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Regional Analysis of Seasonal Maximum Monthly Rainfall Using L-Moments: a Case Study for Brahmaputra Valley Region of Assam, India

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Regional Analysis of Seasonal Maximum Monthly Rainfall Using L-Moments: a Case Study for Brahmaputra Valley Region of Assam, India Regional Analysis of Seasonal maximum monthly rainfall Using L-moments: A case study for Brahmaputra Valley region of Assam, India Rubul Bora ( [email protected] ) Chandra Nath Bezboruah College https://orcid.org/0000-0002-3164-2255 Abhijit Bhuyn C.K.B. College Biju Kumar Dutta The Assam Kaziranga University Research Article Keywords: monthly maximum rainfall, India, Regional Rainfall Frequency Posted Date: July 20th, 2021 DOI: https://doi.org/10.21203/rs.3.rs-703101/v1 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License Regional Analysis of Seasonal maximum monthly rainfall Using L- moments: A case study for Brahmaputra Valley region of Assam, India RUBUL BORA, Department of Mathematics, The Assam Kaziranga University, Jorhat, Assam. (India) E-mail: [email protected] (ORCID: 0000-0002-3164-2255) ABHIJIT BHUYAN, C.K.B. College, Teok, Jorhat, Assam (India) [email protected] BIJU KUMAR DUTTA, Department of Mathematics, The Assam Kaziranga University, Jorhat, Assam. (India) [email protected] Abstract measures. Also, the L-moment ratio diagram, heterogeneity measures, and Z-statistics measures are In this study, Regional rainfall frequency analysis has calculated for regional homogeneity testing. Finding out been carried out in Brahmaputra Valley. For this best fit probability distribution among the Pearson type purpose, daily rainfall data of 11stations are collected III (PE3), generalized extreme value(GEV), generalized for about 15 years from the Indian Meteorological Pareto (GPA), generalized normal(GNO), and the Department (IMD), Guwahati. The daily rainfall data generalized logistic(GLO) for Location, Scale and are then converted to seasonal maximum monthly Shape. Regional growth curves are considered for rainfall such as the Pre-monsoon, Monsoon, and Post- different return periods and develop the regional monsoon periods. Then based on L-moment, we find L- relationship. Monte Carlo simulations are discussed for coefficient variation, L-skewness, L-kurtosis, and large return periods. discordancy measure for regional homogeneity 1 Introduction region. Moreover, the most important reason for low rice production in the entire country is due to a lack of Rainfall is a peculiar phenomenon that varies in adequate and proper water supply in the lake (Panigrahi both space and time. Rainfall distribution is very uneven, and Panda, 2002). The rainfed food production system is and it does not only vary greatly from place to place but under stress as a result of changing rainfall patterns and a also varies year to year. Rainfall is a crucial and lack of adequate land and water resource utilization dominating component in any agricultural program’s (Khan and Hanjra, 2009). Crop planning for a region is development and implementation in any particular primarily influenced by several factors, including 1 irrigation process, drainage, irrigation system quality, soil distributions to express the parameters In1995, according characteristics, topography, and socioeconomic to Bobee and Rasmussen using regional data decreases conditions. However, rainfall magnitude and distribution sampling uncertainty by adding additional data and in space and time are the most important factors in reduces model uncertainty by providing for a better rainfed areas (Shetty et al., 2000). Again, the early end of distribution option. H.J.Fowler and C.G. Kilsby (2003) rains has an impact on production due to several moisture did their research work by using regional rainfall analysis stresses, especially when Kharif crops are in critical from 1961 to 2000 and observed that extreme stages of grain formation and growth (Dixit et al., 2005). precipitation has changed the nature of global climatic change in United Kingdom. Hossein et al. (2014) used L- It is important to manage agriculture on a moment for daily rainfall frequency analysis to develop scientific (technical) basis to make it even more of a rainfall estimation techniques in Iran. region's rainfall pattern in order to maintain crop production at a consistent level. This entails analyzing Frequency analysis gives data that can be used the series of dry and wet spells in a given area to take the to estimate how often a specific occurrence will occur. It necessary steps to prepare a crop plan in rainfed areas. is using probability distributions to collect information on Farmers can find that scientific forecasting of a wet and the volume and frequency of extreme events. (L.V. Noto dry spell analysis is beneficial to improving their fields and G. La Loggia, 2009). Deka et al. (2009) studied and cropping strength, thus improving their economic maximum rainfall daily for 42 years in the North-East condition. There are different