Post on 03-Jul-2020
Flood Frequency Analysis Using Gumbel’s Method: A Case Study of
Lower Godavari River Division, India
Kousik Das Malakar
Centre for the Study of Regional Development,
School of Social Sciences, Jawaharlal Nehru University (JNU),
New Delhi, India.
E-mail: kdmalakargegr92@gmail.com
Abstract:
Quantification of peak flood (extreme-hydrological event) discharge of a channel or
river saying for a desired return period is a pre-requisite for design, planning and
management of hydraulic configurations like, dam, bridges, spillways, barrages etc. this
paper figure out the result of a study carried out at estimation the frequency of Lower
Godavari River division’s flood by using the methods of Gumbel distribution which is one of
the probability distribution methods used to model stream flows. The method was used to
model the annual maximum river discharge for a period of 25 years (1991-92 to 2015-16).
From the analysis of regression equation (R2) gives a values, which is shows that this
distributional method (Gumbel) is suitable for prophesy the expected flow in future on this
river.
Keywords: Flood Frequency; Lower Godavari River; Gumbel‘s method; Flood management
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/33
1. Introduction:
In the management of water resources projects, planner are often interested to quantify the
frequency and magnitude of floods that will occur at the project or management areas. Mainly,
'Flood' is the extreme hydrological event1. This events frequency analysis is one of the most
importance matter of the project area to define the relationship between magnitude and the
frequency of an event, with which that event is exceeded.
Before the estimation of Flood Frequency (FF) need to peak flow data, that‘s plays the
importance role in order to obtain a probability distribution of floods (Ahmad et al., 2011). Flood
Frequency Analysis2 (FFA) is commonly used by hydrologist and engineers and consist of
estimating flood peak for a set of non exceedance probabilities. FFA involves the fitting of a
probability model to the sample of annual flood peaks recorded over a period of observation, for a
project or management area. The model parameters established that, to predict the extreme events of
large recurrence interval.
In Hydrology, flood are the most common natural and anthropogenic disaster (Dilley et al.
2005). It is fall the negative impacts of both property and life that means its fall the affect on
societies around the world (Agritex, 2000; Dilley et al. 2005; Okaka, and Odhiambo, 2018). It was
calculated that, more than 1/3 of the word‘s land area are flood affected and 82% of the world
population (UNDP, 2009). In India, more than 88 lacks peoples are affected of the flood (NERC,
2019). There are main four river (Ganga, Godavari, Brahmaputra, Krishna) contributing the river
water system in India. The river of Godavari are the second largest river of India and it also known
as ‗longest river of South India‘. In the study area,Lower Godavari river basin divisions are
vulnerable for the flood (UNDP, 2005; Dandekar, 2014; IGBP, 2015).The area of lower Godavari
river basin divisions are subjected to flooding during monsoons (IMD, 2019).
FFA is the measurement or estimation of how often a specified even will occur. The
estimation ofFFA has various types of measurement processes like, Maximum Likelihood
estimators (MLE) (Bickel and Doksum, 1977); L-Moment Approach (Greenwood et. al 1979);
Generalised Extreme Value distribution (GEV) (Acreman and Sinclair, 1985); Expected Moments
Algoritham (EMA) (Cohn et. al, 1997); Gumbel mixed model (Yue et. al, 1999); Rainfall-runoff
Model (Lamb, 2005); Weibull formula (Selaman et. al, 2007); Log-Pearson Type III distribution
(Sathe, et. al. 2012); Probability plotting method (Connell and Mohssen, 2017); California Method
(Ganamala, and Kumar, 2017); Hazens Method (Ganamala, and Kumar, 2017); Gumbel‘s method
(Bhagat, 2017) and Probability Models (Okoli et. al., 2019). From this above all methods, Gumbel‘s
Method is most commonly used. So, this study were focus, used the peak discharge data and
selected the method of Gumbel‘s distribution which is widely used for predicting extreme
hydrological events such as floods (Zelenhasic, 1970; Haan, 1977; Shaw, 1983).
------------------------------------------ 1Extreme hydrological events (EHEs), such as droughts and floods. Its vary spatially and temporally in
nature (Corzo and Varouchakis, 2018). Extreme hydrological events represent a focus of considerable
interest in hydrology because such events have the potential to cause considerable harm to human
populations and their related activities (Knox and Kundzewicz, 1997). 2Flood frequency analysis is a measurement of prediction of flood. Its calculate the based on this river‘s
water discharge conditions. I am used this type of data and calculate the flood frequency on the river of
Godavari. Especially lower Godavari basin.
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/34
Map- 1k
Map- 2k
The main objective of the study was to carry out the Flood Frequency (FFA) Analysis for the Lower
Godavari River Divisions using the annual peak discharge data of Polavaram, (Andhra Pradesh);
Somanpally, Perrur, (Telengana); Sangam, Pathagudem, Tumnar, Chindnar, Konta, Ambala,
Sonarpal, Jagdalpur, Cherribeda, (Chhattisgarh) Murthahandi, Nowrangpur, Saradaput
(Odisha);whose are the regulating structure in the Lower Godavari River Basin Division. The
results of the FFA generated from the study gives detailed information of likely flow discharge to
be expected in the river at the various return periods based on the various stations‘ observed annual
data.
2. Study area and Data Collection:
Administrative setup: Asia (continent)—India (Sub continent) -- Maharashtra, Telangana,
Chhattisgarh, Odisha , Andhra Pradesh (River flowing sates / Map no.-1K).
Geographical setup: The Universe – Milky way galaxy – Goldilocks solar system zone3 –
The Earth – Pangia landmass system – Gondwana landmass system – North/East
hemisphere – coordinating system (15*N to 17*30‘ N / 74*E to 83*E) approx. (Malakar,
2019).
