, is equivalent to the Strickler coefficient. Its inverse is the more conventional
Manning’s, n. The value of n is typically in the range 0,01 (smooth channel) to 0,10 (thickly vegetated
channel). The corresponding values for M are from 100 to 10.
The Chezy coefficient is related to Manning’s n by
16/
R
16/
C ==MR (7)
n
Both R and n can vary as a function of x, z, and t. Formula 6 is based on the assumption that the
Manning equation for steady, uniform flow provides a reasonable approximation for S in unsteady,
f
non uniform flow.
Formula (2) can be modified to include a term accounting for the momentum imparted to the water by
a temporally and spatially varying wind. Formulae (1) and (2) also can be written with (1) depth and
velocity, (2) stage and velocity, or (3) stage and discharge as the dependent variables.
Formulae (1) and (2) apply to the unsteady, spatially varied, turbulent free-surface flow of an
incompressible, viscous fluid in an open channel of arbitrary cross-section and alignment. The
equations are solved simultaneously for the unknowns, z (depth of flow) and Q (discharge) as a function
of time (t) and longitudinal position (x).
Formula (3) accounts for the sediment transport and thus the changes in bed levels. Various equations
are available for the calculation of sediment transport rate and alluvial roughness, e.g. the Meyer-Peter
and Muller and the DuBoys’ transport function for the calculation of bed load; the Engelund and Hansen
model, the Ackers and White model, the Yang model and the Smart and Jaeggi model for determination
of the total load and the Engelund and Fredsoe and van Rijn models for the computation of bed load
and suspended load separately. All these models/equations can be applied using a single representative
grain size or using a number of grain sizes representing grain size fractions in graded material.
Formulae (1) and (2) are derived from first principles and may be obtained directly from the three
dimensional equation of mass continuity and the Navier-Stokes equations, which are general, three
dimensional statements of the conservation of momentum for any fluid flow. A number of assumptions
are required to derive Formulae (1) and (2). An unsteady flow model should generally be applied to those
conditions in which none of the major assumptions is severely violated. The assumptions are as follows:
a) flow is approximately one-dimensional, meaning that the predominant spatial variation in dynamic
conditions of hydraulic parameters (discharge, velocity and stage) is in the longitudinal direction;
b) fluid density is homogeneous throughout the modelled reach;
c) vertical accelerations are negligible, i.e. the hydrostatic pressure distribution is applicable;
d) velocity is uniformly distributed in a given cross-section. Inclusion of the momentum coefficient
in Formula (2) allows this assumption to be violated somewhat, however, there should be no flow
separation and streamlines should not be highly curvilinear;
e) neither aggradation nor degradation of the river bed occurs during computational time step;
f) turbulence and energy dissipation can be described by resistance laws formulated for steady,
uniform flow [required for Formula (4)];
g) there are no abrupt changes in channel shape or alignment;
h) velocity is zero at the channel boundary;
i) there is no super elevation of the water level at any cross-section;
j) surface tension and density of air at the free surface are negligible.
6.3 Numerical techniques for solution of governing equations
No known analytical solutions exist for Formulae (1) and (2). Consequently, numerical techniques are
used to convert Formulae (1) and (2) into algebraic equations that may be solved for z and Q at finite,
incremental values of x and t. This solution depends on the proper description of the cross-sectional
area as a function of x and t, and on the availability of accurate boundary condition data.
A variety of numerical techniques have been proposed and used to solve the unsteady flow equations.
The techniques of interest are those based on some type of gridded discretization of the problem at hand,
in which the continuous variables for which the solution is sought are solved only at specific discrete
locations of the physical domain. The algebraic equations that form the numerical model are functions
of those discrete quantities. For the same problem (i.e. the same set of differential governing formulae
and boundary conditions), it is possible to obtain very distinct sets of algebraic numerical equations,
depending on the technique used to discretize the equations. The broad categories of numerical
techniques are method of characteristics, finite differences, finite elements and finite volumes. Generally,
finite-difference techniques are preferred for the solution of the one-dimensional partial differential
equations describing unsteady open-channel flow. The finite difference method includes
a) explicit finite-difference methods, and
b) implicit finite-difference methods.
Numerous variations of each of these general categories of techniques exist. The methods are briefly
reviewed to provide some perspective on advantages and disadvantages of each method.
6 © ISO 2015 – All rights reserved

