Application of copulas for derivation of drought severity-duration-frequency curves

Hydrological Processes

Volumn 26, Issue 11, 2012, Pages 1672-1685

  Janga Reddy, M ^a   Ganguli, Poulomi ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

Author keywords

Copulas; Drought; S D F curves; SPI; Tail dependence

Indexed keywords

AREAL PRECIPITATION; BIVARIATE; COPULAS; DROUGHT MITIGATION; EXPONENTIAL DISTRIBUTIONS; EXTREME VALUE; JOINT DISTRIBUTIONS; LOG-NORMAL DISTRIBUTION; PROBABILISTIC APPROACHES; RAJASTHAN , INDIA; RETURN PERIODS; S-D-F CURVES; SPI; STANDARDIZED PRECIPITATION INDEX; TAIL DEPENDENCE; TIME-SCALES;

STATISTICAL TESTS;

DROUGHT;

DROUGHT; MULTIVARIATE ANALYSIS; NUMERICAL MODEL; PRECIPITATION (CLIMATOLOGY); PROBABILITY; REGIONAL CLIMATE; TIMESCALE; TREND ANALYSIS;

INDIA; RAJASTHAN;

EID: 84861228805     PISSN: 08856087     EISSN: 10991085     Source Type: Journal    
DOI: 10.1002/hyp.8287     Document Type: Article

References (51)