About Godavari River:
The Godavari River (Map no.- 2K) (1465 km) is India‘s second longest river after the
Ganga. The source of the river is Triambakeshwar, Maharashtra. The river of Godavari,
flowing in the Indian state of Maharashtra (48.6%), Telangana (18.8%), Chhattisgarh
(10.9%), Odisha (5.7%), Andhra Pradesh (5.6%) and finally, it estuaries in the Bay of
Bengal. And it has largest river of peninsular India, also known as the ‗Vridha Ganga4‘. This
river has been barricaded by a number of barrages and dams, restricting its flow.
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/35
Map- 3k
Actual study area:
The actual study area (Map no.- 3K)
is Lower Godavari River basin5
divisions. Its occupies the state of
Andhra Pradesh (1 site), Odisha (5
sites), Telangana (3 sites) and
Chhattisgarh (9 sites), and cover up
the total 18 sites. The study
wasbased on only 15 sites because
another 3 sites (Kiwaibalenga,
Kosaguma and Potteru) data are not
available. Following table (1/A)
shows the information about study
area‘s sites.
Database:
I have collected individually, Maximum river discharge data (15 sites) of lower Godavari river
division, data are collected from ‗Central Water Commission, Govt. of India‘ (Godavari Basin,
Daily discharge Data, Vol. - 1, 2017) 6
. And I also showing the location map (Map no. 2K) by using
the SRTM7 data base.
-------------------------------------------------
3In astronomy, based on the kepler data, the Goldilocks Zone refers to the habitable zone around a star where
the temperature is just right not too cold and not too hot/warm for liquid water to exist on this planate.
4Theword of ‗Vridha Ganga‘ is a comparative concept. Its comprise the river of Ganga. Because Godavari
river is a of major/longest/ largest river of south India. And its estuaries in the Bay of Bengal and this place
create a delta formation ‗Krishna-Godavari Delta‘, which is India's second largest delta after Sunderbans.
5Lower Godavari river basin division compares total 18 sites and its covers the state of Andhra Pradesh (1
site), Odisha (5 sites), Telangana (3 sites) and Chhattisgarh (9 sites). This area are flood affected in the
season of Monsoon and presently create the one another problem (sea level rise) of this river‘s estuaries area
(Dandekar, 2014).
6Central Water Commission, Govt. of India (Godavari Basin, Daily discharge Data, Vol. - 1, 2017)to
download the data through the link of:
(http://cwc.gov.in/sites/default/files/admin/10B_K&GBO_Hyderabad_Godavari_WYB_2015-16.pdf
). 7SRTM (Shuttle Radar Topography Mission) to download the DEM file link:
(http://srtm.csi.cgiar.org/srtmdata/).
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/36
3. Site’s Information:
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/37
𝑌𝑛̅̅̅̅
4.Gumbel’s Method:
There are various types of estimation methods are present (Table 2/A). But I am used the only one
fantastic estimation method is Gumbel‘s
method. Gumbel‘s measurement is a
statistical method often used for
predicting extreme hydrological events
such as floods (Zelenhasic, 1970; Haan,
1977; Shaw, 1983). In this study it has
been applied for fold frequency analysis
(FFA) because (i) the river of Godavari is
less regulated, and it is not significantly
affected by reservoir operations,
urbanization or diversions. (ii) flow data
cover a relatively long record (more than
10 years) and is of good quality (Mujere,
2006).
The equation of Gumbel‘s distribution as
well as to the procedure with a return
period T is given as,
XT x + Kt.σx ------ (I)
Where,
XT = Expected flood.
x Average of peak discharge.
σx = Standard deviation of the Sample
Size.
K = Frequency Factor, which is
expressed as,
σn ------ (II) K= YT --
In which, YT = Reduced Variate,
YT = - ln. ln. (Tr/ (Tr-1) ) ------ (III)
Here, Tr = Return Period,
Tr= (n+1/m) ----- (IV)
n= Number of years, m= Order numbers.
Table No.-2/A
Various Methods of Flood Frequency Analysis
(FFA)
Sl_No. Method's Name References
1 Maximum Likelihood
estimators (MLE)
Bickel and Doksum
(1977)
2 L-Moment Approach Greenwood et. al
(1979)
3 Generalised Extreme
Value distribution (GEV),
Acreman, M.C.,
Sinclair, C.D. (1985)
4 Expected Moments
Algoritham (EMA)
Cohn et. Al (1997)
5 Gumbel mixed model Yue et. Al (1999)
6 Rainfall-runoff Model Lamb, R(2005)
7 Weibull formula Selaman et. Al
(2007)
8 Log-Pearson Type III
distribution
Sathe, B.K. (2012)
9 California Method Ganamala, K. and
Kumar, P.S. (2017)
10 Probability plotting
method
Connell, R.J. and
Mohssen, M., (2017)
11 Hazens Method Ganamala, K. and
Kumar, P.S. (2017)
12 Gumbel’s method Bhagat, N. (2017)
13 Probability Models Okoli et. Al (2019)
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/38
𝑌𝑛̅̅̅̅
𝑌𝑛̅̅̅̅
5. Methodology:
The discharge data of lower Godavari division, from at least 20 years were considered for the flood
frequency analysis applying the Gumbel‘s distribution. The steps to estimate the design the flood
for any return period,
Step-I: Annual peak flood data was assembled at least 20years (1991-92/1992-93 to 2015-16).
Step-II: From the maximum flood data for n years, the mean(x ) and standard deviation (σx) are
computed using the excel format; Mean (Average) and standard deviation (stdev.p).
