International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:10 No:02
9
The Verification Of The Best-Fit Equation
To Predict Spatial Sedimentation Rates At
Loagan Bunut Lake, Miri, Sarawak
R.B. Dagang1, S. Lau2, and A.K. Sayok2
1
Swinburne University of Technology, Sarawak, Malaysia
Universiti Malaysia Sarawak, 94300 Kota Samarahan, Sarawak, Malaysia
1
[email protected]
2
Abstract-- Although a number of problems in environmental
science deal with biology, chemistry and social issues, the
applications of physics are also very important. In this paper, the
best-fit model to predict spatial sedimentation rates at Loagan
Bunut Lake is verified using conservation of mass and
comparative equation. The lake is a flood plain lake that is
located within the boundaries of Loagan Bunut National Park in
the northeastern part of the state of Sarawak. Twenty two
cylindrical traps were installed at the lake. The traps were placed
in November 2005 until April 2008. Each sample was collected
after about four to five months of deployment. Dry sedimentation
rates of the traps and their linear distances from Trap 1 located
at the confluencet of Bunut River were measured.
Index Term--
environmental physics, sedimentation rate,
conservation of mass, Loagan Bunut Lake.
completely within less than 60 years [3]. Reports have
mentioned that the sediment flux along the main feeder
stream, the Bunut River and in the lake were 15 kg m-2 y-1 and
0.6 kg m-2 y-1 respectively [4].
The authors of this paper are therefore interested to
contribute by verifying the best-fit model that can be used to
predict sedimentation rates at the distance 0-600 m from the
Bunut River.
2. MATERIALS AND METHODS
Sediment traps
The study site and the sampling stations are as shown in Fig.
1. All the sampling stations were recorded using numbers and
clearly marked on the site with bamboo stilts where the
sediment traps were tied. The trap’s positions and distances
from Trap 1 were recorded (Table I).
1. INTRODUCTION
Loagan Bunut is a fresh water lake situated within the
boundary of Loagan Bunut National Park, at the northeastern
part of the state of Sarawak. It covers 6% of the Park area.
Specifically, the lake area is between Tinjar River and Teru
River of the Baram Basin flood plain. It has its own basin
which is mainly connected with Teru catchments by about 6.6
km of Bunut River.
About 61.9% of the catchments are Stateland on which
logging licenses have been issued and where cultivation by
local community takes place. Satellite images show a high
road density in relatively steep areas [1]. The Teru catchment
is made up of plantations and active subsistence farming areas
[2].
To the locals, the Berawan, the lake and its surrounding
areas play an important livelihood support system and place of
abode for generations. To the Sarawak State, the lake and its
surrounding have economic value for its unique hydrologic
phenomena, exotic fish species, water birds, medicinal plants
and rich local culture that are marketable in terms of tourism.
Even though the retaining of water and the trapping of
sediment at Loagan Bunut are natural downstream flood and
sedimentation controller, an alarmingly high rate of
sedimentation at the lake accelerates the filling of the lake
which threatens its functions, natural physical, hydrological
phenomena and biodiversity. The lake was experiencing 27
years of rapid sedimentation and it was estimated to be infilled
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Fig. 1. Locations of 23 deployed sediment traps.
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International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:10 No:02
T ABLE I
THE TRAP ’ S POSITIONS, DISTANCES FROM TRAP 1 AND WATER speeds.
Trap’s
Water
distance
speed
from
(cm s-1)
Trap
Station
GPS positions
1(m)
N 3o, 45’,
E 114o, 14’,
0.4
1
55.5’’
27.54’’
0
o
o
N 3 , 45’,
E 114 , 14’,
0.3
2
52.86’’
21.18’’
212.16
N 3o, 45’,
E 114o, 14’,
0.1
3
50.76’’
11.40’’
518.2
N 3o, 45’,
E 114o, 14’,
0.2
4
46.92’’
36.90’’
391.47
o
’
o
N 3 , 46 ,
E 114 , 14’,
0.1
5
2.58’’
20.76’’
302.27
N 3o, 46’,
E 114o, 14’,
< 0.1
6
14.64’’
9.06’’
820.37
o
’
o
N 3 , 45 ,
E 114 , 14’,
< 0.1
7
59.40’’
1.02’’
825.64
N 3o, 45’,
E 114o, 14’,
Bunut
< 0.1
8
56.4’’
42.06’’
River
N 3o, 45’,
E 114o, 14’,
0.1
9
51.36’’
25.14’’
147.63
o
’
o
N 3 , 45 ,
E 114 , 14’,
0.1
10
43.26’’
22.62’’
407.07
N 3o, 45’,
E 114o, 14’,
< 0.1
11
28.98’’
17.88’’
870.97
o
’
o
N 3 , 45 ,
E 114 , 14’,
< 0.1
12
36.84’’
41.46’’
718.03
N 3o, 45,
E 114o, 14’,
< 0.1
13
23.22’’
47.34’’
1168.19
N 3o, 45’,
E 114o, 14’,
< 0.1
14
37.5’’
50.04’’
888.23
o
’
o
N 3 , 45 ,
E 114 , 14’,
0.2
15
55.14’’
43.5’’
491.69
N 3o, 46’,
E 114o, 14’,
< 0.1
16
1.68’’
34.2’’
280.12
o
’
o
N 3 , 46 ,
E 114 , 14’,
< 0.1
17
30.48’’
33.36’’
1094.49
N 3o, 46’,
E 114o, 14’,
< 0.1
18
44.04’’
13.5’’
1559.42
N 3o, 47’,
E 114o, 14’,
< 0.1
19
6.96’’
11.1’’
2263.1
o
’
o
N 3 , 46 ,
E 114 , 14’,
< 0.1
20
34.08’’
1.68’’
1432.65
N 3o, 46’
E 114o, 13’,
< 0.1
21
9.24’’
41.58’’
1477.73
o
’
o
N 3 , 46 ,
E 114 , 14’,
0.1
22
0.60’’
9.6’’
574.54
N 3o, 45’,
E 114o, 13’,
< 0.1
23
46.08’’
58.9’’
928.22
A selection of sediment trap design was based on the study
objective, sediment trap review, site condition, material
durability and cost. The sediment trap was design to trap
