Indian Journal of Geo-Marine Sciences
Vol. 41(1), February 2012, pp. 12-18
Evaluating longshore sediment transport rates by integration of beach evolution
model and GIS approach
Li Xing1*, Zhou Yun-xuan2, Zhang Lian-peng1 & Kuang Run-yuan3
1
School of Geodesy and Geomatics, Xuzhou Normal University, Xuzhou 221116, China
State Key Laboratory of Estuarine and Coastal Research, East China Normal University, Shanghai 200062, China
3
School of Architectural and Surveying & Mapping Engineering, Jiangxi University of Science and Technology, Ganzhou 341 000, China
*[E-mail: [email protected]]
2
Received 24 June 2010; revised 29 April 2011
A new integration approach of beach evolution model and Geographical Information System (GIS) is developed to
evaluate the longshore sediment transport rates. Nanhui Beach of Shanghai is selected as study area to demonstrate an
integration scheme. Study area is partitioned into some calculation units. It is further and modified one-line model to meet
complex physical settings of the study area. Firstly, we got the 0-m isobaths, as the beach evolution indicator. It is developed
by digitizing the nautical charts of 1990 and 2004. Shoreline change rates were derived from End Point Rate (EPR) method
based on GIS. Bathymetry was digitized from the nautical charts to calculate the beach evolution complexity factor in the
modified one-line model. The closure depth can be obtained from the published literatures about the study area. Longshore
sediment transport rate of every calculation unit was calculated by inversion of the modified one-line model. Results show
that integration scheme is effective and the precision is high. Total relative error is 8.77%.
[Keywords: longshore sediment transport rate; Geographical Information System; one-line model; End Point Rate; muddy coast]
Introduction
The longshore sediment transport rate is
indispensable in coastal engineering, needed in
applications such as beach evolution, infilling of
dredged channels, and the morphodynamic response
of coastal areas to engineering works1. Wave
energy flux method is one of the most popular
methods to evaluate the longshore sediment transport
rate in engineering practice. There are some
problems encountered in practical case, that is, 1) the
nearshore processes are of a complex nature, and it
is not yet completely clear how some complex
nearshore wave phenomena (e.g., refraction,
diffraction, breaking, transformation, etc.) form,
and correspondences between parameters were
established largely by empirical formula2,3. 2) The
determination of parameters needs extensive
fieldwork and intensive computation, and the
sufficient accuracy usually cannot be achieved3,4.
The models still have to be employed but do so
with careful interpretation of results. 3) Most
studies focused on sandy coasts, but the more
complex muddy coasts were rarely examined.
These problems suggest that the evaluation of
longshore sediment transport rate is still an active
research issue.
Among the common beach evolution models are
the one-line models, which were developed based on
Pelnard-Considère’s method5, that have been used
widely in various studies. Their fundamental
assumption is that the beach profile doesn’t change,
and the longshore sediment transport occurs
uniformly over the beach profile down to the closure
depth6,7. They are ideal models that are mostly used to
study sandy coast. On the other hand, the application
of Geographical Information System (GIS) in the field
of coastal sedimentation and shoreline change
prediction has proliferated in recent years4,8,9. Modern
GIS technology provides the advanced capabilities of
spatio-temporal analysis/visualization, multisource
data fusion/ anagement, interdisciplinary modeling,
and precise positioning, etc. The combination of GIS
and beach evolution models will be a promising
approach to study coastal sedimentation and beach
evolution.
Present study is a new approach which integrates
GIS and one-line model to evaluate the longshore
sediment transport rate. The basic idea is to calculate
inversely the one-line model to get the longshore
sediment transport rate by substituting the shoreline
change rate and the closure depth. Considering the
characteristics of the muddy beach of study area, it is
XING et al.: EVALUATING LONGSHORE SEDIMENT TRANSPORT RATE
introduced, a beach evolution complexity factor
making the one-line model more accurate in this
paper. It also consists the effectiveness of our method
experimentally by comparing with topographic
method.
Materials and Methods
One-line model
The basic mathematical description of the one-line
model is based on the conservation mass balance
equation, as illustrated in Fig. 1, written as,
∂y
1
⎛ ∂Q
⎞
+
− q⎟ = 0
⎜
∂t ( DB + DC ) ⎝ ∂x
⎠
… (1)
Where y is the shoreline position (m), t is the time (s),
and so ∂y/∂t is the shoreline change rate. DB is the
berm elevation (m), DC is the closure depth (m), Q is
the total longshore sediment transport rate (m3/s), x is
the longshore spatial coordinate (m) and q is the line
source or sink of sediment (m3/(s·m)). The suitable
spatial scale is a reach of several kilometers to a few
ten kilometers, and the suitable time scale is several
months to many years for the one-line model6,10.