Step-III: From the Gumbel’s Extreme Value distribution table, collected the values of
and Sn.
Step-IV: From the given return period Tr , the reduced variate YT is computed using equation (III) .
Step-V: From the ,Sn and YT , the flood frequency factors (K) is computed using equation
(II).
Step-VI: With used of equation (I), the magnitude of flood is computed. (Expected flood; XT)
Step-VII: A plot of the reduced variate and magnitude of flood is made on cartographically. If an
eye fits to this plot suggest a straight line, then it is reasonable to conclude that the Gumbel‘s
distribution is a good fit for the observed flood data.
6. Results:
The Gumbel‘s distribution analysis was done following the above methodology (point no. 5) and
calculate the results on each sites and its showing in the format of tubulised format. Also plot of
reduced variate and river discharge was plotted of each site‘s of Lower Godavari Divisions, which
is showing in cartographically. Therefore, the results are showing in bellow
Table No.- 3A;Computation of Expected Flood at the site of Polavaram, Andhra Pradesh
Sl_No. Return
Period
(Tr) in
Years
Reduced Variate
(Yt)
Frequency Factors
(K)
Expected flood (XT)
Yt=-ln.ln(Tr/Tr-
1)
K(T)= ((Yt-Yn)/Sn))
XT= Mean of A1 (X) +KT*Sx
1 2 0.36651292 -0.150606578 27887.085
2 5 1.49993999 0.88780576 39429.060
3 10 2.25036733 1.575325082 47070.851
4 20 2.97019525 2.234810123 54401.041
5 50 3.90193866 3.088445862 63889.220
6 100 4.60014923 3.728125723 70999.276
7 150 5.00729266 4.101138492 75145.320
8 200 5.29581214 4.3654715 78083.387
9 300 5.70211349 4.73771277 82220.857
10 500 6.21360726 5.206328231 87429.527
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/39
Table No.- 4A; Computation of Expected Flood at the site of Konta, Chhattisgarh
Sl_No.
Return Period
(Tr) in Years
Reduced Variate
(Yt) Frequency Factors (K) Expected flood (XT)
Yt=-ln.ln(Tr/Tr-
1) K(T)= ((Yt-Yn)/Sn))
XT= Mean of A1 (X)
+KT*Sx
1 2 0.36651292 -0.150606578 4792.852
2 5 1.49993999 0.88780576 7597.601
3 10 2.25036733 1.575325082 9454.589
4 20 2.97019525 2.234810123 11235.856
5 50 3.90193866 3.088445862 13541.524
6 100 4.60014923 3.728125723 15269.298
7 150 5.00729266 4.101138492 16276.805
8 200 5.29581214 4.3654715 16990.767
9 300 5.70211349 4.73771277 17996.190
10 500 6.21360726 5.206328231 19261.919
Table No.- 5A; Computation of Expected Flood at the site of Saradaput, Odisha
Sl_No.
Return
Period (Tr)
in Years
Reduced Variate
(Yt)
Frequency Factors (K)
Expected flood (XT)
Yt=-ln.ln(Tr/Tr-
1) K(T)= ((Yt-Yn)/Sn)) XT= Mean of A1 (X) +KT*Sx
1 2 0.36651292 -0.150606578 2107.436
2 5 1.49993999 0.88780576 3389.828
3 10 2.25036733 1.575325082 4238.884
4 20 2.97019525 2.234810123 5053.318
5 50 3.90193866 3.088445862 6107.520
6 100 4.60014923 3.728125723 6897.496
7 150 5.00729266 4.101138492 7358.150
8 200 5.29581214 4.3654715 7684.590
9 300 5.70211349 4.73771277 8144.291
10 500 6.21360726 5.206328231 8723.010
Table No.-6A; Computation of Expected Flood at the site of Perrur, Telengana
Sl_No.
Return
Period (Tr)
in Years
Reduced Variate
(Yt)
Frequency
Factors (K) Expected flood (XT)
Yt=-ln.ln(Tr/Tr-1)
K(T)= ((Yt-
Yn)/Sn)) XT= Mean of A1 (X) +KT*Sx
1 2 0.36651292 -0.150606578 28320.973
2 5 1.49993999 0.88780576 42225.348
3 10 2.25036733 1.575325082 51431.255
4 20 2.97019525 2.234810123 60261.781
5 50 3.90193866 3.088445862 71691.991
6 100 4.60014923 3.728125723 80257.326
7 150 5.00729266 4.101138492 85251.979
8 200 5.29581214 4.3654715 88791.407
9 300 5.70211349 4.73771277 93775.730
10 500 6.21360726 5.206328231 100050.506
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/40
Table No.- 7A: Computation of Expected Flood at the site of Pathagudem, Chhattisgarh
Sl_No.
Return Period (Tr)
in Years
Reduced Variate
(Yt) Frequency Factors (K) Expected flood (XT)
Yt=-ln.ln(Tr/Tr-
1) K(T)= ((Yt-Yn)/Sn))
XT= Mean of A1 (X)
+KT*Sx
1 2 0.36651292 -0.150606578 13781.770
2 5 1.49993999 0.88780576 21205.818
3 10 2.25036733 1.575325082 26121.183
4 20 2.97019525 2.234810123 30836.120
5 50 3.90193866 3.088445862 36939.122
6 100 4.60014923 3.728125723 41512.463
7 150 5.00729266 4.101138492 44179.288
8 200 5.29581214 4.3654715 46069.116
9 300 5.70211349 4.73771277 48730.426
10 500 6.21360726 5.206328231 52080.756
Table No.-8A: Computation of Expected Flood at the site of Tumnar, Chhattisgarh
Sl_No. Return Period
(Tr) in Years
Reduced Variate (Yt) Frequency Factors (K) Expected flood (XT)
Yt=-ln.ln(Tr/Tr-1) K(T)= ((Yt-Yn)/Sn)) XT= Mean of A1 (X)
+KT*Sx
1 2 0.366513 -0.15012 1154.699
2 5 1.49994 0.89317 2049.268
3 10 2.250367 1.583917 2641.55
4 20 2.970195 2.246498 3209.681
5 50 3.901939 3.104141 3945.068
6 100 4.600149 3.746824 4496.138
7 150 5.007293 4.121588 4817.48
8 200 5.295812 4.387161 5045.196
9 300 5.702113 4.76115 5365.874
10 500 6.213607 5.231965 5769.575
Table No.-9A; Computation of Expected Flood at the site of Chindnar, Chhattisgarh
Sl_No.
