Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm

Stochastic Environmental Research and Risk Assessment

Volumn 24, Issue 5, 2010, Pages 783-805

  Song, Songbai ^a   Singh, Vijay P ^b,c  

^a NORTHWEST A F UNIVERSITY   (China)

^b Texas A and M University   (United States)

^c Texas AandM University   (United States)

Author keywords

Drought characteristics; Genetic algorithm; Multivariate frequency analysis; Plackett copula; Wei River basin

Indexed keywords

BIVARIATE; DROUGHT DURATION; DROUGHT SEVERITY; FREQUENCY ANALYSIS; FUNCTION METHODS; GAGING STATIONS; GAMMA DISTRIBUTION; INTER-ARRIVAL TIME; JOINT PROBABILITY; MAXIMUM LIKELIHOOD METHODS; MULTIVARIATE FREQUENCY ANALYSIS; PLACKETT COPULA; PROBABILITY WEIGHTED MOMENTS; PSEUDO-LIKELIHOOD; TRIVARIATE; UNIVARIATE DISTRIBUTIONS; WEI RIVER;

DROUGHT; FREQUENCY ESTIMATION; GAGING; GENETIC ALGORITHMS; MAXIMUM LIKELIHOOD ESTIMATION; METHOD OF MOMENTS; MULTIVARIANT ANALYSIS; PROBABILISTIC LOGICS; PROBABILITY; RIVERS; WATERSHEDS; WEIBULL DISTRIBUTION;

PARAMETER ESTIMATION;

DROUGHT; ESTIMATION METHOD; FREQUENCY ANALYSIS; GENETIC ALGORITHM; MULTIVARIATE ANALYSIS; PROBABILITY; STREAMFLOW; WEIBULL THEORY;

CHINA; WEI RIVER;

TAIA;

EID: 77955050386     PISSN: 14363240     EISSN: 14363259     Source Type: Journal    
DOI: 10.1007/s00477-010-0364-5     Document Type: Article

References (71)

