1. Evaluation for the Effects of Flood Control
for Side-weir Detention Basin
using Equivalent Peak Hydrograph
KANG BooSik, Professor/Ph.D.
Dept. of Civil & Environmental Engineering
Dankook University
YOON ByeongMan, Professor/Ph.D.
Dept. of Civil Engineering
Myongji University

2. 1 2 3 4 5 6 Contents Introduction
General Process of Design Flood Estimation 3
Representative Synthetic Unit Hydrograph 4
EPH for the Yeoju site of the detention basin 5
Analysis of the Effects of Flood Control 6
Conclusion 2

3. Introduction : Side-weir detention basin
Side-weir detention basin is an off-line storage located at river side for improving the flood control capacity in the downstream
※ White Oak detention basin, Harris County, U.S.

4. Introduction : Test bed
Yeoju detention basin
outlet
- Watershed Area : 11,361.89km2
storage volume
outflow
16.2 Mm3
금회 작업에서의 대상지점은 여주강변저류지 지점이다. 이지점의 상류유역면적은 11,362km^2이고, 설계홍수량은 16,070cms이다. 여주유역은 전차년도의 정선,평창유역에 비하여 10배이상 큰 대유역으로서 중간에 충주댐에 의하여 유량조절이 이루어지고 있고, 설계홍수량도 5배이상 큰 유역이므로 설계홍수량 산정도 훨씬 복잡한 유역이다.
Side-Weir
inflow
Design flow : 16,070 m3/s 4

5. Introduction : Factors influencing the effects of flood control
Design factors of the side-weir
: side-weir length(Ls), side-weir height(hs), storage volume(Vs)
Environmental factors
: roughness coefficients of river(n), shape of inflow hydrograph
side-weir length (Ls)
river width (B)
side-weir detention basin
detention storage (Vs)
levee height(h)
side-weir height (hs)
river
side-weir detention basin
complete overflow
incomplete overflow

6. Introduction : The effects of flood control
The effects of flood control is a difference between
peak discharge without / with storage.
outflow=streamflow with detention basin
with storage
without storage
effects of flood control
Inflow=streamflow without detention basin B
Overflow out of the detention basin begins. A
Overflow into the detention basin begins.

7. Introduction : Equivalent Peak Hydrographs(EPH)
Why needs EPH?
(In case there is a limitation of size of detention basin) The flood control effects of detention basin can differ according to the peak and shape of the inflow hydrograph.
(In case there is an allocation of target volume of flood control) The optimal size and shape of the detention basin can be determined fitting to the peak and shape of the inflow hydrograph.
The problem is what is the most probable hydrograph at the candidate site.
The definition of the most probable hydrograph for design of detention basin : Equivalent Peak Hydrograph (EPH)
The hydrograph that can happen most likely
The hydrograph that can influence to the design and evaluation of detention basin most critically
For the given design peak flow …
We need to see the flood control effects of the various shape of the hydrographs that produce same design peak flood.
Among the hydrographs of various rainfall duration we need to select hydrographs …
The representative unit hydrograph
Hydrographs by frequency / duration
The hydrograph that can influence to design and evaluation of the detention basin most critically and happen most probably showing same peak flow at the specific site.

8. Introduction : Design Hydrograph with Various Rainfall Duration
Estimation method of representative unit hydrograph : Nash Model
Rainfall duration: Thiessen average by the most frequency quartile Huff distribution (“Han river” Basic plan of river, 2009,Ministry of Land, Transport and Maritime Affairs)
Design flood=16,070m3/sec
These are the examples of EPH. We need to determine the effective range of rainfall duration through IDF analysis. 8

