[PPT] - Low flow regionalization by regression and hybrid methods Monireh PowerPoint Presentation

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Low flow regionalization by regression and hybrid methods

Monireh BIABANAKI Seyed Saeid ESLAMIAN JAHANGIR ABEDI-KOUPAI Alireza TABATABAEI

Isfahan University of Technology

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Low Flow

Knowledge of the magnitude of low flow events is required in order to drought management. The 7-day, 10-year low flow (Q7,10 ) is a commonly used low flow statistic. The (Q7,10 ) is the average annual 7-day minimum flow that is expected to be average every 10 years.

INTRODUCTION

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In this study frequency of the 7-day annual low flow is specified and developed regional regression equations to estimate the low-flow frequency at ungaged sites.

...INTRODUCTION

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Low flow models
Regression method

...MATERIAL & METHODS

Low flow index
Regionalizing the frequency formula

parameters

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Regression method

...MATERIAL & METHODS

X2 . . Q X1 Qa Qb Qc Qd X1 (a) X1 (b) X1 (c) X1 (d) X2 (a) X2 (b) X2 (c) X2 (d)

1 2

b b T 1 2

Q = f[X ,X ,...]

X1 (e) X2 (e)

Qe

. . .

Q (a)=Qa X1 (a) X2 (a) . .

X1 (e) X2 (e)

. .

Q (e)=?

(a) (b) (c) (d) (e) Q (b)=Qb X1 (b) X2 (b) . . X1 (d) X2 (d) . . Q(d)=Qd X1 (c) X2 (c) . . Q (c)=Qc

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Select the best regression model

...MATERIAL & METHODS

Q (a)=Qa X1 (a) X2 (a) . . (a) (b) (c) (d) (e) Q (b)=Qb X1 (b) X2 (b) . . X1 (d) X2 (d) . . Q(d)=Qd X1 (c) X2 (c) . . Q (c)=Qc

X3 . . X2 Q X1 Qa Qb Qc Qd X1 (a) X1 (b) X1 (c) X1 (d) X2 (a) X2 (b) X2 (c) X2 (d) X3 (a) X3 (b) X3 (d) . . . X3 (c) . .

3 1 2

b b b 1 1 2 3

Q = f[X ,X ,X ,...]

1 2

b b 2 1 2

Q = f[X ,X ,...]

1 2

b b 3 1 3

Q = f[X ,X ,...] ei VIFi >5 Qi

j 2 j

1 (VIF = ) 1-R

฀

i i i

(e = Q -Q )

(Rj is the multiple correlation coefficient)

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Low flow index method

...MATERIAL & METHODS

X1 (e) X2 (e) . Q T (e)=?

(a) (b) (c) (d) (e)

QT (b) Q2 (b) X1 (b) X2 (b) . QT (d)=Qd Q2 (d) X1 (d) X2 (d) . QT (b)/Q2 (b) QT (d)/Q2 (d) QT (c)/Q2 (c) QT (a)/Q2 (a) QT (c)=Qc Q2 (c) X1 (c) X2 (c) . QT (a)=Qa Q2 (a) X1 (a) X2 (a) . Q 2 (e)=?

T QT/Q2

1 2

b b 2 1 2

Q = f[X ,X ,...]

X1 (e) X2 (e)

Q 2 (e) Q T (e)

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Regionalizing the frequency formula parameters method

...MATERIAL & METHODS

X1 (e) X2 (e) . MeanQ (e)=?

(a) (b) (c) (d) (e)

MeanQ (b) StdQ(b) X1 (b) X2 (b) . MeanQ (d) StdQ(d) X1 (d) X2 (d) . MeanQ (c) StdQ(c) X1 (c) X2 (c) . MeanQ (c) StdQ(c) X1 (a) X2 (a) . StdQ (e)=?

Q (e)=?

MeanQ (e) Q T (e)

1 2

b b 1 2

StdQ = f[X ,X ,...]

StdQ (e)

( : , ) ( )

G

t e t F x dt t

β β α

α α β β

− ∞

= Γ

∫

1 2

b b 1 2

Mean Q = f[X ,X ,...]

2 parameters gamma distribution

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Hybrid method

1)The study area divide into some homogeneity classes 2)The parameters of Hybrid equation have been calculated: QT is discharge with T-year return period, X1 and X2 are independent hydrologic parameters and k is the constant component and l and m,... are the coefficients

f the regression model.

...MATERIAL & METHODS

l m T 1 2

Q = kX X ...

