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The Application of Mixture Distribution for the Estimation of Extreme Floods in Controlled Catchment Basins

Author

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  • Wiesław Szulczewski

    (Wrocław University of Environmental and Life Sciences)

  • Wojciech Jakubowski

    (Wrocław University of Environmental and Life Sciences)

Abstract

In the estimation of distribution of annual maximum flows it is a generally accepted assumption that the sequence of observations originates from a homogeneous population. This assumption, however, is rarely met. The observed annual maximum flow are only in part generated by flood events. The remaining ones are the result of the effect of other hydrological processes that do not have that character. For this reason, a new solution to this problem is proposed in the paper. It is assumed that the sought distribution is a mixture of two probability distributions: a three-parameter GEV distribution, describing flows generated by events with flood character, and a two-parameter gamma distribution, accounting for maximum annual flows that do not have such a character. The paper presents both the method of estimation of the mixture distribution and its application for gauging stations selected so as to take into account possible the most diverse conditions of meteorological, hydrological and geomorphological character. The area with such a high diversification, selected for the study, is the catchment basin of upper and central river Odra (South-West Poland). In the studied water gauge profiles the proposed mixture distribution indicates correct fit. Its advantages and limitations are presented through a comparative analysis with results obtained during estimation of distributions of maximum annual flows by means of standard methods.

Suggested Citation

  • Wiesław Szulczewski & Wojciech Jakubowski, 2018. "The Application of Mixture Distribution for the Estimation of Extreme Floods in Controlled Catchment Basins," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(10), pages 3519-3534, August.
    • Handle: RePEc:spr:waterr:v:32:y:2018:i:10:d:10.1007_s11269-018-2005-6
    DOI: 10.1007/s11269-018-2005-6
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    References listed on IDEAS

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    1. Felício Cassalho & Samuel Beskow & Carlos Rogério Mello & Maíra Martim Moura & Laura Kerstner & Leo Fernandes Ávila, 2018. "At-Site Flood Frequency Analysis Coupled with Multiparameter Probability Distributions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(1), pages 285-300, January.
    2. Lihua Xiong & Tao Du & Chong-Yu Xu & Shenglian Guo & Cong Jiang & Christopher Gippel, 2015. "Non-Stationary Annual Maximum Flood Frequency Analysis Using the Norming Constants Method to Consider Non-Stationarity in the Annual Daily Flow Series," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(10), pages 3615-3633, August.
    3. Milan Stojković & Stevan Prohaska & Nikola Zlatanović, 2017. "Estimation of flood frequencies from data sets with outliers using mixed distribution functions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(11), pages 2017-2035, August.
    4. Robert F. Engle & Asger Lunde, 2003. "Trades and Quotes: A Bivariate Point Process," Journal of Financial Econometrics, Oxford University Press, vol. 1(2), pages 159-188.
    5. Żyromski, Andrzej & Szulczewski, Wiesław & Biniak-Pieróg, Małgorzata & Jakubowski, Wojciech, 2016. "The estimation of basket willow (Salix viminalis) yield – New approach. Part I: Background and statistical description," Renewable and Sustainable Energy Reviews, Elsevier, vol. 65(C), pages 1118-1126.
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