Development in Earth Science, Volume 4, 2016 www.seipub.org/des doi: 10.14355/des.2016.04.001
Intercomparison of Probability Distributions for Extreme Value Analysis of Rainfall under Missing Data Scenario N. Vivekanandan Central Water and Power Research Station, Pune, Maharashtra, India Abstract Assessment of extreme rainfall is one of the important parameters for planning, design and management of hydraulic structures at the project site. This can be obtained through Extreme Value Analysis (EVA) of rainfall by fitting of probability distributions to the data series of annual 1‐day maximum rainfall. This paper illustrates the adoption of Gumbel (EV1), Frechet (EV2), 2‐parameter Log Normal (LN2) and Log Pearson Type‐3 (LP3) distributions in EVA for Tohana. Methods of moments and Maximum Likelihood Method (MLM) are used for determination of parameters of EV1, EV2, LN2 and LP3 distributions. In addition to above, order statistics approach is used for determination of parameters of EV1 and EV2. The adequacy of fitting of probability distributions is evaluated by Goodness‐of‐Fit tests viz., Anderson‐Darling and Kolmogorov‐Smirnov and diagnostic test using D‐index. By considering the design‐life of the structure, the study suggests the estimated extreme rainfall using LP3 (MLM) distribution could be used for design purposes. Keywords Anderson‐Darling, D‐index, Extreme Value Analysis, Kolmogorov‐Smirnov, Log Pearson, Rainfall
Introduction Rainfall frequency analysis plays an important role in hydrologic and economic evaluation of water resources pro‐ jects. It helps to estimate the return periods and their corresponding event magnitudes thereby creating reasonable design criteria. The basic problem in rainfall studies is an information problem, which can be approached through Extreme Value Analysis (EVA) of rainfall. As the distribution of rainfall varies over space and time, it is required to analyze the data covering long periods and recorded at various locations to obtain reliable information [1]. Out of a number of probability distributions that are adopted in frequency analysis, Gumbel (EV1), Frechet (EV2), 2‐parameter Log Normal (LN2) and Log Pearson Type‐3 (LP3) are extensively used for EVA of rainfall. Based on the applicability, standard parameter estimation procedures viz., Methods of Moments (MoM) and Maximum Like‐ lihood Method (MLM) are generally used for determination of parameters [2]. In addition to MoM and MLM, Atomic Energy Regulatory Board (AERB) guidelines [3] described that the Order Statistics Approach (OSA) can also be considered for determination of parameters of EV1 and EV2 distributions. AERB guidelines also described that the OSA estimates are popular owing to less bias and minimum variance though number of methods are avail‐ able for parameter estimation. In the recent past, numbers of studies have been carried out by researchers adopting probability distributions for EVA of rainfall. Lee [4] expressed that the Pearson Type‐3 (PR3) distribution is better suited amongst five distributions studied for analyzing the rainfall distribution characteristics of Chia‐Nan plain area. Bhakar et al. [5] studied the frequency analysis of consecutive day’s maximum rainfall at Banswara, Rajasthan, India. Study by Saf et al. [6] revealed that the PR3 distribution is better suited for modelling of extreme values in Antalya and Lower‐West Mediterranean sub‐regions whereas the Generalized Logistic distribution for the Upper‐ West Mediterranean sub‐region. Mujere [7] applied EV1 distribution for modelling flood data for the Nyanyadzi River, Zimbabwe. Baratti et al. [8] carried out FFA on seasonal and annual time scales for the Blue Nile River adopting EV1 distribution. Esteves [9] applied EV1 distribution to estimate the extreme rainfall depths at different rain‐gauge stations in southeast United Kingdom. Olumide et al. [10] applied normal and EV1 distributions for prediction of rainfall and runoff at Tagwai dam site in Minna, Nigeria. They have also expressed that the normal distribution is better suited for rainfall pre‐ diction while Log‐Gumbel for runoff. Rasel and Hossain [11] applied EV1 distribution for development of intensity
1