Evaluation of Best-Fit Probability Distribution for Prediction of Extreme Hydrologic Phenomena

Authors: Karim Hamidi Machekposhti, Hossein Sedghi

Abstract:

The probability distributions are the best method for forecasting of extreme hydrologic phenomena such as rainfall and flood flows. In this research, in order to determine suitable probability distribution for estimating of annual extreme rainfall and flood flows (discharge) series with different return periods, precipitation with 40 and discharge with 58 years time period had been collected from Karkheh River at Iran. After homogeneity and adequacy tests, data have been analyzed by Stormwater Management and Design Aid (SMADA) software and residual sum of squares (R.S.S). The best probability distribution was Log Pearson Type III with R.S.S value (145.91) and value (13.67) for peak discharge and Log Pearson Type III with R.S.S values (141.08) and (8.95) for maximum discharge in Jelogir Majin and Pole Zal stations, respectively. The best distribution for maximum precipitation in Jelogir Majin and Pole Zal stations was Log Pearson Type III distribution with R.S.S values (1.74&1.90) and then Pearson Type III distribution with R.S.S values (1.53&1.69). Overall, the Log Pearson Type III distributions are acceptable distribution types for representing statistics of extreme hydrologic phenomena in Karkheh River at Iran with the Pearson Type III distribution as a potential alternative.

Keywords: Karkheh river, log pearson type III, probability distribution, residual sum of squares.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1474877

References:

[1] Abida H, Ellouze M. Probability distribution of flood flows in Tunisia. Hydrology and Earth System Sciences Discussions. 2007; 4(2): 957-981.
[2] Alias NE, Takara K. Probability Distribution for Extreme Hydrological Value-Series in the Yodo River Basin, Japan and Kuala Lumpur, Malaysia. In Proceedings of the 2nd International Conference on Water Resources. Langkawi, Malaysia. 2012.
[3] Atroosh KB, Moustafa AT. An Estimation of the Probability Distribution of Wadi Bana Flow in the Abyan Delta of Yemen. Journal of Agricultural Science. 2012; 4(6): 80-89.
[4] Garba H, Ismail A, Tsoho U. Fitting Probability Distribution Functions to Discharge Variability of Kaduna River. International Journal of Modern Engineering Research (IJMER). 2013; 3(5): 2848-2852.
[5] Haktan Y. Comparison of Various Flood Frequency Distribution using Annual Flood Peaks Data of Rivers in Anatolis. J. Hdrol. 1992; 136: 1-31.
[6] Hamidi machekposhti K, Sedghi H, Telvari A, Babazadeh H. Determination of Suitable Probability Distribution for Annual Discharges Estimation (Case Study: Karkheh River at Iran). International Journal of Probability and Statistics. 2016; 5(3): 73-81.
[7] Hosking JRM, Wallis JR. Some Statistics Useful in Regional Frequency Analysis. Water Resources Research. 1993; 29(2): 271-281.
[8] Ibrahim MH, Isiguzo EA. Flood Frequency Analysis of Guara River Catchment at Jere, Kaduna State, Nigeria. Scientific Research and Essay. 2009; 4(6): 636–646.
[9] Izinyon, OC, Ihimekpen N, Igbinoba GE. Flood Frequency Analysis of Ikpoba River Catchment at Benin City Using Log Pearson Type III Distribution. Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS). 2011; 2(1): 50-55.
[10] Khosravi GH, Majidi A, Nohegar A. Determination of Suitable Probability Distribution for Annual Mean and Peak Discharges Estimation (Case Study: Minab River- Barantin Gage, Iran). International Journal of Probability and Statistics. 2012; 1(5): 160-163.
[11] Mohammed JM, Otache YM, Jibril I, Mohammed ISH. Evaluation of Best-Fit Probability Distribution Models for the Prediction of Inflows of Kainji Reservoir, Niger State, Nigeria. Air, Soil and Water Research. 2017; 10: 1–7.
[12] Ni Lar W, Khin Maung W. The Probability Distributions of Daily Rainfall for Kuantan River Basin in Malaysia. International Journal of Science and Research (IJSR). 2014; 3(8): 977-983.
[13] Sheng Y, Michio H. Probability distribution of annual, seasonal and monthly precipitation in Japan. Hydrological sciences journal. 2007; 52(5): 863-877.
[14] Strupczewski WG, Kochanek K, Markiewicz I, Bogdanowicz E, Weglarczyk S, Singh VP. On the tails of distributions of annual peak flows. Hydrology Research. 2011; 42(2-3): 171-192.
[15] Vogel R, Wilson I. Probability distribution of annual maximum, mean and minimum stream flows in the United States. Journal of Hydrologic Engineering. 1996; 1(2): 69-76.