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…Hybrid method

...MATERIAL & METHODS

Grouping base

n X1

, X2 ,… (a,d) and (c,b) a, d

Q1

(a) Q2 (a) … Q1 (d) Q2 (d) …

QT

(1) c, b

Q1

(c) Q2 (c) … Q1 (b) Q2 (b) …

QT

(2) Calculate k, l, m,… for hybrid model: Calculate l, m, … and k coefficients

Calculate discharge with different return periods

l m T 1 2

Q = kX X ...

f f i Ti i=1 i=1 i Ti i=1 T 2 f i f 2 i=1 i i=1

A Q A Q - f l = A A - f ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ ⎡ ⎤ ⎢ ⎥ ⎣ ⎦

∑ ∑ ∑ ∑ ∑

Put X1 (e), X2 (e) in Hybrid model

QT (e)

(a) (b) (c) (d) (e)

Q1 (d) Q2 (d) … X1 (d) X2 (d) … Q1 (c) Q2 (c) … X1 (c) X2 (c) … Q1 (a) Q2 (a) … X1 (a) X2 (a) … Q1 (b) Q2 (b) … X1 (b) X2 (b) …

Q(e)=?

X1 (e) X2 (e) …

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...MATERIAL & METHODS

Study area

Karkheh Dam Official name Karkheh Dam Location Khūzestān‐Iran Coordinates 32°29′21″N48°07′36″ECoordin ates: 32°29′21″N 48°07′36″E Construction began 1992 Opening date 2001 Construction cost $700 million Dam and spillways Height 127m from foundation Length 3030 m Base width 1100 m (12m at crest) Impounds Karkheh River Reservoir Capacity 5,900,000,000 m

3(4,800,000

acre∙ft) Catchment area 42,000 km

2(16,000

sq mi) Surface area 162 km² Power station Turbines 3 Installed capacity 420 MW (3x140 MW)

[1]

Annual generation 934 GWh

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RESULTS AND DISCUSSION

Low flow models
Multivariate regression

1) 7-day low flows with different return periods (5, 10, 20, 25, 50 and 100 years) used 2) The most important physiographic characteristics that are effective on the low flow estimates have been selected.

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3) Estimated regression models are as follows:

...RESULTS AND DISCUSSION

A: Area (km2), S: Slope (%), BR: Bifurcation Ratio (the ratio of the number of streams of any given order to the number of streams in next higher order (Schumn, 1956)), E: Elevation (m) and QT 7-day low flow with different return periods for a specific basin

4

25

Q = 2.54×10 A+ 0.12S-1.77

4

50

Q = 2.21×10 A+ 0.11S-1.59

4

100

Q =1.95×10 A+ 0.10S-1.44

4
4
0.44BR-5.01×10

E+1.38×10 A+0.54 5

Q =10

4
4
0.46BR-5.44×10

E+1.41×10 A+0.45 10

Q =10

4
4
0.48BR-5.94×10

E+1.411×10 A+0.39 20

Q =10

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Low flow index method

...RESULTS AND DISCUSSION

1) 2) regional frequency

curve

1
4
0.41BR-3.65×10 E+1.38×10

A+0.63 2

Q =10

A: Area (km2), BR: Bifurcation Ratio, E: Elevation (m) and Q2 7- day low flow with 2-year return period

3) calculate QT for a

specific basin

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Regionalizing the frequency formula parameters method

2) Put Mean(Q) and Std(Q) in cumulative distribution function of 2 parameters gamma distribution for calculating 7-day low flow values with different return periods in a specific basin. 1) The relation between average and standard deviation of 7-day low flows and characteristics of the basin are:

...RESULTS AND DISCUSSION

Mean(Q) is the average of 7-day low flows (m3/s), A is the area of basin (km2), BR is bifurcation ratio, E is basin elevation (m), MsL is the mainstream length (km) and Std(Q) is the standard deviation of 7-day low flows series.

3
2

6.15×10 MsL-0.26LogE-0.20BR+4.62×10

Std(Q) =10

4
4

1.44×10 A-2.68LogBR-2.8×10 E+0.59

Mean(Q) =10

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The regional models for estimating low flows by this method are:

...RESULTS AND DISCUSSION

0.01
0.20

25

Q = 1.77 A S

0.00
0.06

50

Q = 1.03A S

0.00
0.02

100

Q = 0.78A S

0.16

5

Q = 4.87 A

0.03
0.81

10

Q = 14.10A S

0.01
0.27

20

Q = 2.35A S

A: Area (km2), S: Slope (%)

Hybrid method

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Validation step

Relative Error (percent) and Root of Mean Square Error (RMSE) for four methods

...RESULTS AND DISCUSSION

For all of return periods, the multivariate regression and low flow index methods have more accuracy in comparison with regionalizing the frequency formula parameters and Hybrid methods.

Multivariate Regression Low Flow Index Hybrid

Return Perion (year) Return Perion (year) Relative Error (percent) Root Mean Square Error

Frequency Formula Frequency Formula Hybrid Multivariate Regression Low Flow Index

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Multivariate regression and low flow index methods are more suitable than Hybrid model. Using climatic data (for example Precipitation, Temperature and ..., that are important in low flows) instead

f physiographic data (Area and Slope) in Hybrid method,

maybe have more accuracy for applying this model (it can consider in future researches)

CONCLUSIONS

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