Intercomparison of Parameter Estimation Methods of EV1 Distribution for Modelling of Annual 1-Day Maximum Rainfall

N. Vivekanandan¹

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.12 , pp.15-22, Dec-2024

Online published on Dec 31, 2024

Copyright © N. Vivekanandan . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

Abstract :
Design rainfall depth is one of the important parameters in the hydraulic modelling of urban drainage systems that directly contributes to runoff. Also, analysis of rainfall characteristics is considered as one of the effective techniques for planning of water resources projects. This can be carried out by applying the Extreme Value Type-1 (EV1) distribution to the series of observed annual 1-day maximum rainfall (AMR) data. This paper presented a study on modelling the AMR series of Akkalkuwa, Kamrej, Navapur, Sakri, Shahada and Taloda rain gauge sites located in the surrounding regions of river Tapi. The parameters of EV1 were determined by Method of Moments (MoM), Maximum Likelihood Method (MLM), Method of L-Moments (LMO) and Method of Least Squares (MLS), and further used for rainfall data analysis. Anderson-Darling (A2) and Kolmogorov-Smirnov (KS) tests were employed for examining the fitting EV1 distribution to the AMR series while the selection of best fit method was made through cross correlation matrix analysis (CCMA) and model performance analysis with various indicators such as correlation coefficient (CC), mean squared error (MSE) and Nash-Sutcliffe model efficiency (NSE). The A2 test results indicated that all four methods of EV1 are acceptable for modelling the AMR of Akkalkuwa, Kamrej, Sakri, Shahada and Taloda whereas MLM and LMO for Navapur. But, the KS test results supported the use of all four methods of EV1 for modelling the AMR of six sites. The outcomes of CCMA showed that there is a perfect correlation between the observed and estimated rainfalls by four methods of EV1, which is nearer to 1.000. The study showed that the NSE given by four methods of EV1 vary from 92.1% to 98.8%. The MSE computed by LMO is minimum than those values of MoM, MLM and MLS. Based on A2 and KS tests results, CCMA and model performance analysis, the LMO was identified as better suited amongst four methods for modelling the AMR data of six sites.

Key-Words / Index Term :
Anderson-Darling, Extreme Value Type-1, Kolmogorov-Smirnov, L-Moments, Rainfall

References :
[1] Montanari, A., & Brath, A., “A stochastic approach for assessing the uncertainty of rainfall-runoff simulations”, Water Resources Research, Paper ID. W0110640, Vol. 1, Pages 1-11, 2004.
https://doi.org/ 10.1029/ 2003WR002540
[2] Singh, V.P., “Extreme value type 1 distribution. In: entropy-based parameter estimation in hydrology”, Water Science and Technology Library, Springer, Vol. 30, 1998.
https://doi.org/10.1007/978-94-017-1431-0_8
[3] Phien, H.N., “A review of methods of parameter estimation for the extreme value type-1 distribution”, Journal of Hydrology, Vol. 90, Issue 3-4, Pages 251-268, 1987.
https://doi.org/10.1016/0022-1694(87) 90070-9
[4] Bhagat, N., “Flood frequency analysis using Gumbel’s distribution method: a case study of lower Mahi Basin, India”, Journal of Water Resources and Ocean Science, Vol. 6, Issue 4, Pages 51-54, 2017.
https://doi.org/ 10.11648/ j.wros.20170604.11
[5] Kumar, R., “Flood frequency analysis of the Tapti river basin using log Pearson type-III and Gumbel extreme value-1 methods”, Journal of the Geological Society of India, Vol. 94, No. 5, Pages 480-484, 2019. https://doi.org/10.1007/s12594-019-1344-0
[6] Sultan Bhat, M., Alam, A., Ahmad, B., Kotlia, B.S., Farooq, H., Taloor, A.K., & Ahmad, S., “Flood frequency analysis of river Jhelum in Kashmir basin”, Quaternary International, Vol. 507, Issue 1, Pages 288-294, 2019.
https://doi.org/10.1016/j.quaint.2018.09.039
[7] Opere, A.O., & Njogu, A.K., “Using extreme value theory to estimate available water in the upper Awach-Kibuon catchment in Nyamira County, Kenya”, American Journal of Water Resources, Vol. 8, Issue 4, Pages 200-210, 2020.
https://doi.org/10.12691/ajwr-8-4-6
[8] Manohar Reddy, V., “Flood frequency analysis using Gumbel’s distribution method and Log-Pearson Type III distribution method in Krishna River, Andhra Pradesh”, Proceedings of Recent Developments in Sustainable Infrastructure (ICRDSI-2020) and Part of the Lecture Notes in Civil Engineering Book Series, Vol. 207, 2022.
https://doi.org/10.1007/978-981-16-7509-6_36
[9] Ranyal, J.A., & Salas, J.D., “Estimation procedures for the type-1 extreme value distribution”, Journal of Hydrology, Vol. 87, Issue 3-4, Pages 315-336, 1986. https://doi.org/10.1016/0022-1694(86) 90022-3
[10] Prabhu, J., George, T., Vijayakumar, B., & Ravi, P.M., “Extreme value statistical analysis of meteorological parameters observed at Kudankulam site during 2004-2014”, Radiation Protection Environment, Vol. 39, Issue 2, Pages 107-112, 2016.
https://doi.org/10.4103/ 0972-0464. 190388
[11] Celik, A.N., “On the distributional parameters used in assessment of the suitability of wind speed probability density functions”, Energy Conversion and Management, Vol. 45, Issue 11-12, Pages 1735-1747, 2004.
https://doi.org/ 10.1016/j.enconman.2003.09.027
[12] Gumbel, E.J., “Statistic of Extremes”, Columbia University Press, New York, 1995.
[13] Arora, K., & Singh, V.P., “On statistical intercomparison of EV1 estimators by Monte Carlo simulation”, Advances in Water Resources, Vol.10, Issue 2, Pages 87-107, 1987.
https://doi.org/10.1016/0309-1708(87)90013-3
[14] Zhang, J., “Powerful goodness-of-fit tests based on the likelihood ratio”, Journal of Royal Statistical Society: Series B (Statistical Methodology), Vol. 64, Issue 2, Pages 281-294, 2002.
https://doi.org/ 10.1111/1467-9868.00337
[15] Vivekanandan, N., Aayusi Ghule, & Vaishnavi Darade, (2021). “Prediction of Seasonal and Annual Rainfall for Pune and Mahabaleshwar Regions Using ANN and Regression Approaches”. Geospatial and Soft Computing Techniques (HYDRO 2021), Lecture Notes in Civil Engineering, Vol. 339, Pages 451-468, 2023, Springer, Singapore. https://doi.org/10.1007/978-981-99-1901-7_36