Return Period
(Tr) in Years
Reduced
Variate (Yt)
Frequency
Factors (K) Expected flood (XT)
Yt=-
ln.ln(Tr/Tr-
1)
K(T)= ((Yt-
Yn)/Sn)) XT= Mean of A1 (X) +KT*Sx
1 2 0.36651292 -0.150606578 5537.739
2 5 1.49993999 0.88780576 8899.818
3 10 2.25036733 1.575325082 11125.807
4 20 2.97019525 2.234810123 13261.029
5 50 3.90193866 3.088445862 16024.854
6 100 4.60014923 3.728125723 18095.953
7 150 5.00729266 4.101138492 19303.660
8 200 5.29581214 4.3654715 20159.494
9 300 5.70211349 4.73771277 21364.703
10 500 6.21360726 5.206328231 22881.945
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/41
Table No-10A: Computation of Expected Flood at the site of Ambala, Chhattisgarh
Sl_No.
Return Period (Tr)
in Years
Reduced Variate
(Yt)
Frequency
Factors (K) Expected flood (XT)
Yt=-ln.ln(Tr/Tr-1)
K(T)= ((Yt-
Yn)/Sn))
XT= Mean of A1 (X)
+KT*Sx
1 2 0.36651292 -0.14965043 1450.535
2 5 1.49993999 0.89875126 2008.523
3 10 2.25036733 1.592884402 2377.960
4 20 2.97019525 2.258713578 2732.332
5 50 3.90193866 3.120561149 3191.031
6 100 4.60014923 3.766394623 3534.761
7 150 5.00729266 4.142995712 3735.198
8 200 5.29581214 4.409871559 3877.237
9 300 5.70211349 4.785693727 4077.260
10 500 6.21360726 5.25881719 4329.069
Table no.-11A :Computation of Expected Flood at the site of Sonarpal, Chhattisgarh
Sl_No.
Return Period (Tr)
in Years
Reduced Variate
(Yt)
Frequency Factors
(K) Expected flood (XT)
Yt=-ln.ln(Tr/Tr-
1) K(T)= ((Yt-Yn)/Sn))
XT= Mean of A1 (X)
+KT*Sx
1 2 0.36651292 -0.150116973 713.393
2 5 1.49993999 0.893170091 1119.980
3 10 2.25036733 1.583916907 1389.176
4 20 2.97019525 2.246497836 1647.395
5 50 3.90193866 3.104140885 1981.634
6 100 4.60014923 3.746823662 2232.098
7 150 5.00729266 4.121587504 2378.150
8 200 5.29581214 4.387161398 2481.649
9 300 5.70211349 4.761150118 2627.399
10 500 6.21360726 5.231965449 2810.884
Table No.-12A; Computation of Expected Flood at the site of Jagdalpur, Chhattisgarh
Sl_No.
Return Period
(Tr) in Years
Reduced Variate
(Yt)
Frequency Factors
(K) Expected flood (XT)
Yt=-ln.ln(Tr/Tr-1) K(T)= ((Yt-Yn)/Sn)) XT= Mean of A1 (X) +KT*Sx
1 2 0.36651292 -0.150606578 1582.509
2 5 1.49993999 0.88780576 2207.066
3 10 2.25036733 1.575325082 2620.577
4 20 2.97019525 2.234810123 3017.226
5 50 3.90193866 3.088445862 3530.648
6 100 4.60014923 3.728125723 3915.386
7 150 5.00729266 4.101138492 4139.736
8 200 5.29581214 4.3654715 4298.720
9 300 5.70211349 4.73771277 4522.606
10 500 6.21360726 5.206328231 4804.456
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/42
Table No.-13A: Computation of Expected Flood at the site of Murthahandi, Orissa
Sl_No.
Return Period
(Tr) in Years
Reduced
Variate (Yt) Frequency Factors (K) Expected flood (XT)
Yt=-ln.ln(Tr/Tr-
1) K(T)= ((Yt-Yn)/Sn)) XT= Mean of A1 (X) +KT*Sx
1 2 0.36651292 -0.150606578 674.282
2 5 1.49993999 0.88780576 1096.838
3 10 2.25036733 1.575325082 1376.607
4 20 2.97019525 2.234810123 1644.968
5 50 3.90193866 3.088445862 1992.333
6 100 4.60014923 3.728125723 2252.635
7 150 5.00729266 4.101138492 2404.423
8 200 5.29581214 4.3654715 2511.987
9 300 5.70211349 4.73771277 2663.461
10 500 6.21360726 5.206328231 2854.152
Table No.-14A: Computation of Expected Flood at the site of Nowrangpur, Orissa
Sl_No.
