Water Resources Management

, Volume 32, Issue 2, pp 547–564 | Cite as

Copulas-Based Drought Characteristics Analysis and Risk Assessment across the Loess Plateau of China

Article
  • 143 Downloads

Abstract

The Loess Plateau (LP) of China is famous with soil erosion and water shortage problems. Droughts were frequently occurred in this region, which becomes a critical limiting factor to the socioeconomic development, ecology and food production. Therefore, the major motivation of the present study is to investigate the drought characteristics and assess the potential drought risk in this area, which is crucial for drought resistance, water resource management as well as agricultural production. This study analyzes the variations of meteorological drought, characterized by the Standardized Precipitation Evapotranspiration Index (SPEI), and assesses the drought hazards in the LP during 1950–2014. The results show that the northwest of LP is more likely to experience long duration and large severity droughts than the southeast of LP. From the perspective of statistical probability models, the exponential distribution and Gamma distribution can well fit the drought duration and severity, respectively. Compared to Frank and Clayton copula, the Gumbel copula can better model the dependence structure between the drought variables in our study area. Moreover, the estimation of the upper tail dependence coefficient between drought duration and severity also demonstrate that Gumbel copula can provide the best description of the upper tail. The spatial distribution of joint return period under different cases indicates that drought risk in northwestern LP is relatively higher than that in other areas of LP. The results presented in this study can provide some scientific basis for the strategic planning of drought resistance and water resource management in the LP.

Keywords

Drought Copula function Tail dependence Loess plateau Drought risk 

Notes

Acknowledgements

This study was supported by the National Natural Science Foundation of China (No. 41501030), and the National Key Research and Development Program of China (No. 2017YFA0603704) and the Open Foundation of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (No. 2016490211). The Standardized Precipitation Evapotranspiration Index (SPEI) data at 3 month time scale were downloaded on the website http://spei.csic.es/database.html.

