World Applied Sciences Journal 13 (2): 376-384, 2011
ISSN 1818-4952
© IDOSI Publications, 2011
Estimate of Sediment Transport Rate at Karkheh River in Iran
Using Selected Transport Formulas
H. Hassanzadeh, S. Faiznia, M. Shafai Bajestan and A. Motamed
Science and Research Branch, Islamic Azad University, Tehran, Iran
Abstract: In this study, the capability of sediment transferring formulas of Bagnold, Engelund and Hansen,
Ackers and White, Yang and Van Rijn in the Karkheh River of Iran had been tested. In pointed formulas about
90 series of field data, had been applied which their suspended load concentration had been measured. The best
sediment load estimate of Karkheh River had been reach by Yang formula which was proper for rivers with high
suspended load concentration. The Engelund and Hansen and Ackers and White methods estimated the total
sediment load more than observation rate and the Van Rijn formula estimated the rate of sediment rate lower
than observation rate. The high scattering in calculated sediment load results by Engelund and Hansen, Ackers
and White and Van Rijn methods, cleared which this methods were not appropriate for estimate sediment load
of Karkheh River. But Yang and the following Bagnold methods delivered the better results. The obvious
difference between estimated sediment load rate, by various methods and its measured rate is the reason of
wash load which has not been accounted in the experimental formulas.
Key words: Sediment
Suspended load
Predict
River
INTRODUCTION
Wash load
The significant difference between results
obtained by different formulas emphasizes the
necessity of
assessing
predicted
values by
different formulas in varying river conditions [7].
Of note is the fact that the existing formulas only
predict the maximum sediment transport capacity of a
river while it is possible that the predicted amount of
sediment is not actually available in the given river and
the measured sediment load is much less than the
calculated sediment load. For example, in mountainous
rivers, bed surface is covered with a coarse layer during
low flow season and the measured sediment load is
actually insignificant while the existing formulas may
predict the amount of transported sediment considerably
high [8].
A large number of comparison studies have been
done to test the predictability of various sediment
transport methods covering a wide range of flow
conditions and sediment types [9-13] But the accuracy of
computational sediment transport models has remained
a “challenging question” yet [14].
In this paper, the applicability and performance of the
commonly used sediment transport formulas in calculating
the sediment transport capacity in Karkheh River are
evaluated.
Since natural rivers are subject to constant erosion
and sediment transport processes, the study of sediment
transport mechanisms and transport capacity of stream
flows is considerably important in river hydraulics and
geomorphology. Sediment transport and sedimentation in
rivers have serious consequences including formation of
sediment bars and reduction of flood sediment transport
capacity, affected dams lifetime and their reservoir
capacity, severe erosion of hydromechanical facilities and
damaging field and water structures, sedimentation at flow
channels and other hydraulic problems. Also, considering
the principles of river material extraction and transported
sediments by river flow in design of river structures, the
study of various methods to predict river sediment
transport rate seems to be necessary.
Sediment transport in natural rivers has been widely
studied in the past few decades and there are many
theoretical or empirical formulas that can be used with
reasonable accuracy to predict the transport rate for sand
bed river. For example, the sediment transport methods
developed by Bagnold [1], Engelund and Hansen [2],
Ackers and white [3], Yang [4] and Van Rijn [5, 6] are
often applied to compute bed- material load in this rivers.
Corresponding Author: H. Hassanzadeh, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Tel: +09166149027, Fax: +06113731769, E-mail: [email protected].
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World Appl. Sci. J., 13 (2): 376-384, 2011
Fig. 1: Map showing the location Karkheh River basin in Iran
Study Area: Karkheh River is the third largest river
in Iran on which the largest reservoir dam in Iran
and Middle East has been built. This river originates in
middle and southwestern parts of Zagros Mountains in
west and northwest Iran and joins Hour Al-Hoveyzeh
wetland at the common borders of Iran and Iraq
(southwest Khuzestan) after traveling 900 km in
north-south direction. Karkheh basin is situated in