6.3.1 Explicit finite-difference methods
Finite-difference methods are probably the most simple and most common methods employed in fluid
flow models, as well as in other disciplines requiring the numerical solution of partial differential
equations. They are based on the approximation of the individual derivative terms in the equations
by discrete differences, thus converting them into sets of simultaneous algebraic equations with the
unknowns defined at discrete points over the entire domain of the problem.
Explicit numerical schemes convert the governing equations to a system of linear algebraic equations
from which the unknowns may be solved directly (explicitly) without iterative computations.
Dependent variables on the advanced time level are determined one point at a time from known values
and conditions at the present or previous time levels. Explicit schemes are only conditionally stable,
meaning that errors may grow as the solution progresses, and the errors are a function of the time and
distance step sizes. Explicit schemes are generally stable when the Courant condition is met, which
results in limitations on the distance step and maximum time step, which can be used.
In order to meet numerical stability requirements, the computational time step must decrease as
the hydraulic depth increases. Consequently, computational time steps may be required to be on the
order of a few minutes for unsteady flow models of large rivers, which make the models somewhat
computationally inefficient. Explicit finite-difference schemes also require that the computational
distance steps be equal throughout the model domain, which may be a disadvantage for some systems.
6.3.2 Implicit finite-difference methods
Implicit numerical schemes convert the governing equations to a system on nonlinear algebraic
equations from which the unknowns must be solved iteratively. Consequently, a system of 2N algebraic
equations is generated for a model having N cross-sections along the x-axis. All of the unknowns within
the model domain are determined simultaneously, rather than point-by-point as with explicit methods.
Weighting factors are typically required in the application of implicit schemes. These factors determine
the time between adjacent time levels at which (1) the spatial derivatives and (2) functional quantities
are evaluated; functional quantities are such features as cross-sectional area, top width and hydraulic
radius, all of which are functions of the computed depth of flow. Some judgment is required in selecting
these weighting factors and the weighting factors often are adjusted as part of the model calibration
process. The accuracy of the numerical scheme generally decreases as the factor approaches one, where
the terms in the governing equations are expressed entirely in terms of the future time step.
Fewer numerical stability problems are encountered with implicit schemes than with explicit schemes.
Numerical instabilities can occur when modelling rapidly varying flows if the time step is large and if
the spatial derivatives are not sufficiently weighted toward the future time step. Nonlinearities caused
by irregular cross-sections having widths that vary rapidly along the channel or with depth also can
cause numerical instabilities in implicit models.
6.3.3 Finite element methods
Finite element methods have been used successfully for fluid flow problems since the 1960s. They are
particularly useful to solve problems with complex geometries, as they do not require the structured
grid system needed in finite difference techniques. In an unstructured grid, the computational nodes
do not need to be defined in an ordered manner, as opposed to structured grids where each node is
identified by an (i - j) pair.
There are two main approaches for the formulation of finite element methods: variational methods and
weighted residual methods. In variational methods, the variational principle for the governing equation
is minimized. In general fluid mechanics problems, exact forms of the variational principles for the
governing nonlinear equations are difficult to find (unlike in the linear equations encountered in solid
mechanics); therefore, weighted residual methods are much more popular. Residual methods are based
on minimizing some sort of error, or residual, of the governing equations.
6.3.4 Finite volume methods
Finite volume methods use conservation laws, i.e. the integral forms of the governing equations. The
domain of computation is subdivided into an arbitrary number of control volumes, and the equations
are discretized by accounting for the several fluxes crossing the control volume boundaries. There are
two main types of techniques to define the shape and position of the control volumes with respect to
the discrete grid points where the dependent variables are calculated: the node-centred scheme and
the cell-centred scheme. The node-centred scheme places the grid nodes at the centroids of the control
volume, making the control volumes “identical” to the grid cells. In cell-centred schemes, the control
volume is formed by connecting adjacent grid nodes.
The main advantage of finite volume methods is that the spatial discretization is done directly in the
physical space, without the need to make any transformations between coordinate systems. It is a very
flexible method that can be implemented in both structured and unstructured grid systems. Because
the method is based directly on physical conservation principles, mass, momentum and energy are
automatically conserved by the numerical scheme.
Under certain conditions, the finite volume method is equivalent to the finite difference method or to
particular forms of lower order finite element methods.
6.4 Sediment transport
Sediment transport rates are calculated for each flow in the hydrograph for each grain size. The
transport potential is calculated for each grain size and multiplied by the corresponding fraction
present in the bed at that time to obtain the transport capacity component. Computations of sediment
transport are carried out using control volume concept.
The basis for adjusting the bed levels for scour or deposition is the continuity equation for sediment, i.e.
the Exner equation. The sediment continuity equation is written for the control volume for each cross-
section. The control volume width is usually equal to the movable bed width and its depth extends from
the water surface to the top of bed rock or other geological control beneath the bed surface. In areas
where no bed rock exists, an arbitrary limit called the model bottom is assigned.
The solution of the continuity of sediment equation assumes that the initial concentration of suspended
bed material is negligible. Therefore, no initial concentration of bed material load needs to be specified
in the control volume. The hydraulic parameters, bed material gradation and calculated transport
capacity are assumed to be uniform in the control volume. The inflowing sediment load is assumed to
be mixed uniformly with sediment existing in the control volume. The model accounts for two sediment
sources, the sediment in the inflowing water and the bed sediment. The inflowing sediment load is
specified as the upstream boundary condition. The bed sediment control volume provides the source
–sink component and is specified in the input data.
The transport capacity is calculated at each cross-section using hydraulic parameters obtained from
the water surface profile computations and the bed material gradation. The difference between
the inflowing sediment load and the reach’s transport capacity is converted to a scour/deposition
volume. After each time step, the cross-section coordinates are lowered/raised by an amount which,
when multiplied by the movable bed width and the representative reach length equals the required
scour/deposition volume.
8 © ISO 2015 – All rights reserved

