N. Vivekanandan | International Journal of Water Resources Engineering | Vol 10, Issue 01 | pp. 1-10 | ISSN: 2456-1606
Abstract
Estimation of peak flood discharge (PFD) for a given return period is required for the design of culverts, dams, spillways, bridges, flood protection and soil conservation work, etc. The dimension and capacity of the hydraulic structures will also depend on design flood magnitude that may have some uncertainty due to model error. This paper presented a study assessment of uncertainty on estimation of PFD using LN2 distribution for river Tapi at Sarangkheda site. For this purpose, the annual maximum discharge (AMD) series with different data length (say, series with 50 years data (DS1), series with 70 years data (DS2) and series with 82 years data (DS3) was generated from the observed AMD data (1941 to 2022) of Sarangkheda and used for estimation of PFD. Goodness-of-Fit (GoF) (viz., Chi-Square and Kolmogorov–Smirnov tests and model performance indicators (viz., correlation coefficient (CC) and mean absolute error (MAE)) was applied for checking the adequacy of fitting three parameter estimation methods viz., method of moments (MoM), maximum likelihood method (MLM) and method of L-Moments (LMO) of LN2 to the series of AMD data. The GoF tests results supported the use of all three methods of LN2 for estimation of PFD for different return periods. The outcomes of the study indicated that (i) there is a good correlation between the observed and estimated AMDs by three methods of LN2, and the CC values vary from 0.985 to 0.991; (ii) the quantum of uncertainty in the estimated PFD measured through MAE by MoM, MLM and LMO is in decreasing order when the data length increases; and (iii) the MAE computed by MLM is minimum than those values of MoM and LMO while applying the DS1, DS2 and DS3 series for estimation of PFD. The study showed that the PFD given by MLM of LN2 distribution could be used for the design of civil and hydraulic structures.
References
1. Ul Hassan M, Hayat O, Noreen Z. Selecting the best probability distribution for at-site flood frequency analysis: A study of Torne River. SN Appl Sci. 2019;1(12):1–10. https://doi.org/10.1007/s42452-019-1584-z. 2. Renard B, Kavetski D, Kuczera G, Thyer M, Franks SW. Understanding predictive uncertainty in hydrologic modelling: The challenge of identifying input and structural errors. Water Resour Res. 2010;46(5):1–22. https://doi.org/10.1029/2009WR008328. 3. Tung Y, Wong C. Assessment of design rainfall uncertainty for hydrologic engineering applications in Hong Kong. Stoch Environ Res Risk Assess. 2014;28(3):583–592. https://doi.org/10.1007/s00477-013-0774-2. 4. Tfwala CM, Van Rensburg LD, Schall R, Mosia SM, Dlamini P. Precipitation intensity-durationfrequency curves and their uncertainties for Ghaap plateau. Clim Risk Manag. 2017;16(1):1–9. https://doi.org/10.1016/j.crm.2017.04.004. 5. Ibrahim MN. Assessment of the uncertainty associated with statistical modelling of precipitation extremes for hydrologic engineering applications in Amman, Jordan. Sustainability. 2022;14(24):1–20. https://doi.org/10.3390/su142417052. 6. Hailegeorgis TT, Thorolfsson ST, Alfredsen K. Regional frequency analysis of extreme precipitation with consideration to uncertainties to update IDF curves for the city of Trondheim. J Hydrol. 2013;498(1):305–318. https://doi.org/10.1016/j.jhydrol. 2013.06.019. 7. Amin MT, Rizwan M, Alazba AA. A best-fit probability distribution for the estimation of rainfall in northern regions of Pakistan. Open Life Sci. 2016;11(1):432–440. https://doi.org/10.1515/biol2016-0057. 8. Kamal V, Mukherjee S, Singh P, Sen R, Vishwakarma CA, Sajadi P, et al. Flood frequency analysis of Ganga River at Haridwar and Garhmukteshwar. Appl Water Sci. 2017;7(4):1979–1986. https://doi.org/10.1007/s13201-016-0378-3. 9. Rosmaini E, Saphira YY. Probability distribution of rainfall in Medan. J Res Math Trends Technol. 2019;1(2):39–45. https://doi.org/10.32734/jormtt.v1i2.2835. 10. Vivekanandan N. Evaluation of estimators of probability distributions for frequency analysis of rainfall and river flow data. Int J Sci Res Civ Eng. 2020;4(4):67–75. http://ijsrce.com/IJSRCE204412. 11. Kaur L, Kumar M, Verma SL, Kumar P. Annual maximum rainfall prediction using frequency analysis for Roorkee, Uttarakhand, India. Mausam. 2021;72(2):359–372. https://doi.org/10.54302/Mausam.v72i2.623. 12. Khan Z, Rahman A, Karim F. An assessment of uncertainties in flood frequency estimation using Bootstrapping and Monte Carlo simulation. Hydrology. 2023;10(1):1–16. https://doi.org/10.3390/hydrology10010018. 13. Bilkova D. Lognormal distribution and using L-moment method for estimating its parameters. Int J Math Models Methods Appl Sci. 2012;6(1):30–44. 14. Hosking JRM. L-moments: Analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc Ser B (Stat Methodol). 1990;52(1):105–124. https://doi.org/10.1111/j.2517-6161.1990.tb01775.x. 15. Zhang J. Powerful goodness-of-fit tests based on the likelihood ratio. J R Stat Soc Ser B (Stat Methodol). 2002;64(2):281–294. https://doi.org/10.1111/1467-9868.00337. 16. Vivekanandan N, Mathew FT, Roy SK. Modelling of wind speed data using probabilistic approach. J Power River Valley Dev. 2012;62(3–4):42–45.
