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History and Perspectives of Hydrologic Frequency Analysis in Japan

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Pioneering Works on Extreme Value Theory

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Abstract

Hydrologic frequency analysis provides basic information for the planning, design, and management of hydraulic and water resources systems for promoting the river basin quality and human health. It uses meteorological/hydrological extreme-value data and probability distribution functions to estimate T-year events (quantiles). Reviewing the history of hydrologic frequency analysis in Japan, this study describes goodness-of-fit criteria such as the standard least-squares criterion and Akaike information criterion and their applications. The jackknife and bootstrap methods are introduced as useful resampling methods for bias correction and quantile variability estimation. As future directions, this study proposes the incorporation of (1) partial duration series or peaks-over-threshold series, if available, instead of the annual maximum series; (2) a nonparametric method using empirical distributions for larger samples with more than 100-year observation period; and (3) probable maximum precipitation or probable maximum flood into frequency analysis.

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Acknowledgements

The author is grateful for the continued support of the Institute of Statistical Mathematics (ISM) for organizing a series of Seminars on Extreme Value Theory and Application for many years. He greatly appreciates Prof. Rinya Takahashi, Prof. Masaaki Sibuya, and Dr. Takaaki Shimura for arranging the seminars every year and the Pioneering Workshop on Extreme Value and Distribution Theories in honor of Prof. Sibuya held at the ISM on March 21–23, 2019.

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Authors and Affiliations

  1. Professor, Graduate School of Advanced Integrated Studies in Human Survivability (Shishu-Kan), Kyoto University, Higashi-Ichijo-Kan, 1 Yoshida-Nakaadachi-Cho, Sakyo-ku, Kyoto, 606-8306, Japan

    Kaoru Takara

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  1. Kaoru Takara
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Correspondence to Kaoru Takara .

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Editors and Affiliations

  1. School of Economics, Kanazawa University, Kanazawa, Ishikawa, Japan

    Nobuaki Hoshino

  2. The Institute of Statistical Mathematics, Tachikawa, Tokyo, Japan

    Shuhei Mano

  3. The Institute of Statistical Mathematics, Tachikawa, Tokyo, Japan

    Takaaki Shimura

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Takara, K. (2021). History and Perspectives of Hydrologic Frequency Analysis in Japan. In: Hoshino, N., Mano, S., Shimura, T. (eds) Pioneering Works on Extreme Value Theory. SpringerBriefs in Statistics(). Springer, Singapore. https://doi.org/10.1007/978-981-16-0768-4_6

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