Bivariate drought frequency analysis using the copula method

Theoretical and Applied Climatology

Volumn 108, Issue 1-2, 2012, Pages 191-206

  Mirabbasi, Rasoul ^a   Fakheri Fard, Ahmad ^a   Dinpashoh, Yagob ^a  

^a UNIVERSITY OF TABRIZ   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

DROUGHT; ECONOMIC IMPACT; ENVIRONMENTAL IMPACT; FREQUENCY ANALYSIS; NATURAL HAZARD; PROBABILITY; WATER MANAGEMENT; WATER PLANNING; WATER RESOURCE;

IRAN;

EID: 84859101609     PISSN: 0177798X     EISSN: 14344483     Source Type: Journal    
DOI: 10.1007/s00704-011-0524-7     Document Type: Article

References (63)

1. Abdous B, Genest C, Rémillard B (2004) Dependence properties of meta-elliptical distributions. In: Duchesne P, Rémillard B (eds) Statistical modeling and analysis for complex data problems. Kluwer, Dordrecht, pp 1-15.
2. AghaKouchak A, Bardossy A, Habib E (2010) Conditional simulation of remotely sensed rainfall fields using a non-Gaussian v-transformed copula. Adv Water Resour 33(6): 624-634. doi: 10. 1016/j. advwatres. 2010. 02. 010.
3. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control AC 19(6): 716-723.
4. Bardossy A (2006) Copula-based geostatistical models for groundwater quality parameters. Water Resour Res 42: W11416. doi: 10. 1029/2005WR004754.
5. Bardossy A, Li J (2008) Geostatistical interpolation using copulas. Water Resour Res 44(7): W07412. doi: 10. 1029/2007WR006115.
6. Cancelliere A, Salas JD (2004) Drought length properties for periodic-stochastic hydrologic data. Water Resour Res 40: W02503. doi: 10. 1029/2002WR001750.
7. Capéraà P, Fougères A-L, Genest C (1997) A nonparametric estimation procedure for bivariate extreme value copulas. Biometrika 84(3): 567-577.
8. Capéraà P, Fougères A-L, Genest C (2000) Bivariate distributions with given extreme value attractor. J Multivariate Anal 72: 30-49.
9. Coles SG, Heffernan JE, Tawn JA (1999) Dependence measures for extreme value analyses. Extremes 2: 339-365.
10. De Michele C, Salvadori G (2003) A generalized Pareto intensity-duration model of storm rainfall exploiting 2-copulas. J Geophys Res Atmos 108: 4067. doi: 10. 1029/2002JD002534.
11. Dracup JA, Lee KS, Paulson EG Jr (1980) On the definition of droughts. Water Resour Res 16(2): 297-302. doi: 10. 1029/WR016i002p00297.
12. Durante F, Salvadori G (2010) On the construction of multivariate extreme value models via copulas. Environmetrics 21: 143-161.
13. Edwards D, McKee T (1997) Characteristics of 20th century drought in the United States at multiple time scales. Climatology report number 972. Technical report, Colorado State University, Fort Collins, USA.
14. Eimanifar A, Mohebbi F (2007) Urmia Lake (Northwest Iran): a brief review. Saline Syst 3(5): 1-8. doi: 10. 1186/1746-1448-3-5.
15. Fang H-B, Fang K-T, Kotz S (2002) The meta-elliptical distributions with given marginals. J Multivariate Anal 82: 1-16.
16. Favre AC, El Adlouni S, Perreault L, Thiémonge N, Bobée B (2004) Multivariate hydrological frequency analysis using copulas. Water Resour Res 40: W01101. doi: 10. 1029/2003WR002456.
17. Fernández B, Salas JD (1999) Return period and risk of hydrologic events. I: mathematical formulations. J Hydrol Eng 4(4): 297-307.
18. Frahm G, Junker M, Schmidt R (2005) Estimating the tail-dependence coefficient: properties and pitfalls. Insur Math Econ 37(1): 80-100.
19. Gebremichael M, Krajewski WF (2007) Application of copulas to modeling temporal sampling errors in satellite-derived rainfall estimates. J Hydrol Eng 12(4): 404-408.
