Quantitative Assessment on Fitting of Gumbel and Frechet Distributions for Extreme Value Analysis of Rainfall

Authors

  • N. Vivekanandan  Central Water and Power Research Station, Pune, Maharashtra, India

Keywords:

Anderson-Darling, D-Index, Frechet, Gumbel, Kolmogorov-Smirnov, Rainfall

Abstract

Rainfall frequency analysis plays an important role in hydrologic and economic evaluation of water resources projects. It helps to estimate the return periods and their corresponding event magnitudes thereby creating reasonable design criteria. Depending on the size, life time and design criteria of the structure, different return periods are generally stipulated for adopting Extreme Value Analysis (EVA) results. This paper illustrates the use of quantitative assessment on fitting of Gumbel (EV1) and Frechet (EV2) probability distributions to the series of annual 1-day maximum rainfall (AMR) data using Goodness-of-Fit (GoF) and diagnostic tests. Order Statistics Approach (OSA) is used for determination of parameters of the distributions. Based on GoF (using Anderson-Darling and Kolmogorov-Smirnov) and diagnostic (using D-index) test results, the study identifies the EV1 distribution is better suited for EVA of rainfall for Fatehabad and Hissar.

References

  1. E.J. Gumbel, Statistic of Extremes, 2nd Edition, Columbia University Press, New York, 1960.
  2. J.A. Carta and P. Ramirez, "Analysis of two-component mixture Weibull statistics for estimation of wind speed distributions", Journal of Renewable Energy, Vol. 32, No.3, pp. 518-531, 2007.
  3. N. Mujere, "Flood frequency analysis using the Gumbel distribution", Journal of Computer Science and Engineering, Vol. 3, No. 7, pp. 2774-2778, 2011.
  4. M.C. Casas, R. Rodriguez, M. Prohom, A. Gazquez, and A. Redano, "Estimation of the probable maximum precipitation in Barcelona (Spain)", Journal of Climatology, Vol. 31, No. 9, pp. 1322-1327, 2011.
  5. E. Baratti, A. Montanari, A. Castellarin, J.L. Salinas, A. Viglione, and A. Bezzi, "Estimating the flood frequency distribution at seasonal and annual time scales", Hydrological Earth System Science, Vol. 16, No. 12, pp. 4651-4660, 2012.
  6. A. Peck, P. Prodanovic and S.P. Simonovic, "Rainfall intensity duration frequency curves under climate change: city of London, Ontario, Canada", Canadian Water Resources Journal, Vol. 37, No. 3, pp. 177-189, 2012.
  7. L.S. Esteves, "Consequences to flood management of using different probability distributions to estimate extreme rainfall", Journal of Environmental Management, Vol. 115, No. 1, pp. 98-105, 2013.
  8. B.A. Olumide, M. Saidu, and A. Oluwasesan, "Evaluation of best fit probability distribution models for the prediction of rainfall and runoff volume (Case Study Tagwai Dam, Minna-Nigeria)", Journal of Engineering and Technology, Vo1. 3, No.2, pp. 94-98, 2013.
  9. V. Rahmani, S.L. Hutchinson, J.M.S. Hutchinson and A. Anandhi, "Extreme daily rainfall event distribution patterns in Kansas," Journal of Hydrologic Engineering, Vol. 19, No. 4, pp. 707-716, 2014.
  10. Zhanling Li, Zhanjie Li, Wei Zhao, and Yuehua Wang, "Probability Modeling of Precipitation Extremes over Two River Basins in Northwest of China," Advances in Meteorology, Vol. 13, Article ID 374127, pp. 1-13, 2015.
  11. J. Zhang, "Powerful goodness-of-fit tests based on the likelihood ratio", Journal of Royal Statistical Society, Vol. 64, No. 2, pp. 281-294, 2002.
  12. A.H. Ang, and W.H. Tang, Probability concepts in engineering planning and design, Vol. 2, John Wiley & Sons, 1984.
  13. Atomic Energy Regulatory Board (AERB), Extreme values of meteorological parameters, AERB Safety Guide No. NF/SG/ S-3, 2008.
  14. P.E. Charles Annis, Goodness-of-Fit Tests for Statistical Distributions,[http://www.statistical engineering.com/goodness.html], 2009.
  15. United States Water Resources Council (USWRC), Guidelines for determining flood flow frequency’, Bulletin No. 17B, 1981.

International Journal of Scientific Research in Science and Technology

Downloads

Published

2015-06-30

Issue

Volume 1, Issue 2, May-June-2015

Section

Research Articles

License

Copyright (c) IJSRST

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
N. Vivekanandan, " Quantitative Assessment on Fitting of Gumbel and Frechet Distributions for Extreme Value Analysis of Rainfall , International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011, Volume 1, Issue 2, pp.68-73, May-June-2015.