Return Period
(Tr) in Years
Reduced Variate
(Yt)
Frequency Factors
(K)
Expected flood (XT)
Yt=-ln.ln(Tr/Tr-
1) K(T)= ((Yt-Yn)/Sn)) XT= Mean of A1 (X) +KT*Sx
1 2 0.36651292 -0.150606578 1038.241
2 5 1.49993999 0.88780576 1627.994
3 10 2.25036733 1.575325082 2018.462
4 20 2.97019525 2.234810123 2393.008
5 50 3.90193866 3.088445862 2877.820
6 100 4.60014923 3.728125723 3241.118
7 150 5.00729266 4.101138492 3452.966
8 200 5.29581214 4.3654715 3603.091
9 300 5.70211349 4.73771277 3814.501
10 500 6.21360726 5.206328231 4080.645
Table No.-15A: Computation of Expected Flood at the site of Somanpally, Telangana
Sl_No.
Return
Period (Tr) in
Years
Reduced
Variate (Yt)
Frequency Factors (K)
Expected flood (XT)
Yt=-
ln.ln(Tr/Tr-1) K(T)= ((Yt-Yn)/Sn)) XT= Mean of A1 (X) +KT*Sx
1 2 0.36651292 -0.150606578 950.703
2 5 1.49993999 0.88780576 1925.616
3 10 2.25036733 1.575325082 2571.093
4 20 2.97019525 2.234810123 3190.251
5 50 3.90193866 3.088445862 3991.686
6 100 4.60014923 3.728125723 4592.250
7 150 5.00729266 4.101138492 4942.453
8 200 5.29581214 4.3654715 5190.622
9 300 5.70211349 4.73771277 5540.100
10 500 6.21360726 5.206328231 5980.060
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/43
Table No.-16A; Computation of Expected Flood at the site of Sangam, Telangana
Sl_No.
Return Period
(Tr) in Years
Reduced
Variate (Yt) Frequency Factors (K) Expected flood (XT)
Yt=-
ln.ln(Tr/Tr-1) K(T)= ((Yt-Yn)/Sn)) XT= Mean of A1 (X) +KT*Sx
1 2 0.36651292 0.106240987 287.960
2 5 1.49993999 1.172694756 491.344
3 10 2.25036733 1.878779947 626.002
4 20 2.97019525 2.556073814 755.169
5 50 3.90193866 3.432761251 922.362
6 100 4.60014923 4.089715117 1047.650
7 150 5.00729266 4.472800776 1120.709
8 200 5.29581214 4.744271869 1172.481
9 300 5.70211349 5.126565194 1245.389
10 500 6.21360726 5.607835213 1337.172
Table No.- 17A: Computation of Expected Flood at the site of Cherribeda, Chhattisgarh
Sl_No.
Return Period (Tr) in Years
Reduced Variate
(Yt)
Frequency Factors
(K) Expected flood (XT)
Yt=-ln.ln(Tr/Tr-1)
K(T)= ((Yt-
Yn)/Sn))
XT= Mean of A1
(X) +KT*Sx
1 2 0.36651292 0.106240987 1118.956
2 5 1.49993999 1.172694756 2200.428
3 10 2.25036733 1.878779947 2916.458
4 20 2.97019525 2.556073814 3603.290
5 50 3.90193866 3.432761251 4492.324
6 100 4.60014923 4.089715117 5158.530
7 150 5.00729266 4.472800776 5547.010
8 200 5.29581214 4.744271869 5822.305
9 300 5.70211349 5.126565194 6209.982
10 500 6.21360726 5.607835213 6698.030
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/44
y = 10031x + 24236 R² = 0.9703
0
10000
20000
30000
40000
50000
60000
- 2 - 1 0 1 2 3 4
RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
POLAVARAM , ANDHRA
PRADESH
y = 2442x + 3903.3 R² = 0.9738
0
2000
4000
6000
8000
10000
12000
14000
- 2 - 1 0 1 2 3 4
RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
KONTA, CHHATTISGARH
y = 1089.8x + 1714.9 R² = 0.9276
0
1000
2000
3000
4000
5000
6000
7000
- 2 - 1 0 1 2 3 4
RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
SARADAPUT, ODISHA
y = 12071x + 23929 R² = 0.9681
0
10000
20000
30000
40000
50000
60000
70000
- 2 - 1 0 1 2 3 4
RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
PERRUR, TELENGANA
y = 6492.6x + 11412 R² = 0.9824
0
10000
20000
30000
40000
- 2 - 1 0 1 2 3 4
RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
PATHAGUDEM ,
CHHATTISGARH
y = 747.91x + 887.56 R² = 0.9371
0
1000
2000
3000
4000
- 2 - 1 0 1 2 3 4
RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
TUM NAR, CHHATTISGARH
y = 2936.2x + 4466.6 R² = 0.9797
0
5000
10000
15000
- 2 - 1 0 1 2 3 4
RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
CHINDNAR, CHHATTISGARH
y = 471.33x + 549.38 R² = 0.9167
0
500
1000
1500
2000
2500
- 2 - 1 0 1 2 3 4
RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
AM B ALA, CHHATTISGARH
6/P: Plot of Reduced Variate v/s River discharge:
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/45
y = 352.94x + 584.98 R² = 0.9681
0
500
1000
1500
2000
- 2 - 1 0 1 2 3 4 RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
SONARPAL, CHHATTISGARH
y = 546.01x + 1383.2 R² = 0.9818
0
1000
2000
3000
4000
- 2 - 1 0 1 2 3 4 RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
JAGDALPUR, CHHATTISGARH
y = 361.34x + 543.74 R² = 0.9393
0
500
1000
1500
2000
- 2 - 1 0 1 2 3 4 RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
M URTHAHANDI, ORISSA
y = 515.32x + 850.21 R² = 0.9807
0
1000
2000
3000
- 2 - 1 0 1 2 3 4
RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
NOWRANGPUR, ORISSA
y = 831.74x + 650.56 R² = 0.935
-1000
0
1000
2000
3000
4000
- 2 - 1 0 1 2 3 4 RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
SOM ANPALLY, TELANGANA
y = 161.34x + 183.23 R² = 0.8084
0
500
1000
1500
- 2 - 1 0 1 2 3 4 RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
SANGAM , TELANGANA
y = 896.32x + 541.95 R² = 0.8825
-2000
0
2000
4000
6000
- 2 - 1 0 1 2 3 4
RIV
ER
DIS
CH
AR
GE
(C
UM
EC
S)
REDUCED VARIATE
CHERRIB EDA,
CHHATTISGARH Figure were managed by based on
Reduced Variate v/s River discharge
quantities of each sites respectively.
