At-site and Regional Flood Frequency Analysis of the Upper Awash Sub Basin in the Ethiopian Plateau

1

AT-SITE AND REGIONAL FLOOD FREQUENCY ANALYSIS OF THE UPPER AWASH SUB – BASIN IN THE ETHIOPIAN

PLATEAU

Leuleseged Tadesse1, Mohamed A. Sonbol2, Willems P.3

1 Ministry of Water Resources, Addis Ababa 5744, Ethiopia, [email protected]

2 Water Resources Research Institute, National Water Research Center, P.O. Box 13621 El-Qanater El-Khairia, Egypt, [email protected] , [email protected]

3 Hydraulics Laboratory, K.U.Leuven, Leuven, B-3001, Belgium,

[email protected]

Abstract The conventional way of flood frequency analysis is applied in determining flood magnitudes of defined return periods by selecting theoretically the best fit probability distributions. The most important part of the distribution is the tail as far as extreme flooding phenomena are utmost concern in water resources development and management. In most cases the central part of the theoretical distribution fits satisfactorily with the empirical points. In FFA, the objective is to estimate flood magnitude (Q) corresponding to any specified recurrent interval of (T) years. The estimation is complicated due to lack of a physical basis for determining the form of the underlying flood frequency distribution and the necessity of evaluating flood event for return periods that exceed the observation period. In order to improve the estimation of the Q-T relationship, the need to use regional information arises so that stabilizing site specific estimates based on limited data can be handled and as well as ungauged catchments. The regional FFA procedure involves the definition and identification of homogeneous regions .In the present frequency analysis, application of index-flood regional method of FFA is considered as one of the tools in overcoming problems of ungauged catchments and streams having small sizes of observation (n). For this purpose as part of FRIEND/Nile research activities, the upper sub-basin of Awash River with 8 gauged streams consisting of stream flow records varying from 15 to 33 years has been analyzed. An extreme value distribution (EV1) is elected as the best fit distribution for the sub-basin and this is also exhibited by other similar analysis in the Nile basin countries (Kenya, Tanzania and the Sudan). Regionalization is the generally accepted term to explain the transfer of information about flood peaks at one catchment derived from other catchments with similar characteristics. The advantage of such procedures is particularly great in the estimation of frequencies for higher flood magnitudes with limited at site data do exist and inference in the tails of probability

2

distributions makes the stabilization of the estimators is difficult. It is quite clear that regionalization is most viable way of improving flood quantile estimation. Although there remain researchable topics in development and application of regionalization methods, the performance of regional EV1 (Extreme Value) distribution is found to be highly satisfactory and can be widely applied. OBJECTIVE OF THE STUDY The objective of the study is to identify appropriate procedure for flood frequency analysis of stream flow gauging stations situated in the upper Awash sub-basin upstream of Koka dam. Study of water resources and designs of hydraulic structures are being conducted based on available techniques and methods of flood frequency analysis with little attention on the tails of the distribution curves which in turn highly influence the provision of appropriate solutions meeting safety and economic considerations. STATEMENT OF THE PROBLEM The main challenge of flood from water resources development and management aspect is its recurring interference with interventions and activities made by society. The loss of life and damage can be pictured in terms of economic losses and danger to human life. The major issue is here to critically analyze the frequency and magnitude of the flooding interference. The basic idea of flood frequency analysis is to obtain an estimate of flood quantile magnitude Q(T), for locations on a river system. Quantile estimates are used in planning, design, construction and operation of water resources projects or decision process relating to hydraulic works or flood alleviation programs and in general for water resources management within river system. The probability that QT is equaled or exceeded in any year is assumed to be 1/T. From this follows that the probability of non-exceedence of QT for each year takes the form

F(QT) = 1-1/T ( 1 ) The major problem of flood quantile estimation stems from type of distribution and availability of observed data for short period of time as compared to extrapolation usually made by upper part of the theoretical curve.

AT- SITE DATA Table (1) gives the characteristics of the selected hydrological stations in the upper Awash area, while figure (1) shows the characteristics (Lengths, slopes and drainage areas) and general location map of the Upper Awash area in Ethiopia. Figure (2) shows plots of annual maximum discharges of stations in the Awash basin, while figure (3) shows plots of dimensionless value of annual maximum discharges. REGIONALIZATION The common situation which we face is the availability of data consisting of small samples at sites. Because of the high sampling variability associated with small sample particularly

3

estimating parameters of distribution with three or more parameters cannot be entirely reliable unless supplemented by regional flood analysis. The transposition of information about maximum discharges at one site is made from other catchments with similar characteristics and this approach is known as regionalization. At present the regionalization approach for flood frequency analysis is widely applied and becoming more popular. The index flood method is one of the commonly applied ones.