References

  1. Allen RG, Pereira LS, Raes D et al (1998) Crop evapotranspiration-Guidelines for computing crop water requirements. FAO Irrig Drain Paper 300(56):1–15Google Scholar
  2. Chen H, Sun J (2015) Changes in drought characteristics over China using the standardized precipitation evapotranspiration index. J Clim 28(13):5430–5447CrossRefGoogle Scholar
  3. Dai A, Trenberth KE, Qian T (2004) A Global Dataset of Palmer Drought Severity Index for 1870–2002: Relationship with Soil Moisture and Effects of Surface Warming. J Hydrometeorol 5(6):1117–1130.  https://doi.org/10.1175/jhm-386.1 CrossRefGoogle Scholar
  4. Das PK, Dutta D, Sharma J et al (2016) Trends and behaviour of meteorological drought (1901–2008) over Indian region using standardized precipitation–evapotranspiration index. Int J Climatol 36(2):909–916CrossRefGoogle Scholar
  5. Favre A-C, El Adlouni S, Perreault L et al (2004) Multivariate hydrological frequency analysis using copulas. Water Resour Res 40(1):W01101.  https://doi.org/10.1029/2003WR002456
  6. Frahm G, Junker M, Schmidt R (2005) Estimating the tail-dependence coefficient: properties and pitfalls. Insur Math Econ 37(1):80–100CrossRefGoogle Scholar
  7. Ganguli P, Reddy MJ (2014) Evaluation of trends and multivariate frequency analysis of droughts in three meteorological subdivisions of western India. Int J Climatol 34(3):911–928CrossRefGoogle Scholar
  8. Genest C, Favre A-C (2007) Everything you always wanted to know about copula modeling but were afraid to ask. J Hydrol Eng 12(4):347–368CrossRefGoogle Scholar
  9. Genest C, Rémillard B, Beaudoin D (2009) Goodness-of-fit tests for copulas: a review and a power study. Insur Math Econ 44(2):199–213CrossRefGoogle Scholar
  10. Heim RR (2002) A review of twentieth-century drought indices used in the United States. Bull Am Meteorol Soc 83(8):1149–1166CrossRefGoogle Scholar
  11. Hosking JRM (1990) L-moments: analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc Ser B Methodol 52(1):105–124Google Scholar
  12. Hosking JRM, Wallis JR (1997) Regional frequency analysis: an approach based on L-moments. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  13. Huard D, Evin G, Favre A-C (2006) Bayesian copula selection. Comput Stat Data Anal 51(2):809–822CrossRefGoogle Scholar
  14. Joe H (1997) Multivariate models and multivariate dependence concepts. CRC Press, Boca RatonCrossRefGoogle Scholar
  15. Kao S-C, Govindaraju RS (2010) A copula-based joint deficit index for droughts. J Hydrol 380(1):121–134CrossRefGoogle Scholar
  16. Kolmogorov A (1933) Sulla Determinazione Empirica di una Legge di Distributione. Giornale dell'Istituto Italiano degli Attuari 4:1–11Google Scholar
  17. Lee T, Modarres R, Ouarda TBMJ (2013) Data-based analysis of bivariate copula tail dependence for drought duration and severity. Hydrol Process 27(10):1454–1463.  https://doi.org/10.1002/hyp.9233 CrossRefGoogle Scholar
  18. Liu X, Zhang J, Ma D et al (2013) Dynamic risk assessment of drought disaster for maize based on integrating multi-sources data in the region of the northwest of Liaoning Province, China. Nat Hazards 65(3):1393–1409CrossRefGoogle Scholar
  19. McKee, T. B., N. J. Doesken, and J. Kleist (1993), The relationship of drought frequency and duration to time scales, paper presented at Proceedings of the 8th Conference on Applied Climatology. American Meteorological Society Boston, MAGoogle Scholar
  20. Miao C, Sun Q, Duan Q et al (2016) Joint analysis of changes in temperature and precipitation on the Loess Plateau during the period 1961–2011. Clim Dyn 47(9):3221–3234.  https://doi.org/10.1007/s00382-016-3022-x CrossRefGoogle Scholar
  21. Mishra AK, Singh VP (2010) A review of drought concepts. J Hydrol 391(1):202–216CrossRefGoogle Scholar
  22. Nelsen RB (2007) An introduction to copulas. Springer, BerlinGoogle Scholar
  23. Palmer WC (1965) Meteorological drought. US Department of Commerce, Weather Bureau, Washington, DCGoogle Scholar
  24. Poulin A, Huard D, Favre A-C et al (2007) Importance of tail dependence in bivariate frequency analysis. J Hydrol Eng 12(4):394–403CrossRefGoogle Scholar
  25. Rajsekhar D, Singh VP, Mishra AK (2014) Hydrologic drought atlas for Texas. J Hydrol Eng.  https://doi.org/10.1061/(ASCE)HE.1943-5584.0001074
  26. Salvadori G, De Michele C (2004) Frequency analysis via copulas: Theoretical aspects and applications to hydrological events. Water Resour Res 40(12):W12511.  https://doi.org/10.1029/2004WR003133 CrossRefGoogle Scholar
  27. Sheffield J, Wood EF (2007) Characteristics of global and regional drought, 1950–2000: Analysis of soil moisture data from off-line simulation of the terrestrial hydrologic cycle. J Geophys Res Atmos 112(D17):115.  https://doi.org/10.1029/2006JD008288
  28. Sheffield J, Wood EF, Roderick ML (2012) Little change in global drought over the past 60 years. Nature 491(7424):435–438CrossRefGoogle Scholar
  29. Shiau J (2006) Fitting drought duration and severity with two-dimensional copulas. Water Resour Manag 20(5):795–815CrossRefGoogle Scholar
  30. Shiau J-T, Modarres R (2009) Copula-based drought severity-duration-frequency analysis in Iran. Meteorol Appl 16(4):481–489CrossRefGoogle Scholar
  31. Shiau J-T, Shen HW (2001) Recurrence analysis of hydrologic droughts of differing severity. J Water Resour Plan Manag 127(1):30–40CrossRefGoogle Scholar
  32. Sklar M (1959) Fonctions de répartition à n dimensions et leurs marges. Université Paris 8, ParisGoogle Scholar
  33. Smirnov N (1948) Table for estimating the goodness of fit of empirical distributions. Ann Math Stat 19(2):279–281CrossRefGoogle Scholar
  34. Stone R (2010) Severe drought puts spotlight on Chinese dams. Science 327(5971):1311–1311.  https://doi.org/10.1126/science.327.5971.1311 CrossRefGoogle Scholar
  35. Su C, Fu B (2013) Evolution of ecosystem services in the Chinese Loess Plateau under climatic and land use changes. Glob Planet Chang 101:119–128CrossRefGoogle Scholar
  36. Tosunoglu F, Kisi O (2016) Joint modelling of annual maximum drought severity and corresponding duration. J Hydrol 543(Part B):406–422CrossRefGoogle Scholar
  37. Trenberth KE, Dai A, van der Schrier G et al (2014) Global warming and changes in drought. Nat Clim Chang 4(1):17–22CrossRefGoogle Scholar
  38. Tsakiris G, Pangalou D, Vangelis H (2007) Regional Drought Assessment Based on the Reconnaissance Drought Index (RDI). Water Resour Manag 21(5):821–833.  https://doi.org/10.1007/s11269-006-9105-4 CrossRefGoogle Scholar
  39. Tsakiris G, Kordalis N, Tigkas D et al (2016) Analysing Drought Severity and Areal Extent by 2D Archimedean Copulas. Water Resour Manag 30(15):5723–5735.  https://doi.org/10.1007/s11269-016-1543-z CrossRefGoogle Scholar
  40. Vicente-Serrano SM, Beguería S, López-Moreno JI (2010) A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index. J Clim 23(7):1696–1718CrossRefGoogle Scholar
  41. Vicente-Serrano SM, López-Moreno JI, Gimeno L et al (2011) A multiscalar global evaluation of the impact of ENSO on droughts. J Geophys Res Atmos 116(D20):D20109.  https://doi.org/10.1029/2011JD016039 CrossRefGoogle Scholar
  42. Vicente-Serrano SM, Van der Schrier G, Beguería S et al (2015) Contribution of precipitation and reference evapotranspiration to drought indices under different climates. J Hydrol 526:42–54CrossRefGoogle Scholar
  43. Wilhite DA (2000) Drought as a natural hazard: concepts and definitions. Drought, a Global Assessment 1:3–18Google Scholar
  44. Yevjevich V, Ingenieur J, Yevjevich V et al (1967) An objective approach to definitions and investigations of continental hydrologic droughts. Colorado State University, Fort CollinsGoogle Scholar
  45. Yu M, Li Q, Hayes MJ et al (2014) Are droughts becoming more frequent or severe in China based on the standardized precipitation evapotranspiration index: 1951–2010? Int J Climatol 34(3):545–558CrossRefGoogle Scholar
  46. Zhang B, He C (2016) A modified water demand estimation method for drought identification over arid and semiarid regions. Agric For Meteorol 230–231:58–66CrossRefGoogle Scholar
  47. Zhang Q, Xiao M, Singh VP et al (2013) Copula-based risk evaluation of droughts across the Pearl River basin, China. Theor Appl Climatol 111(1–2):119–131CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanPeople’s Republic of China
  2. 2.Hubei Provincial Collaborative Innovation Center for Water Resources SecurityWuhanPeople’s Republic of China

Personalised recommendations