GIS-based approach to estimate the shoreline
change rates
In GIS shoreline change modeling, several methods
have been proposed using various mathematical
models such as linear regression, higher order
polynomial, or exponential12,13. Another method, the
End Point Rate (EPR) method, has also been
presented in literatures14,15. The EPR method is the
Fig. 1—One-line model definition scheme (modified from
Silva et al., 200711)
13
most widely applied, especially by coastal planners
and managers, because of its simplicity. It can be
calculated by the following equation,
EPR =
y2 − y1
t2 − t1
… (2)
Where, y1 and y2 are the shoreline positions
respectively at time t1, t2. Usually, the t1, t2 are the
earliest and latest time of the available times.
The advantage of the EPR method lies in the
absence of sediment transport parameters making it
easier to implement. Instead, it assumed reasonably
that the cumulative effect of all the underlying
processes can be captured by modeling the shoreline
position changes12,16. Usually, the EPR can be
computed based on the perpendicular transects
method by creating transects on right angle on a
baseline, and the baseline that serves as the start point
of generating transects, can be created either landward
or seaward from the available historical shorelines17.
And the perpendicular transects method is reliable
over regularly shaped shorelines18.
Here, the GIS-based approach for estimating the
shoreline change rates can be synthesized in the
following steps. First, the indicator of beach evolution
should be determined. Some indicators have been
mentioned in published literatures8, 19-21, including the
mean high tide line, high water line, erosional scarp,
vegetation line, etc., which are easy to be extracted
from special remote sensing images. In this paper, the
0-m isobath of the nautical chart was used as the
indicator of beach evolution to calculate the shoreline
change rates. The second step is to generate the
baseline as the start point of transects. Generally, the
baseline was created by buffering the available
historic shorelines17. And then, the transects were
created along and in a direction perpendicular to the
baseline, and intersect all the historical shorelines.
Finally, we used the Eq. (2) to calculate the shoreline
change rates. The process can be conveniently carried
out using the Digital Shoreline Analysis System
(DSAS) extension to ArcGIS17.
By substituting the values of the shoreline
change rate, derived from Eq. (2) and the closure
depth into the Eq. (1), the longshore sediment
transport rate can be obtained. In the following
sections we will describe the details of implementing
the approach, with the Nanhui beach of Shanghai as
the study area.
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INDIAN J. MAR. SCI., VOL. 41, NO. 1, FEBRUARY 2012
1990 and 2004 were used to extract isobaths for
deriving beach evolution data.
Validation of the method
Study area
In order to validate the proposed approach above,
we selected the Nanhui beach of Shanghai ranged
from Meimaosha shoal to the mouth of Dazhihe River
as the study area, about 20 km long coast, and Fig. 2
shows its physical setting. The Yangtze River Estuary
is one of the largest estuaries in the world. The river
annually transports a runoff discharge of 9.24×1011m3
that carries about 4.86×108 tons of sediment to the
coastal sea22. The huge sediment load has formed the
large subaqueous delta and estuarine sand islands in
coastal area. In the study area, the tide is of the
irregular semi-diurnal shallow-water type, with the
mean and maximum tidal height of 2.66 m and 4.62 m
respectively at Zhongjun tidal station23,24.The wind
direction is typically SSE-SE which generates a
northward longshore current in summer, and NW-NE
which produces a southward longshore current in
winter25. Recent research shows that the sediment
transports upstream at less than 2 m depth, and
downstream at more than 2 m depth in the study
area23. And due to the specific morphodynamics of
the South Passage of Yangtze River estuary, the
sediment exchange between flats and channels is
frequent26. The nautical charts of this study area in
Calculation of the shoreline change rates
The coast has been become anthropogenic coast,
since there are coastal revetments around all coastline
segments in the study area. And the whole segment
was accreting coast during the study period from 1990
to 2004, the coastal revetments were designed and
constructed above the 0-m isobath. So the 0-m isobath
was employed as the indicator of beach evolution
instead of the natural coastline. The baseline was
created based on the coastline from the nautical chart
of 1990. And the 22 transects were generated at
1000m interval along the baseline (see Fig. 3a),
furthermore the 21 calculation units were produced
(see Fig. 3b). Using Eq. (2), we calculated the values
of EPR along all the transects. Then the average
change rate can be derived, by averaging the EPR
values of every two adjacent transects, for every
calculation unit. The results were shown in Fig. 4.
