Naraj barrage with 1302m length and 6.9m height across Kathajodi River is located 14 km west of Cuttack town in Orissa. It is constructed to control flooding in Mahanadi and Kathajodi Rivers. During the past two decades Naraj barrage experienced several high floods in excess of 35,000 m3/s in the years 2001, 2003, 2006, 2008, 2011 and 2018. Kumaraswamy distribution unfortunately not yet been used by statisticians due to less familiarity of the distribution despite being a good number of applications in hydrology. In this work, Kumaraswamy distribution is identified as one of the most suitable alternative flood frequency distribution for maximum flood heights and their return periods at Naraj barrage in Mahanadi River Basin (MRB) by considering commonly used ten candidate distributions along with this distribution. Different techniques of parametric estimation were used to obtain parameters value of the candidate distributions. Performed goodness of fit tests of Kolmogorov?Smirnov and Anderson-Darling for obtaining best fitted distributions, Akaike Information Criteria, Bayesian Information Criteria and graphical techniques (PDF, CDF, Probability Difference, P-P and Q-Q plots) were used for comparing the candidate distributions. Also conducted simulation studies in R Programming for checking whether distribution imitate the observed values of flood heights. High quantiles of extreme flood heights are obtained for their return period.

Keywords: Naraj barrage; Kumaraswamy distribution; Goodness of fit test; MLE; Return period

Rainfall plays a vital role in the state?s economy because Rajasthan is a waterdeficient state. The state of Rajasthan is classified into ten agro-climatic zones. These zones describe the upper and lower limit of the rainfall, a classification given by Indian Agricultural Research Institute (ICAR). This paper presents a new technique Random Effect Model (REM), to estimate these limits. The literature related to estimating rainfall interval using the statistical technique has not observed the heterogeneity among the units. The units may differ in size, magnitude, kind, impact etc. but the REM technique is beneficial for estimating the mean of heterogeneous groups like agro-climate zones. This paper attempts to use this technique to estimate rainfall confidence intervals among the state?s ten agro-climate zones. This technique to estimate the rainfall interval of agroclimate has been used for the first time. The comparison between estimation of rainfall upper and lower limits obtained by these methods? has also been discussed. This paper deals with estimates variability of the rain across all districts, including ten agro-climate zones. The result shows that the REM is a statistically effective method to estimate rainfall intervals. The study shows no statistical difference in average rainfall between humid southern, eastern plain, flood-prone eastern plain, sub-humid southern plains, and the humid southern plain. The minimum level of rain in different agro-climate zones calculated by the ICAR is overestimated because the REM has not proved it. The maximum level of rainfall is almost similar in both estimations. 

 Keywords: Agro-climate zone, Annual rainfall, Confidence interval, Random effect model.