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Semi-parametric and Parametric Inference of Extreme Value Models for Rainfall Data

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  • Amir AghaKouchak
  • Nasrin Nasrollahi

Abstract

Extreme rainfall events and the clustering of extreme values provide fundamental information which can be used for the risk assessment of extreme floods. Event probability can be estimated using the extreme value index (γ) which describes the behavior of the upper tail and measures the degree of extreme value clustering. In this paper, various semi-parametric and parametric extreme value index estimators are implemented in order to characterize the tail behavior of long-term daily rainfall time series. The results obtained from different estimators are then used to extrapolate the distribution function of extreme values. Extrapolation can be employed to estimate the occurrence probability of rainfall events above a given threshold. The results indicated that different estimators may result in considerable differences in extreme value index estimates. The uncertainty of the extreme value estimators is also investigated using the bootstrap technique. The analyses showed that the parametric methods are superior to the semi-parametric approaches. In particular, the likelihood and Two-Step estimators are preferred as they are found to be more robust and consistent for practical application. Copyright Springer Science+Business Media B.V. 2010

Suggested Citation

  • Amir AghaKouchak & Nasrin Nasrollahi, 2010. "Semi-parametric and Parametric Inference of Extreme Value Models for Rainfall Data," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(6), pages 1229-1249, April.
    • Handle: RePEc:spr:waterr:v:24:y:2010:i:6:p:1229-1249
    DOI: 10.1007/s11269-009-9493-3
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    Cited by:

    1. L. Vasiliades & P. Galiatsatou & A. Loukas, 2015. "Nonstationary Frequency Analysis of Annual Maximum Rainfall Using Climate Covariates," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(2), pages 339-358, January.
    2. Linyin Cheng & Amir AghaKouchak & Eric Gilleland & Richard Katz, 2014. "Non-stationary extreme value analysis in a changing climate," Climatic Change, Springer, vol. 127(2), pages 353-369, November.
    3. Lingling Zhao & Jun Xia & Leszek Sobkowiak & Zhonggen Wang & Fengrui Guo, 2012. "Spatial Pattern Characterization and Multivariate Hydrological Frequency Analysis of Extreme Precipitation in the Pearl River Basin, China," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(12), pages 3619-3637, September.
    4. Ali Razmi & Saeed Golian & Zahra Zahmatkesh, 2017. "Non-Stationary Frequency Analysis of Extreme Water Level: Application of Annual Maximum Series and Peak-over Threshold Approaches," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(7), pages 2065-2083, May.
    5. Wendy Shinyie & Noriszura Ismail & Abdul Jemain, 2014. "Semi-parametric Estimation Based on Second Order Parameter for Selecting Optimal Threshold of Extreme Rainfall Events," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(11), pages 3489-3514, September.
    6. Noor Fadhilah Ahmad Radi & Roslinazairimah Zakaria & Julia Piantadosi & John Boland & Wan Zawiah Wan Zin & Muhammad Az-zuhri Azman, 2017. "Generating Synthetic Rainfall Total Using Multivariate Skew-t and Checkerboard Copula of Maximum Entropy," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(5), pages 1729-1744, March.
    7. Wendy Shinyie & Noriszura Ismail & Abdul Jemain, 2013. "Semi-parametric Estimation for Selecting Optimal Threshold of Extreme Rainfall Events," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(7), pages 2325-2352, May.
    8. Paul Leahy & Gerard Kiely, 2011. "Short Duration Rainfall Extremes in Ireland: Influence of Climatic Variability," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(3), pages 987-1003, February.

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