downward flux that is to represent as close as possible with
real sedimentation on the lake bed. An overtraping by
cylindrical trap as reported by Flower [5] and Kozerski and
Leuschner [6] is reduced by using funnel. In this field
sampling, funnel was used to avoid sediment escape and to
reduce overtraping in high energy area. The traps are made of
15.25 cm diameter funnel and 38.0 cm height pvc cylinder
(Fig. 2). A total of 23 sediment traps were first deployed on 24
November 2005. Trap 1 was stationed close to the Bunut
River.
10
Sediment samples
All sediment from the trap was transferred to sealable plastic
bags very carefully to avoid any external material adding into
the sample or to avoid any portion of the sample being
excluded. Every component of the trap was checked and any
damaged part was replaced and reinstalled for the next
deployment.
The sediment sample was collected after four to five months
deployment. The sample was transferred to a metal can for
drying purpose. Oven Drying Method by Purusothama [7] was
employed. The sample was then dried in aired oven at 105 oC
for a period until a constant weight. The sediment was
weighted immediately when cool to get the total sediment
mass.
Correlations between sedimentation rates and distance from
Trap 1 and best fit equations were tested using Microsoft
Excel Analysis ToolPak. A graphical scatterplots were
produced and then regression type was chosen. A selected
regression type was based on the strength of the relationship.
The tool gives the strength of the relationship that is
considered as a strong relationship. Then the best fit equation
was discussed for its validity.
Fig. 2. Cylindrical sediment trap.
Water speed samples
A surface flow speed measurement at Loagan Bunut Lake had
been made at all of the trap’s station using electromagnetic
Flow Meter Valeport Model 801 with precision of 0.1 cm s-1.
During the measurement, the water level of the lake increased
by 1 cm in 5 hours. The water speed readings were from < 0.1
to 0.4 cm s-1 (Table I).
3. RESULTS AND DISCUSSION
Table II shows the general spatial sedimentation rate at each
station for six samples. Trap 8 which was located at Bunut
River has maintained the highest average amount of 47.50 g
day-1 m-2. Then followed by Trap 1 that was located at the
confluence of Bunut River/Lake has 16.36 g day-1 m-2.
Generally, high sedimentation rate area was near to Bunut
River. The lowest rates were at Traps 17, 18 and 20 which
were far from Bunut River.
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International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:10 No:02
11
Averag
e
Sample
6
Sample
5
Sample
4
Sample
3
Sample
2
Sample
1
Traps
T ABLE II
SEDIMENTATION RATES FOR EACH STATION FROM ALL SIX
DEPLOYMENTS .
(g m-2 day-1)
10
11
12
13
14
16.6
7
12.7
0
9.90
9.14
69.3
0
13.6
8
12.5
5
5.03
9.17
2.62
6.57
15
16
17
18
19
20
21
22
23
Av
g.
9.49
3.95
3.34
5.15
2.73
5.25
7.04
7.90
7.39
11.8
7
4
4.75
5
6
7
5.33
4.16
4.18
8
25.7
9
8.02
15.8
5
6.74
13.2
5
7.93
6.17
5.57
11.2
3
9.93
3.40
7.32
6.48
7.17
3.73
2.46
5.25
4.92
5.17
7.64
4.02
6.04
7.01
12.3
9
9.93
3.00
7.06
3.84
7.12
14.3
2
4.20
1.98
4.50
2.78
5.28
8.56
5.96
8.67
13.1
6
12.6
7
6.83
9.76
5.78
8.32
9.26
7.86
16.3
6
12.6
7
6.27
11.9
3
7.08
5.32
5.63
9.68
6.72
6.49
9.28
47.5
11.1
7
7.40
7.28
5.65
7.57
6.26
6.99
1.60
7.43
6.07
4.76
4.53
2.37
6.07
9.21
4.49
7.01
2.61
6.73
6.01
5.38
2.70
4.73
5.48
5.87
6.89
6.87
4.63
5.40
3.59
5.48
3.63
4.84
5.69
5.97
5.47
8.32
4.53
2.81
5.02
3.52
5.20
6.96
6.15
6.44
6.98
5.64
9.03
The graphs and the coefficient of determinant, R2 are in
Fig. 3. The coefficients of determinant were 0.8 or higher. At
this area, sedimentation rate decreased exponentially with
distance from Trap 1. All samples showed highly similar
decay exponential pattern with distance from Trap 1. An
initial value of sedimentation rate before entering the lake was
ranging from 8.42 g day-1 m-2 to 22.24 g day-1 m-2. The
exponential index was ranging from – 0.0007 to – 0.0021. An
average of sedimentation rate with distance from Trap 1 for all
samples at the area has R2 = 0.94 (Fig. 4). The best-fit of
average sedimentation rates distributed by advective force of
inflow at the distance 0-600 m from Bunut River was
0.0017x
Sx = 16.25 e
where 16.25 = sedimentation rate at at Bunut River/Lake
confluence in units g day-1 m-2, Sx = sedimentation rate at x
distance from Trap 1, x = linear distance from Trap 1 in unit
m, 0.0017 = a coefficient of sedimentation rate.
In general, the equation can be written as
 kx
Sx = So e
where so and k are sedimentation rate at x distance from Trap 1
and a coefficient of sedimentation rate respectively.
Fig. 3. Best-fit graphs of sedimentation rates at 0-600 m from Trap 1 for five
samples.
m -2 )
7.65
4.37
19.7
0
16.2
0
7.77
17.1
3
15.3
0
8.98
6.09
16.00
y = 16.253e-0.0017x
R2 = 0.9372
-1
2
3
25.1
9
16.3
9
Sedimentation rate(g day
1
12.00
8.00
4.00
0.00
0
100
200
300
400
500
600
Distance(m)
Fig. 4. Best-fit graph of an average sedimentation rate at 0-600 m from Trap
1.
Reynold theorem
Based on the significant correlation between sedimentation
and distance, this part of the paper will discuss Reynold
theorem.
One needs to understand what really determines the amount of
sediment that is settled in the sediment trap that is installed
vertically upward.
From Reynold theorem,
dB d