Table 1(1): Characteristics of the hydrological stations of upper Awash sub-basin

Coordinates Sl. No. Station Name

Drainage Area ( km2) Lat. (N) Long.(E)

Sample size(n) of MAF in

years

1

Berga River Near Addis Alem

249 9° 01'

UTM 996668

38°21'

428556 25

2 Holeta River Near Holeta 119

9°05'

UTM 1004010

38°31'

446886 25

3

Awash River Near Bello 2566

8°51'

UTM 978231

38°25'

435855 15

4

Tegj River Near Asogri 663 8°47'

UTM 970876

38°20'

426678 23

5

Akaki River at Akaki 884

8°53'

UTM 981872

38°47'

476177 18

6

Awash river at Melka Kunture 4456

8°42'

UTM 961622

38°36'

455998 33

7

Awash River at Hombole

7656 8°23'

UTM 950551

38°47'

476159 33

8

Modjo River at Modjo

1264

8°36'

UTM 950545

39°05'

509170

31

4

%a %a

%a

%a

%a

%a

%a

%a

MOJO@ MOJO Village

AKAKI@ AKAKI

AWASH@ MELKA Hombole

AWASH@ MELKA K

HOLETANr. HOLET

BERGAANr. ADDIS

AWASHNr. BELLO

TEJINr. ASGOR

N

UPPER AWASH Awash @ Melka Hombole River Length =106.151 km

Slope = 0.33 Catchments area=7656 km 2

Awash @ Melka Kuntira River Length =57.353 km Slope = 0.30 Catchments area=4456 km 2

Awas h @ Bello River Length =32.383 km Slope = 0.35 Catchments area=2568 km2

Teji @ Assgori River Length =24.142 km Slope = 0.61 Catchments area=662 km 2

Mojo @ Mojo village River Length =42.526 km Slope = 0.96 Catchments area=2175 km2

Akaki @ Akaki Village River Length =44.799 km Slope = 0.68 Catchments area=884.4 km2

Holota Nr Holota River Length =14.970 km Slope = 0.76 Catchments area=119 km 2

Bergaa Nr Addis Alem River Length =13.485 km Slope = 1.17 Catchments area=248 km2

Figure (1): General Location Map of the Upper Awash Area in Ethiopia. Lengths, slopes and drainage areas for the selected catchments

in the upper Awash River .

5

Graph of Annual flow series

0

100

200

300

400

500

600

700

800

900

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Years

Dis

char

ge

[m3/

s]Berga, Addis AlemHoletaAwash, Bello

Teji, AsgoriAkaki

Awash, Melka KuntureAwash, HomboleMojo river, Mojo Villeg

Figure (2) Plots of annual maximum discharges of stations in the Awash basin

Graph of Q/Qmean series

0

0.5

1

1.5

2

2.5

3

3.5

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Years

Q / Q

mea

n

Berga, Addis Alem

Holeta

Awash, Bello

Teji, AsgoriAkaki

Awash, Melka Kunture

Awash, Hombole

Mojo river, Mojo Villeg

Figure (3) Plots of dimensionless value of annual maximum discharges

6

Table (2) gives the statistical parameters of the available stream flow data. The two major sources of error in flood quantile estimation by index flood procedures are the estimation of the index flood (at-site MAF) and the estimation of standardized quantile. The error of standardized quantile estimation may not be significant since the sub-basin is proved to be hydrologically homogeneous. The accuracy of the estimation of the at-site mean flood value depends highly on the sample size. In most of the cases the risk is associated with inadequate data or small sample size. The availability of data is very vital for planning, development and management of the finite resource "water" in the sub-basin context.

Table2. Statistical parameters of the available stream flow data

Parameters Station name of river

mean CV st.dev skew kurt

Berga@Addis Alem

50.84 0.538 27.353 1.208 4.165

Holeta@Holeta 31.07 0.513 15.930 3.255 16.686 Awash@Bello 37.72 0.072 2.713 1.352 8.587

Tegj @Asgori 80.06 0.325 26.035 -.427 2.661

Akaki@Akaki 181.94 0.434 78.893 .518 5.035

Awash @ Kunture

252.62 0.307 77.581 .625 2.681

Awash @Hombole

438.27 0.348 152.676 .6682 2.877

Modjo@Modjo 120.836 0.575 69.426 1.507 6.114

SELECTION OF DISTRIBUTION AND PARAMETER ESTIMATION METHOD A procedure to this context comprises three things. They are model type, distribution type and method of parameter or quantile estimation.

