Paddy and Water Environment

, Volume 16, Issue 1, pp 153–161 | Cite as

Analysis of hydrological drought characteristics using copula function approach

  • Hamidreza Vaziri
  • Hojat Karami
  • Sayed-Farhad Mousavi
  • Miromid Hadiani


Drought is a natural phenomenon which starts with decreased precipitation and can disrupt the environmental systems by changing the hydrological cycle. This is more conspicuous in hydrological drought. In analysis of hydrological drought, two factors of severity (intensity) and duration play eminent role. These characteristics are highly related and therefore their combined analysis contributes to better understanding of the drought situation. In this research, by using 40-year (1974–2014) daily discharge data of Tajan River, located in Mazandaran province, Iran, and low-flow indices, the best evaluation index of hydrological drought was determined and 10 past hydrological drought events in the region were identified. Then, the best statistical distribution of both drought variables (duration and severity) was selected, based on the goodness-of-fit tests. Five copula functions were fitted to the data. Results showed that Galambos function with the highest maximum log-likelihood (− 8.934) was selected as the best copula function. Results of the bivariate (duration and severity) statistical distribution could be used to analyze the probability of hydrological drought in the region. This bivariate and conditional probability for the worst drought, with duration of 5 months and severity of 0.32, was 6.1 and 28.5%, respectively.


