COMPARISON OF L-MOMENT AND METHOD OF MOMENTS AS PARAMETER ESTIMATORS FOR IDENTIFICATION AND CHOICE OF THE MOST APPROPRIATE RAINFALL DISTRIBUTION MODELS FOR DESIGN OF HYDRAULIC STRUCTURES
In rainfall frequency analysis, the choice of a suitable probability distribution and parameter estimation method is critical in forecasting design rainfall values for varying return periods at every location. Previously, some researchers in Nigeria used the method of moments (MoM) while others used the L-moment method (LMM) as parameter estimators. However, a more accurate result is obtainable if both estimators are used and their results are compared and ranked to obtain the most appropriate distribution models for each location This study compared the performance of two forms of parameter estimation, namely the method of moments (MoM) and the L-moment method (LMM). This was aimed at identifying and selecting the best fit probability distribution models among three distribution models for the design of hydraulic structures. These models are Generalized Pareto (GPA), Generalized Extreme Value (GEV), and Gumbel Extreme Value (EVI). Annual rainfall series of ten gauging stations with data from 33-50 years from ten southern States of Nigeria obtained from NIMET were used for Rainfall Frequency Analysis (RFA). At five locations, the best fit probability model was the GPA probability distribution model with L-Moment. EVI and GEV probability distribution models with the method of moments were the most appropriate probability models at two locations each. EVI probability distribution model with the L-moment was the most appropriate probability model at one place. The findings confirmed that no single distribution outperformed all others at all stations. Since no single model is regarded preferable for all practical purposes, the best-fit probability model with parameter estimator at any location is site-specific. Consequently, available models and parameter estimators are filtered based on the situation at hand and the type of data available. The identified best fit models with the most appropriate parameter estimator would be a tool to help decision-makers in sizing hydraulic structures in the area.
Sankarasubramanian, A. & Srinivasan, K. (1999). Investigation and comparison of sampling properties of L-moments and conventional moments. Journal of Hydrology, 218 (1–2), 13–34. https://doi.org/10.1016/S0022-1694(99)00018-9
Hosking, J. R. (1990). L‐moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society: Series B (Methodological), 52(1), 105-124.https://doi.org/10.1111/j.2517-6161.1990.tb01775.x
Vogel, R. M. & Fennessey, N. M. (1993). L moment diagrams should replace product moment diagrams. Water Resources Research, 29(6), 1745-1752. https://doi.org/10.1029/93WR00341
Hosking, J. R. M. (1986). The theory of probability weighted moments, Res. Report RC12210, IBM Research, Yorktown Heights.
Stedinger, J. R., Vogel, R. M., & Georgiou, E.F. (1993). Frequency analysis of extreme events Chap. 18. In: Maidment, D.J. (Ed.). Handbook of Hydrology, McGraw Hill, New York.
Singh, R. K. (2001). Probability analysis for prediction of annual maximum rainfall of Eastern Himalaya (Sikkimmid hills). Indian Journal of Soil Conservation, 29, 263–265.
Kousar, S., Khan, A. R., Ul Hassan, M., Noreen, Z., & Bhatti, S. H. (2020). Some best‐fit probability distributions for at‐site flood frequency analysis of the Ume River. Journal of Flood Risk Management, 13(3), e12640. https://doi.org/10.1111/jfr3.12640
Mamman, M. J., Martins, O. Y., Ibrahim, J., & Shaba, M. (2017). Evaluation of best-fit probability distribution models for the prediction of inflows of Kainji Reservoir, Niger State, Nigeria. Air, Soil and Water Research, 10, 1-7.
Gocic, M., Velimirovic, L., Stankovic, M., & Trajkovic, S. (2021). Determining the best fitting distribution of annual precipitation data in Serbia using L-moments method. Earth Science Informatics, 14(2), 633-644. https://doi.org/10.1007/s12145-020-00543-9
Eslamian, S. S. & Feizi, H. (2007). Maximum monthly rainfall analysis using L-moments for an arid region in Isfahan Province, Iran. Journal of Applied Meteorology and Climatology, 46(4), 494-503. https://doi.org/10.1175/JAM2465.1
Ghosh, S., Roy, M. K., & Biswas, S. C. (2016). Determination of the best fit probability distribution for monthly rainfall data in Bangladesh. American Journal of Mathematics and Statistics, 6(4), 170-174.