Evaluation criteria can be divided into two categories as follows:

• Criteria relating to ability of a selected model to describe or reproduce the selected

aspects of observed flood (descriptive ability) and

• Criteria relating to procedure's statistical ability to achieve its assigned task, with minimum bias and maximum efficiency and robustness (Predictive ability)

Descriptive ability: Annual Maximum flood series in general are positively skewed with observed average regional skewness (CS) values to the range 0.5 to 3.0 and coefficient of variation (CV) values which vary from 0.1 in tropical rainforest climate to around 1 to semi arid areas. In Ethiopia the CV values

7

range from 0.2 to 0.7 and Cs varies from 0.6 to 1.2. These observations taken together suggest that annual maximum floods are from population with positively skewed distributions. Therefore the most popular possible candidates for the annual maximum flood series are EV1, GEV, Pearson Type III, Log -normal, Log-Pearson Type III and others. Predictive ability: The Study of predictive ability helps to exclude non-robust and inefficient models. Flood frequency analysis: After having the annual flood maximum series, distributions are applied to fit the empirical points obtained by plotting position formulae. The most common distributions are used based on the condition of fitting of the points. The distributions used in the case of the upper Awash gauging sites data are as follows.

• Extreme value type I • 2 parameter Gamma distribution • 2 parameter Log Normal distribution • 3 parameter Log Normal distribution • Pearson type III

Parameter estimation methods : Two parameter estimation methods are applied which commonly used for estimating the parameter of the distributions. These are:

• Method of maximum likelihood • Method of moments

Goodness of fit-tests: By conducting the goodness of fit tests the best distribution is selected for each set of annual maximum series of data. The following methods are used depending on the data set and the length of record.

• The Chi square test • The Deviation method this in turn is divided in to Mean relative deviation and Mean

square deviation • The Class Interval method

AT-SITE CALIBRATION OF FLOOD FREQUENCY DISTRIBUTIONS The extreme value theory for annual maxima has been applied to discriminate the distribution in the upper tail where ? = 0 classified as the normal tail distribution, while ? > 0 the tail is considered as heavy and the light tail is encountered when ? < 0 as explained in Willems P.(1998). In most cases extreme situations are distinguished either normal or heavy tail as far as

8

hydrological application is commonly concerned. In order to evaluate the extreme value theory the following has been used:

• Exponential Q-Q plot with horizontal and vertical axes comprising of

(-ln )1

(+mi

; qi ) (4)

• Pareto Q-Q plot

(-ln )1

(+mi

; ln(qi ) ) (5)

• UH plot

(-ln )1

(+mi

; ln(UHi ) ) (6)

Based on the above plots the behavior of the tail can be described as normal or heavy or light tail depending on the shape of the distribution. In the case of Awash sub-basin flood frequency analysis distributions in upper tails are identified as normal and heavy ones. The tail of the distribution can be identified by the plots of the above mentioned relationships taking in consideration the following conditions. DISTRIBUTION TAIL ANALYSIS Normal tail - Exponential Q-Q plot - upper tail points tend towards straight line - Pareto Q-Q plot - upper tail points tend to bend downwards - UH plot - the slope in the upper tail becomes towards the zero value. Figure (4) shows the Q-Q plots of Akaki River at Akaki for normal tail condition, while Figure (5) shows Comparison of EV1 and Etreme value distributions for Akaki River. Heavy tail - Exponential Q-Q plot - upper tail points tend towards straight line - Pareto Q-Q plot - upper tail points tend to bend downwards - UH plot - the slope in the upper tail becomes towards the zero value Figure (5) Comparison of EV1 and Etreme value distributions for Akaki River. The Teji River flood plain influence- Selection of distribution for the two segments as shown in Figure (6).

9

Exp. Q-Q Plot

0

50

100

150

200

250

300

350

400

0 1 2 3 4-ln(exceedance probability)

Dis

char

ge(m

3/s)

observationsextreme value distributionoptimal threshold

S l o p e E x p . Q - Q p l o t

150

20

40

6080

100120

140

160

180

0 5 10 15 20 25

threshold rank

slop

e

0

50

100

150

200

250

MS

E

slope MSE

UH-plot

0

1

2

3

4

5

6


ln( U

H va

lues

)


Slope UH-Plot

15-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 5 10 15

threshold rank

extr

eme

valu

e in

dex

0

0.10.20.30.4

0.5

0.60.7

0.80.9

1

MSE

extreme value indexMSE

Pareto Q-Q Plot

0

1

2

3

4

5

6

7


ln(D

isch

arge

(m3/

s))


Figure (4) Q-Q plots of Akaki River at Akaki for normal tail condition

10

Comparison between EV-1 (ML, MOM, PWM) and the Extreme Value Distributions

at Akaki Station - Ethiopia .

