Comparison of Probability Distributions for Estimation of Peak Flood Discharge
Author(s)
N. Vivekanandan
ABSTRACT
Estimation of peak flood discharge (PFD) for a given return period is of utmost importance for planning and design of hydraulic structures in the project site. The peak value of a flood discharge having a pre-defined average return period is determined by frequency analysis, known as flood frequency analysis (FFA). The paper compares the eight probability distributions used for estimation of PFD for Malakkara and Neeleswaram. Maximum likelihood method is used for determination of parameters of the probability distributions. Goodness-of-Fit tests such as Anderson-Darling and Kolmogorov-Smirnov are applied for checking the adequacy of fitting of the distributions to the recorded annual maximum discharge. A diagnostic test of D-index is used for the selection of a most suitable distribution for FFA. Based on GoF and diagnostic test results, the study shows the EV1 distribution is better suited for estimation of PFD for Malakkara whereas LP3 for Neeleswaram.
Estimation of peak flood discharge (PFD) for a given return period is of utmost importance for planning and design of hydraulic structures in the project site. The peak value of a flood discharge having a pre-defined average return period is determined by frequency analysis, known as flood frequency analysis (FFA). The paper compares the eight probability distributions used for estimation of PFD for Malakkara and Neeleswaram. Maximum likelihood method is used for determination of parameters of the probability distributions. Goodness-of-Fit tests such as Anderson-Darling and Kolmogorov-Smirnov are applied for checking the adequacy of fitting of the distributions to the recorded annual maximum discharge. A diagnostic test of D-index is used for the selection of a most suitable distribution for FFA. Based on GoF and diagnostic test results, the study shows the EV1 distribution is better suited for estimation of PFD for Malakkara whereas LP3 for Neeleswaram.
Cite this paper
Vivekanandan, N. (2014) Comparison of Probability Distributions for Estimation of Peak Flood Discharge. Open Access Library Journal, 1, 1-7. doi: 10.4236/oalib.1100498.
Vivekanandan, N. (2014) Comparison of Probability Distributions for Estimation of Peak Flood Discharge. Open Access Library Journal, 1, 1-7. doi: 10.4236/oalib.1100498.
References
[1] Neslihan, S., Recep, Y., Tefaruk, H. and Ahmet, D. (2010) Comparison of Probability Weighted Moments and Maximum Likelihood Methods Used in Flood Frequency Analysis for Ceyhan River Basin. Arabian Journal of Science and Engineering, 35, 49-69. [2] 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. Hydrological Earth System Science, 16, 4651-4660.
http://dx.doi.org/10.5194/hess-16-4651-2012 [3] Aksoy, H. (2000) Use of Gamma Distribution in Hydrological Analysis. Turkey Journal of Engineering and Environmental Sciences, 24, 419-428. [4] May, W. (2004) Variability and Extremes of Daily Rainfall during the Indian Summer Monsoon in the Period 1901-1989. Journal of Global & Planetary Change, 44, 83-105.
http://dx.doi.org/10.1016/j.gloplacha.2004.06.007 [5] Sharda, V.N. and Das, P.K. (2005) Modelling Weekly Rainfall Data for Crop Planning in a Sub-Humid Climate of India. Journal of Agricultural and Water Management, 76, 120-138.
http://dx.doi.org/10.1016/j.agwat.2005.01.010 [6] Salami, A.W. (2004) Prediction of the Annual Flow Regime along ASA River Using Probability Distribution Models. AMSE Periodicals. Modelling, Measurement and Control, 65, 41-56. [7] 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, 2, 31-38. [8] 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, 1, 64-67. [9] Fang, B., Guo, S., Wang, S., Liu, P. and Xiao, Y. (2007) Non-Identical Models for Seasonal Flood Frequency Analysis. Journal of Hydrological Sciences, 52, 974-991.
http://dx.doi.org/10.1623/hysj.52.5.974 [10] Chen, L., Guo, S., Yan, B., Liu, P. and Fang, B. (2010) A New Seasonal Design Flood Method Based on Bivariate Joint Distribution of Flood Magnitude and Date of Occurrence. Journal of Hydrological Sciences, 55, 1264-1280.
http://dx.doi.org/10.1080/02626667.2010.520564 [11] Allamano, P., Laio, F. and Claps, P. (2011) Effects of Disregarding Seasonality on the Distribution of Hydrological Extremes. Journal of Hydrology and Earth System Sciences, 15, 3207-3215.
