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A Comparative Study on Gumbel and LP3 Probability Distributions for Estimation of Extreme Rainfall

N VIVEKANANDAN

Abstract


Estimation of extreme rainfall for a given return period has utmost importance for planning, design and management of hydraulic and other civil structures in a region. This can be achieved by Extreme Value Analysis (EVA) that involves fitting of probability distributions to the annual maximum series of rainfall. This paper details a study on EVA of hourly and daily rainfall for Santacruz and Colaba sites by adopting Gumbel and Log Pearson Type-3 (LP3) probability distributions. Parameters of the distributions are determined by maximum likelihood method and used for estimation of rainfall. Goodness-of-Fit (GoF) and diagnostic tests are applied for quantitative assessment whereas the qualitative assessment is made through fitted curves of the estimated values. Anderson-Darling GoF test is applied for checking the adequacy of fitting of probability distributions adopted in EVA of rainfall. The selection of best suitable distribution for estimation of rainfall is evaluated by diagnostic test through model performance indicators viz., correlation coefficient, model efficiency and root mean squared error. The outcome of the study indicates that LP3 distribution could be used for design purposes by considering the risk involved in the operation and management of hydraulic structures.

 

Keywords: Anderson-Darling, correlation coefficient, Gumbel, Log Pearson Type-3, maximum likelihood method, mean squared error, model efficiency, rainfall

Cite this Article: N. Vivekanandan. A Comparative Study on Gumbel and LP3 Probability Distributions for Estimation of Extreme Rainfall. International Journal of Water Resources Engineering. 2020; 6(1): 21–33p.


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References


Afungang, R., and Bateira, C., Statistical modelling of extreme rainfall, return periods and associated hazards in the Bamenda Mountain, NW Cameroon, pp. 5-19, 2016.

AlHassoun, S.A., Developing empirical formulae to estimate rainfall intensity in Riyadh region, Journal of King Saud University-Engineering Sciences, 23(1): 81–88, 2011.

Atomic Energy Regulatory Board (AERB), Extreme values of meteorological parameters (AERB Guide No. NF/SG/ S-3), 2008.

Baratti, E., Montanari, A., Castellarin, A., Salinas, J.L., Viglione, A., and Bezzi, A., Estimating the flood frequency distribution at seasonal and annual time scales, Hydrological Earth System Science, 16(12): 4651–4660, 2012.

Bhakar, S.R., Bansal, A.K., Chhajed, N., and Purohit, R.C., Frequency analysis of consecutive days maximum rainfall at Banswara, Rajasthan, India, ARPN Journal of Engineering and Applied Sciences, 1(1): 64-67, 2006.

Bobee, B., and Askhar, F., The Gamma family and derived distributions applied in hydrology, Water Resources Publications, 1991.

Chen, J., and Adams, B.J., Integration of artificial neural networks with conceptual models in rainfall-runoff modelling, Journal of Hydrology, 318(1-4): 232-249, 2006.

CWC, Development of Hydrological Design Aids (Surface water) under Hydrology Project II: State of the Art Report, Consulting Engineering Services (India) in Association with HR Wallingford, Central Water Commission (CWC), New Delhi, 2010.

Di Balldassarre, G., Castellarin, A., and Brath, A., Relationships between statistics of rainfall extremes and mean annual precipitation: an application for design-storm estimation in northern central Italy, Hydrology and Earth System Sciences, 10(2): 589–601, 2006.

Esteves, L.S., Consequences to flood management of using different probability distributions to estimate extreme rainfall, Journal of Environmental Management, 115(1): 98-105, 2013.

Gumbel, E.J., Statistics of Extremes, Columbia University Press, New York, 1985.

International Atomic Energy Agency (IAEA), Meteorological events in site evaluation for nuclear power plants – IAEA Safety Guide, No.Ns-G-3.4, International Atomic Energy Agency, Vienna, 2003.

Naghavi, B., Yu, F.X., and Singh, V.P., Comparative evaluation of frequency distributions for Louisiana extreme rainfall. Water Resources Bulletin, 29(2): 211-219, 1993.

Rao, A.R., and Hamed, K.H., Flood frequency analysis, CRC Publications, New York, 2000.

Rasel, M., and Hossain, S.M., Development of rainfall intensity duration frequency equations and curves for seven divisions in Bangladesh, International Journal of Scientific and Engineering Research, 6(5): 96-101, 2015.

Sasireka, K., Suribabu, C.R., Neelakantan, T.R., Extreme Rainfall Return Periods using Gumbel and Gamma Distribution, International Journal of Recent Technology and Engineering, 8 (4): 27-29, 2019.

Surwade, K.B., Ramesh, C., Kshirsagar, M.M., and Govindan, S., Assessment of peak maximum rainfall for estimation of peak flood for ungauged Lakya catchment – A case study, Hydrology Journal, Indian Association of Hydrologists, 32(1-2): 1-16, 2009.

Varathan, N., Perera, K., and Nalin., Statistical modelling of extreme daily rainfall in Colombo, Board of Study in Statistics and Computer Science of the postgraduate institute of science, University of Peradeniya, Sri Lanka, 2010.

Vivekanandan, N., Prediction of seasonal and annual rainfall using order statistics approach of Gumbel and Frechet distributions, British Journal of Engineering and Technology, 1(1):140-151, 2012.

Zhang, J., Powerful goodness-of-fit tests based on the likelihood ratio, Journal of Royal Statistical Society Series-B, 64(2): 281-294, 2002.




DOI: https://doi.org/10.37628/jwre.v6i1.609

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