Sains Malaysiana 50(7)(2021): 1843-1856

http://doi.org/10.17576/jsm-2021-5007-02

A Comparative Flood Frequency Analysis of High-Flow between Annual Maximum and Partial Duration Series at Sungai Langat Basin

(Suatu Perbandingan Analisis Kekerapan Banjir Aliran Tinggi antara Siri Maksimum Tahunan dan Siri Tempoh Separa di Lembangan Sungai Langat)

FIRDAUS MOHAMAD HAMZAH*, HAZRINA TAJUDIN & OTHMAN JAAFAR

Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

Diserahkan: 14 Ogos 2020/Diterima: 30 November 2020

ABSTRACT

Flood frequency analysis should consider small and frequent floods. Despite the complexities in partial duration series implementation, it can give a better flood estimation in a way that it does not exclude any significant high flow events, even if it is not the highest event of the year. This study employs the streamflow data recorded at Kajang station, Sungai Langat, Malaysia over a 36-year period spanning from 1978 to 2013. The paper attempts to conduct flood frequency analysis using two approaches, annual maximum and partial duration series. The optimal threshold value is selected to be 48.7 m³/s, where the dispersion index stabilizes at around 1, DI = 1 . The results have shown that generalized extreme value (GEV) distribution describes the annual maximum data while the lognormal (LN3) and generalized Pareto (GPA) distribution is chosen as the best fit distribution at Kajang station for a partial duration series. There is a slight difference between estimated streamflow magnitude when using GPA and LN3 for selected return periods, while a considerable difference was observed when using annual maximum at a higher return period. As a conclusion, PDS gives more relevant magnitude estimation rather than AMS. Flood frequency plays an important role in understanding the nature and magnitude of high flow, which in turn can assist relevant agencies in the design of hydrological structures and reduce flood impacts.

Keywords: Flood frequency analysis; generalized extreme value; generalized Pareto; Sungai Langat; three-parameter lognormal

ABSTRAK

Analisis kekerapan banjir harus mempertimbangkan kejadian banjir dengan magnitud kecil dan kerap. Walaupun terdapat kerumitan dalam pelaksanaan data siri separa, ia memiliki kemampuan untuk memberikan anggaran banjir yang lebih baik, dengan tidak mengecualikan kejadian aliran tinggi yang signifikan, walaupun ia bukan peristiwa tertinggi tahun ini. Kajian ini menggunakan data aliran yang direkodkan di stesen Kajang, Sungai Langat, Malaysia dalam jangka masa 36 tahun yang merangkumi tahun 1978 hingga 2013. Objektif utama kajian ini adalah menjalankan analisis kekerapan banjir menggunakan dua pendekatan iaitu data tahunan maksimum dan data siri separa. Nilai ambang optimum dipilih menjadi 48.7 m³/s dengan indeks penyebaran stabil pada sekitar 1, DI = 1. Taburan nilai ekstrim teritlak (GEV) menerangkan data maksimum tahunan sementara taburan lognormal dan Pareto teritlak dipilih sebagai taburan yang paling sesuai di stesen Kajang untuk data siri separa. Terdapat sedikit perbezaan antara magnitud aliran dengan menggunakan taburan Pareto teritlak dan lognormal untuk tempoh pulangan yang dipilih. Manakala, perbezaan yang cukup besar dapat dilihat apabila menggunakan data tahunan maksima terutamanya pada tempoh pulangan yang lebih tinggi. Secara kesimpulan, PDS memberikan anggaran magnitud yang lebih relevan berbanding AMS. Kekerapan banjir memainkan peranan penting dalam memahami sifat dan besarnya aliran tinggi, yang seterusnya dapat membantu agensi yang berkaitan dalam merancang struktur hidrologi dan mengurangkan kesan kejadian banjir.

