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Exploring Different Probability Distributions for Rainfall Data of Kodagu - an Assisting Approach for Food Security

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Exploring Different Probability Distributions for Rainfall Data of Kodagu - an Assisting Approach for Food Security Int.J.Curr.Microbiol.App.Sci (2020) 9(2): 2972-2980 International Journal of Current Microbiology and Applied Sciences ISSN: 2319-7706 Volume 9 Number 2 (2020) Journal homepage: http://www.ijcmas.com Original Research Article https://doi.org/10.20546/ijcmas.2020.902.339 Exploring Different Probability Distributions for Rainfall Data of Kodagu - An Assisting Approach for Food Security R. Shreyas1*, D. Punith1, L. Bhagirathi2, Anantha Krishna3 and G. M. Devagiri4 1UAHS (Shivamogga), College of Forestry,Ponnampet, Karnataka-571216, India 2Department of Basic Sciences, College of Forestry, Ponnampet, Karnataka-571216, India 3Department of Computer Science, College of Forestry, Ponnampet, Karnataka-571216, India 4Department of Natural Resource Management, College of Forestry, Ponnampet, Karnataka-571216, India *Corresponding author ABSTRACT Rainfall intensity, duration and its distribution play a major role in the growth of agriculture and other related sectors and the overall development of a country. The present study is carried out to know the best fitting K e yw or ds probability distribution for rainfall data in three different taluks of Kodagu Rainfall, probability District. The time series data of average monthly and annual rainfall over a distributions, fitting, period of 61 years (1958-2018) was collected from KSNDMC, Bangalore. goodness-of-fit Around 26 different probability distributions were used to evaluate the best Article Info fit for annual and seasonal rainfall data. Kolmogorov-Smirnov, Anderson Darling and Chi-squared tests were used for the goodness of fit test. The Accepted: 20 January 2020 best fitting distribution was identified by maximum score which is a sum of Available Online: ranks given by three selected goodness of fit test for the distributions which 10 February 2020 is again based on fitting distance. Among various distributions attempted- Log Logistic (3P), Dagum, Gamma (3P), Inverse Gaussian, Generalized Gamma, Pearson Type 5 (3P) and Pearson 6 were found to be the best fit for annual and seasonal rainfall for different taluks of Kodagu district. Introduction amount of rainfall during the monsoon season is very important for economic activity. Indian agriculture sector accounts for around 14 percent of the country’s economy but Rainfall intensity, duration and its distribution accounts for 42 percent of total employment play a major role in the growth of agriculture in the country. About 55 percent of India’s and other related sectors and the overall arable land depends on precipitation, the development of a country. Rainfall intensity, 2972 Int.J.Curr.Microbiol.App.Sci (2020) 9(2): 2972-2980 patterns and its distribution are altered by medicine, climatology, economics and natural climatic variability i.e., decadal agricultural science. Probability distributions changes in circulation (Deepthi K.A, 2015) as of rainfall have been studied by many well as human induced changes i.e., land use researchers. and cover, emission of greenhouse gases, etc. The variability in rainfall affects the The main objective of this study is to identify agricultural production, water supply, a suitable probability distribution for annual transportation, the entire economy of a region, and seasonal rainfall in the different taluks of and the existence of its people. In regions Kodagu. where the year-to-year variability is high, people often suffer great calamities due to Materials and Methods floods or droughts. The damage due to extremes of rainfall cannot be avoided Kodagu district with an area of 4102 km sq. is completely, a forewarning could certainly be one of the smallest districts in the state of useful and it’s possible from analysis of Karnataka, located between 11056’00’’ and rainfall data. 12050’00’’ North latitude and between 75022’00” and 76011’00” East longitude. The In India, the monsoon or rainy season is average annual rainfall is around 2682 mm dominated by the humid South West (Anonymous, 2018). The District is composed Monsoon that sweeps across the country in of three taluks namely Madikeri, Somwarpet early June, first hitting the State of Kerala. and Virajpet. The southwest monsoon is generally expected to begin in early June and end by September Data and the total rainfall of these four months is considered as monsoon rainfall. In Indian Rainfall of three taluks of Kodagu district was agriculture, the contribution of south-west selected with annual and seasonal series from monsoon