Low-flow index Goodness-of-fit test Drought duration Drought severity 


  1. Cancelliere A, Salas JD (2004) Drought length properties for periodic-stochastic hydrologic data. Water Resour Res. Google Scholar
  2. Chen L, Singh VP, Guo S, Mishra AK, Guo J (2013) Drought analysis using copulas. J Hydrol Eng 18(7):797–808. CrossRefGoogle Scholar
  3. Cisty M, Celar L, Becova A (2015) Application of copulas in analysis of drought and irrigation. In: The ninth international conference on advanced engineering computing and applications in sciences, Bratislava, SlovakiaGoogle Scholar
  4. De Michele C, Salvadori G (2003) A generalized Pareto intensity-duration model of storm rainfall exploiting 2-copulas. J Geophys Res 108(D2):4067CrossRefGoogle Scholar
  5. Fleig AK, Tallaksen LM, Hisdal H, Demuth S (2006) A global evaluation of streamflow drought characteristics. Hydrol Earth Syst Sci 10:535–552CrossRefGoogle Scholar
  6. Hadiani MO, Jahanbakhsh Asl S, Rezaei Banafsheh M, Dinpashoh Y, Jahanbani M (2013) Investigating the trend of low flow changes of glacial snow regime rivers in Mazandaran province. Int J Agric Crop Sci 6(14):982–987Google Scholar
  7. Kousari MR, Dastorani MT, Niazi Y, Soheili E, Hayatzadeh M, Chezgi J (2014) Trend detection of drought in arid and semi-arid regions of Iran based on implementation of reconnaissance drought index (RDI) and application of non-parametrical statistical method. Water Resour Manag 28:1857–1872. CrossRefGoogle Scholar
  8. Kwak J, Kim S, Kim G, Singh VP, Park J, Kim HS (2016) Bivariate drought analysis using streamflow reconstruction with tree ring indices in the Sacramento Basin, California, USA. Water 8(4):122. CrossRefGoogle Scholar
  9. Nalbantis I, Tsakiris G (2009) Assessment of hydrological drought revisited. Water Resour Manag 23:881–897CrossRefGoogle Scholar
  10. Nazemi A, Elshorbagy A (2011) Application of copula modelling to the performance assessment of reconstructed watersheds. Stoch Environ Res Risk Assess 26(2):189–205CrossRefGoogle Scholar
  11. Nelsen RB (2006) An introduction to copulas. Springer, New YorkGoogle Scholar
  12. Niu J, Chen J, Sun L (2015) Exploration of drought evolution using numerical simulations over the Xijiang (West River) basin in South China. J Hydrol 526:68–77CrossRefGoogle Scholar
  13. Peters E, Bier G, van Lanen HAJ, Torfs PJJF (2006) Propagation and spatial distribution of drought in a groundwater catchment. J Hydrol 321:257–275CrossRefGoogle Scholar
  14. Piechota TC, Dracup JA (1996) Drought and regional hydrologic variation in the United States: associations with the El Niño-Southern oscillation. Water Resour Res. Google Scholar
  15. Reddy MJ, Ganguli P (2012) Bivariate flood frequency analysis of upper Godavari river flows using Archimedean copulas. Water Resour Manag 26(14):3995–4018CrossRefGoogle Scholar
  16. Serinaldi F, Bonaccorso B, Cancelliere A, Grimaldi S (2009) Probabilistic characterization of drought properties through copulas. Phys Chem Earth 34(10–12):596–605CrossRefGoogle Scholar
  17. Shiau J (2006) Fitting drought duration and severity with two-dimensional copulas. Water Resour Manag 20(5):795–815CrossRefGoogle Scholar
  18. Shiau JT, Feng S, Nadarajah S (2007) Assessment of hydrological droughts for the Yellow River, China, using copulas. Hydrol Process 21:2157–2163CrossRefGoogle Scholar
  19. Sklar A (1959) Distribution functions of n dimensions and margins, vol 8. Institute of Statistics of the University of Paris, Paris, pp 229–231 (in French) Google Scholar
  20. Song S, Singh VP (2010) Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stoch Environ Res Risk Assess 24:425–444CrossRefGoogle Scholar
  21. Tallaksen LM, van Lanen HAJ (2004) Hydrological drought processes and estimation methods for streamflow and groundwater. Developments in Water Science, 48. Elsevier, AmsterdamGoogle Scholar
  22. Tallaksen LM, Hisdal H, van Lanen HAJ (2006) Propagation of drought in a groundwater fed catchment, the Pang in UK. In: Proceedings of the fifth FRIEND world conference (climate variability and change-hydrological impacts), Havana, Cuba, November 2006, IAHS Publ. 308, pp 128–133Google Scholar
  23. Van Huijgevoort MHJ, Van Lanen AHJ, Teuling AJ, Uijlenhoet R (2014) Identification of changes in hydrological drought characteristics from a multi-GCM driven ensemble constrained by observed discharge. J Hydrol 512:421–434CrossRefGoogle Scholar
  24. Vasiliades L, Loukas A, Liberis N (2011) A water balance derived drought index for Pinios River Basin, Greece. Water Resour Manag 25:1087–1101CrossRefGoogle Scholar
  25. Wilhite DA, Glantz MH (1985) Understanding the drought phenomenon: the role of definitions. Water Int 10(3):111–120CrossRefGoogle Scholar
  26. Wilhite DA, Svoboda MD, Hayes MJ (2006) Understanding the complex impacts of drought: a key to enhancing drought mitigation and preparedness. Water Resour Manag 21:763–774CrossRefGoogle Scholar
  27. Wong G, van Lanen HAJ, Torfs PJJF (2013) Probabilistic analysis of hydrological drought characteristics using meteorological drought. Hydrol Sci J 58(2):253–270CrossRefGoogle Scholar
  28. Yevjevich V (1967) An objective approach to definitions and investigations of continental hydrologic droughts. Hydrology Papers, No. 23, Colorado State University, Fort CollinsGoogle Scholar
  29. Zhang L, Singh VP (2012) Bivariate rainfall and runoff analysis using entropy and copula theories. Entropy 14:1784–1812CrossRefGoogle Scholar

Copyright information

© The International Society of Paddy and Water Environment Engineering and Springer Japan KK, part of Springer Nature 2017

Authors and Affiliations

  • Hamidreza Vaziri
    • 1
  • Hojat Karami
    • 1
  • Sayed-Farhad Mousavi
    • 1
  • Miromid Hadiani
    • 2
  1. 1.Faculty of Civil EngineeringSemnan UniversitySemnanIran
  2. 2.College of EngineeringIslamic Azad UniversityGhaemshahrIran

Personalised recommendations