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Copula-based trivariate drought frequency analysis approach in seven climatic sub-regions of mainland China over 1961–2013

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Abstract

In drought analysis, many types of research have applied bivariate analysis. However, a more effective appraisal is achievable by employing three mutually correlated drought variables (i.e., duration, severity, peak) concurrently. This study adopted trivariate copulas for multivariate drought frequency estimation in seven climatic sub-regions and mainland China between 1961 and 2013. The joint distribution is modeled using nine trivariate copula functions, namely Clayton, Ali–Mikhail–Haq (AMH), Gumbel–Hougaard, Frank, M3, M4, M5, M6, and M12. The performance of the different copulas was evaluated using the root mean square error (RMSE), Akaike information criterion (AIC), bias, and graphical test. The results showed that trivariate Clayton copula performed better in modeling joint dependence structure of drought variables in contrast to other class of copulas in sub-regions I–VII and mainland China. Therefore, the Clayton copula–based drought joint distributions were used for the multivariate drought frequency analysis, regarding probabilities and return periods. The joint probabilities in the “OR” cases were greater than that of the “AND” cases in all the seven sub-regions and mainland China. There is every possibility that drought event occurrence will be given for “OR” cases. Accordingly, counter measures of drought hazards need to be set for proactive responses especially in sub-regions III, V, and VI. The trivariate return periods were compared with the univariate and bivariate return periods and discussed the need of multivariate drought frequency analysis. In conclusion, the Clayton trivariate copula is an excellent choice for efficient drought risk evaluation, and results are very handy in the design of water resource hydrologic systems under severe and extreme drought conditions.

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Abbreviations

P, T, ET O :

Precipitation, temperature, potential evapotranspiration

SPEI:

Standardized Precipitation Evapotranspiration Index

Dd, Ds, Dp :

Drought duration, severity, and peak

F(x):

Marginal distribution of drought variables

CDF:

Cumulative distribution function

FNA:

Fully nested Archimedean

Γ(⋅), α, β, λ :

Gamma function, scale, shape, and location parameters

n, x c(i), x 0(i):

Sample size, ith calculated value, ith observed value

\( {P}_{DSP}^{\cap } \) :

Trivariate joint occurrence probability of Dd and Ds and Dp exceeding an actual value

\( {P}_{DSP}^{\cup } \) :

Trivariate joint occurrence probability of Dd or Ds or Dp exceeding an actual value

\( {T}_{DSP}^{\cap } \) :

Trivariate return period of Dd and Ds and Dp exceeding an actual value

\( {T}_{DSP}^{\cup } \) :

Trivariate return period of Dd or Ds or Dp exceeding an actual value

C DS (d, s):

Joint distribution of Dd and Ds

C DP (d, p):

Joint distribution of Dd and Dp

C SP (s, p):

Joint distribution of Ds and Dp

C DSP (d,s,p):

Joint distribution of Dd, Ds, and Dp

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Acknowledgements

We thank the National Meteorological Information Center of China Meteorological Administration (CMA) for sharing the climatic data used in this study. Finally, the authors would like to thank all the anonymous reviewers for their valuable comments and suggestions towards improving the quality of this paper.

Funding

This work was supported by the National Key Research and Development Program of China (grant no. 2017YFC0403303), China Natural Science Foundation (no. U1203182), and the China 111 project (B12007).

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Authors and Affiliations

  1. College of Water Resources and Architectural Engineering, Northwest Agriculture & Forestry University, Yangling, 712100, Shaanxi, China

    Olusola O. Ayantobo, Yi Li & Songbai Song

  2. Key Lab of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Northwest Agriculture & Forestry University, Yangling, 712100, Shaanxi, China

    Olusola O. Ayantobo & Yi Li

  3. Department of Water Resources Management and Agricultural-Meteorology, Federal University of Agriculture, PMB 2240, Abeokuta, Nigeria

    Olusola O. Ayantobo

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  1. Olusola O. Ayantobo
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  2. Yi Li
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  3. Songbai Song
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Correspondence to Yi Li.

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Ayantobo, O.O., Li, Y. & Song, S. Copula-based trivariate drought frequency analysis approach in seven climatic sub-regions of mainland China over 1961–2013. Theor Appl Climatol 137, 2217–2237 (2019). https://doi.org/10.1007/s00704-018-2724-x

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