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International Journal of
eISSN: 2576-4454

Hydrology

Research Article Volume 3 Issue 6

Rainfall probability analysis for crop planning in Rayagada district of Odisha, India

Subudhi CR,1 Nibedita Jena,2 Sukanya Suryavanshi,2 Subudhi R2

1Professor, CAET, OUAT, India
2Ex student, CAET, OUAT, India

Correspondence: Subudhi CR, Professor, CAET, OUAT, Bhubaneswar-751003, Odisha, India

Received: November 07, 2019 | Published: December 26, 2019

Citation: Subudhi CR, Jena N, Suryavanshi S, et al. Rainfall probability analysis for crop planning in Rayagada district of Odisha, India. Int J Hydro.2019;3(6):507-511. DOI: 10.15406/ijh.2019.03.00217

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Abstract

This study was under taken in the U.G. thesis work in the Dept. Of SWCE, CAET, OUAT, Bhubaneswar during the year 2018-19. Rayagada district has a total geographical area of 7584.7sq.km. Rayagada district has latitude of 26oN and a longitude of 94o20’E. The average rainfall at Rayagada district is around 1340.3mm, though it receives high amount rainfall but most of the rainfall occurred during kharif. So most of the crops get low yield due to improper crop planning. Thus, this study is proposed to be undertaken with the following objective: Probability analysis of annual, seasonal and monthly rainfall data of Rayagada district. So rainfall data were collected from OUAT, Agril Meteorology Dept. from 2001 to 2017(17years) monthly, seasonal and annual rainfall were analyzed .Probability analysis have been made and equations were fitted to different distributions and best fitted equations were tested. Monthly, Annual and seasonal probability analysis of rainfall data shows the probability rainfall distribution of Rayagada district in different months, years and seasons. It is observed that rainfall during June to Sep is slightly less than 1000mm and cropping pattern like paddy(110days) may be followed by mustard is suitable to this region. Also if the kharif rain can be harvested and it can be reused for another rabi crop by using sprinkler or drip irrigation, which will give benefit to the farmers. Annual rainfall of Rayagada district is 1340.3mm at 50% probability level.

Keywords: rainfall, probability analysis, crop planning

Introduction

Rayagada district has a total geographical area of 7584.7sq.km. Rayagada district has latitude of 26oN and a longitude of 94o20’E. The average rainfall at Rayagada district is 1340.3mm, most of the rainfall occurred during kharif. Thus, this study is proposed to be undertaken with the following objective: Probability analysis of annual, seasonal and monthly rainfall data of Rayagada district.

Thom1 employed mixed gamma probability distribution for describing skewed rainfall data and employed approximate solution to non-linear equations obtained by differentiating log likelihood function with respect to the parameters of the distribution. Subsequently, this methodology along with variance ratio test as a goodness- of-fit has been widely employed Kar et al,2 Jat et al,3 Senapati et al,4 and Subudhi et al.4 applied incomplete gamma probability distribution for rainfall analysis. In addition to gamma probability distribution, other two-parameter probability distributions (normal, log-normal, Weibull, smallest and largest extreme value), and three-parameter probability distributions (log-normal, gamma, log-logistic and Weibull) have been widely used for studying flood frequency, drought analysis and rainfall probability analysis.5 Gumbel6 Chow,7 have applied gamma distribution with two and three parameter, Pearson type-III, extreme value, binomial and Poisson distribution to hydrological data. Sachan S et al,8 attempted probability analysis using the rainfall data of 30 years(1976-2005) in various influencing raingauge stations viz., Damoh, Hatta, Jabera and Deori falling in Bearma basin of Bundelkhand region, Madhyapradesh. Gumbel,6 Hershfield & Kohlar.9 Have applied gamma distribution with two and three parameter, Pearson type-III, extreme value, binomial and Poisson distribution to hydrological data.10

Materials and methods

The data were collected from District Collector’s Office, Gajapati district for this study. Rainfall data for17years from 2001 to 2017 are collected for the present study to make rainfall forecasting using different methods

Probability distribution functions

For seasonal rainfall analysis of Gajapati district, three seasons- kharif (June-September), rabi (October to January) and summer (February to May) are considered. The data is fed into the Excel spreadsheet, where it is arranged in a chronological order and the Weibull plotting position formula is then applied. The Weibull plotting position formula is given by

p= m N+1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGWb Gaeyypa0tcfa4aaSaaaOqaaKqzGeGaamyBaaGcbaqcLbsacaWGobGa ey4kaSIaaGymaaaaaaa@3DB2@

Where m=rank number

 N=number of years

The recurrence interval is given by

T= 1 p = N+1 m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGub Gaeyypa0tcfa4aaSaaaOqaaKqzGeGaaGymaaGcbaqcLbsacaWGWbaa aiabg2da9Kqbaoaalaaakeaajugibiaad6eacqGHRaWkcaaIXaaake aajugibiaad2gaaaaaaa@421C@

