International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.1, No.3, Jun. 2015, Pub. Date: May 20, 2015
Frequency Analysis of Annual Maximum Flood Discharge Using Method of Moments and Maximum Likelihood Method of Gamma and Extreme Value Family of Probability Distributions
Pages: 141-146 Views: 1584 Downloads: 1112
[01] N. Vivekanandan, Central Water and Power Research Station, Pune, India.
Estimation of Maximum Flood Discharge (MFD) for a given return period is important for planning, design and management of hydraulic structures for the project. This can be achieved through Flood Frequency Analysis (FFA) by fitting of probability distributions to the recorded Annual Maximum Discharge (AMD) data. In this paper, Gamma and Extreme Value family of probability distributions are adopted in FFA. Method of Moments and Maximum Likelihood Method are used for determination of parameters of six probability distributions. Goodness-of-Fit tests such as Chi-square and Kolmogorov-Smirnov are applied for checking the adequacy of fitting of probability distributions to the recorded AMD data. Diagnostic test of D-index is used for the selection of a suitable distribution for estimation of MFD. The study showed that the exponential distribution (using MLM) is found to be better suited amongst six distributions adopted in estimation of MFD at Dedtalai and gamma distribution (using MLM) for Ghala.
Chi-square, D-index, Kolmogorov-Smirnov, Maximum Flood, Probability Distribution
[01] Baratti, E., Montanari, A., Castellarin, A., Salinas, J.L., Viglione, A. and Bezzi, A. (2012); Estimating the flood frequency distribution at seasonal and annual time scales, Hydrology and Earth System Sciences, Vol. 16, No. 12, pp. 4651–4660.
[02] Bhakar, S.R., Bansal, A.K., Chhajed, N. and Purohit R.C. (2006); Frequency analysis of consecutive days maximum rainfall at Banswara, Rajasthan, India. ARPN Journal of Engineering and Applied Sciences, Vol. 1, No. 3, pp. 64-67.
[03] Das, L.M. and Qureshi, Z.H. (2014); Flood frequency analysis for Jiya Dhol river of Brahmaputra valley, Journal of Sciences: Basic and Applied Research, Vol. 14, No. 2, pp. 14-24.
[04] Esteves, L.S. (2013); Consequences to flood management of using different probability distributions to estimate extreme rainfall, Journal of Environmental Management, Vol. 115, No. 1, pp. 98-105.
[05] Ghorbani, A.M., Ruskeep, A.H., Singh, V.P. and Sivakumar, B. (2010); Flood Frequency analysis using mathematica, Turkish Journal of Engineering and Environmental Sciences, Vol. 34, No. 3, pp. 171-188.
[06] Haktanir, T. and Horlacher, H.B. (1993); Evaluation of various distributions for flood frequency analysis, Hydrological Sciences Journal, Vol. 38, No. 1, pp. 15-32.
[07] Hosking, J.R.M. and Wallis, J.R. (1993); Some statistics useful in regional frequency analysis, Water Resources Research, Vol. 29, No. 2, pp. 271-281.
[08] Izinyon, O.C. and Ajumuka, H.N. (2013); Probability distribution models for flood prediction in Upper Benue River Basin, Journal of Civil and Environmental Research, Vo1. 3, No. 2, pp. 62-74.
[09] Kumar, R., Chatterjee, C., Kumar, S., Lohani, A.K. and Singh, R.D. (2003); Development of regional flood frequency relationships using L-moments for Middle Ganga Plains Subzone 1(f) of India, Water Resources Management, Vol. 17, No. 4, pp. 243–257.
[10] Khosravi, Gh., Magidi, A. and Nohegar, A. (2012); Determination of suitable probability distribution for annual and peak discharge estimations (Case Study: Minab River-Barantin Gage, Iran). Journal of Probability and Statistics, Vo1. 1, No. 5, pp. 160-163.
[11] Lee, C. (2005); Application of rainfall frequency analysis on studying rainfall distribution characteristics of Chia-Nan plain area in Southern Taiwan, Journal of Crop, Environment & Bioinformatics, Vol. 2, No. 1, pp. 31-38.
[12] Mujere, N. (2011); Flood frequency analysis using the Gumbel distribution, Journal of Computer Science and Engineering, Vol. 3, No. 7, pp. 2774-2778.
[13] Seckin, N., Yurtal, R., Haktanir, T. and Dogan A. (2010); Comparison of probability weighted moments and maximum likelihood methods used in flood frequency analysis for Ceyhan river basin, Arabian Journal for Science and Engineering, Vol. 35, No. 1B , pp. 49-69.
[14] Rao, A.R. and Hamed, K.H. (2000); Flood frequency analysis, CRC Publications, New York.
[15] Saf, B. (2009); Regional flood frequency analysis using L-moments for the West Mediterranean Region of Turkey, Water Resources Management, Vol. 23, No. 3, pp. 531-551.
[16] United States Water Resources Council (1981); Guidelines for determining flood flow frequency, Bulletin No. 17B.
[17] Vivekanandan N. (2014); Frequency analysis of annual 1-day maximum rainfall using extreme value distributions, Fidelity Journals of Physical Sciences Vol. 1, No. 1 pp. 1-4.
[18] Zhang, J. (2002); Powerful goodness-of-fit tests based on the likelihood ratio, Journal of Royal Statistical Society Series B, Vol. 64, pp. 281-294.
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