Copula-based risk evaluation of hydrological droughts in the East River basin, China

  • Qiang ZhangEmail author
  • Mingzhong Xiao
  • Vijay P. Singh
  • Xiaohong Chen
Original Paper


Probabilistic characteristics of hydrological droughts in a basin are closely related to the variability and availability of water resources of the basin. The East River basin in China is the main source for water supply for mega cities in the Pearl River Delta and cities in the vicinity of the Delta, such as Hong Kong. The water supply is subject to the vagaries of weather and water resources in the basin exhibit probabilistic characteristics. Using daily streamflow data for a period of 1975–2009 from 4 hydrological stations in the East River basin, this study attempts to determine probabilistic characteristics of hydrological droughts using copula functions. The bivariate quantile curves of the secondary return periods for hydrological drought of all the hydrological stations have been built and the results a higher risk of hydrological droughts in the upper East River basin. Furthermore, water resources should be managed by considering the entire East River basin in order to sustain the regional socio-economic development, and the extreme value copula has been used to describe the extreme drought events in the East River basin.


Hydrological drought The East River basin Extreme value Copula Secondary return period 



This work is financially supported by The National Natural Science Foundation of China (Grant No.: 41071020; 50839005), Program for New Century Excellent Talents in University (NCET), a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK405308) and by the Geographical Modeling and Geocomputation Program under the Focused Investment Scheme (1902042) of the Chinese University of Hong Kong. Our cordial gratitude should be owed to the editor-in-chief, Prof. Dr. George Christakos, and two anonymous reviewers for their pertinent and professional comments and suggestions which greatly help to improve the quality of this manuscript.