Mohamed, T. M. & Ibrahim A. A. A. (2016). Fitting probability distributions of annual rainfall in Sudan. SUST Journal of Engineering and Computer Sciences, 17(2), 34-39.
Alam, M. A., Emura, K., Farnham, C., & Yuan, J. (2018). Best-fit probability distributions and return periods for maximum monthly rainfall in Bangladesh. Climate, 6(1), 9. https://doi.org/10.3390/cli601000
Anil, K. (2000). Prediction of annual maximum daily rainfall of Ranichauri (Tehri Garhwal) based on probability analysis. Indian Journal of Soil Conservation, 28(2), 178-180.
Amin, M. T., Rizwan, M., & Alazba, A. A. (2016). A best-fit probability distribution for the estimation of rainfall in northern regions of Pakistan. Open Life Sciences, 11(1), 432-440. https://doi.org/10.1515/biol-2016-0057
Masereka, E. M., Otieno, F. A. O., Ochieng, G. M., & Snyman, J. (2015). Best fit and selection of probability distribution models for frequency analysis of extreme mean annual rainfall events. International Journal of Engineering Research and Development, 11(4), 34-53.
Langat, P. K., Kumar, L., & Koech, R. (2019). Identification of the most suitable probability distribution models for maximum, minimum, and mean streamflow. Water, 11(4), 734. https://doi.org/10.3390/w11040734
Okeke, O. B. & Ehiorobo, J. O. (2017). Frequency analysis of rainfall for flood control in Patani, Delta State of Nigeria. Nigerian Journal of Technology, 36(1), 282-289. https://doi.org/10.4314/njt.v36i1.34
Izinyon, O. C. & Ajumuka, H. N. (2013). Probability distribution models for flood prediction in Upper Benue River Basin-Part II. Civil and Environmental Research, 3(2), 62-74.
Ologhadien, I. (2021). Selection of probabilistic model of extreme floods in Benue river basin, Nigeria. European Journal of Engineering and Technology Research, 6(1), 7-18. https://doi.org/10.24018/ejers.2021.6.1.2300
Anandan, V. (2014). Comparison of probability distributions for frequency analysis of annual maximum rainfall. International Journal of Research and Innovative Technology 1(3), 50-55.
Vivekanandan, N. (2015). Flood frequency analysis using method of moments and L-moments of probability distributions. Cogent engineering, 2(1), 1018704, https://doi.org/10.1080/23311916.2015.1018704
Greenwood, J. A., Landwehr, J. M., Matalas, N. C., & Wallis, J. R. (1979). Probability weighted moments: definition and relation to parameters of several distributions expressable in inverse form. Water resources research, 15(5), 1049-1054. https://doi.org/10.1029/WR015i005p01049
Chadwick, A., Morfett, J., & Borthwick, M. (2021). Hydraulics in civil and environmental engineering. CRC Press. Taylor & Francis Group, 5TH Edition, 340-342. https://doi.org/10.1201/b14556
Ojha, C., Berndtsson, R., & Bhunya, P. (2008). Engineering Hydrology, Oxford University Press, New Delhi, India Ch 7, 248-289.
Filliben, J. J. (1975). The probability plot correlation coefficient test for normality. Technometrics, 17(1), 111-117. https://doi.org/10.1080/00401706.1975.10489279
Agbonaye A. I. & Izinyon O. C. (2017). Best-fit probability distribution model for rainfall frequency analysis of three cities in South-Eastern Nigeria. Nigerian Journal of Environmental Sciences and Technology, 1(1), 34-42. https://doi.org/10.36263/nijest.2017.01.0024
Hao, W., Hao, Z., Yuan, F., Ju, Q., & Hao, J. (2019). Regional frequency analysis of precipitation extremes and its spatio-temporal patterns in the Hanjiang River Basin, China. Atmosphere, 10(3), 130. https://doi.org/10.3390/atmos10030130
Izinyon, O. C. & Ehiorobo, J. O. (2015). L-moments method for flood frequency analysis of river Owan at Owan in Benin Owena River basin in Nigeria. Current Advances in Civil Engineering, 3(1), 1-10. https://doi.org/10.4314/njt.v33i1.2
Kumar, R. (2019). Flood frequency analysis of the Rapti river basin using log pearson type-III and Gumbel Extreme Value-1 methods. Journal of the Geological Society of India, 94(5), 480-484. https://doi.org/10.1007/s12594-019-1344-0
National Water Development Authority (2019). Detailed Project Report (DPR) Burhi Gandak-Noon-Baya-Ganga intra-state link of Bihar (Chapter III Hydrology). http://nwda.gov.in/upload/uploadfiles/files/DPR_BG_N_BG_Ch_3.pdf. Accessed 28 March 2019.
