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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,
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
0 1 2 3 4-ln(exceedance probability)
ln( U
H va
lues
)
observationsextreme value distributionoptimal threshold
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
0 1 2 3 4-ln(exceedance probability)
ln(D
isch
arge
(m3/
s))
observationsextreme value distributionoptimal threshold
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
0 0.5 1 1.5 2 2.5 3 3.5-ln(exceedance probability)
obse
rvat
ions
observations
extreme value distribution
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
0 0.5 1 1.5 2 2.5 3 3.5-ln(exceedance probability)
ln(o
bser
vati
ons)
observations
extreme value distribution
optimal threshold
Slope Pareto Q-Q Plot
150
0.2
0.4
0.6
0.8
1
1.2
1.4
0 5 10 15 20threshold rank
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
0 5 10 15 20threshold rank
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
0 0.5 1 1.5 2 2.5 3 3.5-ln(exceedance probability)
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).