46° 7´ to 49° 10 E and 31° 18 to 34° 58 N. The basin has an
area of 50,000 km². The main tributaries contributing to
the basin include Gamasiab, Ghareh Soo, Seimareh,
Chordoval and Kashkan rivers (Fig. 1) flowing on a
mountainous bed. The Karkheh River is finally formed by
Seimareh and Kashkan rivers in Khuzestan Plain. Average
annual flow of Karkheh River at a hydrometric station
close to Karkheh Dam is 5582,000,000 m³ with average
discharge of 177 m³/s. In this paper, in order to estimate
Karkheh River sediment load, data were used from Jelogir
Hydrometric Station. The correct estimation of annual
sediment at this station seemed to be quite necessary due
to its high flow in small and big agricultural and industrial
schemes and fish farms, developing large irrigation
networks and the increase of dead volume of dam
reservoir.
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World Appl. Sci. J., 13 (2): 376-384, 2011
Table 1: Methods used to estimate sediment load
Calculate of sediment load
------------------------------------------------------------Procedure
Bed load
Suspended load
Total load
Application orders
Bagnold (1966)
*
*
*
For rivers which has the bed form
Engelund and Hansen (1972)
-
-
*
For rivers which has dune bed form, this model developed basis of
laboratory flume data and by the use of the size of bed material particles,
as entrance
Ackers and white (1973)
-
-
-
For all kind of bed form and flow under critical, the coefficients modified
Yang (1996)
-
-
*
This method modified for rivers by high concentration suspended load,
for small particles bed materials , as entrance model
the size of suspended load particles used as entrance model
Van Rijn (2004)
-
-
-
Develop base of field data and the size of bed material particles
Geological formations of Karkheh basin, specially
formations around Karkheh Dam, are sensitive to erosion
and include Marl evaporation sediments, thick Limestone
layers, Lime Sandstones, colorful Siltstones and large part
of Conglomerate and Conglomerate Sand formations
along with alluvial deposits play an important role in
erosion and sedimentation processes, specially supply of
wash load, of Karkheh River.
Since rivers with narrow and deep flow channels
carry less sediment as bed load when compared to wide
and less deep channels [15], Karkheh River with a wide
and deep flow channel transports the largest portion of its
sediment load as suspended load. Suspended load
composition of this river at Jelogir Station mainly includes
59% silt, 37% clay and 4% sand [16] while bed load
sediments are mostly sandy. The X-ray tests have shown
that the sand minerals in this river are Quartz, Feldspar,
Kaolinite and Calcite, respectively [17].
short introduction to the sediment transport formulas is
given below. Because of the lengthy expressions of some
of these formulas, only the basic equations are presented
here.
Bagnold (1966): Bagnold extended his sediment transport
function in relation to the concept of flow power. He
focused on the relation between existing energy in a given
alluvial system and the amount of work by that system to
transport sediment and developed the formula below for
bed load transport:
s
−
qbw tan
= veb
Where
and s are specific weights of water and
sediment, respectively, qbw is bed load transport rate by
weight per unit width, tan proportion of tangential shear
force to Vertical shear force, shear stress along the bed,
eb efficiency coefficient and V average flow velocity.
Considering experimental flume data Bagnold obtained
efficiency function for suspended load transport and
presented the following formula to calculate suspended
load:
Methods
Sediment Transport Formulas: The commonly used
formulas for calculate bed material load (or total load)
developed by Bagnold [1], Engelund and Hansen [2],
Ackers and white [3], Yang [4] and van Rijn [5, 6] were
selected for the comparison in this study. For Yang’s
method, the modified version by Yang [7] was used
because this version was specially modified for high
concentrations rivers of fine suspended materials. For Van
Rijn’s method, the 2004 version [18, 19] was selected
because the new formulas were improved greatly
especially for fine sizes of sediment and with greater
consideration of the physics in natural. In order to
calculate suspended load and bed load separately,
Bagnold [1] formulas and Van Rijn [18, 19] were used.
A total of five sediment transport methods were selected
for comparison in this paper as listed in Table (1). A very
qsw = 0.01(
s
−
2
)
Engelund and Hansen (1972): Engelund and Hansen
applied Bagnold’s stream power concept and the
similarity principle to obtain a sediment transport
function.
qs = 0.05V 2 s (
1
d50
)2 (
g (Gs − 1) (