Kata kunci: Analisis kekerapan banjir; lognormal tiga-parameter; nilai ekstrim teritlak; Pareto teritlak; Sungai Langat

RUJUKAN

Agilan, V. & Umamahesh, N.V. 2017. Non-stationary rainfall intensity-duration-frequency relationship: A comparison between annual maximum and partial duration series. Water Resources Management 31(6): 1825-1841.

Alahmadi, F.S., Abd Rahman, N. & Abdulrazzak, M. 2014. Evaluation of the best fit distribution for partial duration series of daily rainfall in Madinah, Western Saudi Arabia. Proceedings of the International Association of Hydrological Sciences 364. Göttingen: Copernicus Publications. pp. 159-163.

Anderson, T.W. & Darling, D.A. 1954. A test of goodness of fit. Journal of the American Statistical Association 49(268): 765-769.

Beguería, S. 2005. Uncertainties in partial duration series modelling of extremes related to the choice of the threshold value. Journal of Hydrology 303(1-4): 215-230.

Bezak, N., Brilly, M. & Šraj, M. 2014. Comparison between the peaks-over-threshold method and the annual maximum method for flood frequency analysis. Hydrological Sciences Journal 59(5): 959-977.

Bílková, D. 2014. Alternative tools of statistical analysis: L-moments and TL-moments of probability distributions. Pure and Applied Mathematics Journal 3(2): 14-25.

Chang, K.B., Lai, S.H. & Othman, F. 2016. Comparison of annual maximum and partial duration series for derivation of rainfall intensity-duration-frequency relationships in Peninsular Malaysia. Journal of Hydrologic Engineering 21(1): 1-11.

Cheong, R.Y. & Gabda, D. 2018. Frequency analysis of annual maximum river flow by generalized extreme value distribution with Bayesian MCMC. Journal of Computer Science & Computational Mathematics 8(4): 77-81.

Claps, P. & Laio, F. 2003. Can continuous streamflow data support flood frequency analysis? An alternative to the partial duration series approach. Water Resources Research 39(8): 1-11.

Cunnane, C. 1979. A note on the Poisson assumption in partial duration series models. Water Resources Research 15(2): 489-494.

Department of Statistics Malaysia. 2019. Poket stats negeri – Selangor. https://www.dosm.gov.my/v1/index.php?r=column/cone&menu_id=dFc3aExhVktPbUpoZys1dWoyUWFPQT09.

Engeland, K., Wilson, D., Borsányi, P., Roald, L. & Holmqvist, E. 2018. Use of historical data in flood frequency analysis: A case study for four catchments in Norway. Hydrology Research 49(2): 466-486.

Franchini, M., Galeati, G. & Lolli, M. 2005. Analytical derivation of the flood frequency curve through partial duration series analysis and a probabilistic representation of the runoff coefficient. Journal of Hydrology 303(1-4): 1-15.

Gado, T. & Nguyen, V.T.V. 2016. Regional estimation of floods for ungauged sites using partial duration series and scaling approach. Journal of Hydrologic Engineering 21(12): 1-12.

Garba, H., Ismail, A. & Tsoho, U. 2013. Fitting probability distribution functions to discharge variability of Kaduna River. International Journal of Modern Engineering Research 3(5): 2848-2852.

Gharib, A., Davies, E.G.R., Goss, G.G. & Faramarzi, M. 2017. Assessment of the combined effects of threshold selection and parameter estimation of generalized Pareto distribution with applications to flood frequency analysis. Water 9(9): 692-708.

Ghasemi, A. & Zahediasl, S. 2012. Normality tests for statistical analysis: A guide for non-statisticians. International Journal of Endocrinology and Metabolism 10(2): 486-489.

Jiang, S. & Kang, L. 2019. Flood frequency analysis for annual maximum streamflow using a non-stationary GEV model. E3S Web of Conferences: International Symposium on Architecture Research Frontiers and Ecological Environment 79, 03022. United Kingdom: EDP Sciences. pp. 1-5.

Karim, F., Hasan, M. & Marvanek, S. 2017. Evaluating annual maximum and partial duration series for estimating frequency of small magnitude floods. Water 9(7): 481-497.