The values are then subjected to various probability distribution functions namely- normal, log-normal (2-parameter), log-normal (3-parameter), gamma, generalized extreme value, Weibull, generalized Pareto distribution, Pearson, log-Pearson type-III and Gumbel distribution. Some of the probability distribution functions are described as follows:

Normal distribution

The probability density is

p( x )=( 1/σ 2π )  e ( xμ ) 2 2 σ 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaadchajuaGpaWaaeWaaOqaaKqzGeWdbiaadIhaaOWdaiaa wIcacaGLPaaajugib8qacqGH9aqpjuaGpaWaaeWaaOqaaKqzGeWdbi aaigdacaGGVaGaeq4Wdmxcfa4aaOaaaOqaaKqzGeGaaGOmaiabec8a WbWcbeaaaOWdaiaawIcacaGLPaaajugib8qacaGGGcGaamyzaKqbao aaCaaaleqabaqcLbmacqGHsisll8aadaqadaqaaKqzadWdbiaadIha cqGHsislcqaH8oqBaSWdaiaawIcacaGLPaaapeWaaWbaaWqabeaaju gWaiaaikdaaaGaeyirGqQaaGOmaiabeo8aZTWaaWbaaWqabeaajugW aiaaikdaaaaaaaaa@5B74@

Where x is the variate, μ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH8o qBaaa@383B@ is the mean value of variateand σ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaHdp WCaaa@3848@ is the standard deviation. In this distribution, the mean, mode and median are the same. The cumulative probability of a value being equal to or less than x is

p( x )=1/σ 2π x e ( xμ ) 2 2 σ 2  dx MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaadchajuaGpaWaaeWaaOqaaKqzGeWdbiaadIhacqGHKjYO aOWdaiaawIcacaGLPaaajugib8qacqGH9aqpcaaIXaGaai4laiabeo 8aZLqbaoaakaaakeaajugibiaaikdacqaHapaCaSqabaqcfa4aa8qC aeaajugibiaadwgalmaaCaaajuaGbeqaaKqzadGaeyOeI0YcpaWaae WaaKqbagaajugWa8qacaWG4bGaeyOeI0IaeqiVd0gajuaGpaGaayjk aiaawMcaaSWdbmaaCaaajuaGbeqaaKqzadGaaGOmaaaacqGHebcPca aIYaGaeq4Wdm3cdaahaaqcfayabeaajugWaiaaikdaaaaaaaqcfaya aKqzadGaeyOeI0IaeyOhIukajuaGbaqcLbmacaWG4baajugibiabgU IiYdGaaiiOaiaacsgacaGG4baaaa@6876@

This represents the area under the curve between MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqGHsi slcqGHEisPaaa@38E3@ and x.

Log-normal (2-parameter) distribution

The probability density is

p( x )=( 1 σ y   e y 2π )  e ( yμy ) 2 2 σ y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCamaabm aabaaeaaaaaaaaa8qacaWG4baapaGaayjkaiaawMcaa8qacqGH9aqp paWaaeWaaeaapeGaaGymaiabgseiKkabeo8aZnaaBaaaleaacaWG5b aabeaakiaacckacaWGLbWaaWbaaSqabeaacaWG5baaaOWaaOaaaeaa caaIYaGaeqiWdahaleqaaaGcpaGaayjkaiaawMcaa8qacaqGGaGaam yza8aadaahaaWcbeqaa8qacqGHsislpaWaaeWaaeaapeGaamyEaiab gkHiTiabeY7aTjaadMhaa8aacaGLOaGaayzkaaWdbmaaCaaameqaba GaaGOmaaaaliabgseiKkaaikdacqaHdpWCdaWgaaadbaGaamyEaaqa baaaaaaa@5703@

Where y =ln x, where x is the variate, μ y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH8o qBjuaGdaWgaaqaaKqzadGaamyEaaqcfayabaaaaa@3BA4@ is the mean of y and σ y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaHdp WCjuaGdaWgaaqaaKqzadGaamyEaaqcfayabaaaaa@3BB1@ is the standard deviation of y.