20. Genest C, Favre AC (2007) Everything you always wanted to know about copula modeling but were afraid to ask. J Hydrol Eng 12(4): 347-368.
21. Genest C, Ghoudi K, Rivest L-P (1995) A semiparametric estimation procedure of dependence parameters in multivariate families of distribution. Biometrika 82(3): 543-552. doi: 10. 1093/biomet/82. 3. 543.
22. Genest C, Rémillard B, Beaudoin D (2009) Goodness-of-fit tests for copulas: a review and a power study. Insur Math Econ 44: 199-213.
23. Genest C, Rivest L-P (1993) Statistical inference procedures for bivariate archimedean copulas. J Am Stat Assoc 88: 1034-1043.
24. Ghosh S (2010) Modelling bivariate rainfall distribution and generating bivariate correlated rainfall data in neighbouring meteorological subdivisions using copula. Hydrol Process 24: 3558-3567. doi: 10. 1002/hyp. 7785.
25. Ghoudi K, Khoudraji A, Rivest L-P (1998) Propriétés statistiques des copules de valeurs extrêmes bidimensionnelles. Can J Stat 26: 187-197.
26. Grimaldi S, Serinaldi F (2006a) Asymmetric copula in multivariate flood frequency analysis. Adv Water Resour 29(8): 1115-1167. doi: 10. 1016/j. advwatres. 2005. 09. 005.
27. Grimaldi S, Serinaldi F (2006b) Design hyetograph analysis with 3-copula function. Hydrol Sci J 51(2): 223-238. doi: 10. 1623/hysj. 51. 2. 223.
28. Hayes MJ, Svoboda MD, Wilhite DA, Vanyarkho OV (1999) Monitoring the 1996 drought using the standardized precipitation index. Bull Am Met Soc 80(3): 429-438.
29. Joe H (1997) Multivariate models and dependence concepts. Chapman and Hall, New York.
30. Kao SC, Govindaraju RS (2007) Probabilistic structure of storm surface runoff considering the dependence between average intensity and storm duration of rainfall events. Water Resour Res 43: W06410. doi: 10. 1029/2006WR005564.
31. Kao SC, Govindaraju RS (2010) A copula-based joint deficit index for droughts. J Hydrol 380: 121-134. doi: 10. 1016/j. jhydrol. 2009. 10. 029.
32. Kao SC, Govindaraju RS, Niyogi D (2009) A spatio-temporal drought analysis for the midwestern US. In: Proceedings of World Environmental and Water Resources Congress, Great Rivers, 4654-4663.
33. Kim TW, Valdés JB, Yoo C (2003) Nonparametric approach for estimating return periods of droughts in arid regions. J Hydrol Eng 8(5): 237-246.
34. Loukas A, Vasiliades L (2004) Probabilistic analysis of drought spatiotemporal characteristics in Thessaly region, Greece. Nat Hazards Earth Syst Sci 4: 719-731.
35. Mathier L, Perreault L, Bobe B, Ashkar F (1992) The use of geometric and gamma-related distributions for frequency analysis of water deficit. Stoch Hydrol Hydraul 6(4): 239-254.
36. McKee TB, Doeskin NJ, Kleist J (1993) The relationship of drought frequency and duration to time scales. In: Proceedings of the 8th conference on applied climatology, 17-22 January, Anaheim, CA, Am Meteor Soc, pp 179-184.
37. Mirakbari M, Ganji A, Fallah SR (2010) Regional bivariate frequency analysis of meteorological droughts. J Hydrol Eng 15(12): 985-1000. doi: 10. 1061/(ASCE)HE. 1943-5584. 0000271.
38. Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models. 1. A discussion of principles. J Hydrol 10: 282-290. doi: 10. 1016/0022-1694(70)90255-6.
39. Nelsen RB (2006) An introduction to copulas. Springer, New York.
40. Poulin A, Huard D, Favre A, Pugin S (2007) Importance of tail dependence in bivariate frequency analysis. J Hydrol Eng 12(4): 394-403.