Modification of the one-line model
The beach evolution is a complex process,
including the shoreline retreat/advance and beach
erosion/accretion27. Generally speaking, the shoreline
retreat or advance doesn’t mean the beach erosion or
Fig. 2—The location and physical setting of the study area in 2004
XING et al.: EVALUATING LONGSHORE SEDIMENT TRANSPORT RATE
15
Fig. 3—Transects and calculation units. (a) 22 transects are used for calculating the change rate of 0-m isobath. (b) 21 calculation units
are used for calculating the longshore sediment transport rates, and the background topographic data was from the nautical chart of 1990.
Fig. 4—The mean EPR for every calculation unit
accretion, and also can’t reflect comprehensively the
beach profile evolution. The one-line model is an
ideal model, as described above, which based on the
assumption that the profile shape maintains invariable
over time. Obviously, the physical setting of the study
area does not accord with the assumption, since there
exist successively Meimaosha shoal, South Passage,
and Jiuduansha shoal seaward from nearshore
(see Fig. 3b), especially the frequently subaqueous
topography variations. In order to simulating
accurately, we introduced beach evolution complexity
factor, denoted by λ, into Eq. (1). Meanwhile as to the
study area, DB can be taken as 0, and neglecting the q
item, let ∂y/∂t=r, then Eq. (1) can be rewritten as,
∂Q = −rDC λ∂x
… (3)
Firstly, Referring to Chen Xiqing (1998)’s
research results to the closure depth of Changjiang
Delta28, the DC is given as 10 m based on the
nautical charts. Let's suppose that beach evolution
processes are natural continuous, the subaqueous
topographic variation in slope reveals the beach
topographic fluctuation to a great extent, which
indirectly implies the beach evolution complexity.
On the premise of the closure depth being
determined, the beach evolution complexity factor λ
can be described approximately by the variation of
average depth in study area.
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INDIAN J. MAR. SCI., VOL. 41, NO. 1, FEBRUARY 2012
From the nautical charts of 1990 and 2004, we can
see that the position of 2-m isobath in 2004 has
exceeded over the 5-m isobath of 1990 in the south of
Jiuduansha shoal. It is reasonable to assume that the
longshore sediment transport in the range of 5-m
isobath to 0-m isobath of 1990, lying in the south of
Jiuduansha shoal in study area, was just used to
fabricate the Jiuduansha shoal, not being involved in
the beach evolution of study area. Consequently, for
the sake of calculating λ, a calculation area
(the gray area in Fig. 3b) was bounded by the 0-m and
5-m isobaths of 1990, Transect 1 and 22 (denoted as
T1 and T22 in Fig. 3a), which is partitioned into
21 calculation units by 22 transects. Here, owing to
the irregularity of calculation units, it is necessary to
multiply the right side of Eq. (3) by a harmonic
coefficient. And then for the ith calculation unit,
Eq. (3) can be expressed as follows,
∂Qi = − ri DC ΔH i ki ( s ) ∂x
which the left ones are less than 50%. Results seem
encouraging since the Q fits well with the Q0 in
Fig. 5. On the one hand, our study was installed on a
straight coast that assures the proposed approach is
reliable. On the other hand, we made some
modifications to the one-line model, by adding extra
parameters and partitioning calculation units, that
facilitates the integration of one-line model with GIS
and promotes authenticity of results. Moreover, as
mentioned above, the GIS-based EPR method
captures the cumulative effect of all the underlying
processes, we therefore have reason to think that the
derived sediment transport rate Q incorporated the
effect of storms, sediment runoff transport, and crossshore sediment transport, etc. to some degree. One
point to beware is that the results are the annual
averages, and the unit of Q and Q0 is m3/yr.
