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Multivariate Drought Frequency Analysis using Four-Variate Symmetric and Asymmetric Archimedean Copula Functions

Author

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  • Olusola O. Ayantobo

    (Northwest Agriculture & Forestry University
    Northwest Agriculture & Forestry University
    Federal University of Agriculture)

  • Yi Li

    (Northwest Agriculture & Forestry University
    Northwest Agriculture & Forestry University)

  • Songbai Song

    (Northwest Agriculture & Forestry University)

Abstract

In drought frequency analysis, as the number of drought variables increases, the joint behavior between these variables needs to be studied. Therefore, this study aims to develop a flexible four-variate joint distribution function of the regional stochastic nature of drought. Using run theory, drought duration, severity, peak, and inter-arrival time were abstracted from the Standardized Precipitation Evapotranspiration Index (SPEI) aggregated at six months, observed in mainland China between 1961 and 2013. As these drought variables showed significant dependence properties and followed different marginal distributions, we employed and compared six four-variate symmetric and asymmetric Archimedean copulas (i.e., Frank, Clayton, Gumbel–Hougaard). The best-fitting model for each region was carefully selected using RMSE, AIC, and BIAS goodness-of-fit tests. Results revealed that the empirical and theoretical probabilities of the symmetric Clayton in regions NE (Northeast), CS (Central and Southern China), EMC (Entire China), and symmetric Frank in regions NC (North China), SC (South China), IM (Inner Mongolia), NW (Northwest), TP (Tibet Plateau) agreed well. Symmetric Frank copula was considered the best-fit for station-based drought analysis in EMC. Based on these copulas, the drought probabilities and return periods for the occurrence of drought events over the next 5, 10, 20, 50, and 100 years in each region were hereby comprehensively explained, and the results shown here could be helpful in the appraisal of the adequacies of water supply systems under drought conditions in all regions. This study showed that a four-variate copula approach is a vital tool for probabilistic interpretation of hydrological and meteorological data in the different climatic region of mainland China.

Suggested Citation

  • Olusola O. Ayantobo & Yi Li & Songbai Song, 2019. "Multivariate Drought Frequency Analysis using Four-Variate Symmetric and Asymmetric Archimedean Copula Functions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(1), pages 103-127, January.
    • Handle: RePEc:spr:waterr:v:33:y:2019:i:1:d:10.1007_s11269-018-2090-6
    DOI: 10.1007/s11269-018-2090-6
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    References listed on IDEAS

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    1. Cornelia Savu & Mark Trede, 2010. "Hierarchies of Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 295-304.
    2. J. Shiau, 2006. "Fitting Drought Duration and Severity with Two-Dimensional Copulas," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 20(5), pages 795-815, October.
    3. Niall Whelan, 2004. "Sampling from Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 339-352.
    4. George Tsakiris & Nikos Kordalis & Dimitris Tigkas & Vasileios Tsakiris & Harris Vangelis, 2016. "Analysing Drought Severity and Areal Extent by 2D Archimedean Copulas," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(15), pages 5723-5735, December.
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    2. Chen Wang & Yizi Shang & Majid Khayatnezhad, 2021. "Fuzzy Stress-based Modeling for Probabilistic Irrigation Planning Using Copula-NSPSO," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(14), pages 4943-4959, November.
    3. Zhan, Cun & Liang, Chuan & Zhao, Lu & Zhang, Yaling & Cheng, Long & Jiang, Shouzheng & Xing, Liwen, 2021. "Multifractal characteristics analysis of daily reference evapotranspiration in different climate zones of China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    4. Elaheh Motevali Bashi Naeini & Ali Mohammad Akhoond-Ali & Fereydoun Radmanesh & Jahangir Abedi Koupai & Shahrokh Soltaninia, 2021. "Comparison of the Calculated Drought Return Periods Using Tri-variate and Bivariate Copula Functions Under Climate Change Condition," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(14), pages 4855-4875, November.
    5. Ihsan F. Hasan & Rozi Abdullah, 2022. "Agricultural Drought Characteristics Analysis Using Copula," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(15), pages 5915-5930, December.
    6. Wu Zening & He Chentao & Huiliang Wang & Qian Zhang, 2020. "Reservoir Inflow Synchronization Analysis for Four Reservoirs on a Mainstream and its Tributaries in Flood Season Based on a Multivariate Copula Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(9), pages 2753-2770, July.
    7. Rajabzadeh, Vida & Hekmatzadeh, Ali Akbar & Tabatabaie Shourijeh, Piltan & Torabi Haghighi, Ali, 2023. "Introducing a probabilistic framework to measure dam overtopping risk for dams benefiting from dual spillways," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    8. Homa Razmkhah & Alireza Fararouie & Amin Rostami Ravari, 2022. "Multivariate Flood Frequency Analysis Using Bivariate Copula Functions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(2), pages 729-743, January.

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