9. Process of design flood estimation
Dividing subbasin
Collecting a rainfall data
Estimation point probabilistic precipitation
Estimating rainfall intensity formula
Estimating IDF curve
Estimation area probabilistic precipitation
Thiessen Method
Area reduction factor
Set a rainfall statistical distribudion
Mononobe Method
Huff Method
Estimating effective precipitation
Fixed loss
Initial and Fixed loss
Infiltration curve
SCS
Estimating time of concentration
Kirpich
Rziha
Kraven
Applying unit hydrograph
Snyder
Nash
Clark
Flood routing in subbasin
Reservoir routing
Channel routing
Estimating design flood
Basic flood
Design flood
대규모유역에서의 일반적인 설계홍수량 산정 절차이다. 이러한 절차는 교과서나 홍수량산정지침에서 찾아볼 수 있는 내용이지만 각 과정마다 학술적 이론정립이 필요하고 불확실성을 유발하는 요소들이 존재하기때문에 결과적으로 표준적인 절차에 의하여 산정된 홍수량이라 할지라도 상당한 불확실성을 내표하고 있다. 이를테면 … (하늘색박스안의 내용을 설명)
특정 지점에서의 대표홍수수문곡선을 제시한다는 것이 매우 어려운 작업이 된다. 9

10. <Linear reservoir theory by Nash >
Estimating Instaneous Unit Hydrograph
Theory of Nash Model
The entire basin consists of succesive n reservoirs, and the inflows and outflows at each reservoir have linear relationship.
The IUH is determined through the flood routing from the first to the n-th reservoir using linearity.
differenciating
Simultaneous eq.
본 연구에서 단위도 산정은 Nash의 순간단위도를 유도하고 이를 통하여 지속시간별 단위도를 산정하였다. 화면은 Nash단위도의 기본이론이다.
Computing till nth reservoir
<Linear reservoir theory by Nash >

11. Estimating Instaneous Unit Hydrograph
Estimating parameter of Nash model
The parameters of the IUH formula, i.e. 2-param. Gamma distribution become n, K, the 1st and 2nd moments for the original point(t=0) follows;
The 1st moment, : the delayed time from the origin to the centroid of the IUH curve.
: The 1st moments of the effective rainfall and direct runoff divided by the total effective rainfall and direct runoff.
Nash단위도의 기본매개변수는 K와 n값이며 화면은 매개변수를 추정하는 기본과정이다.
: The 2st moments of the effective rainfall and direct runoff divided by the total effective rainfall and direct runoff.

12. Estimating Instaneous Unit Hydrograph
Estimating representative unit hydrograph
The representative peak flow and time can be estimated by taking averages of peak flows and times of individual rainfall events.
The formulas of peak specific flow and time can be obtained by differentiating Nash model formulas.
differentiate
where is the peak specific flow (cm/hr) and time (hr) of unit hydrograph, n, the # of reservoirs, can be determined if the peak specific flow and time are given. The storage constant K can be estimated using the n.
만일 단위도의 첨두유량과 첨두발생시간을 알면 이를 통하여 역으로 K와 n값을 추정하여 단위도곡선을 만들어낼 수도 있다. Nash방법의 장점이기도 하다.
Therefore, if the peak flow and time are determined using the unit hydrographs of the rainfall events, the parameters n and K can be determined using the trial and error method for the differentiated Nash Model.

13. Composite unit hydrograph considering basin characteristic
Composite unit hydrograph method of Korea Institute of Construction Technology(KICT) (2000)
The new methodology for composing unit hydrograph using the multiple linear regression, which derived using the UH from 70 sites and their basin charateristics.
단위유량도의 첨두유량과 첨두발생시간에 대한 식이 과거 2000년 건기원보고서에서 제시된 바 있다.
The Tp and Qp are applied to the Nash model for the purpose of estimating the ordinates of the UH.

14. Improvement of composite unit hydrograph method
Composite unit hydrograph considering basin characteristic
Improvement of composite unit hydrograph method
Primary factor
KICT’s formula
Proposed formula
Separating base flow
Horizontal method
Local Minimum Method
Unit hydrograph
Ridge Regression
Nash Model
Rainfall
Complex rainfall
Single rainfall
Parameter of unit hydrograph
Basin Area, River length, River slope
Basin Area, Shape factor, River slope
The previous studies for the composite unit hydrograph are the results of different rainfall events, method of effective rainfall, baseflow separation, method of representative UH, which makes difficult in showing consistence outcome.
In this study, the improved methodology for composing UH will be suggested by differing in estimating the major components of the UH even though the composing method is basically the same as the existing the method of composing UH.
본 연구에서는 전차년도에 다양한 규모의 유역과 강우사상자료를 수집하여 건기원식을 개선하여 제시한 바 있다.