is immense as more than 70% of 1958 to 2018. The required rainfall data for India’s annual rainfall is from the south west the study was collected from Karnataka State monsoon and supports nearly 75% of the Natural Disaster Monitoring Centre kharif crop which is critical to India’s food (KSNDMC) situated at Bangalore. security. Methodology The prediction of rainfall at a particular place and time can be made by studying the The procedures adopted for this work can be behavior of rainfall of that place over several summarized in the following steps: years during the past. This behavior is best studied by fitting a suitable distribution to the Statistics of annual and seasonal period time series data on the rainfall (Kainth 1996). rainfall The rainfall is predicted with the help of the probability estimates. Probability and Using the sample data (i=1, 2…, n) the basic frequency analysis of rainfall data enables to statistical descriptors of the annual rainfall determine the expected rainfall at different series, the mean, standard deviation, probability level (Mishra et al., 2013). coefficient of variation (CV), skewness, kurtosis, minimum and maximum values, The probability distributions are used in have been estimated for each taluk of Kodagu different fields of science such as engineering, district. 2973 Int.J.Curr.Microbiol.App.Sci (2020) 9(2): 2972-2980 Distribution Fitting (0.05) level of significance for the selection of the best fit distribution. The hypothesis under The annual average and seasonal period the GOF test is: rainfall data for each of the 3 taluk of Kodagu district are fitted to the selected 26 continuous H0: MMR data follow the specified probability distributions as presented in table 1. distribution, H1: MMR data does not follow the specified Testing the goodness of fit distribution. The goodness-of-fit tests namely, The best fitted distribution is selected based Kolmogorov Smirnov test, Anderson-Darling on the minimum error produced, which is test and Chi-Squared test were used at α evaluated by the following techniques: Table.1 Description for continuous probability distribution Sl Distributio Probability Distribution Function f(x) Range/values Parameters No n 1 1 Burr (3P) x , , 0 ,as hape ak 0 x scale fx() 1 x 1 1 2 Burr (4P) x ,as hape ak x scale fx() 1 location xy 1 3 Dagum 1 ,as hape x (3P) ak scale 1 x 1 1 4 Dagum x ,as hape (4P) ak scale 1 location xy 1 5 Fatigue xx// 1 x , , 0 as hape Life . 0 x scale 2 (x y ) x 2974 Int.J.Curr.Microbiol.App.Sci (2020) 9(2): 2972-2980 6 Fatigue , , 0 as hape Life (3P) ()//()xx 1 x x scale . 2 (x y ) x location 7 Gamma ()x 1 , , 0 as hape (2P) f( x ) exp( x / ) () 0 x scale 8 Gamma ()x 1 , , 0 (3P) f( x ) exp( ( x ) / ) () x 9 1 Gen. 1 1 1 , , 0 exp( (1 zz ) )(1 ) 0 Extreme x fx( ) 1 Value exp(zz exp( )) 0 Gen. k 1 k, a s hape kx x k Gamma exp( ( ) ) scale 10 k () , , 0 11 Gen. kx() k 1 0 x f( x ) exp( (( x ) )k ) Gamma k () (4P) 12 Gumbel 1 x ,as scale hape f( x ) exp( z exp( z )) Max x locationscale Where, location x fx() 13 Inv. ()x 2 ,0 shape Gaussian 32exp 22xx 0 x location 14 2 shape Inv. ()x ,0 Gaussian exp 2 (xx )32 2 ( ) x , location (3P) 15 2 Johnson 1 z x , shape fx( ) exp ln SB 2zz (1 ) 21 z scale location 16 2 Log- 1 Logistic xx 1 2975 Int.J.Curr.Microbiol.App.Sci (2020) 9(2): 2972-2980 17 2 Log- 1 , , 0 as hape Logistic xx 1 x scale (3P) location , , 0 as hape 18 Log- 1 0 1 ln(XX ) ln( ) fx( ) exp 0 x scale Pearson 3 X () 0 , , 0 00xe y x exy 0 19 Log- 2 0 shape 1 ln(x Normal exp scale 2 0 x x2 20 Log- 2 0 shape 1 ln(x ) Normal exp scale (3P) 2 x (x ) 2 location 21 Pearson 5 exp( x ) ( )(x ) 1 22 Pearson 5 exp( (x )) (3P) 1 ( )((x ) ) 23 1 1 Pearson 6 ()x 12, , 0 12, shape fx() 12 scale Bx( 12 , )(1 ) 0 x 24 1 1 Pearson 6 ((x ) ) 12, , 0 12, shape fx() (4P) 12 scale Bx( 12 , )(1 ( ) ) x location 25 Weibull 1 xx fx( ) exp , , 0 26 Weibull 1 xx (3P) fx( ) exp 0 x 2976 Int.J.Curr.Microbiol.App.Sci (2020) 9(2): 2972-2980 Kolmogorov-Smirnov test Where Oiis the observed frequency for bin i, 2 and Eiis the expected (theoretical) x Is used to decide if a sample (x1, x2,xn ) with frequency for bin I calculated by Ei=F(X2) - CDF F(x) comes from a hypothesized F(X1), F is the CDF of the probability continuous distribution. The Kolmogorov- distribution being tested, X1 and X2 limits for Smirnov statistic (D) is based on the largest bin i. vertical difference between the theoretical CDF and the empirical (observed) CDF and is Based on Kolmogorov-Smirnov, Anderson- given by Darling and Chi-squared GOF test statistic ii1 values, 3 different rankings have been given Dmax F ( xii ) , F ( x ) to each of the distributions for all the taluk. 1innn No rank is given to a distribution when the concerned test fails to fit the data.
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