Intercomparison of Estimators of Seven Probability Distributions for Assessment of Peak Flood Discharge

N. Vivekanandan¹ , C. Srishailam² , R.G. Patil³

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.3 , pp.21-28, Jun-2023

Online published on Jun 30, 2023

Copyright © N. Vivekanandan, C. Srishailam, R.G. Patil . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Assessment of Peak Flood Discharge (PFD) for a given return period is considered as one of the important aspects in hydrological studies as also for planning, design and management of civil and hydraulic structures. This can be carried out by Flood Frequency Analysis (FFA) that consists of fitting probability distribution to the annual maximum series of discharge data. In this paper, seven probability distributions such as 2-parameter Log Normal, Pearson Type-3, Log Pearson Type-3, Generalized Extreme Value (GEV), Extreme Value Type-1 (EV1), Extreme Value Type-2 and Pareto are adopted in FFA for river Cauvery at Kollegal and river Sutlej at Powari. The parameters of the distributions are determined by method of moments, maximum likelihood method and method of L-Moments (LMO) wherever applicable, and used for estimation of PFD. Quantitative assessment using Goodness-of-Fit (viz., Chi-square and Kolmogorov-Smirnov) and diagnostic (viz., D-index) tests, and qualitative assessment by fitted curves of the estimated PFD are employed for checking the adequacy of fitting distributions adopted in FFA. The GoF and diagnostic tests results indicates that the EV1 (LMO) is better suited amongst seven distributions studied for estimation of PFD at Kollegal whereas GEV (LMO) for Powari. The study suggests that the estimated PFD by the selected probability distribution could be used for arriving at a design flood for designing civil and hydraulic structures, and for disaster management related activities at Kollegal and Powari sites.

Key-Words / Index Term :
Chi-Square, D-index, Generalized Extreme Value, Kolmogorov-Smirnov, Peak Flood