15. Parameter of Nash model
Representative Unit Hydrograph
Representative unit hydrograph for Yeoju site
Parameter of Nash model n K
2.115
11.514
여주수위표지점의 대표단위유량도의 매개변수값과 단위도의 형태이다.

16. Probable rainfall-intensity formula (Yangpyeong)
Estimating IDF Curve
Probable rainfall-intensity formula (Yangpyeong)
Class
2 yr
5 yr
10 yr
100 yr
200 yr
Short term
Long term
여주지점에서 가장 가까운 양평기상관측소의 강우강도곡선이다. 하천기본계획이나 유역종합치수계획상에서는 지속시간기준으로 대략 2시간을 기준으로 단기간과 장기간에 대한 강우강도식이 제시되어 있는데, 본과제에서는 6시간이상의 지속시간에 대하여 검토하므로 장기간에 대한 강우강도식이 해당되지만 동시에 유역내 강우관측소에 대한 강우자료를 수집하여 직접 IDF분석을 수행하였다. 16

17. Estimating IDF Curve
- The 100-yr IDF couve in the AWS in Han river basin
Yangpyeong, Icheon, Wonju, Hongcheon, Chungju, Jecheon, etc.
Taking average using Thiessen areal ratio.
유역내 양평, 이천,원주,홍천, 충주, 제천 관측소자료에 대한 개별 IDF곡선과 평균강우에 대한 IDF곡선을 제시하였다.
(이 IDF곡선과 22번 슬라이드의 IDF곡선을 비교해보라는 질문이 나올 수 있음)

18. Estimating Precipitation producing equivalent peak flow
Design (Peak) flood : 16,070 m3/s
Duration
(hr)
Effective precipitation
(mm)
Effective intensity
(mm/hr)
Precipitation producing equivalent peak flow (mm)
Precipitation intensity producing equivalent peak flow (mm)
6 hr
168.3
28.05
422.3
70.88
12 hr
171.3
14.27
390.8
32.56
18 hr
176.5
9.81
395.5
21.97
24 hr
184.5
7.69
385.7
16.07
36 hr
206.2
5.73
424.1
11.78
48 hr
227.3
4.73
452.6
9.42
60 hr
249.0
4.15
680.6
8.01
72 hr
271.9
3.78
509.3
7.07
96 hr
320.6
3.34
583.1
6.07
120 hr
372.0
3.10
666.7
5.56
144 hr
425.1
2.95
751.3
5.22
168 hr
479.6
2.85
835.7
4.97
여주지점의 목표홍수량 16070에 대한 등가강우량과 유효강우량이다. 이를 그림으로 도시하면…

19. Frequency analysis
Analyzing the probability that cause the rainfall producing the design flood.
The transform of the real precipitation considering runoff ratio is necessary because the input of UH is the effective rainfall.
100년빈도 재현기간에 대하여 등가강우곡선과 IDF곡선을 비교해보면 임계지속시간 48시간을 중심으로 등가강우곡선이 IDF곡선에 접하고 있음을 알수 있으며 이에서 멀어질수록 등가강우곡선과 IDF곡선의 차가 증가하고 있다. 대략적으로 24시간에서 길게는 72시간사이에서 등가강우가 IDF강우와 비슷한 홍수량을 보이고 있으며 이를 벗어나게 되면 등가강우곡선은 비현실적인 재현기간을 보이고 있으므로 설계에 반영하는 것이 무의미해짐을 알수가 있다. 따라서 이때의 유효지속시간을 24시간에서 72시간으로 제시할 수 있고 이에 해당하는 수문곡선은 앞서 제사한 다음과 같은 수문곡선이 된다. 19

20. Representative Hydrograph for Various Rainfall Duration
Estimation method of representative unit hydrograph : Nash Model
Rainfall duration: Thiessen average by the most frequency quartile Huff distribution
(“Han river” Basic plan of river, 2009,Ministry of Land, Transport and Maritime Affairs)
Design flood=16,070m3/sec
(Return period = 100yr)
24시간~72시간의 수문곡선만 제시할 것!! 20

21. Analysis on the effects of flood control
Numerical analysis : HEC-RAS
stream lengths
bed slope
river width
peak discharge
side-weir height
side-weir width
44 km
0.0005
360 ~1830m
16030m3/s
36.4 EL.m
300 m
[volume elevation relationship]
[unsteady boundary condition]
[flow hydrograph]