Log-normal (3-parameter) distribution

A random variable X is said to have three-parameter log-normal probability distribution if its probability density function (pdf) is given by:

f( x )={ 1 ( xλ )σ 2π exp{ 1 2 ( log( xλ )μ) σ ) 2 },λ<x<,μ>0,σ>0@ 0,otherwise)} MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaajugiba baaaaaaaaapeGaamOzaKqba+aadaqadaGcbaqcLbsapeGaamiEaaGc paGaayjkaiaawMcaaKqzGeGaeyypa0Jaai4EaKqbaoaaleaaleaaju gib8qacaaIXaaal8aabaqcfa4aaeWaaSqaaKqzGeWdbiaadIhacqGH sislcqaH7oaBaSWdaiaawIcacaGLPaaajugib8qacqaHdpWCjuaGda GcaaWcbaqcLbsacaaIYaGaeqiWdahameqaaaaajugibiaadwgacaWG 4bGaamiCa8aacaGG7bWdbiabgkHiTKqbaoaalaaakeaajugibiaaig daaOqaaKqzGeGaaGOmaaaajuaGdaqadaGcbaqcfa4damaalaaakeaa jugib8qacaWGSbGaam4BaiaadEgajuaGpaWaaeWaaOqaaKqzGeWdbi aadIhacqGHsislcqaH7oaBaOWdaiaawIcacaGLPaaajugib8qacqGH sislcqaH8oqBpaGaaiykaaGcbaqcLbsapeGaeq4WdmhaaaGccaGLOa GaayzkaaWcdaahaaqabeaajugWaiaabkdaaaqcLbsacaGG9bGaaiil aiabeU7aSjabgYda8iaadIhacqGH8aapcqGHEisPcaGGSaGaeqiVd0 MaeyOpa4JaaGimaiaacYcacqaHdpWCcqGH+aGpcaaIWaGaaiiqaaGc baqcLbsacaaIWaGaaiilaiaad+gacaWG0bGaamiAaiaadwgacaWGYb Gaam4DaiaadMgacaWGZbGaamyza8aacaGGPaGaaiyFaaaaaa@88A7@

Where μ,σandλ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH8o qBcaGGSaGaeq4WdmNaaGPaVlaadggacaWGUbGaamizaiabeU7aSbaa @40AF@ are known as location, scale and threshold parameters, respectively.

Pearson distribution

The general and basic equation to define the probability density of a Pearson distribution

p( x )=e x a+x b 0 + b 1  x+ b 2   x 2   dx MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaadchajuaGpaWaaeWaaOqaaKqzGeWdbiaadIhaaOWdaiaa wIcacaGLPaaajugib8qacqGH9aqpcaWGLbqcfa4aa8qmaOqaaKqbao aalaaakeaajugibiaadggacqGHRaWkcaWG4baakeaajugibiaadkga juaGdaWgaaWcbaqcLbmacaaIWaaaleqaaKqzGeGaey4kaSIaamOyaS WaaSbaaeaajugWaiaaigdaaSqabaqcLbsacaqGGaGaamiEaiabgUca RiaadkgalmaaBaaabaqcLbmacaaIYaaaleqaaKqzGeGaaeiiaiaadI halmaaCaaabeqaaKqzadGaaGOmaaaajugibiaabccaaaaaleaajugW aiabgkHiTiabg6HiLcWcbaqcLbmacaWG4baajugibiabgUIiYdGaam izaiaadIhaaaa@612B@

Where a,b0,b1andb2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGHb GaaiilaiaadkgajugWaiaaicdajugibiaacYcacaWGIbqcLbmacaaI XaqcLbsacaWGHbGaamOBaiaadsgacaaMc8UaamOyaKqzadGaaGOmaa aa@46A6@ are constants.

The criteria for determining types of distribution are β 1 , β 2 andk MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdi2aaS baaSqaaiaaigdaaeqaaOGaaiilaiabek7aInaaBaaaleaacaaIYaaa beaakiaadggacaWGUbGaamizaiaaykW7caWGRbaaaa@4108@ where

β 1 = μ 3 2 μ 2 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdi2aaS baaSqaaiaaigdaaeqaaOGaeyypa0ZaaSaaaeaacqaH8oqBdaqhaaWc baGaaG4maaqaaiaaikdaaaaakeaacqaH8oqBdaqhaaWcbaGaaGOmaa qaaiaaiodaaaaaaaaa@4060@

β 2 = μ 4 μ 2 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdi2aaS baaSqaaiaaikdaaeqaaOGaeyypa0ZaaSaaaeaacqaH8oqBdaWgaaWc baGaaGinaaqabaaakeaacqaH8oqBdaqhaaWcbaGaaGOmaaqaaiaaik daaaaaaaaa@3FA4@

k= β 1 ( β 2 +3 ) 2 4( 4 β 2 3 β 1   )( 2 β 2 3 β 1 6 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGRbGaeyypa0ZaaSaaaeaacqaHYoGydaWgaaWcbaGaaGymaaqa baGcpaWaaeWaaeaapeGaeqOSdi2aaSbaaSqaaiaaikdaaeqaaOGaey 4kaSIaaG4maaWdaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaaa k8qabaGaaGina8aadaqadaqaa8qacaaI0aGaeqOSdi2aaSbaaSqaai aaikdaaeqaaOGaeyOeI0IaaG4maiabek7aInaaBaaaleaacaaIXaaa beaakiaabccaa8aacaGLOaGaayzkaaWaaeWaaeaapeGaaGOmaiabek 7aInaaBaaaleaacaaIYaaabeaakiabgkHiTiaaiodacqaHYoGydaWg aaWcbaGaaGymaaqabaGccqGHsislcaaI2aaapaGaayjkaiaawMcaaa aaaaa@571F@

Where μ 2 , μ 3 and μ 4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH8o qBjuaGdaWgaaqaaKqzadGaaGOmaaqcfayabaqcLbsacaGGSaGaeqiV d02cdaWgaaqcfayaaKqzadGaaG4maaqcfayabaqcLbsacaWGHbGaam OBaiaadsgacqaH8oqBlmaaBaaajuaGbaqcLbmacaaI0aaajuaGbeaa aaa@49C5@ are second, third and fourth moments about the mean.