Keast, D. & Ellison, J. 2013. Magnitude frequency analysis of small floods using the annual and partial series. Water 5(4): 1816-1829.

Khan, S.A., Hussain, I., Hussain, T., Faisal, F., Muhammad, Y.S. & Shoukry, A.M. 2017. Regional frequency analysis of extremes precipitation using L-moments and partial L-moments. Advances in Meteorology 2017: Article ID. 6954902.

Leščešen, I. & Dolinaj, D. 2019. Regional flood frequency analysis of the Pannonian Basin. Water 11(193): 1-15.

Madsen, H., Rasmussen, P.F. & Rosbjerg, D. 1997. Comparison of annual maximum series and partial duration series methods for modelling extreme hydrologic events. Water Resources Research 33(4): 747-757.

Makkonen, L. 2006. Plotting positions in extreme value analysis. Journal of Applied Meteorology and Climatology 45(2): 334-340.

Malamud, B.D. & Turcotte, D.L. 2006. The applicability of power-law frequency statistics to floods. Journal of Hydrology 322(1-4): 168-180.

Mierlus-Mazilu, I. 2010. On generalized Pareto distributions. Romanian Journal of Economic Forecasting 13(1): 107-117.

Özonur, D., Gökpinar, E., Gökpinar, F., Bayrak, H. & Gül, H.H. 2013. Comparison of the goodness of fit tests for the geometric distribution. Gazi University Journal of Science 26(3): 369-375.

Pettitt, A.N. & Stephens, M.A. 1977. The Kolmogorov-Smirnov goodness-of-fit statistic with discrete and grouped data. Technometrics 19(2): 205-210.

Pham, H.X., Shamseldin, A.Y. & Melville, B.W. 2014. Statistical properties of partial duration series and its implication on regional frequency analysis. Journal of Hydrologic Engineering 19(7): 1471-1480.

Scarrott, C. & Macdonald, A. 2012. A review of extreme value threshold estimation and uncertainty quantification. Revstat Statistical Journal 10(1): 33-60.

Schlögl, M. & Laaha, G. 2017. Extreme weather exposure identification for road networks - A comparative assessment of statistical methods. Natural Hazards and Earth System Sciences 17(4): 515-531.

Singla, N., Jain, K. & Sharma, S.K. 2016. Goodness of fit tests and power comparisons for weighted gamma distribution. Revstat Statistical Journal 14(1): 29-48.

Srinivasa Murthy, D., Aruna Jyothy, S. & Mallikarjuna, P. 2017. Probability distributions of annual maximum daily streamflows using L-moments - A case study. International Journal of Civil Engineering and Technology 8(6): 290-302.

Syed Hussain, T.P.R. & Ismail, H. 2013. Flood frequency analysis of Kelantan River basin, Malaysia. World Applied Sciences Journal 28(12): 1989-1995.

Tallaksen, L. & Hewa, G. 2008. Extreme value analysis. In Manual on Low-flow Estimation and Prediction, edited by Gustard, A. & Demuth, S. Geneva, Switzerland: World Meteorological Organization. pp. 57-70.

Tekolla, A.W. 2010. Rainfall and flood frequency analysis in Pahang River basin, Malaysia. Master of Science Thesis. Lund University, Lund, Sweden (Unpublished).

Ummi Nadiah, A., Shabri, A. & Zakaria, Z.A. 2013. An analysis of annual maximum streamflows in Terengganu, Malaysia using TL-moments approach. Theoretical and Applied Climatology 111(3-4): 649-663.

van Westen, C.J. & Jetten, V. 2015. Magnitude-frequency analysis. In Caribbean Handbook on Risk Information Management, edited by van Westen, C.J., Jetten, V., Sliuzas, R., Brussel, M., Alkema, D., Van den Bout, B. & Hazarika, M. Washington D.C., United States: World Bank.

*Pengarang untuk surat-menyurat; email: fir@ukm.edu.my