The results (Table no.- 3A to 17A ) show the expected floods in the river reach (each sites)
for return periods of 2yrs, 5yrs, 10yrs, 20yrs, 50yrs, 100yrs, 150yrs, 200yrs, 300yrs and 500yrs.
From here, other values not shown in chart can be extrapolated or can be computed using the above
mentioned method.
The above site (Polavaram, Andhra Pradesh) results (Table no.-3A) show that the
maximum flow of 52811 cumecs was recorded in 2006-07 while the lowest flow of 11249
cumecswas recorded in 2009-10. The 25 –years mean river discharge is 29561.08 cumecs with a
CV (Coefficient of Variation) is 37.60%. Finally, using the Gumbel‘s distribution analysis, the
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/46
floods with different recurrence intervals were also computed and the scatter same are shown in
between Reduced Variate v/s River discharge (Point no: 6/P respectively).
The above site (Konta, Chhattisgarh) results (Table no.-4A) show that the maximum flow
of 12181 cumecs was recorded in 2006-07 while the lowest flow of 1696 cumecswas recorded in
1993-94. The 25 –years mean river discharge is 5199.64 cumecs with a CV (Coefficient of
Variation) is 51.94%. Finally, using the Gumbel‘s distribution analysis, the floods with different
recurrence intervals were also computed and the scatter same are shown in between Reduced
Variate v/s River discharge (Point no: 6/P respectively).
The above site (Saradaput, Odisha) results (Table no.-5A) show that the maximum flow of
6480 cumecs was recorded in 2006-07 while the lowest flow of 879.7 cumecswas recorded in
1997-98. The 25 –years mean river discharge is 2293.43 cumecs with a CV (Coefficient of
Variation) is 53.84%. Finally, using the Gumbel‘s distribution analysis, the floods with different
recurrence intervals were also computed and the scatter same are shown in between Reduced
Variate v/s River discharge (Point no: 6/P respectively).
The above site (Perrur, Telengana) results (Table no.-6A) show that the maximum flow of
57245 cumecs was recorded in 2013-14 while the lowest flow of 8996 cumecswas recorded in
1996-97. The 25 –years mean river discharge is 30337.60 cumecs with a CV (Coefficient of
Variation) is 44.13%. Finally, using the Gumbel‘s distribution analysis, the floods with different
recurrence intervals were also computed and the scatter same are shown in between Reduced
Variate v/s River discharge (Point no: 6/P respectively).
The above site (Pathagudem, Chhattisgarh) results (Table no.-7A) show that the
maximum flow of 35392cumecs was recorded in 2006-07 while the lowest flow of 4564
cumecswas recorded in 1996-97. The 25 –years mean river discharge is 14858.52 cumecs with a
CV (Coefficient of Variation) is 48.11%. Finally, using the Gumbel‘s distribution analysis, the
floods with different recurrence intervals were also computed and the scatter same are shown in
between Reduced Variate v/s River discharge (Point no: 6/P respectively).
The above site (Tumnar, Chhattisgarh) results (Table no.-8A) show that the maximum
flow of 3584cumecs was recorded in 2004-05 while the lowest flow of 407 cumecswas recorded in
2011-12. The 24 –years mean river discharge is 1283.42 cumecs with a CV (Coefficient of
Variation) is 66.81%. Finally, using the Gumbel‘s distribution analysis, the floods with different
recurrence intervals were also computed and the scatter same are shown in between Reduced
Variate v/s River discharge (Point no: 6/P respectively).
The above site (Chindnar, Chhattisgarh) results (Table no.-9A) show that the maximum
flow of 13351cumecs was recorded in 2006-07 while the lowest flow of 1508 cumecswas recorded
in 1998-99. The 25 –years mean river discharge is 6025.36 cumecs with a CV (Coefficient of
Variation) is 53.73%. Finally, using the Gumbel‘s distribution analysis, the floods with different
recurrence intervals were also computed and the scatter same are shown in between Reduced
Variate v/s River discharge (Point no: 6/P respectively).
The above site (Ambala, Chhattisgarh) results (Table no.-10A) show that the maximum
flow of 2243cumecs was recorded in 2006-07 while the lowest flow of 145.5 cumecswas recorded
in 1998-99. The 23 –years mean river discharge is 1530.18 cumecs with a CV (Coefficient of
Variation) is 34.78%. Finally, using the Gumbel‘s distribution analysis, the floods with different
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/47
recurrence intervals were also computed and the scatter same are shown in between Reduced
Variate v/s River discharge (Point no: 6/P respectively).
The above site (Sonarpal, Chhattisgarh) results (Table no.-11A) show that the maximum
flow of 1546 cumecs was recorded in 2010-11 while the lowest flow of 245.1cumecswas recorded
in 2011-12. The 24 –years mean river discharge is 711.90 cumecs with a CV (Coefficient of
Variation) is 50.48%. Finally, using the Gumbel‘s distribution analysis, the floods with different
recurrence intervals were also computed and the scatter same are shown in between Reduced
Variate v/s River discharge (Point no: 6/P respectively).
