A Study on the Hydraulic Characteristics of the Drainage System
through the Interaction between the Tidal Surge and the River's Flood
J.F. Yen
Department of Civil Engineering, Kao Yuan Institute of Technology, Kaohsiung, Taiwan, R.O.C.
C.H. Lin
Hydraulic Planning and Research Institute, WCA, MOEA, Taiwan, R.O.C.
C.T. Tsai
Department of Hydraulic and Ocean, National Cheng Kung University, Tainan, Taiwan, R.O.C.
ABSTRACT : The flooding phenomenon of torrential rains occurs mainly due to the river's
overflow and poor drainage. A local area's drainage depends on the storm sewer system. Due to the
flat terrain of Taiwan's western coastal area, the drainage systems are often blocked by the estuary
tidal upsurges. In particular, during the tidal period of typhoons, if the river's upstream flood peak
also arrives at the same time, it would raise the water level downstream, thereby causing poor
drainage or flooding. This research studies the drainage behavior by examining the interaction
between the tidal surge and river's flood peak, in order to provide a basis for the improvement of the
drainage system design. This study used the Sinbow drainage system (Fig. 1) in Chang-Hwa County
as an illustration. From the tidal surges by Typhoon Herb, July 31 ~ August 1, 1996, the design
flood hydrographs of the drainage system's boundary (Fig. 3), and the application of the unsteady
flow model of drainage networks, this research investigates the drainage behavior through the
interaction between the tidal surge and river's flood peak (Fig. 7). In addition to the case of upstream
flood peak and downstream tidal upsurge happening at the same time (Case 1), this study also
simulates the cases which the flood peak arrives at two hours earlier than the tidal upsurge (Case 2),
or two hours later (Case 3), in order to compare the river's water levels at several sections in
different upstream and downstream boundary conditions. The results show that the tidal surge
travels upstream apparently, and the river's maximum water level occurs when the upstream flood
peak and downstream tidal upsurge converge at the same time. Since the propagation of the flood
relates to river's length, this study shows that the unsteady flow model of drainage networks can be
used for the application and understanding of estuary drainage system's hydraulic characteristics and
behaviors, and provide the basis for planning and design of the coastal drainage system.
1
INTRODUCTION
Taiwan is situated in the subtropics, and the
torrential rains during the typhoon season
resulted in floods to bring on tremendous
flows and high stages. Furthermore, the tidal
surges induced by the typhoons could block
drainage in collision with the river's floods.
However, the steady backwater algorithm,
which calculates the water profiles of
channels by use of the water level of
downstream estuary and the designed flow of
channels as the initial conditions, is
inadequate to simulate such case.
There have been studies on the
above-mentioned surges of estuaries. The
research on the exact solutions of the
propagation of the tides only in the ideal
rectangular cross-section channels have been
extensive. For the actual rivers, the analysis
of tidal surges uses harmonic analysis or
numerical analysis, for example, the finite
difference or the characteristic curve method.
When there are interactions between the tidal
surges and the river's floods, the studies on
the combined wave speed and related
experiments also have been carried out.
However, the flood conditions, the
astronomical and the meteorological tides,
and the geometry of estuaries are so
sophisticated and vary with time and space,
thus numerical models become the main
method to simulate the interactions between
the tidal surges and the river's floods.
This study used Sinbow drainage system
in Chang-Hwa County of western Taiwan, as
an illustration. By use of the storm tides,
caused by Typhoon Herb, July 31 ~ August 1,
1996, and the designed flood hydrographs of
channels as the downstream and upstream
boundary conditions, together with the actual
surveyed cross-sections, the unsteady flow
model of drainage networks is used to
investigate the hydraulic characteristics of the
estuaries.
Since the slope of the coastal drainage
system is relatively flat, the flow can be
simplified as gradually varied flow. Thus, the
continuity and momentum equations of the
channels are expressed as follows,
Q
y
B
 q l  qo
x
t
(1)
Q
Q
y
 2V
V 2 B
V 2 Axy
t
x
x
 y z

 gA

 S f   q lV l  qoV
 x x

(2)
which Q : discharge, y : water depth, ql :
lateral inflow per unit channel's length, qo :
overbank outflow per unit channel's length, z :
bottom elevation of river, Sf : friction slope,
Vl : velocity component of lateral inflow
along main flow direction, V : average
velocity of flow section, =Q/A, A : flow area
when water depth equals to y, x : distance
along main flow direction, t : time, B : flow
width when water depth equals to y, Axy :
change in cross-section area along x direction
for non-prismatic channel at water depth y.
The drainage system is a network
composed of converging channels, with some
nodes, at which the channels intersect.
