variable parameter unsteady flow model for the han river - kyung-soo jun.pdfvariable parameter...

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


Contents

1. Introduction

2. Model Description

3. Numerical Model for the Han River

4. Model Application

5. Conclusions



1. Introduction


1. Introduction

Hydraulic computational model


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.


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



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




Paldang Dam

23.4km

Yellow Sea

Goyang

Incheon

Junryu

N

2012 Google

Jamsil submerged Weir

SeoulSingok submerged Weir

Hangang Br.

Han River



Han River


Jamsil submerged weir



Singok submerged weir



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



The schematic of the modeled river reach



Flood events used for model calibration and verification


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



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


Model calibration: n = constant & n = n(x)



Model calibration: applied step functions, n = n(x, Q)




Model calibration: n = n(x, Q(x,t)) (2-step & 3-step functions)

18/21Upstream reach Downstream reach



Model calibration: n = n(x, Q(x,t)) (4-step & 5-step functions)

18/21Upstream reach Downstream reach


Upstream reach Downstream reach


Model calibration: n = n(x, Q(x,t)) (power function)


Model calibration: RMS errors


RMS errors for various step functions RMS errors for various parameter models


Model validation: average n functions, n = n(x, Q)

Upstream reach Downstream reach



Model validation : stage hydrographs for flood event 2



Model validation : RMS errors


RMS errors for various step functions RMS errors for various parameter models


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 !

variable parameter unsteady flow model for the han river - kyung-soo jun.pdfvariable parameter...

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