1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 4, July-August (2013), © IAEME
113
APPROACHES FOR OBTAINING DESIGN FLOOD PEAK DISCHARGES IN
SARADA RIVER
Dr.YerramsettyAbbulu1
, Dr.P. Chandan Kumar2
, V.K.V.Bhadrudu3
1
Associate Professor, Dept. of Civil Engineering, Andhra University College of Engineering (A),
Visakhapatnam, Andhra Pradesh- 530 003.
2
Assistant Professor, GITAM Institute of Technology, GITAM University, Visakhapatnam, Andhra
Pradesh-530 045.
3
Student of M.E. (H, C& H Engg.), Dept. of Civil Engineering, Andhra University College of
Engineering (A), Visakhapatnam, Andhra Pradesh- 530 003.
ABSTRACT
One of the approach for the flood frequency studies is Estimation of flood quantile
magnitudes in a river. In developing countries like India availability of the observed flood duration
data is insufficient for analysis of flood frequency studies. Hence, using theoretical probability
distributions and empirical probability distribution by different plotting positions applying method of
least squares has been done. Flood frequency data for year 2000 to 2013 was considered for river
Sarada in Visakhapatnam district of Andhra Pradesh. It has been concluded that Weibull 3
distribution methodology was perfectly represented in theoretical distribution and Gamma 3
distribution was perfectly represented in empirical distribution. This is quite useful for determining
the dead level of the river, which is useful in term for determining the elevation of bridges.
INTRODUCTION
Floods can take thousands of lives and cause damage in billions of dollars. Annual maxima
for successive years can generally be considered to be independent and identically distributed,
making the required frequency analysis straight forward. Flood frequency analysis is concerned with
the estimation of flood quantile magnitudes for different return periods at a station or at a number of
stations in a river system. A difficulty associated with flood frequency analysis is the lack of
sufficient data. Consequently, it is difficult to identify the parent errors of estimate result because of
small sample sizes. Estimation of the magnitude of floods greater than the length of standard error
estimate increases rapidly with increasing return periods. If there are sufficient flood data at a gauged
station, flood estimates are often made based on at-site flood frequency analyses. However, observed
flood data at the site are generally insufficient to obtain reliable estimates of the flood quantiles,
especially in developing and underdeveloped countries. [7]
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND
TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 4, Issue 4, July-August (2013), pp. 113-118
© IAEME: www.iaeme.com/ijciet.asp
Journal Impact Factor (2013): 5.3277 (Calculated by GISI)
www.jifactor.com
IJCIET
© IAEME

2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 4, July-August (2013), © IAEME
114
Annual maximum river flood data were observed at Sarada river, and then investigated. The
following distribution functions were used to investigate this data: the Generalized Pareto (GPAR),
the Generalized Extreme Value (GEV), Generalized Logistic (GLO), Generalized Normal (GNOR),
and Pearson Type III (P3) distributions. Different Plotting-Position formulas (VenTe Chow, 1964;
Yevjevitch,1972) were proposed to evaluate the empirical probabilities: Hazen, Weibull, Cegodaev,
Blum, Tukey, Gringorten. [6]
Flood has been defined by various researchers in various ways. According to chow (1956), a
flood is a relatively high flow, which overflows the natural channel provided for the runoff. A
general definition by ward (1978), states that a flood is a body of water which rises to overflow land
which is not normally submerged. In India, a river is said to be in flood when its water level crosses
the danger level (DL) at that particular site. [8]
In this paper, mainly the method of least squares was used for the evaluation of the statistical
distributions. The maximum annual discharges registered at Godari anicut river gauge station for 13
years (2000- 2012) were used for the statistical analysis. The maximum discharges (Fig.1) are in the
range 1607.36 m3
/s (in 2007) and 2548.07 m3
/s (in 2012). [9]
Fig. 1. The series of maximum discharges at Godari anicut river gauge station between
2000-2013.
