variable parameter unsteady flow model for the han river - kyung-soo jun.pdfvariable parameter...
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Variable Parameter Unsteady Flow Model
for the Han River
Kyung Soo Jun
Graduate School of Water Resources,
Sungkyunkwan University, Korea
2016.05.24
2016 APEC Typhoon Symposium
2016 APEC Typhoon Symposium
Contents
1. Introduction
2. Model Description
3. Numerical Model for the Han River
4. Model Application
5. Conclusions
2016 APEC Typhoon Symposium
2016 APEC Typhoon Symposium
1. Introduction
2016 APEC Typhoon Symposium
1. Introduction
Hydraulic computational model
2016 APEC Typhoon Symposium
1. Introduction
Study objectives:
To develop a variable parameter unsteady flow model,
which allows variable roughness coefficients for each
computational point according to its spatial position and
discharge.
To apply the model to the Han River, and evaluate the
performance.
2016 APEC Typhoon Symposium
2. Model Description
2016 APEC Typhoon Symposium
Governing Equations for Looped-network Model
Link
Fluvial Flow: Weir-type Flow:
Node
2/31K AR
n
Numerical Solution• Preissmann’s four-point implicit scheme
• Newton-Raphson method
• Double-sweep algorithm
0A Q
t x
( )2
20
Q QQ Q ygA gA
t x A x K
u dQ Q
2
2
3
u s u d d w
d w u w
Q b g y y y y
y y y y
3/22
3
2
3
u f u w
d w u w
gQ b y y
y y y y
, , , , , 1
0 1jL
j k ext
k
Q Q j t j J
, , , , , , , 1 1j k j jy y k L j J
2. Model Description
2016 APEC Typhoon Symposium
Three roughness coefficient models are investigated:
1. 𝑛 =constant
2. 𝑛 = 𝑛(𝑥) 𝑛 =
3. 𝑛 = 𝑛 𝑥, 𝑄 𝑥, 𝑡 𝑛 =
𝑛 = 𝑛(𝑥)
𝑛 = 𝑛(𝑄) 𝑛 = 𝑛(𝑄)
𝑛1 upstream reach
𝑛2 downstream reach
𝑛1 𝑄 𝑥, 𝑡 upstream reach
𝑛2 𝑄 𝑥, 𝑡 downstream reach
Step function 𝒏 = 𝜶𝑸𝜷Power function :
𝑛 𝑄
2. Model Description
2016 APEC Typhoon Symposium
3. Numerical Model for the Han River
2016 APEC Typhoon Symposium
3. Numerical Model for the Han River
Paldang Dam
23.4km
Yellow Sea
Goyang
Incheon
Junryu
N
2012 Google
Jamsil submerged Weir
SeoulSingok submerged Weir
Hangang Br.
Han River
2016 APEC Typhoon Symposium
3. Numerical Model for the Han River
Han River
2016 APEC Typhoon Symposium
Jamsil submerged weir
3. Numerical Model for the Han River
2016 APEC Typhoon Symposium
Singok submerged weir
3. Numerical Model for the Han River
2016 APEC Typhoon Symposium
Weir flowChannel
flow
Q yu
yw yd
flooded
free-flowing
Flow direction
ReachLink
Point
Upstream
Tributary
Downstream
Weir-type
link
Fluvial
link
Fully opened
during flood
periods
Jamsil and Singok submerged weirs
3. Numerical Model for the Han River
2016 APEC Typhoon Symposium
The schematic of the modeled river reach
3. Numerical Model for the Han River
2016 APEC Typhoon Symposium
4. Model Application
2016 APEC Typhoon Symposium
Flood events used for model calibration and verification
4. Model Application
Flood
EventPeriod
Peak Discharge of
Upstream BC
(𝐦𝟑/𝐬)
Flood
EventPeriod
Peak Discharge of
Upstream BC
(𝐦𝟑/𝐬)
108.07.24
- 07.2816,146 2
04.07.15
- 07.1912,104
311.07.03
- 07.0512,099 4
07.08.08
- 08.1210,024
504.07.12
- 07.149,909 6
09.08.11
- 08.149,463
703.08.23
- 08.309,369 8
11.06.29
- 07.019,066
911.07.11
- 07.198,386 10
05.06.31
- 07.026,995
1108.07.19
- 07.236,773 12
04.08.17
- 08.215,147
2016 APEC Typhoon Symposium
4. Model Application
Objective function
𝑯𝒕𝒌: observed water levels, 𝒉𝒕
𝒌: computed water levels,
t : time level, k : kth gauging station, n : parameter vector.
Optimization technique
• The Gauss-Marquardt-Levenberg algorithm: Combine the advantage of
the steep descent method and the inverse Hessian method.
• PEST
3
2
1 1
Minimize -
n
Tk kt t
k t
S H h
2016 APEC Typhoon Symposium
Model calibration: n = constant & n = n(x)
4. Model Application
2016 APEC Typhoon Symposium
Model calibration: applied step functions, n = n(x, Q)
4. Model Application
2016 APEC Typhoon Symposium
4. Model Application
Model calibration: n = n(x, Q(x,t)) (2-step & 3-step functions)
18/21Upstream reach Downstream reach
2016 APEC Typhoon Symposium
4. Model Application
Model calibration: n = n(x, Q(x,t)) (4-step & 5-step functions)
18/21Upstream reach Downstream reach
2016 APEC Typhoon Symposium
Upstream reach Downstream reach
4. Model Application
Model calibration: n = n(x, Q(x,t)) (power function)
2016 APEC Typhoon Symposium
Model calibration: RMS errors
4. Model Application
RMS errors for various step functions RMS errors for various parameter models
2016 APEC Typhoon Symposium
Model validation: average n functions, n = n(x, Q)
Upstream reach Downstream reach
4. Model Application
2016 APEC Typhoon Symposium
Model validation : stage hydrographs for flood event 2
4. Model Application
2016 APEC Typhoon Symposium
Model validation : RMS errors
4. Model Application
RMS errors for various step functions RMS errors for various parameter models
2016 APEC Typhoon Symposium
5. Conclusions
A variable parameter unsteady flow model is developed, which allows
variable roughness coefficients for each computational point according to its
spatial position and discharge
The model being applied to the Han River, spatial variation and discharge
dependence of Manning’s n are clearly identified.
The upstream reach of the Wangsook stream junction is proved to have
greater values of Manning’s n than that of the downstream reach.
The Manning’s n decreases as the discharge increases and this tendency is
more noticeable for the upstream reach of the Wangsook stream junction
compared to the downstream reach which is subject to the tidal effects.
Model performance is improved by using variable roughness coefficients
which change with space and discharge.
Defining the step function as a functional relation between Manning’s n and
discharge is subjective with regard to the number of steps and discharge
values at which step rise/fall occurs.
The power function appears to be the most appropriate. RMS errors from
the power function model is smaller than the average of errors from various
step function models.
Thank you !