1. Akaike H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control AC-19(6): 716-723.
2. Ane T, Kharoubi C. 2003. Dependence structure and risk measure. Journal of Business 76(3): 411-438.
3. Bozdogan H. 2000. Akaike's Information Criterion and recent developments in information complexity. Journal of Mathematical Psychology 44: 62-91.
4. Cancelliere A, Salas JD. 2004. Drought length properties for periodic-stochastic hydrological data. Water Resources Research 40. DOI: 10.1029/2002WR001750.
5. Capéraá P, Fougéres A-L, Genest C. 1997. A non-parametric estimation procedure for bivariate extreme value copulas. Biometrika 84: 567-577.
6. Chung CH, Salas JD. 2000. Drought occurrences probabilities and risks of dependent hydrologic processes. Journal of Hydrologic Engineering 5(3): 259-268.
7. CMP Report. 2010. Crisis Management Plan - Drought (National). Dept. of Agriculture and cooperation, Ministry of Agriculture, Govt. of India. [available at: ]. [accessed: January 2011].
8. Coles SG, Heffernan JE, Tawn JA. 1991. Modeling multivariate extreme events. Journal of the Royal Statistical Society B 53: 377-392.
9. Dalezios NR, Loukas A, Vasiliades L, Liakopoulos E. 2000. Severity-duration-frequency of droughts and wet periods in Greece. Hydrological Sciences Journal 45: 751-769.
10. Dracup JA, Lee KS, Paulson EG. 1980a. On the definition of droughts. Water Resources Research 16(2): 297-302.
11. Dracup JA, Lee KS, Paulson EG. 1980b. On the statistical characteristics of drought events. Water Resources Bulletin 26(5): 823-829.
12. Fernandez B, Salas JD. 1999. Return period and risk of hydrologic events I: mathematical formulation. Journal of Hydrologic Engineering 4(4): 297-307.
13. Frahm G, Junker M, Schimdt R. 2005. Estimating the tail-dependence coefficient: properties and pitfalls. Insurance, Mathematics and Economics 37: 80-100.
14. Genest C, Favre AC. 2007. Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering 12(4): 347-368.
15. Genest C, Ghoudi K, Rivest LP. 1995. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82(3): 543-552.
16. Genest C, Rivest L-P. 1993. Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association 88(423): 1034-1043.
17. González J, Valdés JB. 2003. Bivariate drought recurrence analysis using tree ring reconstructions. Journal of Hydrologic Engineering 8(5): 247-258.
18. Joe H. 1997. Multivariate Models and Dependence Concepts. Monographs on Statistics and Applied Probability, vol. 73. Chapman and Hall: London; 399.
19. Joe H, Smith RL, Weissman I. 1992. Bivariate threshold models for extremes. Journal of the Royal Statistical Society B 54: 171-183.
20. Kao SC, Govindaraju RS. 2010. A copula-based joint deficit index for droughts. Journal of Hydrology 380: 121-134.
21. Keyantash J, Dracup JA. 2002. The quantification of drought: an evaluation of drought indices. Bulletin of the American Meteorological Society 83: 1167-1180.
22. Kim TW, Valdés JB, Yoo C. 2003. Nonparametric approach for estimating return periods of droughts in arid regions. Journal of Hydrologic Engineering 8(5): 237-246.
23. Kim T-W, Valdés JB, Yoo C. 2006. Nonparametric approach for bivariate drought characterization using Palmer drought index. Journal of Hydrologic Engineering 11(2): 134-143.
24. Laux P, Wagner S, Wagner A, Jacobeit J, Bárdossy A, Kunstmann H. 2009. Modelling daily precipitation features in the Volta Basin of the West Africa. International Journal of Climatology 29(7): 937-954.
25. Mashal R, Zeevi A. 2002. Beyond correlation: Extreme co-movements between financial assets. Technical Report, Columbia University; 47.
26. McKee TB, Doesken NJ, Kliest J. 1993. The relationship of drought frequency and duration time scales. Proceedings of the 8th International Conference on Applied Climatology, Boston, MA; 179-184.
27. McNeil AJ, Frey R, Embrechts P. 2005. Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press: Princeton; 538.
28. Mirakbari M, Ganji A, Fallah SR. 2010. Regional bivariate frequency analysis of meteorological droughts. Journal of Hydrologic Engineering 15(12): 985-1000.
29. Mohan S, Sahoo PK. 2008. Stochastic simulation of droughts: Part-I: point droughts. Hydrological Processes 22: 854-862.
30. Nadarajah S. 2009. A bivariate pareto model for drought. Stochastic Environmental Research and Risk Assessment 23(6): 811-822.
31. Narain P, Khan MA, Singh G. 2005. Potential for water conservation and harvesting against drought in Rajasthan, India. Working paper 104 (Drought Series: 7). IWMI: Sri Lanka.
32. Nelsen RB. 1999. An Introduction to copulas. Springer: New York, NY; 209.
33. Obasi GOP. 1994. WMO's role in the international decade for natural disaster reduction. Bulletin of the American Meteorological Society 75: 1655-1661.
34. Panofsky HA, Brier GW. 1958. Some applications of statistics to meteorology. Pennsylvania State University Press: University Park, PA; 224.
35. Poulin A, Huard D, Favre A-C, Pugin S. 2007. Importance of tail dependence in bivariate frequency analysis. Journal of Hydrologic Engineering 12(4): 394-403.
36. Saghafian B, Shokoohi A, Raziei T. 2003. Drought spatial analysis and development of severity-duration-frequency curves for an arid region. Proceedings of International Conference on Hydrology of the Mediterranean and Semiarid Regions. Montpellier, 278: 305-311.
37. Sen Z. 1980. Regional drought and flood frequency analysis: Theoretical consideration. Journal of Hydrology 340: 1-11.
38. Serinaldi F. 2008. Analysis of inter-gauge dependence by Kendall's, upper tail dependence coefficient, and 2-copulas with application to rainfall fields. Stochastic Environmental Research and Risk Assessment 22(6): 671-688.
39. Serinaldi F, Bonaccorso B, Cancelliere A, Grimaldi S. 2009. Probabilistic characterization of drought properties through copulas. Physics and Chemistry of the Earth B 34(10-12): 596-605.
40. Shiau JT. 2006. Fitting drought duration and severity with two-dimensional copulas. Water Resources Management 20: 795-815.
41. Shiau JT, Modarres R. 2009. Copula-based drought severity-duration-frequency analysis in Iran. Meteorological Applications 16(4): 481-489.
42. Shiau JT, Feng S, Nadarjah S. 2007. Assessment of hydrological droughts for the Yellow River, China, using copulas. Hydrological Processes 21(16): 2157-2163.
43. Shiau JT, Shen HW. 2001. Resource analysis of hydrologic droughts of different severity. Journal of Water Resources Planning and Management 127(1): 30-40.
44. Sklar A. 1959. Fonctions de répartition á n dimensions et leurs marges. Publications de l'Institut de Statistique de l'Université de Paris 8: 229-231.
45. Song S, Singh VP. 2010. Meta-elliptical copulas for drought frequency analysis of periodic hydraulic data. Stochastic Environmental Research and Risk Assessment 24(3): 425-444.
46. Svoboda M, Lecomte D, Hayes M, Heim R, Gleason K, Angel J, Rippey B, Tinker R, Palecki M, Stooksbury D, Miskus D, Stephens S. 2002. The drought monitor. Bulletin of the American Meteorological Society 83: 1181-1190.
47. Tallaksen LM, Madsen H, Clausen B. 1997. On the definition and modeling of stream drought duration and deficit volume. Hydrological Sciences Journal 42(1): 15-33.
48. Tawn JA. 1988. Bivariate extreme value theory: models and estimation. Biometrika 75(3): 397-415.
49. Wu H, Svoboda MD, Hays MJ, Wilhite DA, Wen F. 2007. Appropriate application of the standardized precipitation index in arid locations and dry seasons. International Journal of Climatology 27: 65-79.
50. Yoo C, Kim D, Kim T-W, Hwang K-N. 2008. Quantification of drought using a rectangular pulses Poisson process model. Journal of Hydrology 355: 34-48.
51. Yue S. 2001. A bivariate extreme value distribution applied to flood frequency analysis. Nordic Hydrology 32(1):49-64.