LITERATURE REVIEW
AhamadShukriYahayaet et.al. (2012) Concluded that to determine the best probability plotting
positions, three-error measures were used which are normalized absolute error, mean absolute error
and root mean square error. Probability position methods was compared to estimate the shape and
scale parameters, simulation technique was used to obtain random variable for Weibull distributions.
A regression method is one of several techniques to estimate parameters of a distribution such as the
Weibull distribution. The best quantile estimate made from the plotting formula should be unbiased
and should have the smallest root means error among all estimates.
Carlos Escalante-Sandoval (2007)stated that frequency analysis is to estimate the flood magnitude
corresponding to any return period of occurrence through the use of probability distributions. The
return period, also referred to as the recurrence interval, selected depends on the nature of the project
and the consequences of the design flood being exceeded. Most flood studies have been analyzed
through the use of univariate distributions, and those with three (or) more parameters provide high
flexibility for fitting the data. Estimation of peak flow of a design return period is a standard
0
500
1000
1500
2000
2500
3000
1998 2000 2002 2004 2006 2008 2010 2012 2014
annual discharge

3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 4, July-August (2013), © IAEME
115
requirementin many projects such as design of bridge openings and culverts, drainage networks,
flood relief/protection schemes and determination of flood risk and large scale residential
developments.
Keshav P Bhattarai (2005)focused mainly on the at-site method of flood frequency analysis,
involving the method of L-moments and the generalized extreme value (GEV) distribution, three
variants of L-moments, namely the simple L-moments, the higher L-moments and the partial L-
moments are applied for fitting the GEV distribution to annual maximum series and the results thus
obtained are compared.
Onni S. Saelamanet et. al. (2007)determines the magnitude and frequency of floods using Gumbel
distribution. The probability plot and flood frequency curves by Gumbel distribution of the station
are prepared using three different plotting position formulae’s which are Weibull, Gringorten and L-
moments. Analysis of the station Gumbel distribution based on L-moments always give the least
ratio of peak discharge of T-years recurrence-interval over mean annual flood (QT/MAF) but at
some stations, it gives unreasonable return period (T) and reduced variate ‘y’ range. Also L-moment
method is best plotting position but have some limitations so Gringorten formula is still the best
plotting position method with Gumbull distribution.
UmmiNadiah Ahmad et. al. (2011)Flood frequency analysis (FFA) is the estimation of how often a
specified event will occur. Before the estimation can be done, analyzing the stream flows data are
important in order to obtain the probability distribution of flood. By knowing the probability
distribution, prediction of flood events and their characteristics can be determined. The study is to
perform the flood frequency analysis of annual maximum stream flows by using the L-moments and
TL-moment with trimming only one smallest value approach. The most suitable distribution was
determined by the use of MADI and moments ratio diagram. Estimate that GLO distribution of the
best distribution fitted the data of annual maximum stream flows.
Yevjevitch,V.(1972) concluded that statistical values can be obtained by selecting each year the
maximum annual discharge, or keeping only the maximum discharges over a threshold. No matter
the procedure used, the statistical values of the flood peaks are affected by statistic and epistemic
uncertainties. As a result, an interval containing the statistical values of the maximum discharges
should be considered. This approach is totally different of the classic approach when a unique value
characterize the maximum discharges corresponding to a certain probability of exceed. two methods
are proposed for obtaining the interval containing the maximum discharge. The results obtained by
the two methods are compared using as a case study the discharges registered at Budapest gauge
station.
NATURE OF STUDY
The Sarada river, one of the river in Visakhapatnam district, is located on north eastern
coastal district of Andhra Pradesh. Sarada river is spread over the Devarapalli, Chodavaram,
Anakapalli and Kasimkota mandals of the Visakhapatnam district.
The study was carried by collecting daily discharges in Sarada river at Godari anicut river
gauge station is 2 km away from Anakapalli mandal, Visakhapatnam district. Sarada river flows
almost north to east and joins the Bay of Bengal at Revupolavaram Village.