  1. American Meteorological Society (AMS) (2004) AMS statement on meteorological drought. Bulletin of the American Meteorological Society, vol 85, pp 771–773Google Scholar
  2. Cancelliere A, Salas DJ (2010) Drought probabilities and return period for annual streamflow series. J Hydrol 391:77–89CrossRefGoogle Scholar
  3. Chen YD, Zhang Q, Lu XX, Zhang SR, Zhang ZX (2011) Precipitation variability (1956–2002) in the Dongjiang River (Zhujiang River basin, China) and associated large-scale circulation. Quat Int 244:130–137CrossRefGoogle Scholar
  4. Edward RC, Richard S, Mark AC, David WS (2007) North American drought: reconstructions, causes, and consequences. Earth Sci Rev 81:93–134CrossRefGoogle Scholar
  5. Falk M, Reiss RD (2005) On pickands coordinates in arbitrary dimensions. J Multivar Anal 92(2):426–453CrossRefGoogle Scholar
  6. Fleig AK, Tallaksen LM, Hisdal H, Demuth S (2006) A global evaluation of streamflow drought characteristics. Hydrol Earth Syst Sci 10(4):535–552CrossRefGoogle Scholar
  7. Genest C, Rivest LP (1993) Statistical inference procedures for bivariate Archimedean copulas. J Am Stat Assoc 88(423):1034–1043CrossRefGoogle Scholar
  8. Genest C, Segers J (2009) Rank-based inference for bivariate extreme-value copulas. Ann Stat 37(5):2990–3022CrossRefGoogle Scholar
  9. Genest C, Kojadinovic I, Nešlehová J, Yan J (2011) A goodness-of-fit test for bivariate extreme-value copulas. Bernoulli 17(1):253–275CrossRefGoogle Scholar
  10. Kao S-C, Govindaraju R (2008) Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas. Water Resour Res 44:W02415CrossRefGoogle Scholar
  11. Kao S-C, Govindaraju SR (2010) A copula-based joint deficit index for droughts. J Hydrol 380:121–134CrossRefGoogle Scholar
  12. Kim DH, Yoo C, King TW (2011) Application of spatial EOF and multivariate time series model for evaluating agricultural drought vulnerability in Korea. Adv Water Resour 34:340–350CrossRefGoogle Scholar
  13. Madsen H, Rosbjerg D (1995) On the modelling of extreme droughts. IAHS Publ Ser Proc Reports-Intern Assoc Hydrol Sci 231:377–386Google Scholar
  14. Mishra KA, Singh PV (2010) A review of drought concepts. J Hydrol 391:202–216CrossRefGoogle Scholar
  15. Nelsen RB (2006) An introduction to copulas. Springer, BerlinGoogle Scholar
  16. Pickands J (1981) Multivariate extreme value distributions. Bull Int Stat Inst 49:859–878Google Scholar
  17. Plackett RL (1965) A class of bivariate distributions. J Am Stat Assoc 60(310):516–522CrossRefGoogle Scholar
  18. Salvadore G, De Michele C, Kottegoda NT, Rosso R (2007) Extremes in nature: an approach using copulas. Springer, BerlinGoogle Scholar
  19. Salvadori G, De Michele C (2004) Frequency analysis via copulas: theoretical aspects and applications to hydrological events. Water Resour Res 40(12):W12511CrossRefGoogle Scholar
  20. Salvadori G, De Michele C (2011) Estimating strategies for multiparameter multivariate extreme value copulas. Hydrol Earth Syst Sci 15(1):141–150CrossRefGoogle Scholar
  21. Serinaldi F, Bonaccorso B, Cancelliere A, Grimaldi S (2009) Probabilistic characterization of drought properties through copulas. Phys Chem Earth 34:596–605CrossRefGoogle Scholar
  22. Shiau J (2006) Fitting drought duration and severity with two-dimensional copulas. Water Resour Manage 20(5):795–815CrossRefGoogle Scholar
  23. Sklar A (1959) Fonctions de répartition àn dimensions et leurs marges. Publ. Inst. Stat. Univ. Paris, Paris, France, pp 229–231Google Scholar
  24. Song S, Singh VP (2010) Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stoch Environ Res Risk Assess 24(3):425–444CrossRefGoogle Scholar
  25. Tallaksen LM, Madsen H, Clausen B (1997) On the definition and modelling of streamflow drought duration and deficit volume. Hydrol Sci J 42(1):15–33CrossRefGoogle Scholar
  26. Wilhite DA (2000) Drought as a natural hazard: concepts and definitions. In: Wilhite DA (ed) Drought: a global assessment. Routledge, London, pp 3–18Google Scholar
  27. Wilhite DA, Glantz MH (1985) Understanding the drought phenomenon: the role of definitions. Water Int 10:111–120CrossRefGoogle Scholar
  28. Yevjevich V (1967) Objective approach to definitions and investigations of continental hydrologic droughts. Hydrology paper 23, Colorado State Uiversity, Fort CollinsGoogle Scholar
  29. Zelenhasic E, Salvai A (1987) A method of streamflow drought analysis. Water Resour Res 23(1):156–168CrossRefGoogle Scholar
  30. Zhang L, Singh VP (2007) Bivariate rainfall frequency distributions using Archimedean copulas. J Hydrol 332(1–2):93–109CrossRefGoogle Scholar
  31. Zhang Q, Xu C-Y, Zhang Z (2009a) Observed changes of drought/wetness episodes in the Pearl River basin, China, using the standardized precipitation index and aridity index. Theor Appl Climatol 98(1):89–99CrossRefGoogle Scholar
  32. Zhang Q, Xu C-Y, Yu Z, Liu C-L, Chen YQ (2009b) Multifractal analysis of streamflow records of the East River basin (Pearl River), China. Phys A 388:927–934CrossRefGoogle Scholar
  33. Zhang Q, Singh VP, Li JF, Chen XH (2011) Analysis of the periods of maximum consecutive wet days in China. J Geophys Res. doi: 10.1029/2011JD016088
  34. Zhang Q, Zhang W, Lu X, Chen YD (2012) Landfalling tropical cyclones activities in the south China: intensifying or weakening? Int J Climatol. doi: 10.1002/joc.2396
  35. Zhou Y, Zhang Q, Li K, Chen X (2012) Hydrological effects of water reservoirs on hydrological processes: complexity evaluations based on the multi-scale entropy analysis. Hydrol Process. doi: 10.1002/hyp.8406
  36. Zolina O, Kapala A, Simmer C, Gulev SK (2004) Analysis of extreme precipitation over Europe from different reanalysis: a comparative assessment. Global Planet Change 44:129–161CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Qiang Zhang
    • 1
    • 2
    • 3
    Email author
  • Mingzhong Xiao
    • 1
    • 2
    • 3
  • Vijay P. Singh
    • 4
    • 5
  • Xiaohong Chen
    • 1
    • 2
    • 3
  1. 1.Department of Water Resources and EnvironmentSun Yat-sen UniversityGuangzhouChina
  2. 2.Key Laboratory of Water Cycle and Water Security in Southern China of Guangdong High Education InstituteSun Yat-sen UniversityGuangzhouChina
  3. 3.School of Geography and Planning, and Guangdong Key Laboratory for Urbanization and Geo-simulationSun Yat-sen UniversityGuangzhouChina
  4. 4.Department of Biological & Agricultural EngineeringTexas A & M UniversityCollege StationUSA
  5. 5.Department of Civil and Environmental EngineeringTexas A & M UniversityCollege StationUSA

Personalised recommendations