Log-pearson type III distribution

In this the variate is first transformed into logarithmic form (base 10) and the transformed data is then analyzed. If X is the variate of a random hydrologic series, then the series of Z variates where

z=logx MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWG6b Gaeyypa0JaciiBaiaac+gacaGGNbGaamiEaaaa@3C57@

Are first obtained. For this z series, for any recurrence interval T and the coefficient of skew C S MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGdb qcfa4aaSbaaeaajugWaiaadofaaKqbagqaaaaa@3A90@

σ Z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaHdp WClmaaBaaabaqcLbmacaWGAbaaleqaaaaa@3A8C@ = Standard deviation of the Z variate sample

 = ( ( z z ¯ ) 2 /( N1 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qadaGcaaqaa8aadaqadaqaa8qacqGHris5paWaaeWaaeaapeGaamOE aiabgkHiTiqadQhagaqeaaWdaiaawIcacaGLPaaadaahaaWcbeqaai aabkdaaaGccaGGVaWaaeWaaeaapeGaamOtaiabgkHiTiaaigdaa8aa caGLOaGaayzkaaaacaGLOaGaayzkaaaal8qabeaaaaa@4409@

And C S MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGdb qcfa4aaSbaaeaajugWaiaadofaaKqbagqaaaaa@3A90@ = coefficient of skew of variate Z

 = ( z z ¯ ) 3 ( N1 )( N2 ) σ z 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qadaWcaaqaaiabggHiL=aadaqadaqaa8qacaWG6bGaeyOeI0IabmOE ayaaraaapaGaayjkaiaawMcaamaaCaaaleqabaGaaG4maaaaaOWdbe aapaWaaeWaaeaapeGaamOtaiabgkHiTiaaigdaa8aacaGLOaGaayzk aaWaaeWaaeaapeGaamOtaiabgkHiTiaaikdaa8aacaGLOaGaayzkaa Gaeq4Wdm3aa0baaSqaaiaadQhaaeaacaaIZaaaaaaaaaa@498A@

z ¯ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qaceWG6bGbaebaaaa@372D@ = mean of z values

N= sample size = number of years of record

Generalized pareto distribution

The family of generalized Pareto distributions (GPD) has three parameters μ,σandξ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH8o qBcaGGSaGaeq4WdmNaamyyaiaad6gacaWGKbGaeqOVdGhaaa@3F33@ .

The cumulative distribution function is

F ( ξ,μ,σ ) ( x )={ 1 ( 1+ ξ( xμ ) σ ) 1 ξ for ξ0 1exp( ( xμ ) σ ) for ξ=0 } MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGgb WcdaWgaaqaamaabmaabaqcLbmaqaaaaaaaaaWdbiabe67a4jaacYca cqaH8oqBcaGGSaGaeq4Wdmhal8aacaGLOaGaayzkaaaabeaajuaGda qadaGcbaqcLbsapeGaamiEaaGcpaGaayjkaiaawMcaaKqzGeGaeyyp a0tcfa4aaiWaaOqaaKqzGeqbaeqabiqaaaGcbaqcLbsacaaIXaGaey OeI0scfa4aaeWaaOqaaKqzGeWdbiaaigdacqGHRaWkjuaGdaWcaaGc baqcLbsacqaH+oaEjuaGpaWaaeWaaOqaaKqzGeWdbiaadIhacqGHsi slcqaH8oqBaOWdaiaawIcacaGLPaaaa8qabaqcLbsacqaHdpWCaaaa k8aacaGLOaGaayzkaaqcfa4aaWbaaSqabeaajugWaiabgkHiTSWaaS aaaeaajugWaiaaigdaaSqaaKqzadWdbiabe67a4baaaaqcLbsacaWG MbGaam4BaiaadkhacaqGGaGaeqOVdGNaeyiyIKRaaGimaaGcpaqaaK qzGeGaaGymaiabgkHiT8qacaWGLbGaamiEaiaadchajuaGpaWaaeWa aOqaaKqzGeWdbiabgkHiTKqbaoaalaaakeaajuaGpaWaaeWaaOqaaK qzGeWdbiaadIhacqGHsislcqaH8oqBaOWdaiaawIcacaGLPaaaa8qa baqcLbsacqaHdpWCaaaak8aacaGLOaGaayzkaaqcLbsapeGaaiiOai aadAgacaWGVbGaamOCaiaabccacqaH+oaEcqGH9aqpcaaIWaaaaaGc paGaay5Eaiaaw2haaaaa@8821@