b d +
dt dt 
 b (V.n) dA tells a rate change of property at one control
volume and control surface of suspended sediment is equal to
the sum of a rate change of property in a control volume and
net outward flux of the property out of the control surface. It is
assumed that a change of sediment mass due to organic matter
decomposition and organic matter oxidation are very small.
Hence, the first term in Reynold theorem does not apply. The
second term is the input and output through a control area. It is
considered that the sediment that is trapped will not be
resuspended since the resuspension needs at least 6 cm s-1 of
water speed. It is the second term in the theorem that is used to
count an input rate of sediment flux through the control
surface of the sediment trap’s opening, thus the rate of
sediment flux in this case is written,
 b (V.n) dA where b =
1, ρ = concentration of suspended sediment outside the trap, V
= velocity of sediment which is a resultant of horizontal water
velocity and Stoke’ settling velocity, A = trap’s opening area
and n = normal line to the trap’s opening area. Sedimentation
rate into the trap’s surface depends on suspended solid
concentration (ρ) and a dot product of velocity and a direction
normal to the control surface (V.n). The term (V.n) is equal to
(V cosθ) which is positive for water entering and negative for
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International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:10 No:02
water leaving the volume. The effective (V cosθ) at the trap’s
opening is equivalent to Stoke’s settling velocity. Therefore,
g  s  w  2
(V.n) = Stoke’s settling velocity, ws = 