22. Analysis on the effects of flood control
Duration : 24 hours
inflow
inflow
roughness
coefficient
(n)
peak flow
(m3/s)
effects of
flood control
0.025
15922
108
0.030
15619
411
0.035
15722
308
n=0.025에 비하여 n=0.03일때 홍수저감효과가 높은데, n=0.035일때 홍수저감효과가 급격히 떨어지는 이유에 대한 설명이 필요함.
n=0.035일때 peak 후반부에 secondary peak가 발생하는 이유에 대한 설명이 필요함.
[답변]
강변저류지의 홍수조절효과는 하천 수위에 따라 결정됩니다.
따라서 조도계수가 큰 경우는 동일한 수문곡선에서도 하천 수위가 높게 계산되기 때문에 월류량이 많게 됩니다.
그리고 수문곡선을 보시면 조도계수가 클수록 월류되는 시점이 빠른 것을 확인할 수 있습니다.
이와 같은 이유로 저류용량이 제한적인 경우 월류량이 많게 되면 저류지가 가득차게 되어
하천에서 저류지로 완전월류가 발생하다가 하천수위와 저류지 수위가 같이 올라갔다가 내려가는 상황이 발생합니다.
따라서 완전 월류시보다 불완전 월류시에는 월류량이 작아져서 직하류의 홍수조절효과가 작아지게 됩니다.
secondary peak 이후에는 월류턱 보다 높게 발생한 수위가 저류지에서 하천으로 들어오면서 upstream의 수문곡선의 같은 시각 유량보다 약간 높게 발생하게 됩니다.
이와 같은 부분이 강변저류지의 용량이 제한적인 경우이기 때문입니다.
마찬가지로 수문곡선의 첨두 지속시간이 긴 경우에 홍수조절효과가 없을 수도 있는 이유가 peak가 길어지면서 저류지가 가득차게되기 때문입니다.

23. Analysis on the effects of flood control
Duration : 36 hours
inflow
roughness
coefficient
(n)
peak flow
(m3/s)
effects of
flood control
0.025
15927
103
0.030
15626
404
0.035
15895
135
inflow

24. Analysis on the effects of flood control
inflow
Duration : 48 hours
roughness
coefficient
(n)
peak flow
(m3/s)
effects of
flood control
0.025
15926
104
0.030
15625
404
0.035
15909
121
inflow

25. Analysis on the effects of flood control
Duration : 60 hours
inflow
roughness
coefficient
(n)
peak flow
(m3/s)
effects of
flood control
0.025
15922
108
0.030
15622
408
0.035
15945 84
inflow

26. Analysis on the effects of flood control
Duration : 72 hours
inflow
roughness
coefficient
(n)
peak flow
(m3/s)
effects of
flood control
0.025
15925
105
0.030
15626
404
0.035
15985 45
inflow

27. peak flow of inflow hydrograph
Analysis on the effects of flood control
Results analysis
duration
(hour)
roughness
coefficient
(n)
peak flow of inflow hydrograph
(m3/s)
effects of
flood control
rate
(%) 24
0.025
16030
107.25
0.66
0.030
393.29
2.45
0.035
286.15
1.78 36
102.79
0.64
403.94
2.52
137.45
0.85 48
102.56
404.41
122.63
0.76 60
107.06
405.92
2.53
81.32
0.50 72
104.18
401.58
2.50
46.34
0.28
강변저류지의 홍수조절효과는 수문곡선과 하천 조도계수에 따라 불확실성이 있으므로 발생 가능한 범위에 대한
충분한 검토 후 안전측으로 제시하여야 한다.

28. Conclusion
Analysis on the effects of flood control for side-weir detention basin should consider the prediction uncertainty of water level and hydrograph.
The effects of flood control are analyzed for possible roughness coefficients to remove the uncertainty of prediction of the water level.
The effects of flood control are analyzed for various hydrograph considering a possible rainfall characteristics to remove the uncertainty of the hydrograph.
Because the Yeoju detention basin is located at the mid-stream of the Han River basin, its flood mitigation effects reveals relatively low under the condition of disregarding control gate. However, if we can consider the control gate, we can expect much higher mitigation effects by controlling secondary peak.