References :
[1] Isameldin A. Atiem and Nilgün B. Harmanciolu, “Assessment of Regional Floods Using L-Moments Approach: The Case of the River Nile”, Water Resources Management, Vol. 20, Issue 5, pp.723-747, 2006.
[2] Tefaruk Haktanir and Hans B. Horlacher, “Evaluation of Various Distributions for Flood Frequency Analysis”, Hydrological Sciences Journal, Vol.38, Issue 1, pp.15-32, 1993.
[3] Rakesh Kumar and Chandranath Chatterjee, “Regional Flood Frequency Analysis Using L-Moments for North Brahmaputra Region of India”, Journal of Hydrologic Engineering, Vol.10, Issue 1, pp.1-7, 2005.
[4] Mohammad Ali Ghorbani, Heikki Ruskeepa AA,Vijay P. Singh and Bellie Sivakumar, “Flood Frequency Analysis Using Mathematica”, Turkish Journal of Engineering and Environmental Sciences, Vol.34, Issue 3, pp.171-188, 2010.
[5] Neslihan Seckin, Tefaruk Haktanir and Recep Yurtal, “Flood Frequency Analysis of Turkey Using L-Moments Method”, Hydrological Process, Vol.25, No.22, pp.3499-3505, 2011.
[6] Zhang Ziyang, Stadnyk Tricia A and Burn Donald H, “Identification of a Preferred Statistical Distribution for At-Site Flood Frequency Analysis in Canada”, Canadian Water Resources Journal, Vol.45, Issue 1, pp.43-58, 2019.
[7] Babak Naghavi, Fang Xin Yu and Vijay P. Singh, “Comparative Evaluation of Frequency Distributions for Louisiana Extreme Rainfall”, Journal of the American Water Resources Association, Vol.29, Issue 2, pp.211-219. 1993.
[8] Sheng Yue and Chun Yuan Wang, “Possible Regional Probability Distribution Type of Canadian Annual Stream Flow by L-Moments”, Water Resources Management, Vol.18, Issue 5, pp.425-438, 2004.
[9] Tatiana Gubareva and Boris Gartsman, “Estimating Distribution Parameters of Extreme Hydrometeoro-Logical Characteristics by L-Moments Method”, Water Resources, Vol.37, Issue 4, pp.437-445, 2010.
[10] Haberlandt U and Radtke I, “Hydrological Model Calibration for Derived Flood Frequency Analysis Using Stochastic Rainfall and Probability Distributions of Peak Flows”, Hydrology and Earth System Sciences, Vol.18, Issue 1, pp.353-365, 2014.
[11] Kjeldsen TR, Smithers JC and Schulze RE, “Regional Flood Frequency Analysis in the Kwazulu-Natal Province, South Africa Using the Index-Flood Method”, Journal of Hydrology, Vol.255, Issue 1-4, pp.194-211, 2002.
[12] Rakesh Kumar, Chatterjee C, Sanjay Kumar, Lohani AK and Singh RD, “Development of Regional Flood Frequency Relationships Using L-Moments for Middle Ganga Plains Subzone 1(f) of India”, Water Resources Management, Vol.17, Issue 4, pp.243-257, 2003.
[13] Abida H and Ellouze M, “Probability Distribution of Flood Flows in Tunisia”, Hydrology and Earth System Sciences, Vol.12, Issue 3, pp.703-714, 2008.
[14] Betül Saf, “Regional Flood Frequency Analysis Using L-Moments for the West Mediterranean Region of Turkey”, Water Resources Management, Vol.23, Issue 3, pp.531-551, 2009.
[15] Malekinezhad H, Nachtnebel HP and Klik A, “Regionalization Approach for Extreme Flood Analysis Using L-Moments”, Agricultural Science and Technology (Iran), Vol.13, Supplementary Issue, pp.1183–1196, 2011.
[16] Kossi Komi, Barnabas A Amisigo, Bernd Diekkrüger and Fabien CC Hountondji, “Regional Flood Frequency Analysis in the Volta River Basin, West Africa”, Hydrology, Vol.3, Issue 1, pp.1-15, 2016.
[17] Ery Suhartanto, Lily Montarcih Limantara, Dina Noviadriana, Febri Iman Harta and Dwi Aryani K “Estimation of Design Flood with Four Frequency Analysis Distributions”, Asian Journal of Applied Science and Technology, Vol.2, Issue 1, pp.13-27, 2018.
[18] Mahmood Ul Hassan, Omar Hayat and Zahra Noreen, “Selecting The Best Probability Distribution for At-Site Flood Frequency Analysis; A Study of Torne River”, SN Applied Science, Vol.1, Issue 12, Article ID: 1629, 2019.
[19] Vivekanandan N, “Comparison of estimators of five probability distributions for estimation of peak flood”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue 5, pp.53-59, 2020.
[20] Van derSpuy D and Du Plessis JA, “Flood Frequency Analysis - Part 1: Review of the Statistical Approach in South Africa”, Water SA, Vol.48, Issue 2, pp.110-119, 2022.
[21] Hosking JRM, “L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics”, Royal Statistical Society (Series B: Statistical Methodology), Vol.52, Issue 1, pp.105-124, 1990.
[22] Hosking JRM and Wallis JR, “Some Statistics Useful in Regional Frequency Analysis”, Water Resources Research, Vol.29, Issue 2, pp.271-281, 1993.
[23] Rao AR and Hamed KH, Flood frequency analysis, CRC Press, Florida, USA, 2000.
[24] Jin Zhang, “Powerful Goodness-of-Fit Tests Based on the Likelihood Ratio”, Journal of Royal Statistical Society: Series B (Statistical Methodology), Vol.64, Issue 2, pp. 281-294, 2002.
[25] USWRC, “Guidelines for Determining Flood Flow Frequency”, United States Water Resources Council (USWRC), Bulletin No. 17B (Revised), Washington, DC, New York, 1982.