1. Aas K, Czado C, Frigessi A, Bakken H (2007) Pair-copula constructions of multiple dependence. Insur Math Econ. doi: 10. 1016/j. jnsmatheco. 2007. 02. 001: 1-17.
2. Amal SH (2005) Goodness-of-fit for the generalized exponential distribution. http://interstat. statjournals. net/YEAR/2005/articles/0507001. pdf.
3. Bárdossy A (2006) Copula-based geostatistical models for groundwater quality parameters. Water Resour Res 42: W11416. doi: 10. 1029/2005WR004754.
4. Bárdossy A, Li J (2008) Geostatistical interpolation using copulas. Water Resour Res 44: W07412. doi: 10. 1029/2007WR006115.
5. Bonaccorso B, Bordi I, Cancelliere A, Rossi G, Sutera A (2003a) Spatial variability of drought: an analysis of SPI in Sicily. Water Resour Manag 17: 273-296.
6. Bonaccorso B, Cancelliere A, Rossi G (2003b) An analytical formulation of return period of drought severity. Stoch Env Res Risk Assess 17(3): 157-174.
7. Cabrera E, García-Serra J (1999) Drought management planning in water supply systems: proceedings from the Uimp International Course Held in Valencia, December 1997. Kluwer, Dordrecht.
8. Cancelliere A, Salas JD (2004) Drought length properties for periodic-stochastic hydrological data. Water Resour Res 10(2): 1-13.
9. Chang LC (2008) Guiding rational reservoir flood operation using penalty-type genetic algorithm. J Hydrol 354(1-4): 65-74.
10. Cunnane C (1978) Unbiased plotting positions-a review. J Hydrol 37(3-4): 205-222.
11. De Michele C, Salvadori G (2003) A generalized Pareto intensity-duration model of storm rainfall exploiting 2-copulas. J Geophys Res 108(D2): 4067. doi: 10. 1029/2002JD002534.
12. Dobrić J, Schmid F (2007) A goodness of fit test for copulas based on Rosenblatt's transformation. Comput Stat Data Anal 51: 4633-4642.
13. Dupuis DJ (2007) Using copulas in hydrology: benefits, cautions, and issues. J Hydrol Eng 12(4): 381-393.
14. Evin G, Favre AC (2008) A new rainfall model based on the Neyman-Scott process using cubic copulas. Water Resour Res 44(3): W03433. doi: 10. 1029/2007WR006054.
15. Favre AC, El Adlouni S, Perreault L, Thiémonge N, Bobée B (2004) Multivariate hydrological frequency analysis using copulas. Water Resour Res 40(1): W01101. doi: 10. 1029/2003WR002456.
16. 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.
17. Genest C, Favre AC (2007) Everything you always wanted to know about copula modeling but were afraid to ask. J Hydrol Eng 12(4): 347-367.
18. Genest C, Rémillard B, Beaudoin D (2007a) Goodness-of-fit tests for copulas: a review and a power study. Insur Math Econ. doi: 10. 1016/j. insmatheco. 2007. 10. 005.
19. Genest C, Favre AC, Béliveau J, Jacques C (2007b) Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data. Water Resour Res 43: W09401. doi: 10. 1029/2006WR005275.
20. Goel NK, Seth SM (1998) Multivariate modeling of flood flows. J Hydraul Eng 124(2): 146-155.
21. González J, Valdés JB (2003) Bivariate drought recurrence analysis using tree ring reconstructions. J Hydrol Eng 8(5): 247-258.
22. Grimaldi S, Serinaldi F (2006) Asymmetric copula in multivariate flood frequency analysis. Adv Water Resour 29(8): 1155-1167.
23. Gringorten II (1963) A plotting rule for extreme probability paper. J Geophys Res 68(3): 813-814.
24. Gumbel EJ (1958) Statistics of extremes. Columbia University Press, New York.
25. Kao SC, Govindaraju RS (2008) Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas. Water Resour Res 44(2): W02415. doi: 10. 1029/2007WR006261.
26. Kao SC, Govindaraju RS (2009) A copula-base joint deficit index for droughts. J Hydrol. doi: 10. 1016/j. jhydrol. 2009. 10. 029.
27. Kim TW, Valdés JB, Yoo C (2006) Nonparametric approach for bivariate drought characterization using Palmer Drought Index. J Hydrol Eng 11(2): 134-143.
28. Laux P, Wagner S, Wagner A, Jacobeit J, Bardossy A, Kunstmann H (2009) Modelling daily precipitation features in the Volta Basin of West Africa. Int J Climatol 29(7): 937-954.
29. Mardia KV (1967) Some contributions to contingency-type bivariate distributions. Biometrika 54(1-2): 235-249.
30. McCuen RH (2002) Modeling hydrologic change: statistical methods. Taylor & Francis, Boca Raton.
31. Mishra AK, Singh VP, Desai VR (2008) Drought characterization: a probabilistic approach. Stoch Environ Res Risk Assess. doi: 10. 1007/s00477-007-0194-2.
32. Molenberghs G, Lesaffre E (1994) Marginal modeling of correlated ordinal data using a multivariate Plackett distribution. J Am Stat Assoc 89: 633-644.
33. Nadarajah S (2007) A bivariate gamma model for drought. Water Resour Res 43(8): W08501. doi: 10. 1029/2006WR005641.
34. Nelsen RB (1999) An introduction to copulas. Springer, New York.
35. O'Reilly UM, Yu T, Riolo R, Worzel B (2005) Genetic programming theory and practice II. Springer, Boston.
