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Hydrological Uncertainty Processor (HUP) with Estimation of the Marginal Distribution by a Gaussian Mixture Model

Author

Listed:
  • Kuaile Feng

    (Huazhong University of Science and Technology
    Hubei Key Laboratory of Digital Valley Science and Technology)

  • Jianzhong Zhou

    (Huazhong University of Science and Technology
    Hubei Key Laboratory of Digital Valley Science and Technology)

  • Yi Liu

    (Huazhong University of Science and Technology
    Hubei Key Laboratory of Digital Valley Science and Technology)

  • Chengwei Lu

    (Huazhong University of Science and Technology
    Hubei Key Laboratory of Digital Valley Science and Technology)

  • Zhongzheng He

    (Huazhong University of Science and Technology
    Hubei Key Laboratory of Digital Valley Science and Technology)

Abstract

Uncertainty assessments of hydrological prediction results can reflect additional hydrological information and reveal important hydrological characteristics of river basins, which is of great significance to disaster prevention and reduction. The hydrological uncertainty processor (HUP), which is a key part of the Bayesian forecasting system (BFS), has derived a variety of methods for hydrological uncertainty forecasting. The HUP allows for any form of marginal distributions of hydrological data and does not require a unified estimation structure for the marginal distribution function. The Gaussian mixture model (GMM) is a probability distribution estimation model that can approximate any probability distribution with arbitrary precision. In this paper, the GMM was used to estimate the marginal distribution of observed and modelled data, and this method is called HUP-GMM. The uncertainty of river discharge at the Yichang hydrological station on the main stem of the Yangtze River in China is predicted by the HUP-GMM. The Weibull and Gamma distributions, which are commonly used hydrological probability distributions, are compared to analyse the performance of the GMM. In June, when the measured flow h3 is 13,850 m3/s and the GMM, Gamma and Weibull distributions are used, the prior probabilities are 1.63E-04, 1.05E-04 and 9.50E-05 and the posterior probabilities are 2.57E-04, 1.61E-04 and 1.38E-04, respectively. In September, when the measured flow h3 is 35,400 m3/s and the GMM, Gamma and Weibull distributions are used, the prior probabilities are 5.98E-05, 2.21E-05 and 2.18E-05 and the posterior probabilities are 1.64E-04, 9.15E-05 and 8.43E-05, respectively. The results show that the performance of the uncertainty estimation of the prior and posterior probability distributions in the HUP-GMM has been improved.

Suggested Citation

  • Kuaile Feng & Jianzhong Zhou & Yi Liu & Chengwei Lu & Zhongzheng He, 2019. "Hydrological Uncertainty Processor (HUP) with Estimation of the Marginal Distribution by a Gaussian Mixture Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(9), pages 2975-2990, July.
    • Handle: RePEc:spr:waterr:v:33:y:2019:i:9:d:10.1007_s11269-019-02260-5
    DOI: 10.1007/s11269-019-02260-5
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    References listed on IDEAS

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    1. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    2. Wei Li & Jianzhong Zhou & Huaiwei Sun & Kuaile Feng & Hairong Zhang & Muhammad Tayyab, 2017. "Impact of Distribution Type in Bayes Probability Flood Forecasting," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(3), pages 961-977, February.
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    Cited by:

    1. Shuai Zhou & Yimin Wang & Ziyan Li & Jianxia Chang & Aijun Guo, 2021. "Quantifying the Uncertainty Interaction Between the Model Input and Structure on Hydrological Processes," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(12), pages 3915-3935, September.
    2. Zhangjun Liu & Jingwen Zhang & Tianfu Wen & Jingqing Cheng, 2022. "Uncertainty Quantification of Rainfall-runoff Simulations Using the Copula-based Bayesian Processor: Impacts of Seasonality, Copula Selection and Correlation Coefficient," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(13), pages 4981-4993, October.
    3. Jianzhong Zhou & Kuaile Feng & Yi Liu & Chao Zhou & Feifei He & Guangbiao Liu & Zhongzheng He, 2020. "A Hydrologic Uncertainty Processor Using Linear Derivation in the Normal Quantile Transform Space," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(11), pages 3649-3665, September.
    4. Binquan Li & Zhongmin Liang & Qingrui Chang & Wei Zhou & Huan Wang & Jun Wang & Yiming Hu, 2020. "On the Operational Flood Forecasting Practices Using Low-Quality Data Input of a Distributed Hydrological Model," Sustainability, MDPI, vol. 12(19), pages 1-16, October.

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