The process of scour and deposition is converted for numerical algorithms for computer simulation.
The basis for simulating vertical movement of the bed is the continuity equation for sediment material
viz., the Exner equation.
∂Y
∂G
s
+B = 0 (8)
∂X ∂t
where
B is width of movable bed;
t is time;
G is average sediment discharge rate during time step;
X is distance along the channel;
Y is depth of sediment in control volume.
s
Computational region
P
FLOW
G G
t
u d
P
L L
ud
0 Channel distance
X
(Upstream)
(Downstream)
Figure 2 — Computation grid
The following formulae represent the Exner equation expressed in finite difference form for point P
shown in Figure 2
′
BY −Y
GG− ()
sp sp sp
du
+ =0 (9)
Δt
05, LL+
()
du
Time (t)
Section 4
Section 3
Section 2
Section 1
   
GG−
 Δt 
 
du
′
YY=− (10)
 
 
sp sp
 05, B   LL+ 
() ()
sp du
   
where
B is the width of movable bed at point P;
sp
G , G are the sediment loads at the upstream and downstream cross-sections respectively;
u d
L , L are the upstream and downstream reach length respectively between cross-sections;
u d
Y , Y’ is the depth of sediment before and after time step, respectively at point P;
sp sp
0,5 is the ‘volume shape factor’ which weights the upstream and downstream reach lengths;
t is the computational time step.
The initial depth of bed material at point P defines the initial value of Y . The sediment load, G , is the
sp u
amount of sediment, by grain size, entering the control volume. For the uppermost reach, this is the
inflowing load boundary condition. The sediment leaving the control volume, G , becomes the G for the
d u
next downstream control volume.
The sediment load, G , is calculated by considering the transport capacity at point P, the sediment
d
inflow, availability of material in the bed and armoring. The difference between G and G is the amount
d u
of material deposited or scoured in the reach and is converted to a change in bed level.
The transport potential of each grain size is calculated for the hydraulic conditions at the beginning
of the time interval and is not recalculated during that interval. However, the gradation of the bed
material is recalculated during the time interval because the amount of material transported is very
sensitive to the gradation of bed material.
7 Data requirements
In general, the basic data requirements for loose boundary hydraulic models can be grouped in three
broad categories: geometric data, hydraulic data and sediment data. These data establish the boundary
conditions necessary to solve the governing equations and are an integral part of a model. The term
“model” thus refers to the ensemble of the set of governing equations, their numeric solution technique,
their implementation in a computer program, and the data that define the prototype. Data are required
to construct, calibrate, test, validate and apply unsteady flow and sediment deposition models. Data
collection and preparation often play the dominant role in determining the accuracy and applicability
of the final numerical solutions generated by the computer.
The geometry data defines the topography of the reach to be simulated, i.e. the channel bed, banks and
flood plains. In two and three-dimensional models, the data are most often presented as a set of points
given by its x, y and z coordinates. The data are then interpolated to the locations of the grid nodes used
in the discretization of the problem. In one-dimensional models, the geometry is usually defined by
cross-sections. Each cross-section is a line representing a particular section of the modelled reach and
is given by a set of points, each defined by a lateral distance and a bed elevation above a common datum.
This line provides the information about the section shape and the locations of the sub-channels, and
should be taken between locations above the highest stage levels. It should be perpendicular to the
flow streamlines. Additionally, the distance between the cross-sections needs to be specified, and this
distance should be measured along the flow streamlines. In addition, the movable bed portion of each
cross-section and the depth of sediment material in the bed are required in some models.
Hydraulic data encompasses the necessary upstream and downstream flow conditions, as well as
friction factors and local head losses. Subcritical flows require the flow discharge at the upstream
boundary and the stage at the downstream end, while supercritical flows require both the discharge
and the stage at the upstream boundary.
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Stage-discharge rating curves, an elevation hydrograph, or a water-surface-slope hydrograph are
common ways to define the stage. In the case in which the downstream boundary is a dam, the reservoir
operational scheme may be used to define the stage. When the dam outlet works are used, relationships
for the gates and spillways may have to be employed. These relationships are a function of the head at the
dam, and more complex iterative schemes need to be used. Some models include capabilities to specify
gate operations either a priori or as a user specified function of simulated hydraulic parameters (e.g. gates
are opened and closed during the simulation in response to the reservoir stage in the previous time step).
Friction factors play an important role in determining stages and flow velocities. They can vary
spatially (laterally and longitudinally) and temporally as a function of flow, hydraulic depth, season,
temperature and ch
...