36. Park WJ, Kim YG (1992) Goodness-of-fit tests for the power-law process. IEEE Trans Reliab 41(1): 107-111.
37. Plackett RL (1965) A class of bivariate distributions. J Am Stat Assoc 60(310): 516-522.
38. Poulin A, Huard D, Favre AC, Pugin S (2007) Importance of tail dependence in bivariate frequency analysis. J Hydrol Eng 12(4): 394-403.
39. Rossi G, Cancelliere A, Pereira L, Oweis T, Shatanawi M, Zairi A (2003) Tools for drought mitigation in Mediterranean regions. Kluwer, Dordrecht.
40. Rossi G, Vega T, Bonaccorso B (2007) Methods and tools for drought analysis and management. Springer, Dordrecht.
41. Salvadori G, De Michele C (2004) Frequency analysis via copulas: theoretical aspects and applications to hydrological events. Water Resour Res 40(12): W12511. doi: 10. 1029/2004WR003133.
42. Salvadori G, De Michele C (2007) On the use of copulas in hydrology: theory and practice. J Hydrol Eng 12(4): 369-380.
43. Salvadori G, De Michele C, Kottegoda NT, Rosso R (2007) Extremes in nature: an approach using copulas. Springer, Dordrecht.
44. Serinaldi F, Grimaldi S (2007) Fully nested 3-copula: procedure and application on hydrological data. J Hydrol Eng 12(4): 420-430.
45. Serinaldi F, Bonaccorso B, Cancelliere A, Grimaldi S (2009) Probabilistic characterization of drought properties through copulas. J Phys Chem Earth 34(10-12): 596-605.
46. Shiau JT (2003) Return period of bivariate distributed hydrological events. Stoch Env Res Risk Assess 17(1-2): 42-57.
47. Shiau JT (2006) Fitting drought duration and severity with two-dimensional copulas. Water Resour Manag 20: 795-815.
48. Shiau JT, Modarres R (2009) Copula-based drought severity-duration-frequency analysis in Iran. Meteorol Appl. doi: 10. 1002/met. 145.
49. Shiau JT, Shen HW (2001) Recurrence analysis of hydrologic droughts of differing severity. J Water Resour Plan Manag 127(1): 30-40.
50. Shiau JT, Wang HY, Chang TT (2006) Bivariate frequency analysis of floods using copulas. J AmWater Resour Assoc 42(6): 1549-1564.
51. Shiau JT, Feng S, Nadarajah S (2007) Assessment of hydrological droughts for the Yellow River, China, using copulas. Hydrol Process 21(16): 2157-2163.
52. Shimokawa T, Liao M (1999) Goodness-of-fit tests for type-I extreme-value and 2-parameter Weibull distribution. IEEE Trans Reliab 48(1): 79-86.
53. Singh K, Singh VP (1991) Derivation of bivariate probability density functions with exponential marginals. Stoch Hydrol Hydraul 5(1): 55-68.
54. Singh VP, Zhang L (2007) IDF curves using the Frank Archimedean copula. J Hydrol Eng 12(6): 651-662.
55. Sklar A (1959) Fonctions de repartition án dimensions et leurs marges. Publ Inst Stat Univ Paris 8: 229-231.
56. Song SB, Singh VP (2009) Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stoch Environ Res Risk Assess. doi: 10. 1007/s00477-009-0331-1.
57. Tayfur G, Moramarco T (2008) Predicting hourly-based flow discharge hydrographs from level data using genetic algorithms. J Hydrol 352(1-2): 77-93.
58. Vose MD (1999) The simple genetic algorithm: foundations and theory. MIT Press, Cambridge.
59. Wong G, Lambert MF, Metcalfe AV (2008) Trivariate copulas for characterization of droughts. ANZIAM J 49: 306-323.
60. Wong G, Lambert MF, Leonard M, Metcalfe AV (2009) Drought analysis using trivariate copulas conditional on climate states. J Hydrol Eng. doi: 10. 1061/(ASCE)HE. 1943-5584. 0000169.
61. Yue S (1999) Applying bivariate normal distribution to flood frequency analysis. Water Int 24(3): 248-254.
62. Yue S (2000a) Joint probability distribution of annual maximum storm peaks and amounts as represented by daily rainfalls. Hydrol Sci J 45(2): 315-326.
63. Yue S (2000b) The Gumbel logistic model for representing a multivariate storm event. Adv Water Resour 24(2): 179-185.
64. Yue S (2000c) The Gumbel mixed model applied to storm frequency analysis. Water Resour Manag 14(5): 377-389.
65. Yue S, Rasmussen P (2002) Bivariate frequency analysis: discussion of some useful concepts for hydrological application. Hydrol Process 16(14): 811-819.
66. Yue S, Ouarda TBMJ, Bobée B, Legendre P, Bruneau P (1999) The Gumbel mixed model for flood frequency analysis. J Hydrol 226: 88-100.
67. Yue S, Ouarda TBMJ, Bobée B (2001) A review of bivariate gamma distributions for hydrological application. J Hydrol 246: 1-18.
68. Zhang L, Singh VP (2006) Bivariate flood frequency analysis using the copula method. J Hydrol Eng 11(2): 150-164.
69. Zhang L, Singh VP (2007a) Gumbel-Hougaard copula for trivariate rainfall frequency analysis. J Hydrol Eng 12(4): 409-419.
70. Zhang L, Singh VP (2007b) Bivariate rainfall frequency distributions using Archimedean copulas. J Hydrol 332: 93-109.
71. Zhang L, Singh VP (2007c) Trivariate flood frequency analysis using the Gumbel-Hougaard copula. J Hydrol Eng 12(4): 431-439.