http://dx.doi.org/10.5194/hess-15-3207-2011 [12] Bowers, M.C., Tung, W.W. and Gao, J.B. (2012) On the Distributions of Seasonal River Flows: Lognormal or Power Law? Journal of Water Resources Research, 48, Paper No. W05536. [13] Vijayagopal, P., Vivekanandan, N. and Kannan, S. (2013) Assessing Adequacy of Probability Distribution for Development of IDF Relationships for Mandla and Jabalpur. Journal of Scientific Research and Reviews, 2, 99-114. [14] Rao, A.R. and Hamed, K.H. (2000) Flood Frequency Analysis. CRC Publications, New York. [15] Zhang, J. (2002) Powerful Goodness-of-Fit Tests Based on the Likelihood Ratio. Journal of Royal Statistical Society Series B, 64, 281-294.
http://dx.doi.org/10.1111/1467-9868.00337 [16] United States Water Resources Council (USWRC) (1981) Guidelines for Determining Flood Flow Frequency. Bulletin No. 17B, 15-19.
[1] Neslihan, S., Recep, Y., Tefaruk, H. and Ahmet, D. (2010) Comparison of Probability Weighted Moments and Maximum Likelihood Methods Used in Flood Frequency Analysis for Ceyhan River Basin. Arabian Journal of Science and Engineering, 35, 49-69. [2] 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. Hydrological Earth System Science, 16, 4651-4660.
http://dx.doi.org/10.5194/hess-16-4651-2012 [3] Aksoy, H. (2000) Use of Gamma Distribution in Hydrological Analysis. Turkey Journal of Engineering and Environmental Sciences, 24, 419-428. [4] May, W. (2004) Variability and Extremes of Daily Rainfall during the Indian Summer Monsoon in the Period 1901-1989. Journal of Global & Planetary Change, 44, 83-105.
http://dx.doi.org/10.1016/j.gloplacha.2004.06.007 [5] Sharda, V.N. and Das, P.K. (2005) Modelling Weekly Rainfall Data for Crop Planning in a Sub-Humid Climate of India. Journal of Agricultural and Water Management, 76, 120-138.
http://dx.doi.org/10.1016/j.agwat.2005.01.010 [6] Salami, A.W. (2004) Prediction of the Annual Flow Regime along ASA River Using Probability Distribution Models. AMSE Periodicals. Modelling, Measurement and Control, 65, 41-56. [7] 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, 2, 31-38. [8] 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, 1, 64-67. [9] Fang, B., Guo, S., Wang, S., Liu, P. and Xiao, Y. (2007) Non-Identical Models for Seasonal Flood Frequency Analysis. Journal of Hydrological Sciences, 52, 974-991.
http://dx.doi.org/10.1623/hysj.52.5.974 [10] Chen, L., Guo, S., Yan, B., Liu, P. and Fang, B. (2010) A New Seasonal Design Flood Method Based on Bivariate Joint Distribution of Flood Magnitude and Date of Occurrence. Journal of Hydrological Sciences, 55, 1264-1280.
http://dx.doi.org/10.1080/02626667.2010.520564 [11] Allamano, P., Laio, F. and Claps, P. (2011) Effects of Disregarding Seasonality on the Distribution of Hydrological Extremes. Journal of Hydrology and Earth System Sciences, 15, 3207-3215.
http://dx.doi.org/10.5194/hess-15-3207-2011 [12] Bowers, M.C., Tung, W.W. and Gao, J.B. (2012) On the Distributions of Seasonal River Flows: Lognormal or Power Law? Journal of Water Resources Research, 48, Paper No. W05536. [13] Vijayagopal, P., Vivekanandan, N. and Kannan, S. (2013) Assessing Adequacy of Probability Distribution for Development of IDF Relationships for Mandla and Jabalpur. Journal of Scientific Research and Reviews, 2, 99-114. [14] Rao, A.R. and Hamed, K.H. (2000) Flood Frequency Analysis. CRC Publications, New York. [15] Zhang, J. (2002) Powerful Goodness-of-Fit Tests Based on the Likelihood Ratio. Journal of Royal Statistical Society Series B, 64, 281-294.
http://dx.doi.org/10.1111/1467-9868.00337 [16] United States Water Resources Council (USWRC) (1981) Guidelines for Determining Flood Flow Frequency. Bulletin No. 17B, 15-19.