s
− ) d50
3
)2
where qs is the bed- material sediment discharge by weight
per unit width; V is the depth- average flow velocity;
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World Appl. Sci. J., 13 (2): 376-384, 2011
d50 is the median diameter of the bed materials; g is the
gravitational acceleration; is the shear stress along the
depth of more than 1 m. The proposed formula to predict
bed load for current and wavy flows is as follows:
bed; Gs is the specific gravity given by
; and and
=
qb
s
s are the specific weights of water and sediment,
respectively.
Engelund and Hanson found the formula would be
applicable for dun beds and upper flow regime with
sediment size larger than 0.15 mm.
F gr
A


− 1


qs =
m
Where Ct weight concentration of bed material, V* is shear
velocity, h is average depth of flow section and C, A, n
and m are coefficients. This formula was derived using
1000 laboratory data with particle size larger than 0.04 mm
and Froude number less than 0.8.
Yang (1996): By modifying Yang’s main relation [4] for
rivers with highly- concentrated suspended materials,
Yang [7] developed the following relation which was used
in the present paper accordingly:
+(1.780 − 0.36 Log
m d50
m d50
− 0.297 Log
V*
m
 VS
− 0.48 Log
) Log 
m
 m
V*


− m
m
s
h
∫a ucdZ
Field Measurements: Prediction of bed load flux remains
a significant problem in understanding river
morphodyanmics for geomorphic and engineering
applications [20]. In most watershed and river engineering
projects, 20 to 30% of suspended load is generally
considered as bed load. This assumption may not be
correct in some cases [21]. In this study, since the bed
load of Karkheh River was not measured systematically
and continuously at Jelogir measuring Station and due to
necessity comparing its measurements with computed
values by experimental formulas and to prevent any error
resulting from the assumed suspended load 20 to 30% as
bed load, samples were taken from bed load for a
monitoring period of 6 months (once a two weeks).
A Helley- smith sampler with a 75mm x 75mm
entrance and 25 kg weight was used to estimate bed
load transport rates [22]. Sampling duration was almost
15 min. Bed load catches range from 408 to 5.8 gr with a
mean of 54 gr. The medium diameter is 0.35 mm but 10% of
the bed load is coarser than 1.5 mm, the medium diameter
(d50) of the bed material. This reveals the motion of
particles coarse enough to induce changes in the bed
configuration.
The results of particle size analysis of samples
showed that, on average, bed load of Karkheh River is
composed of 93.26% sand, 4.63% gravel and 2.08% mud
(silt and clay).


V*n
V


gd 50 (GS − 1)  32 Log (10h / d 50 ) 
LogCt =
5.165 − 0.153Log
b, cr ) / b ,cr 
Where u is the velocity profile including wave-current
interaction; C is the concentration profile; and z is an
integration variable.
1− n
Fgr =
) 0.5  ( 'b ,cw −
where fsilt is a silt factor; ´b,cr is the instantaneous grainrelated bed-shear stress due to both currents and waves;
is the critical bed-shear stress according to shields; ñ is
is the
the density of water; ç is an exponent and
dimensionless particle size.
The suspended sediment transported is computed by:
Ackers and White (1973): Ackers and White used
dimensional analysis based on flow power concept, as
explained by Bagnold, in order to express sediment
transport rate by several dimensionless parameters. Their
proposed formula was as follows:
n
d50  V  
=
Ct CGs
  