The above site (Jagdalpur, Chhattisgarh) results (Table no.-12A) show that the maximum
flow of 2956 cumecs was recorded in 1992-93 while the lowest flow of 831.6cumecswas recorded
in 2009-10. The 25 –years mean river discharge is 1673.09 cumecs with a CV (Coefficient of
Variation) is 35.95%. Finally, using the Gumbel‘s distribution analysis, the floods with different
recurrence intervals were also computed and the scatter same are shown in between Reduced
Variate v/s River discharge (Point no: 6/P respectively).
The above site (Murthahandi, Orissa) results (Table no.-13A) show that the maximum
flow of 1882 cumecs was recorded in 2010-11 while the lowest flow of 295.9cumecswas recorded
in 2009-10. The 25 –years mean river discharge is 735.57 cumecs with a CV (Coefficient of
Variation) is 55.32%. Finally, using the Gumbel‘s distribution analysis, the floods with different
recurrence intervals were also computed and the scatter same are shown in between Reduced
Variate v/s River discharge (Point no: 6/P respectively).
The above site (Nowrangpur, Orissa) results (Table no.-14A) show that the maximum flow
of 2510 cumecs was recorded in 1992-93 while the lowest flow of 365.8cumecswas recorded in
2011-12. The 25 –years mean river discharge is 1123.78 cumecs with a CV (Coefficient of
Variation) is 50.54%. Finally, using the Gumbel‘s distribution analysis, the floods with different
recurrence intervals were also computed and the scatter same are shown in between Reduced
Variate v/s River discharge (Point no: 6/P respectively).
The above site (Somanpally, Telangana) results (Table no.-15A) show that the maximum
flow of 3336 cumecs was recorded in 2006-07 while the lowest flow of 25.79cumecswas recorded
in 2004-05. The 25 –years mean river discharge is 1092.10 cumecs with a CV (Coefficient of
Variation) is 85.96%. Finally, using the Gumbel‘s distribution analysis, the floods with different
recurrence intervals were also computed and the scatter same are shown in between Reduced
Variate v/s River discharge (Point no: 6/P respectively).
The above site (Sangam, Telangana) results (Table no.-16A) show that the maximum flow
of 970.6 cumecs was recorded in 2005-06 while the lowest flow of 92.57cumecswas recorded in
1997-98. The 20 –years mean river discharge is 267.70 cumecs with a CV (Coefficient of
Variation) is 71.24%. Finally, using the Gumbel‘s distribution analysis, the floods with different
recurrence intervals were also computed and the scatter same are shown in between Reduced
Variate v/s River discharge (Point no: 6/P respectively).
The above site (Cherribeda, Chhattisgarh) results (Table no.-17A) show that the
maximum flow of 4348 cumecs was recorded in 2014-15 while the lowest flow of 76.57cumecswas
recorded in 1998-99. The 20 –years mean river discharge is 1011.22 cumecs with a CV (Coefficient
of Variation) is 100.28%. Finally, using the Gumbel‘s distribution analysis, the floods with
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/48
different recurrence intervals were also computed and the scatter same are shown in between
Reduced Variate v/s River discharge (Point no: 6/P respectively).
7. Applicability of Flood Frequency analysis:
This information (FFA) will be very useful for various management purposes such as
floodplain management, to designing of bridge, dam, spillways, barrages etc., to protect the public,
minimised the flood related costs of Government and Socio-public sector, to maintain (designing
and locating) the Assessing Hazards (AH) and Hydraulic Structures (HS) to the development of
flood affected plain. And this information also include the design of flood control structures which
will be reduce flood related disaster in the plain or catchment area as well as assist the considerably
in storm water resource management along with social-economic benefits.
8. Conclusion:
From the flood frequency analysis carried out for lower Godavari division based on 15th
sites and used the at least 25 year‘s annual peak flow data. Figure (point no 6/P respectively); shows
a plot of the reduced Variate and river discharge on each site‘s. From the trend line equation, the
value of ―r‖ (Table no.-18A) shows that the pattern of the scatter trend and that Gumbel‘s
distribution method is suitable for predicting expected flow in the river.
Table No.- 18A: Values of ‘r’ of each site’s
Sl_No. Sites Name Value of ‘r’ Sl_No. Sites Name Value of ‘r’
1 Polavaram 0.97 9 Sonarpal 0.96
2 Konta 0.97 10 Jagdalpur 0.98
3 Saradaput 0.92 11 Murthahandi 0.93
4 Perrur 0.96 12 Nowrangpur 0.98
5 Pathagudem 0.98 13 Somanpally 0.93
6 Tumnar 0.93 14 Sangam 0.80
7 Chindnar 0.97 15 Cherribeda 0.88
8 Ambala 0.91 Source: Scatter figure (Point no 6/P) respectively.
This prediction of flood in each site‘s can be utilized in the designing of important hydraulic
structures and bridges in the river reach. Also in case of extreme floods emergency evacuation of
people can be carried out well in advance. Similar study can also be carried out on some other study
region, as the method used for the study is having a constant formula, which remains spatially
constant.
Acknowledgement
The author thank anonymous reviewer for constructive comments. Also thanks toDr.
Sreekesh, Dr. Sanjeev Sharma (CSRD, JNU) and Dr. Nieuwaal (Director Delta Alliance, The
Netherlands) for the theoretical and applied helps of this paper.
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/49
7. References:
1. Acreman, M.C., Sinclair, C.D., (1985): Classification of drainage basins according to their
physical characteristics; an application for flood frequency analysis in Scotland. Journal of
Hydrology, Vol. 84, pp. 365-380.