Table 1—Longshore sediment transport rates and relative error
… (4)
Where, ΔH i is the difference of average depth in 1990
and 2004 in the ith calculation unit. The harmonic
coefficient ki(s) is linearly correlated with the area of
ith calculation unit, and the range is [1, 2.5]. By
substituting the values of relevant parameters into the
Eq. (4), the total longshore sediment transport rates Q
(see Table 1) can be derived by an integral with
respect to x in calculation unit. It is worthwhile to
mention that the modified one-line model will be
more accordance with its theoretical prerequisites,
since it is applied in small calculation unit. And the
+/- sign of results can indicate the state of beach
accretion/erosion totally in calculation unit.
Results and Discussion
The proposed approach was validated by
comparison with the topographic method, by which
the total accretion/erosion volume in calculation units
can be calculated by means of GIS technique, using
the subaqueous topographic data from the nautical
charts of 1990 and 2004. And the volume can be
converted into average sediment transport rate Q0,
which is treated as the truth value. Then the relative
errors were calculated by |Q-Q0|/|Q0|, the results were
shown in Table 1 and Fig. 5.
From Table 1, we can see that the total relative
error is 8.77%, and about half of relative errors are less
than 30%. The largest ones are 58.90% and 58.29%
respectively in calculation units of 2 and 21, except
calculation
units
1
Q/m3/yr
Q0/m3/yr
66.44×104
113.37×104
relative
error/%
41.40
2
89.09×104
216.77×104
58.90
3
58.44×10
4
73.93×10
4
106.05×10
69.94×10
4
66.26×10
4
5.56
83.18×10
4
4.31
44.69×10
4
16.94
36.00×10
4
43.90
99.24×10
4
40.78
82.24×10
4
47.47
55.58×10
4
21.98
4
5
6
7
8
89.42×10
4
86.77×10
4
52.26×10
51.80×10
4
139.71×10
4
10
121.29×10
4
11
4
9
67.79×10
4
12
132.37×10
13
94.92×10
4
14
15
16
17
18
19
20
21
4
34.64
4
122.43×10
4
30.29
8.11
4
33.90
47.24×104
36.54×104
29.30
31.16×10
4
30.20×10
4
3.20
32.49×10
4
32.00×10
4
1.52
35.32×10
4
43.70×10
4
19.18
48.78×10
4
68.19×10
4
28.46
46.98×10
4
73.45×10
4
36.04
13.76×10
4
25.95×10
4
47.00
-3.81×10
70.89×10
4
-9.14×10
4
4
58.29
4
1487.01×10
8.77
total
1356.64×10
Notes: negative values indicate erosion, positive values
indicate accretion.
XING et al.: EVALUATING LONGSHORE SEDIMENT TRANSPORT RATE
17
Fig. 5—Q and Q0 for every calculation unit
Whereas, we also find that the errors fluctuate
greatly over the calculation units, with the minimum
of 1.52% and the maximum of 58.90%. There are
7 calculation units, respectively denoted as Unit 1
and Unit 2, Unit 8 and Unit 9 and Unit 10, Unit 20
and Unit 21 (see Fig. 3b), whose relative errors are
larger than 40%. Among them, the Unit1 and Unit 2
locate outside the mouth of Dazhi River, the Unit 8
and Unit 9 and Unit 10 are opposite the entrance of
the tidal channel between Shangsha shoal and
Zhongsha shoal of Jiuduansha shoal, and the Unit 20
and Unit 21 lie outside the mouth of the tidal
channel between Jiangya shoal and Shangsha shoal.
It hints that some complex dynamic processes don’t
be incorporated into the model. So it necessitates a
further improvement in order to achieve more
reliable results.
Conclusion
GIS has been applied successfully in many fields.
Present is an attempt to integrate GIS and beach
evolution model to evaluate the longshore sediment
transport rates. The integration scheme was
established by partitioning the study area into some
calculation units and modifying one-line model to
meet complex physical settings of study area. The
whole procedure is implemented in GIS platform.
The results were compared with the ones of the
topographic method. The total relative error is only
8.77%. It shows the potential of combination of GIS
and the coastal engineering discipline. The results
are promising but further improvements is still
needed. It indicates that the proposed approach is
effective and can offer significant reference for
deeper research.
Acknowledgement
This work was funded by the Programme Strategic
Scientific Alliances between China and the
Netherlands (2008DFB90240), the state key
laboratory special fund from the Ministry of Science
and Technology of China and School Foundation of
Xuzhou Normal University (11XLR04). Special
thanks are due to the anonymous reviewers for their
valuable comments and suggestions for the
improvement of the manuscript.
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