d
18   
which is proportional to the particle’s diameter square. This
means that sedimentation rate is also determined by suspended
sediment size. Therefore, sedimentation rate, S = ρws.
Equation of conservation of mass
Assuming an average of settling velocity is approximately
constant, the concentration,  , is proportional to
sedimentation rate, S. It can be written that

o
=
e  kx (Equation of suspended sediment

concentration) where
and
o
are suspended sediment
concentration at distance x and Trap 1 respectively.
In an attempt to put cross-sectional area and horizontal
speed in the lake to the suspended sediment concentration
 kx
equation, ρ = ρo e , if a change in suspended sediment
concentration was mainly attributed to a change of cross
sectional area, a principle of conservation of mass can be used.
In a small time interval Δt, at the Bunut River
confluence, the water moves through a distance of Δxo = vo Δt.
The suspended sediment mass contained in the volume of Ao
Δxo is given by Δmo = ρo Ao Δxo = ρo Ao vo Δt. Likewise, at x1
distance from Trap 1, in the same time interval Δt, mass Δm =
ρ A v Δt where A and x are cross sectional area and horizontal
distance respectively. Assuming the mass of the suspended
sediment is conserved, the mass of the suspended sediment
entering the lake from Bunut River per second is equal to the
mass of the suspended sediment per second at x distance from
Trap 1 provided that sedimentation from Trap 1 to x distance
does not contribute much to a change in density ρ and that a
change of sediment concentration is merely by a change of
cross-section.
m o  m
=
t
t
 o Ao vo t Avt
=
(g/s)
t
t
Therefore,  o Ao vo = Av is a rate flow of suspended
Hence,
sediment mass moving horizontally.
Next, 


 o Ao vo
Av
Av
 ρo e

Rx
ws
e
Rx
ws
(Equation of conservation of
mass)
Where Av represents the horizontal rate flow at distance x
from Trap 1 while v and A are the horizontal speed of the
suspended sediment and cross sectional area that is occupied
by suspended sediment which is parallel to the direction of the
velocity v at distance x from the Bunut River respectively. The
exponential decay equation shows horizontal rate flow, Av,
increased exponentially with distance from Bunut River into
the lake. Even though, suspended particle speed decreased as
it moves from Bunut River further into the lake, but,
tremendous increases in cross-sectional area is able to offset
that particle’s speed changes. From the equation

 o Ao vo
Av
, suspended sediment concentration, ρ is
inversely proportional to Av. It shows that a change of
suspended sediment concentration and water volume were
mainly influenced by cross-sectional area, A.
Comparative equations
All particles of suspended sediment that come from Bunut
River settled at specific location and time were determined by
kinematics parameters: initial height and initial horizontal
velocity at the confluence, downward settling velocity and
horizontal and vertical acceleration/deceleration of that
suspended particle. Equations of motions are the simplest
tools that could be used to describe the sedimentation pattern
but
need
great
assumption
of
constant
acceleration/deceleration. The equation of motion in
horizontal that might be used is
h
dx = Vox  y
w
 s
2
1  hy 

 + a x  2  where dx = horizontal distance
2  ws 

from Bunut River/lake confluence, Vox = particle’s horizontal
velocity at the point source, hy = the displacement of that
particle from the initial elevation at the point source to the
elevation of trap’s opening, a x = an average horizontal
deceleration of the particle and
ws = an average Stoke’s
settling velocity.

S = So
ρ = ρo e
by assuming that a change of concentration in the
model is only due to a change in cross-section, and one can
write that
 o Ao vo

Sedimentation rate with distance exponential decay equation,
is fitted to the model
Rx
ws
1
1

Av Ao vo
12
e
1  ho2
ax 
2  ws2
Rx
ws
 ho
w
 s
and kinematic equation, dx = Vo 



+

 are needed to be discussed at the same time to

provide an insight into the relationship between them.