-50

0

50

100

150

200

250

300

350

400

0 0.5 1 1.5 2 2.5 3 3.5-ln(exceedance probability)

obse

rvat

ions(

Q m

3/s)

EV1/Gumbel, MOM

EV1/Gumbel, PWM

EV1/Gumbel, ML

observations

extreme value distribution

optimal threshold

Figure (5) Comparison of EV1 and Extreme value distributions for Akaki River.

Further the heavy tail situation is shown in the case of Teji River at Asgori as shown in Figure (6). The flooding influence is observed as it is affected by the flood plain where water is temporarily ponded and gradually released at later time ( Sonbol M.A, Willems P.) as shown in Figure (7) for Teji River. In this case threshold should be marked and two distributions are fitted to realistically represent the conditions. The regulation effect is highly pronounced in the case of high flow period. INDEX-FLOOD PROCEDURE The index flood method basically takes the assumption that, floods from different catchments within a region normalized by their mean annual flood come from a single distribution. The important condition for this procedure is the standardization of the flood data from sites with different flood magnitudes. The common practice is to get the dimensionless data by dividing the values by an estimate of the at-site mean.

X T =

QmeanQi

(2)

Then the quantile QT is estimated as QT = ( ) X T

Qmean ∗ (3) Thus, the mean annual flood is the index flood. Parameters of the distribution of X are found from the combined set of regional data. If at site data are not available, the index flood can be estimated from regionally established empirical formula. The estimation of mean annual flood from cathment characteristics is widely applicable in particular where our point of interest is unguaged. An insight examination of the temporal and special variability of hydrological elements is important in predicting variables based on the knowledge of regionally pooled data base and relationships established with physical parameters. Some examples of such types are shown below.

11

EXP. Q-Q Plot

0

20

40

60

80

100

120

140


obse

rvat

ions

observations


optimal threshold

Slope EXP Q-Q Plot

140

10

20

30

40

50

60

70

0 5 10 15 20threshold rank

slop

e

0

100

200

300

400

500

600

700

800

900

1000

MS

E

slope MSE

Pareto Q-Q Plot

0

1

2

3

4

5

6


ln(o

bser

vati

ons)

observations


optimal threshold

Slope Pareto Q-Q Plot

150

0.2

0.4

0.6

0.8

1

1.2

1.4


extr

eme

valu

e in

dex

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

MS

E

extreme value index MSE

Slope UH-Plot

23

-35

-30

-25

-20

-15

-10

-5

0


extr

eme

valu

e in

dex

-1

49

99

149

199

249

MS

E

extreme value index MSE

Figure (6) Teji River at Asgori Q-Q plot for heavy tail condition.

12

0

50

100

150

200

250

300


obse

rvat

ions

observationsextreme value distribution

optimal thresholdcensored POT values

EV1/Gumbel, MOM

Figure (7) Calibration result for the flood frequency distribution at Teji River for

the flooded and non-flooded events. It is identified that the station on the Awash River near Bello is situated down-stream of flood plain where flows spread in the plain rather than confined to the natural channel. This in turn highly smoothened the peaks and low magnitudes of maximum flows were registered which did not at all correspond to the drainage sizes as compared to the other stations situated in similar climatic, physico-geographical condition and receiving more or less the same magnitude of rainfall. The Akaki river catchment highly urbanized and partly regulated by old reservoirs presumably reached their service life, which in reality has completely silted up. In this condition higher values of peak could be anticipated, which do not represent the naturalized flow. Regional Frequency Analysis The use of regional information to estimate flood magnitudes at sites with little or no observed data has become increasingly important since many projects which require design flood information are located in areas where observed flood data are either missing or inadequate. Regional analysis consist of analyzing the record of all gauged sites in a hydrologically homogeneous region, in order to be able to use or transfer information contained in the record of many sites to estimate quintiles at any individual gauged or ungauged catchments in the region. Hosking and Wallis (1993) have discussed the various aspects of regional frequency analysis such as identification of homogeneous regions and described the different steps of regional analysis. In the present application, the discharge -return period (Q-T) relationships for all sites as obtained from extreme value analysis were plotted together with the discharge being expressed in dimensionless or standardized form (by dividing by the mean) and the results are shown in Figure (8). It is clearly observed that the region is consedered homogeneous and this, as has been mentioned before due to the same hydrological phenomena responsible for generating the flood events over the region. Consequently, a regional frequency curve has been developed for the region as shown in Figure (9). Also Various relations have been developed based on multiple linear regression, between the Mean Annual Flood ( MAF), and catchment area (A) and mean annual rainfall (MAR) as shown in figures (10) and (11) respectively. It has been found that all catchment characteristics

13

give correlation to the MAF.A and MAR can be combined in one mathematical relationship for the best fit of the line of correlation.