For xμ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWG4b GaeyyzImRaeqiVd0gaaa@3AFE@ when ξ0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH+o aEcqGHLjYScaaIWaaaaa@3AC8@ and xμ σ ξ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWG4b GaeyizImQaeqiVd0MaeyOeI0scfa4aaSaaaeaajugibiabeo8aZbqc fayaaKqzGeGaeqOVdGhaaaaa@41AA@ when ξ<0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH+o aEcqGH8aapcaaIWaaaaa@3A06@ ,where μR MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH8o qBcqGHiiIZcaWGsbaaaa@3A96@ is the location parameter, σ>0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaHdp WCcqGH+aGpcaaIWaaaaa@3A0A@ the scale parameter and ξR MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH+o aEcqGHiiIZcaWGsbaaaa@3AA3@ the shape parameter.

The probability density function is

f ( ξ,μ,σ ) ( x )= 1 σ ( 1+ ξ( xμ ) σ ) ( 1 ξ 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGMbWdamaaBaaaleaadaqadaqaa8qacqaH+oaEcaGGSaGaeqiV d0Maaiilaiabeo8aZbWdaiaawIcacaGLPaaaaeqaaOWaaeWaaeaape GaamiEaaWdaiaawIcacaGLPaaapeGaeyypa0ZaaSaaaeaacaaIXaaa baGaeq4Wdmhaa8aadaqadaqaa8qacaaIXaGaey4kaSYdamaalaaaba Wdbiabe67a49aadaqadaqaa8qacaWG4bGaeyOeI0IaeqiVd0gapaGa ayjkaiaawMcaaaqaa8qacqaHdpWCaaaapaGaayjkaiaawMcaamaaCa aaleqabaWaaeWaaeaapeGaeyOeI0YaaSaaaeaacaaIXaaabaGaeqOV dGhaaiabgkHiTiaaigdaa8aacaGLOaGaayzkaaaaaaaa@593B@

Or
f ( ξ,μ,σ ) ( x )= σ 1 ξ (σ+ξ( xμ )) 1 ξ +1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGMbWdamaaBaaaleaadaqadaqaa8qacqaH+oaEcaGGSaGaeqiV d0Maaiilaiabeo8aZbWdaiaawIcacaGLPaaaaeqaaOWaaeWaaeaape GaamiEaaWdaiaawIcacaGLPaaapeGaeyypa0ZaaSaaaeaacqaHdpWC daahaaWcbeqaamaalaaabaGaaGymaaqaaiabe67a4baaaaaakeaaca GGOaGaeq4WdmNaey4kaSIaeqOVdG3damaabmaabaWdbiaadIhacqGH sislcqaH8oqBa8aacaGLOaGaayzkaaGaaiykamaaCaaaleqabaWdbm aalaaabaGaaGymaaqaaiabe67a4baacqGHRaWkcaaIXaaaaaaaaaa@575D@
again, for xμ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWG4b GaeyyzImRaeqiVd0gaaa@3AFE@ , and xμ σ ξ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWG4b GaeyizImQaeqiVd0MaeyOeI0scfa4aaSaaaeaajugibiabeo8aZbqc fayaaKqzGeGaeqOVdGhaaaaa@41AA@ when ξ<0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH+o aEcqGH8aapcaaIWaaaaa@3A06@

Generalized extreme value distribution

Generalized extreme value distribution has cumulative distribution function

f ( x;μ,σ,ξ ) ( x )= 1 σ [ 1+ξ( xμ σ ) ] ( 1 ξ 1 ) exp( [ 1+ξ ( xμ σ ) ( 1 ξ ) ] ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaadAgajuaGpaWaaSbaaSqaaKqbaoaabmaaleaajugib8qa caWG4bGaai4oaiabeY7aTjaacYcacqaHdpWCcaGGSaGaeqOVdGhal8 aacaGLOaGaayzkaaaabeaajuaGdaqadaGcbaqcLbsapeGaamiEaaGc paGaayjkaiaawMcaaKqzGeWdbiabg2da9Kqbaoaalaaakeaajugibi aaigdaaOqaaKqzGeGaeq4WdmhaaKqbaoaadmaakeaajugibiaaigda cqGHRaWkcqaH+oaEjuaGpaWaaeWaaOqaaKqba+qadaWcaaGcbaqcLb sacaWG4bGaeyOeI0IaeqiVd0gakeaajugibiabeo8aZbaaaOWdaiaa wIcacaGLPaaaa8qacaGLBbGaayzxaaWcpaWaaWbaaeqabaWaaeWaae aajugWaiabgkHiTSWdbmaalaaabaqcLbmacaaIXaaaleaajugWaiab e67a4baacqGHsislcaaIXaaal8aacaGLOaGaayzkaaaaaKqzGeGaci yzaiaacIhacaGGWbqcfa4aaeWaaOqaaKqzGeGaeyOeI0scfa4aamWa aOqaaKqzGeWdbiaaigdacqGHRaWkcqaH+oaEjuaGpaWaaeWaaOqaaK qba+qadaWcaaGcbaqcLbsacaWG4bGaeyOeI0IaeqiVd0gakeaajugi biabeo8aZbaaaOWdaiaawIcacaGLPaaalmaaCaaabeqaamaabmaaba qcLbmacqGHsisll8qadaWcaaqaaKqzadGaaGymaaWcbaqcLbmacqaH +oaEaaaal8aacaGLOaGaayzkaaaaaaGccaGLBbGaayzxaaaacaGLOa Gaayzkaaaaaa@883D@