41. Raziei T, Saghafian B, Paulo AA, Pereira LS, Bordi I (2009) Spatial patterns and temporal variability of drought in western Iran. Water Resour Manag 23: 439-455. doi: 10. 1007/s11269-008-9282-4.
42. Rossi G, Benedini M, Tsakiris G, Giakoumakis S (1992) On regional drought estimation and analysis. Water Resour Manag 6(4): 249-277. doi: 10. 1007/BF00872280.
43. Salvadori G, De Michele C (2010) Multivariate multiparameter extreme value models and return periods: a copula approach. Water Resour Res 46: W10501. doi: 10. 1029/2009WR009040.
44. Salvadori G, De Michele C, Durante F (2011) Multivariate design via copulas. Hydrol Earth Syst Sci Discuss 8: 5523-5558. doi: 10. 5194/hessd-8-5523-2011.
45. Salvadori G, De Michele C, Kottegoda NT, Rosso R (2007) Extremes in nature. An approach using copulas. Springer, Dordrecht.
46. Serinaldi F (2008) Analysis of inter-gauge dependence by Kendall's τK, upper tail dependence coefficient, and 2-copulas with application to rainfall fields. Stoch Environ Res Risk Assess 22: 671-688. doi: 10. 1007/s00477-007-0176-4.
47. Serinaldi F, Bonaccoroso B, Cancelliere A, Grimaldi S (2009) Probabilistic characterization of drought properties through copulas. Phys Chem Earth Parts A/B/C 34(10-12): 596-605.
48. Shiau JT (2006) Fitting drought duration and severity with two-dimensional copulas. Water Resour Manag 20: 795-815. doi: 10. 1007/s11269-005-9008-9.
49. Shiau JT, Feng S, Nadarajah S (2007) Assessment of hydrological droughts for the Yellow River, China, using copulas. Hydrol Process 21: 2157-2163.
50. Shiau JT, Modarres R (2009) Copula-based drought severity-duration-frequency analysis in Iran. J Appl Meteorol 16(4): 481-489. doi: 10. 1002/met. 145.
51. Shiau JT, Shen HW (2001) Recurrence analysis of hydrologic droughts of differing severity. J Water Resour Plan Manag 127(1): 30-40.
52. Shiau JT, Wang HY, Tsai CT (2006) Bivariate frequency analysis of floods using copulas. J Am Water Resour Assoc 42: 1549-1564.
53. Sibuya M (1960) Bivariate extreme statistics. Ann Inst Stat Math 11: 195-210.
54. Singh VP, Zhang L (2007) IDF curves using the Frank Achimedean copula. J Hydrol Eng 12(6): 651-662.
55. Sklar A (1959) Fonctions de répartition à n dimensions et leurs marges. Publ Inst Statist Univ Paris 8: 229-231.
56. Song S, Singh VP (2010a) Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm. Stoch Environ Res Risk Assess 24: 783-805. doi: 10. 1007/s00477-010-0364-5.
57. Song S, Singh VP (2010b) Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stoch Environ Res Risk Assess 24: 425-444. doi: 10. 1007/s00477-009-0331-1.
58. Wong G, Lambert MF, Metcalfe AV (2008) Trivariate copulas for characterization of droughts. ANZIAM J 49: 306-323.
59. Wong G, Lambert MF, Leonard M, Metcalfe AV (2010) Drought analysis using trivariate copulas conditional on climatic states. J Hydrol Eng 15(2): 129-141.
60. Xu Y-P, Booij MJ, Tong Y-B (2010) Uncertainty analysis in statistical modeling of extreme hydrological events. Stoch Environ Res Risk Assess 24: 567-578. doi: 10. 1007/s00477-009-0337-8.
61. Yevjevich V (1967) An objective approach to definitions and investigations of continental hydrologic drought. Hydrol paper 23. Colorado State University Fort Collins, USA.
62. Zhang L, Singh VP (2006) Bivariate flood frequency analysis using the copula method. J Hydrol Eng 11(2): 150-164.
63. Zhang L, Singh VP (2007) Gumbel-Hougaard copula for trivariate rainfall frequency analysis. J Hydrol Eng 12(4): 409-419.