Intercomparison of Rainfall Estimates of EV1 Distribution for Estimation of Peak Flood Discharge for Ungauged Catchments
Keywords:
Anderson-Darling, Gumbel, Kolmogorov-Smirnov, Probability Weighted Moments, Rainfall, Peak Flood DischargeAbstract
Estimation of Peak Flood Discharge (PFD) for a return period is one of the important parameters for planning, design and management of hydraulic structures such as dams, bridges, barrages and storm water drainage systems. For ungauged catchments, rainfall depth becomes an important input for estimation of PFD. The rainfall depth can be determined through Extreme Value Analysis (EVA), which involves fitting of probability distribution to the series of Annual 1-day Maximum Rainfall (AMR) data. In this paper, the AMR series derived from the daily rainfall data observed at Dehra site is used for EVA adopting Extreme Value Type-1 (EV1) distribution. Standard parameter estimation methods such as method of moments, method of least squares, maximum likelihood method, principle of maximum entropy, Probability Weighted Moments (PWM) and L-moments are applied for determination of parameters of the EV1 distribution. The adequacy of fitting of EV1 distribution adopted in EVA is evaluated by Goodness-of-Fit tests viz., Anderson-Darling and Kolmogorov-Smirnov (KS) and diagnostic tests viz., root mean squared error and mean absolute error. The KS and diagnostic tests results indicated that the PWM is better-suited method for determination of parameters of EV1 distribution, which is adopted for EVA of rainfall. The 1-hour distributed rainfall computed from the estimated extreme rainfall adopting EV1 (using PWM) distribution is used to estimate the PFD by rational formula. The estimated PFD for river Nakehr and its tributaries could be used for design of hydraulic structures.
Downloads
References
M.C. Casas, R. Rodriguez, M. Prohom, A. Gazquez and A. Redano. 2011. Estimation of the probable maximum precipitation in Barcelona (Spain). Journal of Climatology, Vol. 31, No. 9, pp. 1322-1327.
J.H. Lee and J.H. Heo. 2011. Evaluation of estimation methods for rainfall erosivity based on annual precipitation in Korea. Journal of Hydrology, Vol. 409, Nos. 1-2, pp. 30-48.
R.D. Singh, S.K. Mishra and H. Chowdhary. 2001. Regional flow duration models for 1200 ungauged Himalayan watersheds for planning micro-hydro projects. ASCE Journal of Hydrologic Engineering, Vol. 6, No. 4, pp. 310-316.
B.H. Lee, D.J. Ahn, H.G. Kim and Y.C. Ha. 2012. An estimation of the extreme wind speed using the Korea wind map. Renewable Energy, Vol. 42, No. 1, pp. 4-10.
R. Daneshfaraz, S. Nemati, H. Asadi and M. Menazadeh. 2013. Comparison of four distributions for frequency analysis of wind speed: A case study. Journal of Civil Engineering and Urbanism, Vol. 3, No. 1, pp. 6-11.
L.S. Esteves. 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.
M.M. Rasel and S.M. Hossain. 2015. Development of rainfall intensity duration frequency equations and curves for seven divisions in Bangladesh. International Journal of Scientific and Engineering Research, Vol. 6, No. 5, pp. 96-101.
H.A. Ewea, A.M. Elfeki and N.S. Al-Amri. 2017. Development of intensity-duration-frequency curves for the Kingdom of Saudi Arabia. Journal of Geomatics, Natural Hazards and Risk, Vol. 8, No. 2, pp. 570-584.
K. Arora and V.P. Singh. 1987. On statistical intercomparison of EVI estimators by Monte Carlo simulation. Advances in Water Resources, Vol. 10, No. 2, pp. 87-107.
J.M. Landwehr, N.C. Matalas and J.R. Wallis. 1979. Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles. Water Resources Research, Vol. 15, No. 5, pp. 1055-1064.
J.A. Ranyal and J.D. Salas. 1986. Estimation procedures for the type-1 extreme value distribution. Journal of Hydrology, Vol. 87, Nos. 3-4, pp. 315-336.
P.F. Rasmussen and N. Gautam. 2003. Alternative PWM-estimators of the Gumbel distribution. Journal of Hydrology, Vol. 280, Nos. 1-4, pp. 265-271.
E.J. Gumbel. 1960. Statistic of Extremes, 2nd Edition, Columbia University Press, New York, USA.
J. Lieblein. 1974. Note on simplified estimates for Type I extreme value distribution (NBSIR 75-647). National Bureau of Standards, US Department of Commerce, Washington.
Atomic Energy Regulatory Board (AERB). 2008. Extreme values of meteorological parameters. AERB Safety Guide No. NF/SG/ S-3.
D. Manik and S.K. Datta. 1998. A comparative study of estimation of extreme value. Journal of River Behaviour & Control, Vol. 25, No. 1, pp. 41-47.
H.N. Phien. 1987. A review of methods of parameter estimation for the extreme value type-1 distribution, Journal of Hydraulics, Vol. 90, Nos. 3-4, pp. 251-268.
J. Zhang. 2002. Powerful goodness-of-fit tests based on the likelihood ratio. Journal of Royal Statistical Society, Vol. 64, No. 2, pp. 281-294.
P.E. Charles Annis. 2009. Goodness-of-Fit tests for statistical distributions.
CWC. 1994. Flood estimation report for Western Himalayas-Zone 7. Central Water Commission (CWC) Design Office Report No.: WH22/1994, New Delhi.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0