The re-construction of Godari anicut project comes under the jurisdiction of Irrigation and
Command Area Developing (I&CAD) Department in June 8th
1999, total length of anicut 673 feet;
343 feet in masonry portion and 330 feet rough stone portion and is having 4 number of scouring
vents were located on left flank of anicut.
To conduct a study on analysis of flood frequency in Sarada river at Anakapalli region, data
available from the year 2000 onwards was used. A field study was carried out for a year in the post
monsoon months of October, November and December; rainy season for the observations of the river

4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 4, July-August (2013), © IAEME
116
discharges in Godari anicut river gauge station and the daily discharge reading of Sarada river were
collected. The max discharge obtained in the month of the November 2012 which is about 2550
m3
/sec. due to Neelam thunder storm, the flood continue to take a heavy toll on life and property in
Anakapalli region, many roads and bridges have been washed away and all major highways have
been shut down or damaged.
It is estimated that more than 25 villages are affected by this massive disaster. Hundreds of
houses, schools, farmlands and shops have been completely damaged and swept away.
METHODOLOGY
The purpose is the identification of those distributions whose values present large charts from
most of the other distributions, in order to exclude them, as well as to identify the range of the
remaining distributions. Beside a graphic criterion, statistic tests will be used to achieve an objective
evaluation.
One may notice that for a certain probability of exceeding the maximum discharges are quite
close, except the values in the red rectangles. Thus, the maximum discharges computed using the
Log-Logistic distribution for the probabilities of exceeding of 0.01% and 0.1% are very large if
compared with the similar values for the other distributions, while Gamma 3 distribution has almost
all values totally different.
The following graphs will justify the decision of rejection or acceptance of those distributions
which fit well the empirical distribution.
The graph empirical probability-theoretical probability (Fig. 2) allows the evaluation of the
agreement between the theoretical and empirical distributions; the better their agreement, the closest
the points to a straight line of equation y=x. The probabilities empirical and theoretical correspond to
the same maximum discharge.
Fig. 2. Empirical probability – theoretical probability graph for the maximum annual discharges at
Godarianicutriver gauge station.
The graph empirical quantile - theoretical quantile (Fig. 3) also allows the comparison of
these distributions; the point coordinates are represented by the discharges corresponding to the same
probability of exceeding for both distributions.
P-P Plot
Gamma (3P) Weibull (3P)
P (Empirical)
10.90.80.70.60.50.40.30.20.1
P(Theoritical)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 4, July-August (2013), © IAEME
117
Fig. 3. Empirical quantile - theoretical quantile graph for the maximum annual discharges
atGodarianicut river gauge station.
If the theoretical distribution would perfectly represent the empirical distribution the points
from Figures 2 and 3 should be on a line at 450
. While Weibull 3 distribution is quite close to this
line, the Gamma 3 distribution is quite far from it.
DISCUSSIONS
This study was conducted years from 2000 to 2013 observed mean daily discharge data
obtained from calculate annual peak discharges. Fitting a distribution to data sets provides a compact
and smoothed representation of the frequency distribution revealed by the available data, and leads to
a systematic procedure for extrapolation to frequencies beyond the range of the data set.
In the present study, the danger level 2.5m of Sarada river at godari river gauge station. In
year of 2012 Neelam thunder storm, the peak discharge was recorded very high and was affected.
Usually, the maximum annual discharges corresponding to a probability of exceedance P%
are obtained using only one theoretical distribution. The analysis of the maximum discharges using 7
theoretical distributions (Kri ki-Menkel, Pearson III, Weibull 3, GEV, Lognormal, Log-Logistic and
Gamma 2) put into evidence an interval which contains the discharges. As a result, to a given
probability of exceedance P% correspond not a unique value, but an interval containing the
discharges. This interval, called uncertainty interval is defined by its lower and upper limits. That
means that there are an infinite values for the maximum discharge corresponding to a probability of
exceedance P%.
The entire study was done in different discharge readings in single river gauge station.
CONCLUSIONS
1. This study area was conducted at Sarada River, 13 years observed mean daily discharge data
obtained from calculate annual peak discharges.
