The Best Fit Flood Probability Distribution for Alibeyköy Basin in İstanbul, Türkiye

Yıl 2023, Cilt: 5 Sayı: 2, 40 - 51, 01.09.2023

Mehmet Dikici , Cevza Kazezyılmaz Alhan , Bihrat Önöz

https://doi.org/10.46740/alku.1323214

Öz

Determination of peak flow rates is crucial in reducing the economic and social impact of flood. Therefore, the investigation of various methods for estimating flood is of paramount importance. Flood frequency analysis can be used as a practical method in predicting the peak flow values as the flood peaks have return periods that are typically much larger than the recording length. In this study, 7 different probability distributions (normal (N), two-parameter lognormal (LN2), three-parameter lognormal (LN3), extreme value type I (Gumbel), generalized extreme value (GEV), Pearson Type III (P3) and Log-Pearson Type III (LP3)) are employed for flood frequency analysis of Alibeyköy Watershed using 44-years of measured annual maximum flow. K-S and PPCC tests are applied to determine the most suitable distributions to estimate the flood flow rate. Based on these tests, GEV and Gumbel distributions appear to be the most preferable distributions in flood flow estimation.

Anahtar Kelimeler

flood frequency analysis, probability distribution, return period, peak flow

Alibeyköy Havzası İçin En Uygun Taşkın Olasılık Dağılımı

Öz

Taşkın debisinin belirlenmesi, taşkının ekonomik ve sosyal etkisinin azaltılmasında önemli bir rol oynar. Hem kırsal hem de kentleşmiş alanlardaki taşkın hasarı ülke ekonomisini önemli ölçüde etkilemektedir. Bu nedenle, taşkın tahmini için çeşitli hesaplama yöntemlerinin araştırılması büyük önem taşımaktadır. Taşkın frekansı analizi, genellikle ölçülenden çok daha büyük olan geri dönüş dönemlerine karşılık gelen ve bir olasılık eğrisinin üst kuyruğunda taşkın zirveleri göründüğünden, taşkın büyüklüklerinin tahmin edilmesinde pratik bir yöntem olarak kullanılabilir. Bu analiz, özellikle akış verisi olmayan nehirler için çok önemlidir. Bu çalışmada 7 farklı olasılık dağılımı (normal (N), iki parametreli lognormal (LN2), üç parametreli lognormal (LN3), uç değer tip I (Gumbel), genelleştirilmiş uç değer (GEV), Pearson Tip III (P3 ) ve hidrolojik frekans analizinde yaygın olarak kullanılan Log-Pearson Tip III (LP3)), Alibeyköy Havzası taşkın frekans analizinde kullanılmıştır. Her bir olasılık dağılımı, Alibeyköy Havzası'ndaki bir ölçüm istasyonunda ölçülen yıllık maksimum akışlar kullanılarak geliştirilmiştir. Olasılık dağılımını elde etmek için 44 yıllık maksimum akış verileri kullanılmıştır. Daha sonra bu dağılımlar, T-yıllık taşkın tekrarlama aralıklarının (50, 100, 200 ve 500 yıl) tahmin edilmesinde kullanılmıştır. Son olarak, taşkın akış oranını tahmin etmek için en uygun dağılımları belirlemek için K-S ve PPCC uygunluk testleri yapılmıştır. Bu testlerin değerlendirmesine göre GEV ve Gumbel dağılımları taşkın akış tahmininde en tercih edilebilir dağılımlar olarak görünmektedir.