Figure (8) Flood magnitudes versus return periods

Plot of Regional curve

0

0.5

1

1.5

2

2.5

3

3.5

1 10 100

Return period [yrs]

Q/Q

mea

n

Berga, Addis Alem

Holeta

Teji, Asgori

Akaki

Awash, Melka Kunture

Awash, Hombole

Mojo river, Mojo at Village

Regional curve

river flood curve, Holeta

river flood curve, Teji

river flood curve, Awash MelkaKuntureriver flood curve, AwashHombole

Figure (9) Regional flood curve

Plot of Q vs T

0

200

400

600

800

1000

1200

1400

1 10 100 1000

T,years

Q,m

3/s

BergaHoletaAwash-Bel loTejiA k a k iAwash-M.Kunt.HomboleMojo

14

Figure (10) Mean annual floods as a function of drainage areas.

Figure (11) Mean annual flood as a function of drainage area & mean annual rainfall

M e a n A n n u a l F l o o d v s ( A r e a * M A R )

y = 0 . 0 1 3 2 x0 . 6 5 5 1

R 2 = 0 . 9 8 0 1

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0 0 . 0 0 0 1 0 0 0 0 0 0 . 0 0 0 1 0 0 0 0 0 0 0 . 0 0 0

A r e a [ k m 2 ] * M A R [ m m ]

MA

F [m

3/s]

A w a s h - B e l l o( F l o o d e d a r e a )

A k a k i( U r b a n a r e a )

Graph of Mean Annual Flood vs Drainage Area

y = 1.7795x0.5907

R 2 = 0 .9665

10

100

1000

1 0 0 1000 10000

Area [km2]

MA

F [m

3/s]

Power fit

Awash-Bel lo(Flooded area)

Akak i(Urban area)

15

CONCLUSIOS In the case of this particular regional analysis, catchments characteristics, mean annual flood and annual rainfall are considered in order to establish regional relationship that can be applied to the unguaged catchments of the sub-basin. Currently regional flood frequency curves are derived for the Nile basin under the collaborative works of FRIEND/Nile project. This type of joint study undertakings promotes cooperation among the Nile basin countries and the results obtained could be applied for water resources management and planning. The present outputs can be further examined in light of catchment land use, land cover and soil type. In addition to this, stationarity test, statistical trend analysis and identification of cycles could be considered for improving the analysis so far performed. ACKNOWLEDMENTS This paper was prepared based on the research activities of the FRIEND/Nile Project which is funded by the Flemish Government of Belgium through the Flanders-UNESCO Science Trust Fund cooperation and executed by UNESCO Cairo Office. The authors would like to express their great appreciation to the Flemish Government of Belgium, the Flemish experts and universities for their financial and technical support to the project. The authors are indebted to UNESCO Cairo Office, the FRIEND/Nile Project management team, overall coordinator, thematic coordinators, themes researchers and the implementing institutes in the Nile countries for the successful execution and smooth implementation of the project. Thanks are also due to UNESCO Offices in Nairobi, Dar Es Salaam and Addis Ababa for their efforts to facilitate the implementation of the FRIEND/Nile activities. REFERENCES

Hosking and Wallis (1993) , Estimation of the general extreme value distribution by the method of probability weighted moments. Techno metrics, 27(3):251-261. Sonbol M.A, Willems P. (2005) , "Flood frequency analysis of the Eastern Nile rivers" Willems P. (1998), 'Hydrological applications of extreme value analysis’, In: Hydrology in a changing environment, H. Wheater and C. Kirby (ed.), John Wiley & Sons, Chichester, vol. III, 15-25; (ISBN 0-471-98680-6).

At-site and Regional Flood Frequency Analysis of the Upper Awash Sub Basin in the Ethiopian Plateau

Documents

Transcript of At-site and Regional Flood Frequency Analysis of the Upper Awash Sub Basin in the Ethiopian Plateau