h  V*  

−0.3
( 'b,cw /
s f silt d50 d*
In which Ct weight concentration of sediment in ppm,
V is kinematic velocity of sediment- laden flow, m is
special weight of sediment- laden flow and m is particle
fall velocity.
Van Rijn (2004): Van Rijn revised his formula upon
hydrodynamic parameters and main sediment particulars
for current and wavy flows whose results are reflected in
TR 2004 Model (18, 19). This model is applied for
sediments with particle size of 0.008 mm or larger and
sediment concentration higher than 150 kg/m³ with water
Comparison: In order to determine the accuracy of
selected formulas, predicted sediment rates by different
methods were compared with measured amounts using
three statistical methods below.
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World Appl. Sci. J., 13 (2): 376-384, 2011
Table 2: Summary of applied data in total, bed and suspended load calculations of Karkheh River
Sediment discharge Flow discharge
(Ton/Day)
(m3/s)
1392757-61.6
Eshell (m) Depth (m)
1395-23
4.2-0.31
D50 (mm)
7.96-4.1 0.012-0.00008
D90 (mm)
Slope %
0.0325-0.00015
0.002
Difference Ratio; This ration is defined as follows:
Ri =
Section
width (m)
32-7
114.3-80.7
Section area
(m2)
624.1-270.4
measured at the same time, were selected and used in
formulas. Table (2) presents a summary of the available
hydraulic data at Jelogir Station.
Suspended load concentration of Karkheh River is
measured at specified intervals following a regular
schedule while bed load is measured occasionally. Hence,
the reported sediment discharge in Table (2) contains only
suspended load measurements. Data of gradation in Table
(2) related to the bed material particles size were measured
regularly during intended statistical period while that of
suspended load particles size might have been measured
occasionally therefore in this research material bed
gradation was used in total formula.
Cci
Cmi
Where Cci and Cmi are calculated and measured sediment
rates, respectively. To obtain a ‘fit perfect’, R1 should be
one. In analyzing long series of data, average difference
ration (R) should be used.
Mean Standard Error: Mean Standard Error was used in
order to select the best formula since due to high
difference between predicted and measured sediment
rates at various intervals, specially during flood periods,
the difference ratio can not be used alone for this
purpose:
MNE =
Temperature
(Degree)
RESULTS
By measuring bed load, which was done at the same
time with measuring suspended load over a monitoring
period of 6 months, bed load coefficient of the study area
was obtained from 0.2% to 0.6% which was used to
determine the total observed sediment load at Jelogir
Station. The total sediment concentration was calculated
by the selected formulas (Engelund and Hanson, Ackers
and White, Yang, Bagnold and Van Rijn) while bed load
and suspended load rates were calculated by Bagnold and
Van Rijn methods. Since the measured sediment load at
Jelogir Station only was suspended load of Karkheh River
and sediment load obtained by Engelund and Hanson,
Ackers and White and Yang methods was total load, thus
the calculated total load by these three methods along
with bed load percent obtained from field measurements
[bed load = 0.2 to 0.6 suspended load percent] plus
measured suspended load were compared. In order to
prevent any errors resulting from application of
approximated bed load percent, in Bagnold and Van Rijn
methods, only measured and calculated suspended loads
were compared. The results are shown in Table (3) and
figure (2) below.
Engelund and Hanson method predicted total
sediment load of Karkheh River more than measured
values. The prediction process of sediment load by
Ackers and White and Van Rijn method is unclear and
imprecise (Fig. 2 b, d) while Yang and Bagnold method is
less imprecise (Fig. 2c, e) and seems to produce the best
prediction among the selected methods.
n
100
S0 − Sc
N i =1 Sc
∑
In which MNE is Mean Standard Error, So observed
sediment rate, Sc is predicted sediment load and N is the
number of predicted values. In this method, a lower
statistical criterion (close to zero) shows a higher
accuracy in model performance.
Average Geometric Deviation (AGD):
1
(AGD): N