methods for rainfall region taking 9 sites by using L-moment and LQ- frequency analysis such as daily, weekly, monthly, moment. Ishfaq et al. (2016) observed the annual daily seasonally annually, and consecutive days maximum maximum rainfall by using different moments in Pakistan rainfall. All are important to forecasting rainfall patterns and concluded that the fit probability distribution was and help the farmers to take better steps during selected by using Goodness of fit estimation. Md. agricultural plantation. It also helps to construct small Ashraful Alam et al. (2017) observed the best fit and big damps, bridges, drainage systems, and different probability distribution for monthly maximum rainfall by engineering projects relating to hydrology. For at-site using the L-moment method in Bangladesh from rainfall data analysis, we have required long-term data commonly use nine distributions. sets because the accuracy of the estimate is directly The probability distribution chosen is crucial proportional to the length of data. But in the case of since a bad choice could lead to significant bias and regional frequency analysis, the biggest advantage is seen inaccuracy in new design flood predictions, especially to be an increase in record length. Many studied have for longer return periods. This can lead to either an been done for regional flood and rainfall frequency underestimation or an overestimation, which can have analysis. Out of these, Hosking and Wallis (1997) major consequences in the operation of our real life. A, developed the L-moment which has a significant S. Rahman et al. (2013) gave stress for finding best- advantage over than ordinary moment that it combines a fitting probability distributions for flood in Australia in probability-weighted moment (PWM) and a linear their research work. In this research paper, we are trying function of the data set in a linear way. Greenwood et al. (1979) had explained the inverse form of the different 2 to find out the best fit probability distribution to get an 1 −2 1 accurate return period for seasonal rainfall analysis. 푘 −1 (푥−휉) 푘−1 (푥−휉) 푓(푥) = 훼 {1 − 푘 훼 } [1 + {1 − 푘 훼 }] (1) The quantile function is in the form 2 Study region and data collection Q(F) In this study, we collect the rainfall data for the 훼 (1−퐹) 푘 11 sites in the Brahmaputra valley of Assam. They are 푄(퐹) = 휉 + 푘 [1 − { 퐹 } ] (2) Beki, Dibrugarh, Goalpara, Golaghat, Guwahati, Jorhat, 3.1.2 Generalized extreme value distribution (GEV) Kokrajahar, North Lakhimpur, Sibsagar, Tezpur, and A three- parameter distribution for maximum is Kampur from IMD, Guwahati for about 15 years of which gives shape, scale and location parameters. GEVThe rainfall data. We take the Brahmaputra valley region for probability distribution function and the quantile function our research because the maximum numbers of Tea of the are given by gardens are found in this area. This is the main pillar of GEV our economy. Also, maximum numbers of mini tea- 1 1 푘−1 garden are found in this region. The production of tea 1 (푥−휉) (푥−휉) 푘 훼 훼 훼 mainly depends on the amount of rainfall. So, the study 푓(푥) = [1 − 푘 ] 푒푥푝 [−{1 − 푘 } ] (3) of rainfall frequency is necessary for providing the 훼 푘 knowledge of the future rainfall patterns of these types of 푄(퐹) = 휉 + 푘 [1— (−푙푛퐹) ] (4)) 3.1.3 Generalized Pareto distribution (GPA) mini tea planters as they are not able to manage water in the dry season like a big tea garden. In precipitation analysis, the GPA distribution is applied. This is also three parameters distribution. The 3 Methods parameters can be estimated by using L-moments 3.1 Different probability distributions utilizing in our methods. The pdf and cdf are as follows: investigation −1 Hosking and Wallis ( ) and Rao and 푓(푥) = 훼 exp[−(1 − 푘)푦] (5) Where Hamed used different probability1997 distributions −1 −푘 log {1 − 푘(푥 − 휉)/훼, 푘 ≠ 0 under . We used these methods in this (2000) 푓(푥) = { (푥 − 휉) ⁄ , 푘 = 0 훼 discussion. L − moment And we consider five distributions, for that the probability density functions and quantile 0 ≤ 푥 ≤ 훼⁄ 푖푓 푘 > 0, 0 ≤ 푥 <∝ 푖푓 푘 ≤ 0. 푘 functions are given below. (PDFs) 퐹(푥) = 1 − exp(−푦) 3.1.1 Generalized logistic distribution (GLO) 푘 훼{1−(1−퐹) } 휉 + 푘 , 푘 ≠ 0 A three-parameter distribution consisting of 푥(퐹) = 푓(푥) = { (6) 휉 − 훼 log (1 − 퐹) , 푘 = 0 location , scale , and shape is GLO. The 3.1.4 Generalized Normal (lognormal) (GNP and(휉) quantile functions(훼) for this are(푘) given by PDF 3 A three- parameter distribution is which where X is a real valued random variable with and are real. A special gives shape, scale and location parameters.GNO The probability distribution function and quantile function of distributioncase for the two function F p, r, sand are the are given by 1,0.s 1,r,0 generally used andmoments defined asM M GNO (푥−휉) 1 1 (푥−휉) 2 1 exp [− log{1−푘 훼 }−2[−푘 log{1−푘 훼 }] 푠 1 훼푟 = 푀1,0.푟 = ∫0 푥(퐹)(1 − 퐹) 푑퐹 (12) 푓(푥) = 훼(2휋)2 (7) The quantile function is in the form 1 푟 훽where푟 = 푀 1,푟,0 = ∫ℝ0 푥(퐹)퐹 푑퐹is the,푟 =conventional 표,1.2,.
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