Suppose L(m) denotes the number of
channels intersect at node m, each
converging channel can be seen as a link
between node m and another neighboring
node. The continuity equation at node m will
be
Lm 
Q m t j 1  Q m , l  0
 
(3)
l 1
which Qm(tj+1) : the external inflow of
node m at time tj+1, Qm,l : the inflow or
outflow of node m from link l at time tj+1.
The non-linear partial differential
equations (1) and (2), through linear fully
implicit scheme, are transformed into the
difference equations, with discharge and
water depth as the dependent variables. In
this network model, the flow area of a link
converging at node m, depending upon its
flow direction, will be set as inflow or
outflow, and substituted into the node
continuity equation (3). Due to the flat slope
of the coastal plains, assume the water level
of converging channels at each node is equal,
in order to derive the node water depth
equations, thus the water depth at each node
can be solved.
Once the water depths at nodes are known,
the discharge and water depth at each channel
section can be obtained, through double scan
calculation method, to complete the
calculation of drainage system at the
specified time interval. Then continuing on to
the next time interval, the model simulation
of the overall time duration will be
accomplished.
2
ILLUSTRATION OF APPLICATION
sections for calculation, the main channel
from estuary to the intersecting point, 0 to
1,104 meters, the tributary channel from
1,104 to 1,800 meters, and the main channel
from 1,104 to 1,920 meters, as shown in Fig.
2.
St
ra
it
s
The Sinbow drainage system, as shown in Fig.
1, including the main and tributary channels,
is situated at the southern Chang-Hwa County
of Taiwan. The main channel is 1,800 meters
long, and the tributary channel converges at
1,104 meters away from estuary of main
channel. This system is divided into three
an
Chang-Hwa
iw
D.B.S
Ta
h
t
Q
Sta.(-700)m
Bed EL.-0.50m
Dr
ai
Ch
an
ne
l
Si
nb
ow
na
ge
t
U.B.C.1
Sta.1800m
Main
Sta.1104m
Si
nb
ow
Drain
a
0
350
700m
Q
ge
Tributary
Channel
U.B.C.2
t
(Sta.1920m)
Figure 1 : Map of Sinbow drainage system, with estuary as origin
Reach 1
h2
ac
e
R
Re
ach
3
Figure 2 : Sketch of channel divisions for
simulation
 DOWNSTREAM BOUNDARY
CONDITIONS
In 1996, Typhoon Herb brought on
torrential rains in Taiwan, and caused storm
surges in the western coastal area. This paper
used the storm surges by Typhoon Herb, from
July 31 to August 1, and the record of seawater
level, 700 meters away from estuary, as the
downstream boundary conditions, the solid line
D.B.C. as shown in Fig. 3.
 UPSTREAM BOUNDARY
CONDITIONS
Since there are no flow gauge station in this
drainage system, the upstream boundary
conditions are set to be the flood hydrographs,
derived from 24-hours rainfall for five years'
RESULTS AND DISCUSSIONS
The upstream designed flood hydrograph of
channels and the downstream water level
hydrograph of storm surge are used for the
unsteady flow simulation. The time step for
calculation is three minutes, and the overall
time duration is 24 hours. The results are
shown in Fig. 4 ~ Fig. 9, with conclusions
summarized as follows :
1. When seawater level of estuary rises, the
discharge of drainage system decreases to
induce the inundation of seawater. If the
upstream flood arrives at the same time, the
seawater inundation and the flood will collide
to fluctuate the discharge of drainage system.
2. In the estuarine section of Sinbow main
channel, 0 ~ 600 meters, the closer the channel
approaches to the downstream estuary, the
more seawater inundation gets. If the upstream
flood becomes larger, along with the release of
the flood storage in the channels, the peak
discharge will also be bigger, as it approaches
to the downstream.
3. The influence of tides is more apparent
as the drainage channels approach to the
estuary. The pushing impacts of tides and
floods become less when the distance away
from the estuary increases.
4. When compared to the discharge
fluctuations in the estuarine section due to the
collision of the tides and floods, the water level
hydrographs vary uniformly. In general, the
water level hydrographs in the estuarine section
is similar, in outline, to the tidal water level
hydrographs.
5. The peak water level of the drainage
system is very close to the peak water level of
the downstream tidal hydrograph. This implies
when the tides go upstream to meet with the
floods, the water level in the estuarine section
does not rise dramatically. The main influence
on the downstream channels is the tides, and
20
18
16
14
12
10
8
6
4
2
0
-2
U.B.C.1
U.B.C.2
D.B.C.
Tidal level (m)
3
the discharge has no obvious relationship with
the water level. However, the main influence
on the upstream channels, far away from the
estuary, is the floods, and the discharge relates
positively with the water level.