 N


Ri 


 i =1 
∏
 Sc if S ≥ S
c
0
 S0

Ri = 
 S0 if S0 ≥ Sc
 Sc
For a perfect fit, A G D = 1.
Data Used in the Study: Jelogir Station, at which
hydrometric statistics of Karkheh River are recorded, is a
first order hydrometric station providing long, relatively
reliable data. Hydraulic data of this station used as the
basis for calculations were selected from the period of
1974 to 2008. More than 90 series of data regarding
measured suspended sediments, flow discharge, eshell,
particle size of bed materials, water temperature, water
surface slope and cross-section of station, which were
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World Appl. Sci. J., 13 (2): 376-384, 2011
Table 3: Summary of comparison between computed and measured bed material load of Karkheh River
No.
Method
0.5= R = 2
%MNE
AGD
1
Engelund & Hansen (1972)
22.5
2
Ackers & White (1973)
62.8
11.1
88.6
11.5
22.5
304.5
3
Yang (1996)
12.9
4.6
41.1
85.2
4
3.3
Bagnold(1966)
1.2
55.5
486.1
3.4
5
Van Rijn (2004)
0.1
3.3
12256640.1
50.3
R
(a)
10000000
(b)
1E+14
1000000
1E+12
100000
1E+10
10000
1E+08
1000
1E+06
100
10000
10
100
1
1
1
100
1
10000 1E+06 1E+08
(c)
10000000
100
10000
(d)
1000000
100000
1000000
1000000 1E+08
10000
1000
100000
100
10
10000
1000
1
0.1 1
100
10
1
1
100
10000 1E+06 1E+08
1000000
0.01
0.001
0.0001
100
10000 1000000 1E+08
Measured concentration (T/D)
(e)
100000
10000
1000
100
10
1
1
100
10000 1000000 1E+08
Measured concentration (T/D)
Fig. 2: Comparison between computed and measured load sediment concentration for Karkheh River data: (a) Englelund
and Hansen, (b) Ackers and White, (c) Yang, (d) Van Rijn, (e) Bagnold
DISCUSSION
closer to R = 1, the selected method performs more
accurately and should the depicted points are scattered in
direction of R = 1, the selected method can be modified by
applying a corrective coefficient. Considering Fig. (3), one
can infer that Yang method produced a relatively accurate
prediction as such that the points are depicted along
R = 1 and around R = 4 and can be corrected by applying
a ¼ corrective coefficient to produce better results (Fig.4).
Overall, no accurate method exists to determine the
best sediment prediction formula since the use of various
statistical methods produce different results.
Fig. (3) Shows sediment load ratios (calculated load
/ measured load) with different periods for the selected
methods. As the depicted points are in direction and
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World Appl. Sci. J., 13 (2): 376-384, 2011
(a)
1000
100
100
10
10
1
0.1 0
20
40
60
80
1
0.1 0
100
0.01
0.01
0.001
0.001
60
80
(d)
1
10
0.1
0
20
40
60
80
100
0
20
40
60
80
100
0.01
0.001
0.01
0.001
40
10
100
1
20
(c)
1000
0.1
(b)
1000
0.0001
Number of period
Number of period
(e)
1000
100
10
1
0.1
0
20
40
60
80
100
0.01
0.001
Number of period
Fig. 3: Proportion computed and measured load sediment concentration for Karkheh River data in various procedure:
(a) Englelund and Hansen, (b) Ackers and White, (c) Yang, (d) Van Rijn, (e) Bagnold
1000
100
10
1
0.1
0
20
40
60
80
100
0.01
0.001
Number of period
Fig. 4: Estimate of sediment load in Yang procedure after application correction coefficient
Bagnold method underestimated sediment load of
Karkheh River and sometimes overestimated sediment rate
mainly due to flow high-velocity.
Large scatter of calculated results by Van Rijn and
Ackers and White methods and to a lesser extent those
by Engelund and Hanson method show that these
methods are not appropriate to determine sediment load
of Karkheh River which contains abundant fine and
suspended materials
while they perform more
successfully in laboratory flumes. Weak performance of
these three methods can be attributed to delay of
sediment deposition velocity which is not normally
considered in such methods. This weak performance can
also be caused by application of corrective coefficients
calibrated by laboratory data so that Sediment transfer
formulas developed based on such data can not
accurately predict sediment load under field conditions
[13]. In all the selected methods, the bed particle size was
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World Appl. Sci. J., 13 (2): 376-384, 2011
used due to the lack of data regarding suspended particle
size and Also average flow velocity was used instead of
direct measurement of flow velocity from different river
profiles, hence scatter of depicted points was larger in
Van Rijn and Ackers and White, which are more sensitive
to flow velocity and sediment particle size [12].
The calculated sediment load by experimental
formulas is total bed material which excludes wash load.
On the other hand, with the existence of fine, erosionsensitive formations around the study area, a large wash
load is expected to occur in Karkheh River. Thus, the large
portion of difference between measured sediment load
and calculated sediment load by the selected methods can
be related to the washed load of the river. Also, since
sediment load is calculated by experimental formulas for
averaged river depth and width while morphological
features of a river are different in time, thus a difference is
always expected between the calculated sediment load
and observed sediment load.
Extreme scatter of results by Engelund and
Hanson, Ackers and White and Van Rijn
methods in the study area shows that such
methods were not proper to predict sediment
load material of Karkheh River and the
coefficient applied in these formulas, which were
obtained on lab flumes, are not good to be used for
natural rivers.
The results produced by different formulas were
different and were considerably different than the
observed values which can be related to the wash
load from loose formations of the basin not
considered in experimental formulas.
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CONCLUSIONS
Various experimental formulas including Engelund
and Hanson, Ackers and White, Yang and Bagnold
methods in order to determine total sediment load and Van
Rijn and Bagnold methods to determine bed load and
suspended load of Karkheh River were used at Jelogir
Station using 90 series of field data and the results were
compared by the measured suspended load along with the
measured bed load in a short period to calculate bed load
coefficient for the whole statistical period. The following
conclusions can be drawn:
The results of direct filed measurement of bed load
showed that it is almost 0.2 to 0.6 percentage of
suspended load.
The sediment particle size analysis showed that
Karkheh bed load is composed of 93.26% sand,
4.63% gravel and 2.08 silt and clay; hence a large
portion of bed load material of this river is sandy
material.
The best estimates of Karkheh sediment load were
produced by Yang and Bagnold methods as less
erroneous predictions were obtained. In the Yang
method Due to less scattered points around R = 1
(calculated/observed load), a corrective coefficient of
¼ can be used to obtain better results.
Engelund and Hanson and Ackers and White
methods overestimated the total sediment load while
Van Rijn underestimated the total sediment load.
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World Appl. Sci. J., 13 (2): 376-384, 2011
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