For 1+ξ( xμ )/σ>0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaaIXaGaey4kaSIaeqOVdG3damaabmaabaWdbiaadIhacqGHsisl cqaH8oqBa8aacaGLOaGaayzkaaWdbiaac+cacqaHdpWCcqGH+aGpca aIWaaaaa@4315@ , where μR MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH8o qBcqGHiiIZcaWGsbaaaa@3A96@ is the location parameter, σ>0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaHdp WCcqGH+aGpcaaIWaaaaa@3A0A@ the scale parameter and ξR MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqaH+o aEcqGHiiIZcaWGsbaaaa@3AA3@ the shape parameter. The density function is, consequently

f ( x;μ,σ,ξ ) ( x )= 1 σ [ 1+ξ( xμ σ ) ] ( 1 ξ 1 ) exp( [ 1+ξ ( xμ σ ) ( 1 ξ ) ] ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaadAgajuaGpaWaaSbaaSqaaKqbaoaabmaaleaajugib8qa caWG4bGaai4oaiabeY7aTjaacYcacqaHdpWCcaGGSaGaeqOVdGhal8 aacaGLOaGaayzkaaaabeaajuaGdaqadaGcbaqcLbsapeGaamiEaaGc paGaayjkaiaawMcaaKqzGeWdbiabg2da9Kqbaoaalaaakeaajugibi aaigdaaOqaaKqzGeGaeq4WdmhaaKqbaoaadmaakeaajugibiaaigda cqGHRaWkcqaH+oaEjuaGpaWaaeWaaOqaaKqba+qadaWcaaGcbaqcLb sacaWG4bGaeyOeI0IaeqiVd0gakeaajugibiabeo8aZbaaaOWdaiaa wIcacaGLPaaaa8qacaGLBbGaayzxaaWcpaWaaWbaaeqabaWaaeWaae aajugWaiabgkHiTSWdbmaalaaabaqcLbmacaaIXaaaleaajugWaiab e67a4baacqGHsislcaaIXaaal8aacaGLOaGaayzkaaaaaKqzGeGaci yzaiaacIhacaGGWbqcfa4aaeWaaOqaaKqzGeGaeyOeI0scfa4aamWa aOqaaKqzGeWdbiaaigdacqGHRaWkcqaH+oaEjuaGpaWaaeWaaOqaaK qba+qadaWcaaGcbaqcLbsacaWG4bGaeyOeI0IaeqiVd0gakeaajugi biabeo8aZbaaaOWdaiaawIcacaGLPaaalmaaCaaabeqaamaabmaaba qcLbmacqGHsisll8qadaWcaaqaaKqzadGaaGymaaWcbaqcLbmacqaH +oaEaaaal8aacaGLOaGaayzkaaaaaaGccaGLBbGaayzxaaaacaGLOa Gaayzkaaaaaa@883D@

Again, for 1+ξ( xμ )/σ>0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaaIXaGaey4kaSIaeqOVdG3damaabmaabaWdbiaadIhacqGHsisl cqaH8oqBa8aacaGLOaGaayzkaaWdbiaac+cacqaHdpWCcqGH+aGpca aIWaaaaa@4315@

Gumbel’s method: The extreme value distribution was introduced by Gumbel6 and is commonly known as Gumbel’s distribution. It is one of the most widely used probability-distribution functions for extreme values in hydrologic and meteorological studies. According to this theory of extreme events, the probability of occurrence of an event equal to or larger than a value x 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWG4b qcfa4aaSbaaeaajugWaiaaicdaaKqbagqaaaaa@3AA7@ is