Putting dx into x in S = So
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e
Rx
ws
gives,
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International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:10 No:02

e
S = So
confluence to approximately the center of the lake. From
observation, the lake cross-sectional area decreases from
Bunut River/Lake confluence to approximately 600m into the
lake.
The calculated speeds using comparative equation are
comparable to the measured speeds. The measured average
water speed was from 0.4 cm s-1 at the Trap 1 to less than 0.1
cm s-1 at the center of the lake (Table I).
The similarities between the indications from the equation of
conservation of mass and the observation and comparable
water speeds provide verification of the best-fit equation, Sx =
Rd x
ws
dx =
ln S o
ln S

R / ws R / ws
Comparing the two equations shows that
 ho
w
 s
Vo 
1  ho2
 ln S o
and
ax 
 =
2  ws2
 R / ws

ln S
 = 
.
R / ws

h
In the first comparative equation, Vox  o
w
 s
13

 =

ln S o
, Vox which is an horizontal speed at Trap 1 or at the
R / ws
Bunut River/Lake confluence might be used for comparison.
In the best-fit model of total sedimentation rate with distance,
R/ws or k is 0.0017 and So is 16.25 g day-1 m-2. An average
depth of 2.5 m at Station 1 is taken as ho. From Wetzel (1975)
[8], settling velocities of silt, clay and small particulate carbon
are 3 – 30 m day-1, 0.3 – 1 m day-1 and 0.2 m day-1
respectively. The smallest silt settling velocity, 3.0 m day-1, an
average of clay settling velocity, 0.65 m day-1 and organic
settling velocity, 0.2 m day-1 are used. An amount of silt and
clay within the model area was approximately equal and an
average percentage of organic at the modeling area was about
13 %. Hence, the calculated initial horizontal velocity, Vox, at
Station 1 or at the Bunut River/Lake confluence using the
equation is 1.2 cm s-1, which is reasonable and comparable to
the measured value 5.26 cm s-1 at Bunut River near the
Teru/Bunut confluence. The speed measurements at most
areas of the lake were < 0.1 – 0.4 cm s-1 (Table 3) when the
water level rise was 4.8 cm day-1. An average water rise
during the entire period of sediment trap deployment was 5.2
cm day-1.
So e
 kx
.
ACKNOWLEDGEMENTS
The authors would like to thank Yayasan Sarawak Tunku
Abdul Rahman Scholarship for financial support.
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
REFERENCES
UNDP/GEF, “Multi-Disciplinary Assessment of the Peat Swamp
Forest of Loagan Bunut National Park,” Technical Report,
UNDP/GEF, 2007.
G.T. Noweg, W.H. Sulaiman, M. Murtedza, N. Bessaih, and A. K.
Sayok, “Estimation of Sediment Yield in the Loagan Bunut Lake,”
Report to UNDP/GEF, 2006.
C. Hunt, R.M. Banda, B. Badang and A.U. Ambun, “Geology and
soil survey of Loagan Bunut National Park,” Paper presented at the
Seminar on the Loagan Bunut Scientific Expedition, Kuching, August
2004.
S. Lau, S.F Sim, K. Devagi, A.C.H. Bong and A.K. Sayok, “Organic
matter and heavy metal contents in the sediment of Loagan Bunut,”
In Scientific Journey Through Borneo: Loagan Bunut, pp. 51-58,
UNDP/GEF, 2006.
R. J. Flower, “Field calibration and performance of sediment traps in
a eutrophic holomictic lake,” Journal of Paleolimnoloy, 5(2):175188, 1991.
H.P. Kozerski, and K. Leuschner, “Plate sediment traps for slowly
moving waters,” Water Research, 33:2913-2922, 1999.
R.P Purusothama, Geotechnical Engineering. New Delhi: Tata
McGraw-Hill, p.320, 1995.
R. G. Wetzel , Limnology. Saunders. Philadelphia, pp. 15-36, 1975.
T ABLE III
WATER CURRENTS AT DISTANCES CALCULATED USING THE FIRST
COMPARATIVE EQUATION
Distance (m)
Sedimentation rate (g
day-1 m-2)
Velocity (cm s-1)
100
13.8
1.1
200
11.6
1.06
300
9.8
0.99
400
8.2
0.92
4. CONCLUSIONS
In this paper, the exponential decay equation to predict
sedimentation rate at 0-600 m from the Bunut River is verified
by the equation of conservation of mass and comparative
equations. The mass conservation equation indicates that the
cross-sectional area and water speed increases and decreases
respectively with distance from the Bunut River/Lake
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