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A New Estimation Method for Copula Parameters for Multivariate Hydrological Frequency Analysis With Small Sample Sizes

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Abstract

Multivariate hydrological frequency analysis is important when designing hydraulic and civil infrastructures. However, hydrologic data scarcity and insufficiency are common. By studying the relationship between copula entropy and total correlation estimated by the matrix-based Renyi's α-order entropy functional, a new estimation method (total correlation estimation, TCE) for parameters of the Gumbel-Hougaard copula and Clayton copula was proposed when the sample size was equal to or less than 30. A total of 11,802 simulations were performed to evaluate the performance of TCE for sample sizes ranging from 30 to 5, and were compared with traditional estimation methods that require a large amount of data. As for the Gumbel-Hougaard copula, the performance of TCE is satisfactory regardless of sample size, while the traditional methods perform poorly when the sample size is equal to or less than 20. For the Clayton copula, TCE is reliable and robust and performs well if the sample size is greater than 10, while the traditional methods are unreliable when the sample size is less than 25. Also, TCE is applied to construct the joint distributions of annual runoff and sediment discharge in the Xiliugou River, China. The method based on Renyi's α-order entropy functional provides a new way for multivariate hydrological frequency analysis with small sample sizes.

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Funding

The study was supported by the National Science Foundation for Distinguished Young Scholars of China (Grant No. 52025093), the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Grant NO. IWHR-SKL-KF202009, National Natural Science Foundation of China (Grant Nos. 51609254 and 41875061), and NUPTSF (Grant Nos. NY219161 and NY220035).

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Authors and Affiliations

  1. School of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Longxia Qian & Hanlin Li

  2. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing, 100038, China

    Longxia Qian & Yong Zhao

  3. Water resources and reservoir dispatching center of Shaanxi Province, Xian, 710004, China

    Jianhong Yang

  4. College of Water Sciences, Beijing Normal University, Beijing, 100875, China

    Hongrui Wang

  5. Beijing Institute of Applied Meteorology, Beijing, 100029, China

    ChengZu Bai

Authors
  1. Longxia Qian
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  2. Yong Zhao
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  3. Jianhong Yang
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  4. Hanlin Li
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  5. Hongrui Wang
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  6. ChengZu Bai
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Contributions

The contribution of Longxia Qian is project design, model construction and case study. The contribution of Yong Zhao includes project design and result analysis. The contribution of Jianhong Yang is algorithmic programming. The contribution of Hanlin Li is model validation. The contribution of Chengzu Bai is model comparison.

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Correspondence to Yong Zhao.

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Qian, L., Zhao, Y., Yang, J. et al. A New Estimation Method for Copula Parameters for Multivariate Hydrological Frequency Analysis With Small Sample Sizes. Water Resour Manage 36, 1141–1157 (2022). https://doi.org/10.1007/s11269-021-03016-w

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  • DOI: https://doi.org/10.1007/s11269-021-03016-w

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