Data-based bivariate uncertainty assessment of extreme rainfall-runoff using copulas: comparison between annual maximum series (AMS) and peaks over threshold (POT)

  • Esmaeel Dodangeh
  • Kaka Shahedi
  • Karim Solaimani
  • Jenq-Tzong Shiau
  • John Abraham


Bivariate frequency analysis of extreme rainfall and runoff is crucial for water resource planning and management in a river basin. This study is aimed at accounting for uncertainties in bivariate analysis of extreme rainfall-runoff frequency in the Taleghan watershed, one of the major watersheds in northern Iran, using copulas. Two types of paired rainfall and runoff data, including annual maximum series (AMS) and peaks over threshold (POT) are adopted to investigate the uncertainties that arose due to the input data. The Cramer von-Mises goodness-of-fit test and Akaike information criteria (AIC) reveal that the Student’s t copula is the best-fit copula for PAMS-QAMS with Gaussian–Pearson III (P3) margins, while the Plackett copula is the best-fit copula for PPOT-QPOT with generalized Pareto (GPAR–GPAR) margins. A nonparametric bootstrapping method for sampling from p-level curves is established to investigate the effects of univariate and bivariate models selection and uncertainties induced by input data. The results indicated that the sampling uncertainty reduces POT data compared to AMS data due to the increased sample size. However, the parameterization uncertainty of the POT data increases because of the weaker dependence structure between rainfall and runoff for the POT data. The results also reveal that the larger sampling uncertainties are associated with higher p-level curves for both AMS and POT data which are induced by lower data density in the upper tail. For the study area, the input-data uncertainty is most significant in bivariate rainfall-runoff frequency analysis and quantile estimation, while the uncertainty induced by probabilistic model selection is least significant.


Uncertainty analysis Bivariate model Copula Rainfall-runoff process Annual maximum series Peaks over threshold 



The authors would like to thank Dr. Stefan Gelissen for his technical supports. They also appreciate Iran Ministry of Power for their kind help and providing the data for this study.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Esmaeel Dodangeh
    • 1
  • Kaka Shahedi
    • 1
  • Karim Solaimani
    • 1
  • Jenq-Tzong Shiau
    • 2
  • John Abraham
    • 3
  1. 1.Department of Watershed ManagementSari Agriculture Science and Natural Resources UniversitySariIran
  2. 2.Department of Hydraulic and Ocean EngineeringNational Cheng Kung UniversityTainanTaiwan
  3. 3.School of EngineeringUniversity of St. ThomasSt. PaulUSA

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