2. It has been concluded that Gamma 3 distribution it well into the empirical distribution (fig.2)
and Weibull 3 distribution (fig.3) methodology was perfectly represented in theoretical
distribution.
3. This study may be useful in highway bridge construction and must to pass the design
discharge of specified magnitude without being flooded during its life-span.
Q-Q Plot
Gamma (3P) Weibull (3P)
Quantile (Emperical)
2500200015001000500
Quantile(Theoritical)
2400
2200
2000
1800
1600
1400
1200
1000
800
600
400

6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 4, July-August (2013), © IAEME
118
4. The places having elevation greater than 10m with respect to Dead Level (DL) have to be
identified and the housing colonies shall be developed in these identified areas.
5. The drainage system should be improved by forming embankments on either sides and
removing the silt deposited and cleaning the vegetation in the bed of the drains, so as to
minimize the damages caused to the crops.
6. The towns and villages lying below 10m contour need attention to prevent damages caused
by floods.
7. Drinking water supply pipeline should be laid connecting all the villages and town situated in
the flood affected area by supplying water from outside the area.
8. Maximum discharge and its frequency are required for flood risk assessment of the projects
Maximum discharge in the study period, for the Sarada river is 2548.07 m3
/s.
9. It was concluded that 2 years recurrence interval of peak flood discharges in Sarada river
which could be used as measures for flood protection like embankments, check dam etc.
REFERENCES
1. Ahmad ShukriYahaya, Chong Suat Yee, NorAzamRamli and Fauziah Ahmad
(2012).“Determination of the Best Probability Plotting Position for Predicting Parameters of
the Weibull Distribution”, International Journal of Applied Science and Technology Vol. 2
No. 3; March 2012 (106-111).
2. Carlos Escalante-Sandoval (2007). “Application of Bivariate Extreme Value Distribution to
Flood Frequency Analysis: A Case Study of Northwestern Mexico”, Nat Hazards November
2007, 42: (37–46).
3. Keshav P. Bhattarai (2005). “Flood frequency analysis of Irish river flow data Using variants
of L-moments”, National Hydrology Seminar 2005(46-55).
4. Onni S. Selaman, Salim Said and F.J. Putuhena (2007). “Flood Frequency Analysis for
Sarawak Using weibull, Gringorten and L-Moments Formula”,The Institution of Engineers,
Malaysia Vol. 68, No. 1, March 2007, (43-52).
5. UmmiNadiah Ahmad, AniShabri and ZahrahtulAmaniZakaria (2011).“Flood Frequency
Analysis of Annual Maximum Stream Flows using L-Moments and TL-Moments”, Applied
Mathematical Sciences, Vol. 5, June 2011, no. 5, (243 – 253).
6. Yevjevitch,V.(1972).“Probability and statistics in Hydrology”. Water Resources Publications,
Fort Collins. Colorado.
7. A text book on “Irrigation Engineering and Hydraulic Structures” by Santhosh Kumar Garg,
vol No.1, 2012.
8. A text book on “Hydrology” by Wisler&Brater, 1990.
9. Discharge data obtained from O/O Executive Engineer, Department of Irrigation and
Command Area Development (I & CAD), Visakhapatnam Circle.
10. Mustafa Hamid Abdulwahid and Kadhim Naief Kadhim, “Application of Inverse Routing
Methods to Euphrates River (Iraq)”, International Journal of Civil Engineering &
Technology (IJCIET), Volume 4, Issue 1, 2013, pp. 97 - 109, ISSN Print: 0976 – 6308,
ISSN Online: 0976 – 6316.
11. A.Raja Jeya Chandra Bose, Dr.T.R.Neelakantan and Dr.P.Mariappan, “Peak Factor in The
Design of Water Distribution- An Analysis”, International Journal of Civil Engineering &
Technology (IJCIET), Volume 3, Issue 2, 2012, pp. 123 - 129, ISSN Print: 0976 – 6308,
ISSN Online: 0976 – 6316,