Ul Hassan, M., Hayat, O., & Noreen, Z. (2019). Selecting the best probability distribution for at-site flood frequency analysis; a study of Torne River. SN Applied Sciences, 1(12), 1-10. https://doi.org/10.1007/s42452-019-1584-z
Drissia, T. K., Jothiprakash, V., & Anitha, A. B. (2019). Flood frequency analysis using L moments: a comparison between at-site and regional approach. Water Resources Management, 33(3), 1013-1037. https://doi.org/10.1007/s11269-018-2162-7
Ul Hassan, M., Noreen, Z., & Ahmed, R. (2021). Regional frequency analysis of annual daily rainfall maxima in Skåne, Sweden. International Journal of Climatology, 41(8), 4307-4320. https://doi.org/10.1002/joc.7074.
Bajirao, T. S. (2021). Comparative performance of different probability distribution functions for maximum rainfall estimation at different time scales. Arabian Journal of Geosciences, 14(20), 1-15. https://doi.org/10.1007/s12517-021-08580-4
Copyright (c) 2022 UNIMAS Publisher
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Upon acceptance of an article, the corresponding author on behalf of all authors will be asked to complete and upload the Copyright Transfer Form (refer to Copyright Issues for more information on this) alongside the electronic proof file.
Copyright Transfer Statement for Journal
1) In signing this statement, the author(s) grant UNIMAS Publisher an exclusive license to publish their original research papers. The author(s) also grant UNIMAS Publisher permission to reproduce, recreate, translate, extract or summarize, and to distribute and display in any forms, formats, and media. The author(s) can reuse their papers in their future printed work without first requiring permission from UNIMAS Publisher, provided that the author(s) acknowledge and refer the publication in the Journal.
2) For open-access articles, the author(s) agree that their articles published under UNIMAS Publisher are distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0) which permits unrestricted use, distribution, and reproduction in any medium, for non-commercial purposes, provided the original work of the author(s) is properly cited.
3) For subscription articles, the author(s) agree that UNIMAS Publisher holds the copyright or an exclusive license to publish. Readers or users may view, download, print, and copy the content, for academic purposes, subject to the following conditions of use: (a) any reuse of materials is subjected to permission from UNIMAS Publisher; (b) archived materials may only be used for academic research; (c) archived materials may not be used for commercial purposes, which include but not limited to monetary compensation by means of sale, resale, license, transfer of copyright, loan, etc.; and (d) archived materials may not be re-published in any part, either in print or online.
4) The author(s) are responsible to ensure their submitted work is original and does not infringe any existing copyright, trademark, patent, statutory right, or propriety right of others. The corresponding author has obtained permission from all co-authors prior to submission to the journal. Upon submission of the manuscript, the author(s) agree that no similar work has been or will be submitted or published elsewhere in any language. If the submitted manuscript includes materials from others, the authors have obtained permission from the copyright owners.
5) In signing this statement, the author(s) declare that the researches which they have conducted comply with the current laws of the respective country and UNIMAS Journal Publication Ethics Policy. Any experimentation or research involving humans or the use of animal samples must obtain approval from the Human or Animal Ethics Committee in their respective institutions. The author(s) agree and understand that UNIMAS Publisher is not responsible for any compensational claims or failure caused by the author(s) in fulfilling the above-mentioned requirements. The author(s) must accept the responsibility for releasing their materials upon request by Chief Editor or UNIMAS Publisher.
6) The author(s) should have participated sufficiently in the work and ensured the appropriateness of the content of the article. The author(s) should also agree that they have no commercial attachments (e.g. patent or license arrangement, equity interest, consultancies, etc.) that might pose any conflict of interest with the submitted manuscript. The author(s) also agree to make any relevant materials and data available upon request by the editor(s) or UNIMAS Publisher.