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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: [email protected]

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

mailto:[email protected]

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.



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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.



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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/).



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3. Site’s Information:



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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)



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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



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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



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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


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



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Table No-10A: Computation of Expected Flood at the site of Ambala, Chhattisgarh

Sl_No.

Return Period (Tr)

in Years

Reduced Variate

(Yt)

Frequency


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


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



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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 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 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



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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


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



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y = 10031x + 24236 R² = 0.9703

0

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REDUCED VARIATE

POLAVARAM , ANDHRA

PRADESH

y = 2442x + 3903.3 R² = 0.9738

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REDUCED VARIATE

KONTA, CHHATTISGARH

y = 1089.8x + 1714.9 R² = 0.9276

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REDUCED VARIATE

SARADAPUT, ODISHA

y = 12071x + 23929 R² = 0.9681

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REDUCED VARIATE

PERRUR, TELENGANA

y = 6492.6x + 11412 R² = 0.9824

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REDUCED VARIATE

PATHAGUDEM ,

CHHATTISGARH

y = 747.91x + 887.56 R² = 0.9371

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REDUCED VARIATE

TUM NAR, CHHATTISGARH

y = 2936.2x + 4466.6 R² = 0.9797

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REDUCED VARIATE

CHINDNAR, CHHATTISGARH

y = 471.33x + 549.38 R² = 0.9167

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AM B ALA, CHHATTISGARH

6/P: Plot of Reduced Variate v/s River discharge:



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y = 352.94x + 584.98 R² = 0.9681

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REDUCED VARIATE

SONARPAL, CHHATTISGARH

y = 546.01x + 1383.2 R² = 0.9818

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REDUCED VARIATE

JAGDALPUR, CHHATTISGARH

y = 361.34x + 543.74 R² = 0.9393

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REDUCED VARIATE

M URTHAHANDI, ORISSA

y = 515.32x + 850.21 R² = 0.9807

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REDUCED VARIATE

NOWRANGPUR, ORISSA

y = 831.74x + 650.56 R² = 0.935

-1000

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REDUCED VARIATE

SOM ANPALLY, TELANGANA

y = 161.34x + 183.23 R² = 0.8084

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REDUCED VARIATE

SANGAM , TELANGANA

y = 896.32x + 541.95 R² = 0.8825

-2000

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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



ISSN NO: 1524-2560


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





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





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





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




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





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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





The above site (Jagdalpur, Chhattisgarh) results (Table no.-12A) show that the maximum






The above site (Murthahandi, Orissa) results (Table no.-13A) show that the maximum






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





The above site (Somanpally, Telangana) results (Table no.-15A) show that the maximum






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





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



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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.



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