P( X x 0   )=1 e e y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGqbWdamaabmaabaWdbiaadIfacqGHLjYScaWG4bWaaSbaaSqa aiaaicdaaeqaaOGaaeiiaaWdaiaawIcacaGLPaaapeGaeyypa0JaaG ymaiabgkHiTiaadwgadaahaaWcbeqaaiabgkHiTiaadwgadaahaaad beqaaiabgkHiTiaadMhaaaaaaaaa@459A@

in which y is a dimensionless variable and is given by

y=α( xa ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWG5bGaeyypa0JaeqySde2damaabmaabaWdbiaadIhacqGHsisl caWGHbaapaGaayjkaiaawMcaaaaa@3E40@

a= x ¯ 0.45005 σ x MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGHbGaeyypa0JabmiEayaaraGaeyOeI0IaaGimaiaac6cacaaI 0aGaaGynaiaaicdacaaIWaGaaGynaiabeo8aZnaaBaaaleaacaWG4b aabeaaaaa@420C@

Thus y= 1.2825( x x ¯ ) σ x +0.577...... MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaadMhacqGH9aqpjuaGdaWcaaGcbaqcLbsacaaIXaGaaiOl aiaaikdacaaI4aGaaGOmaiaaiwdajuaGpaWaaeWaaOqaaKqzGeWdbi aadIhacqGHsislceWG4bGbaebaaOWdaiaawIcacaGLPaaaa8qabaqc LbsacqaHdpWCjuaGdaWgaaWcbaqcLbsacaWG4baaleqaaaaajugibi abgUcaRiaaicdacaGGUaGaaGynaiaaiEdacaaI3aGaaiOlaiaac6ca caGGUaGaaiOlaiaac6cacaGGUaaaaa@522A@ …….. (i)

Where x ¯ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qaceWG4bGbaebaaaa@372B@ = mean and σ x MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaHdpWCdaWgaaWcbaGaamiEaaqabaaaaa@3902@ = standard deviation of the variate X. In practice it is the value of X for a given P that is required and such Eq. (i) is transposed as

y p =ln[ln(1p)] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWG5bWaaSbaaSqaaiaadchaaeqaaOGaeyypa0JaeyOeI0IaciiB aiaac6gacaGGBbGaeyOeI0IaaiiBaiaac6gacaGGOaGaaGymaiabgk HiTiaacchacaGGPaGaaiyxaaaa@449A@

Noting that the return period T=1/P MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivaiabg2 da9iaaigdacaGGVaGaaiiuaaaa@3A17@ and designating y T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWG5bWaaSbaaSqaaiaadsfaaeqaaaaa@3819@ =the value of y, commonly called the reduced variate, for a given T

y T =[ ln.ln T ( T1 ) ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaadMhajuaGdaWgaaWcbaqcLbsacaWGubaaleqaaKqzGeGa eyypa0JaeyOeI0scfa4damaadmaakeaajugib8qaciGGSbGaaiOBai aac6caciGGSbGaaiOBaKqbaoaalaaakeaajugibiaadsfaaOqaaKqb a+aadaqadaGcbaqcLbsapeGaamivaiabgkHiTiaaigdaaOWdaiaawI cacaGLPaaaaaaacaGLBbGaayzxaaaaaa@4B87@

Or y T =[ 0.834+2.303 loglog  T ( T1 ) ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaadMhajuaGdaWgaaWcbaqcLbmacaWGubaaleqaaKqzGeGa eyypa0JaeyOeI0scfa4damaadmaakeaajugib8qacaaIWaGaaiOlai aaiIdacaaIZaGaaGinaiabgUcaRiaaikdacaGGUaGaaG4maiaaicda caaIZaGaaeiiaiaadYgacaWGVbGaam4zaiaaykW7caWGSbGaam4Bai aadEgacaqGGaqcfa4aaSaaaOqaaKqzGeGaamivaaGcbaqcfa4damaa bmaakeaajugib8qacaWGubGaeyOeI0IaaGymaaGcpaGaayjkaiaawM caaaaaaiaawUfacaGLDbaaaaa@584C@

Now rearranging Eq. (i), the value of the variate X with a return period T is

x T = x ¯ +K σ x MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWG4bWaaSbaaSqaaiaadsfaaeqaaOGaeyypa0JabmiEayaaraGa ey4kaSIaam4saiabeo8aZnaaBaaaleaacaWG4baabeaaaaa@3EDB@

Where K= ( y T 0.577 ) 1.2825 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGlbGaeyypa0ZdamaalaaabaWaaeWaaeaapeGaamyEamaaBaaa leaacaWGubaabeaakiabgkHiTiaaicdacaGGUaGaaGynaiaaiEdaca aI3aaapaGaayjkaiaawMcaaaqaa8qacaaIXaGaaiOlaiaaikdacaaI 4aGaaGOmaiaaiwdaaaaaaa@44D0@

The above equations constitute the basic Gumbel’s equations and are applicable to an infinite sample size (i.e. N MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGob GaeyOKH4QaeyOhIukaaa@3AB6@ ).