Since the timing of tidal surges may not be
the same as that of floods, in addition to the
simulation of the simultaneous happening of
the downstream tidal surge and the upstream
flood, this paper also simulates case 2 - the
downstream tidal surge arrives at two hours
earlier than the upstream flood, and case 3 two hours later, in order to compare the
differences of the peak water level of
downstream channels under combinations of
upstream and downstream boundary conditions.
The result shows that the highest peak water
level occurs when the downstream tidal surge
and the upstream river's flood happens at the
same time, as shown in Fig. 10. If the length of
drainage channels varies, the results will be
different. Thus, the arrival time of the storm
tidal surge and flood will influence the water
level in the estuarine section, and is related to
the length of drainage channels. The unsteady
flow model of drainage network can be used
for safe design.
Discharge (cms)
frequency coming from the recorded rainfall
data, through the modified triangular unit
hydrograph design model, which is often used
by Taiwan Water Resources Bureau, the
U.B.C.1 and U.B.C.2 as shown in Fig. 3.
1 2 3 4 5 6 7 8 9 101112131415161718192021222324
Time (hr)
Figure 3 : Graph of upstream boundary
condition, U.B.C.1 and U.B.C.2, and
downstream boundary condition, D.B.C.
4.00
Stage (m)
400m
3.00
200m
2.50
0m
2.00
1.50
1.00
Discharge (cms)
600m
3.50
0.50
1 2 3 4 5 6 7 8 9 101112131415161718192021222324
30
25
20
15
10
5
0
-5
-10
-15
-20
-25
-30
Time (hr)
1800m
1104m
600m
0m
1 2 3 4 5 6 7 8 9 101112131415161718192021222324
Time (hr)
30
25
20
15
10
5
0
-5
-10
-15
-20
-25
-30
Figure 7 : Graph of simulated discharge
hydrographs of main channel, with distance
from the estuary
5.00
4.50
4.00
600m
400m
Stage (m)
Discharge (cms)
Figure 4 : Graph of simulated water level
hydrographs of the estuarine section, with
distance from the estuary
200m
3.50
3.00
1920m
2.50
1400m
2.00
0m
760m
1.50
0m
1.00
1 2 3 4 5 6 7 8 9 101112131415161718192021222324
Time (hr)
1 2 3 4 5 6 7 8 9 101112131415161718192021222324
Time (hr)
Figure 5 : Graph of simulated discharge
hydrographs of the estuarine section, with
distance from the estuary
Figure 8 : Graph of simulated water level
hydrographs of tributary channel, with distance
from the estuary
4.50
4.00
3.00
1800m
2.50
2.00
1104m
1.50
600m
1.00
0m
0.50
1 2 3 4 5 6 7 8 9 101112131415161718192021222324
Time (hr)
Discharge (cms)
Stage (m)
3.50
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
1920m
1400m
760m
0m
1 2 3 4 5 6 7 8 9 101112131415161718192021222324
Time (hr)
Figure 6 : Graph of simulated water level
hydrographs of main channel, with distance
from the estuary
Figure 9 : Graph of simulated discharge
hydrographs of tributary channel, with distance
from the estuary
3.74
installation of tide-proof gates and the
consideration of terrain along the drainage
channels, are recommended.
Peak Stage (m)
Case 1
3.73
Case 2
3.72
Case 3
REFERENCES
3.71
3.70
3.69
-600 -400 -200
0
200
400
600
800 1000 1200
Distance (m)
Figure 10 : Graph of comparison of simulated
peak water level of three cases, with distance
from the estuary
4
CONCLUSIONS AND
RECOMMENDATIONS
During the typhoon season, the flooding of
drainage system in Taiwan's coastal areas was
aggravated by seawater inundation. This study
applied the unsteady flow model to simulate
the flow conditions in the estuarine section of
Sinbow drainage system in Chang-Hwa County.
Since there is interaction between the tidal
surge and the river's flood in the estuarine
section, the steady backwater calculation is
inadequate, but instead the unsteady flow
model of drainage network can reasonably
investigate the hydraulic characteristics of the
estuarine section and reflect the collision
between the tidal surge and the river's flood.
This simulation also concludes that the
closer the drainage channels approach to the
estuary, the more the tidal surges influence.
The dynamic governing factor in the upstream
channel is the flood mainly. The interaction
between the tidal surge and the river's flood is
related to the tidal currents, flood hydrographs,
and the length of drainage channels, so the
simulation should be performed under the flow
conditions of the drainage system, through the
flow model of drainage network.
Since there is seawater inundation in the
drainage channels, and the flooding in the main
channel will obstruct the alleviation of flooding
in the lower ground level areas, therefore,
further researches on the flow discharge and
the flooding conditions, including the
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