2. Agritex, H., (2000): Assessment of the Impact of Cyclone Eline (February 2000) on the
Food, Agriculture and Natural resource Sector in Zimbabwe.
3. Ahmad, U.N., Shabri, A., and Zakaria, Z.A., (2011): Flood frequency analysis of annual
maximum stream flows using L-Moments and TL-Moments. Applied Mathematical
Sciences, vol. 5, pp. 243– 253.
4. Bhagat, N., (2017): Flood Frequency Analysis Using Gumbel's Distribution Method: A Case
Study of Lower Mahi Basin, India. Journal of Water Resources and Ocean Science, Vol.- 6,
pp. 51-54.
5. Bickel, P.J., Doksum, K.A., (1977): Mathematical Statistics: Basic Ideas and Selected
Topics. Holden-Day, San Francisco.
6. Cohn, T.A., Lane, W.L., Baier, W.G., (1997): An algorithm for computing moments-based
flood quantile estimates when historical flood information is available. Water Resources
Research, vol.-33, pp. 2089–2096.
7. Connell, R.J. and Mohssen, M., (2017): Estimation of Plotting Position for Flood Frequency
Analysis. HWRS Conference paper, pp.1-4.
8. Corzo, G. Varouchakis, E., (2018): Spatiotemporal Analysis of Extreme Hydrological
Events. Elsevier, pp. 179. eBook ISBN: 9780128117316.
9. Dandekar, P., (2014): Shrinking and Sinking Deltas: Major role of Dams in delta subsidence
and effective sea level rise. South Asia Network on Dams, Rivers and People, pp. 2-16.
10. Deltas at Risk. International Geosphere-Biosphere Programme. Retrieved 21 May 2019.
11. Dilley, M., Chen, R.S., Deichmann, U., Lerner-Lam, A.L., and Arnold, M., (2005): Natural
disaster hotspots: A global risk analysis. World Bank, pp.1.
12. Ganamala, K. and Kumar, P.S., (2017): A case study on flood frequency analysis.
International Journal of Civil Engineering and Technology, Vol.-8, pp. 1762-68.
13. Greenwood, J. A., Landwehr, J. M., Matalas, N. C., and Wallis, J. R. (1979): Probability
weighted moments: Definition and relation to parameters of several distributions expressible
in inverse form. Water Resour. Res, Vol.-15, pp.1049–1054.
14. Haan, C.T., (1997): Statistical Methods in Hydrology. Iowa State University Press, Ames,
Iowa. I '. Haefner, Journal of Water,
15. IMD (Indian Meteorological Department), Government of India (2019)
16. International Geosphere-Biosphere Programme; IGBP, (2015). Link: http://www.igbp.net/
17. Knox, J.C., and Kundzewicz, Z.W., (2009): Extreme hydrological events, palaeoinformation
and climate change. Hydrological Sciences Journal, Vol-42, pp. 765.
18. Lamb, R., (2005): Rainfall-runoff Modeling for Flood Frequency Estimation. Encyclopedia
of Hydrological Sciences, pp. 1-5.
19. Malakar, K.D., (2019): Regional Studies: some thinkable subjective discussion, LAP
LAMBERT Academic Publishing, Mauritius. pp. 18, 20. ISBN: 978-620-0-24914-2.
20. Mujer, N., (2006): Flood Frequency Analysis Using the Gumbel Distribution. International
Journal on Computer Science and Engineering, Vol.-3, pp. 2724-27.
21. National Emergency Response Centre; NERC , (2019) link: https://ndma.gov.in/en/
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/50
22. Okaka, F.O., and Odhiambo, B.D.O., (2018): Relationship between Flooding and Out Break
of Infectious Diseasesin Kenya: A Review of the Literature. Journal of Environmental and
Public Health, pp. 1-2.
23. Okoli, K., Breinl, K., Mazzoleni, M., and Baldassarre, G.D., (2019): Design Flood
Estimation: Exploring the Potentials and Limitations of Two Alternative Approaches.
Journal of Water, Vol-11, pp. 1-11.
24. Sathe, B.K., Khire, M.V., Sankhua, R.N., (2012): Flood Frequency Analysis of Upper
Krishna River Basin 8atchment area using Log Pearson Type III Distribution. IOSR Journal
of Engineering, Vol-2, pp. 69-69.
25. Selaman, O.S., Said, S., and Putuhena, F.J., (2007): Flood frequency analysis for sarawak
using weibull, gringorten and l-moments formula. The Institution of Engineers, Malaysia,
Vol. 68, pp.43-46.
26. Shaw, E. M. (1983): Hydrology in Practice. Van Nostrand Reinhold, UK.
27. UN Development Programme (2005): India: Andhra Pradesh Flood 2005 situation report.
(https://reliefweb.int/report/india/india-andhra-pradesh-flood-2005-situation-report-21sep-
2005)
28. UNDP (2005): United Nations Global Assessment Report on Disaster Risk Reduction.
International Strategy for Disaster Reduction, UNDP.
29. UNDP (2009): United Nations Global Assessment Report on Disaster Risk Reduction.
International Strategy for Disaster Reduction, UNDP, pp.7-8.
30. Yue, S., Ouarda, T.B.M.J., Bobee, B., Legender, P., Burneau, P., (1999): The Gumbel
mixed model for flood frequency analysis. Journal of Hydrology, Vol- 226, pp. 88–100.
31. Zelenhasic, E. (1970): Theoretical Probability Distributions for Flood Peaks. Colorado
University Press, Colorado.
Journal of Scientific Computing
Volume 9 Issue 2 2020
ISSN NO: 1524-2560
http://jscglobal.org/51