Anahtar Kelimeler

taşkın frekans analizi, olasılık dağılımı, dönüş periyodu, taşkın debisi

Kaynakça

• [1] Önöz B., and Bulu A., “Frequency analysis of low flows by the PPCC test in Turkey” FRIEND '97 — Regional Hydrology: Concept sand Models for Sustainable Water Resource Management (Proceedings of the Postojna, Slovenia, Conference, September-October Î997). IAHS Pubj. no. 246, 1997.
• [2] Xiong L., Du T., Xu C.Y., Guo S., Jiang C., Gippel J.C. “Non station annual maximum flood frequency analysis using the NMC method consider non-stationarty in the annual daily flow series” Water resource manage, 29:3615-3633, 2015. DOI: 10.1007/s11269-015-1019-6
• [3] Haktanir T., “Statistical modelling of annual maximum flows in Turkish rivers.” Hydrological Sciences Journal, 36:4, 367-389, 2009. DOI: 10.1080/02626669109492520
• [4] He, J., Anderson, A., and Valeo, C., “Bias compensation in flood frequency analysis”. Hydrological Sciences Journal, 60:3, 381-401, 2015. DOI: 10.1080/02626667.2014.885651
• [5] Seckin N., Haktanir T., and Yurtal R., “Flood frequency analysis of Turkey using L-moments method.” Hydrologıcal Processes 25, 3499–3505, 2011.
• [6] Önöz B. and Bayazit M., “Best-fit distributions of largest available flood samples. Journal of Hydrology 167,195-208, 1995.
• [7] Li Z., Li Z., Zhao W. and Wang Y., “Probability modeling of precipitation extremes over two river basins in Northwest of China”, Advances in Meteorology, 374127, 2015.
• [8] Phien HN. And Laungwattanapong N., “At-site flood frequency analysis for Thailand”, ISSN 0378-4738= Water SA Vol. 17 No.2, April 1991.
• [9] Aydoğan D., Kankal M., Önsoy H., “Regional flood frequency analysis for Çoruh Basin of Turkey with L-moments approach”, Flood Risk Management, 2016. DOI: 10.1111/jfr3.12116
• [10] Sarmadi F. and Shokoohi A. “Regionalizing precipitation in Iran using GPCC gridded data via multivariate analysis and L-moment methods” The Application Climatology, 2015. 122:121–128. DOI: 10.1007/s00704-014-1292-y
• [11] Vogel R.M. and Wilson I., “Probability distribution of annual maximum mean and minimum stream flows in the United States, Journal of Hydrologic Engineering, Pages 69-76, April 1996.
• [12] Atiem A. and Harmancioğlu N.B., “Assessment of regional floods using l-moments approach: The case of the river Nile” Water Resources Management, 2006. 20: 723–747 DOI: 10.1007/s11269-005-9004-0
• [13] Zalina M.D., M. Desa, M.N., Nguyen, V-T-V and M. Kassim, A.H., “Selecting a probability distribution for extrem era infall series in Malaysia.” Water Science Technology Journal, Vol. 45, No. 2, pp 63 – 68, 2002.
• [14] Vogel R.M., Wilbert O.,Thomas J. and McMahon T.A., “Flood-flow frequency model selection in southwestern United States”. Journal of Water Resources Planning and Management, Vol. 119, No.3, May/June 1993. ISSN 0733-9496/9310003-03531
• [15] Rahman S.A., Rahman A., Zaman M.A., Haddad K., Ahsan A and Imteaz M., “A study on selection of probability distributions for at-site flood frequency analysis in Australia.” Natural Hazards, 2013. 69:1803–1813 DOI: 10.1007/s11069-013-0775-y
• [16] Senocak S. and Acar R., “Modelling of short-duration rainfall intensity equation for the Agean region of Turkey. Fresenius Environmental Bulletin January, 16(9):1220-1226, 2007.
• [17] Ferdows M. and Hossain M. “Flood frequency analysis at different rivers in Bangladesh: a comparison study on probability distribution functions”. Thammasat International Journal Science Technology, Vol 10, No 3, July-September, 2005.
• [18] Choo T.H., Maeng S.J., Kim H.S., and Lee S.W., "Characteristic of design floods using l-moment based on gradual composition of annual maximum flood flow” Irrigation and Drainage 61: 497–506, 2012. DOI: 10.1002/ird.687
• [19] Salinas J.L., Castellarin A., Viglione A., Kohnová S., and Kjeldsen T.R., “Regional parent flood frequency distributions in Europe – Part 1: Is the GEV model suitable as a pan-European parent?”. Hydrology Earth System Science, 18, 4381–4389, 2014. www.hydrol-earth-syst-sci.net/18/4381/2014/ doi:10.5194/hess-18-4381-2014
• [20] Olofintoye O.O., Sule B.F. and Salami A.W. “Best–fit Probability distribution model for peak daily rainfall of selected Cities in Nigeria” New York Science Journal, 2(3), ISSN 1554-0200, 2009.
• [21] Saghafian B., Golian S. and Ghasemi A., “Flood frequency analysis based on simulated peak discharges” Natural Hazards, 2014.71:403–417. DOI 10.1007/s11069-013-0925-2
• [22] Can, I. Tosunoglu, F., “Estimating T-year flood confidence intervals of rivers in Çoruh basin, Turkey”, Journal of Flood Risk Management, 2013. https://doi.org/10.1111/jfr3.12000
• [23] Mkhandi S.H., Kachroo R.K. and Guo S.L., “Uncertainty analysis of flood quantile estimates with reference to Tanzania” Journal of Hydrology 185 0996) 317-333, 1996.
• [24] Sharma A.M. and Singh B.J., “Use of probability distribution in rainfall analysis. New York Science Journal, 3, (9), 40–49. 2010.
• [25] Önöz B. and Bayazit M., “Flood and drought hydrology” İstanbul, P 46-48, 2007.
• [26] Rao R.A. and Hamed H.K., “Flood frequency analysis”, London: CRC Press, 2000.
• [27] Singh V.P., “Entropy-based parameter estimation in Hydrology” Dordrecht: Kluwer Academic Publishers, 1996.
• [28] Hosking, J.R.M., “L-moments: analysis and estimation of distributions using linear combinations of order statistics” Journal Royal Statistic Society, Series B, 52, 105–124, 1990.
• [29] Hosking, J.R.M. and Wallis, J.R., “Regional flood-frequency analysis using L-moments” IBM Research, Yorktown Heights, New York, Rep. 15658, 1990.
• [30] Filliben JJ., “The probability plot correlation test for Normality”, Technometrics 17 (1):111-117, 1975.
• [31] Looney S.W. and Gulledge T.R. Jr., “Use of the correlation coefficient for the normal probability plots” The American Statistician 39(1):75-79, 1985.