Three-dimensional identification of hydrological drought and multivariate drought risk probability assessment in the Luanhe River basin, China

  • Xu Chen
  • Fa-wen LiEmail author
  • Jian-zhu Li
  • Ping Feng
Original Paper


It is critical to assess drought risk probability based on a really spatio-temporal continuum identification and characterization method, which is of great importance for drought resistance, planning, and management of water resource as well as agricultural production. Therefore, the major motivation of this study is to identify and characterize hydrological drought events in a three-dimensional framework and further assess the potential drought risk probability in a multivariate framework in the Luanhe River basin during 1961–2011. The study adopts a really spatio-temporal continuum identification method to characterize drought, and copula functions for multivariate risk probability assessment of hydrological drought. First, the Soil and Water Assessment Tool (SWAT) model is used to simulate the watershed runoff and the cubic spline interpolation method is used to obtain the gridded data sets. Second, the Standardized Runoff Index (SRI) and the three-dimensional identification method are employed to identify hydrological drought. Third, according to three drought parameters of drought severity (S), duration (D), and affect area (A), the marginal distribution, bivariate, and trivariate joint distribution are constructed, and the optimal ones are selected based on different evaluation methods of goodness-of-fit. Fourth, based on the derived marginal and joint distributions, drought risk probability is fully assessed. Results indicate that: (1) SWAT model is a reliable tool to simulate the watershed hydrologic processes; (2) the three-dimensional identification method used in this study is robust and efficient; (3) the optimal marginal distributions for S, D, and A are GEV, GEV, and lognormal distribution; the optimal bivariate copula function for S-D, S-A, and D-A are Joe, Gumbel, and Joe copula; and the optimal trivariate copula function for S-D-A is Nested Gumbel copula; (4) return periods of the first five most serious drought events are 80, 75, 46, 45, and 40 years, respectively; (5) to completely characterize the spatio-temporal variability of hydrological drought, it is necessary to completely consider the three characteristic variables of S, D, and A.



The authors sincerely acknowledge the insightful comments and corrections of editors and reviewers.

Funding information

This investigation is supported by the Natural Science Foundation of China (Nos. 51579169, 51479130, 51279123, 51179117) and the National Key R & D Program of China (Grant No. 2016YFC0401407).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.

Supplementary material

704_2019_2780_MOESM1_ESM.doc (647 kb)
ESM 1 (DOC 647 kb)


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Hydraulic Engineering Simulation and SafetyTianjin UniversityTianjinPeople’s Republic of China

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