Result and discussion

The various parameters like mean, standard deviation, RMSE value were obtained and noted for different distributions. The rainfall at 90%, 75%, 50%, 25% and 10% probability levels are determined. The distribution “best” fitted to the data is noted down in a tabulated form in Table 1. In the present study, the parameters of distribution for the different distributions have been estimated by FLOOD frequency analysis software. The rainfall data is the input to the software programme. The best fitted distribution of different month and seasons and annual were presented in Table 1.The annual rainfall in 50% probability was found to be 1340.3mm for Rayagada block of Odisha. During Kharif at 50% probability level, the rainfall is 1066.2mm where as only125.9mm and 136.0mm was received during rabi and summer respectively. In the present study, the parameters of distribution for the different distributions have been estimated by FLOOD-flood frequency analysis software. The rainfall data is the input to the software programme. The best fitted distribution of different month and season and annual were presented in Table 1. The annual rainfall in 50% probability was found to be 1340.3mm for Rayagada district of Odisha. During Kharif at 50% probability level, the rainfall is 1066.2mm where as only125.9mm and 136.0mm was received during rabi and summer respectively.

Months

Best- fit Distribution

RMSE Value

Rainfall at probability levels

 

 

90%

75%

50%

25%

10%

January

EV type-III

0.05662

-

-

-

13.15

32.85

February

Pareto

0.04265

-

-

-

-

10.64

March

Exponential

0.0577

-

-

11.44

34.43

64.84

April

Gamma

0.06436

-

-

22.92

68.44

130.69

May

Gumbel-max

0.03242

1.11

35.5

73.41

119.17

170.71

June

Weibull

0.0447

65

115.44

190.89

283.75

379.27

July

Pareto

0.05212

119.24

166.98

262.77

397.94

532.8

August

Log-Normal

0.03976

161.14

219.33

308.98

435.3

592.76

September

Log-Normal

0.03585

93.91

135.02

202.16

302.71

435.47

October

Pareto

0.03324

-

8.18

81.85

182.44

278.02

November

Pearson

0.04999

-

-

3.79

25.12

51.87

December

Pareto

0.06214

-

-

-

-

30.06

Annual

Pareto

0.05995

1022.03

1131.26

1340.3

1610.28

1846.79

Kharif (June-Sept)

Pareto

0.0567

699.38

830.75

1066.2

1335.35

1532.34

Rabi (Oct-Jan)

Log-Pearson

0.03913

-

52.26

125.9

219.57

313.53

Summer (Feb-May)

Pearson

0.05757

54.78

86.47

136

202.89

279.36

Table 1 Rainfall analysis of Rayagada district at different probability levels for different months and seasons

In the present study, the parameters of distribution for the different distributions have been estimated by FLOOD-flood frequency analysis software. The rainfall data is the input to the software programme. The best fitted distribution of different month and season and annual were presented in Table 1. The annual rainfall in 50% probability was found to be 1340.3mm for Rayagada district of Odisha. During Kharif at 50 % probability level, the rainfall is 1066.2mm where as only125.9mm and 136.0mm was received during rabi and summer respectively, so water harvesting structures may be made to grow crops during rabi and summer to utilize the water from the water harvesting structures to increase the cropping intensity of the area. It is also observed that at 75% probability level the June, July, Aug and Sept received more than 100 mm, so farmers of these area can grow crops in upland areas suitably paddy can be grown followed by any rabi crop in rabi season like mustard or kulthi in upland areas. In Figure 1 the plot between different months and amount of rainfall in different probabilities were shown, It is observed that September month gets highest amount of rainfall compared to other months. Figure 2 shows the different cropping pattern in Rayagada district as per the rainfall available in different weeks.11‒16

Figure 1 Rainfall at different probabilities of monthly, seasonal and annual at Rayagada block.

Figure 2 Different cropping patterns for Rayagada district.

Conclusion

Forecasting of rainfall is essential for proper planning of crop production. About 70% of cultivable land of Odisha depends on rainfall for crop production. Prediction of rainfall in advance helps to accomplish the agricultural operations in time. It can be concluded that, excess runoff should be harvested for irrigating post-monsoon crops. It becomes highly necessary to provide the farmers with high-yielding variety of crops and such varieties which require less water and are early-maturing in Rayagada district of Mahanadi command area of Odisha. It is also observed that at 75% probability level the June, July, Aug and Sept received more than 100 mm, so farmers of these area can grow crops in upland areas suitably paddy can be grown followed by any rabi crop in rabi season like mustard or kulthi in upland areas. Annual rainfall of Rayagada district is 1340.3mm at 50% probability level. It is observed that September month gets highest amount of rainfall compared to other months. Different cropping pattern selected may be may be practiced in this district.

Acknowledgments

None.

Conflicts of interest

The authors declare that there is no conflict of interest.

Funding

None.

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