Bivariate flood frequency analysis using the copula function: A case study of the Litija station on the Sava River

Hydrological Processes

Volumn 29, Issue 2, 2015, Pages 225-238

  Sraj, Mojca ^a   Bezak, Nejc ^a   Brilly, Mitja ^a  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

Author keywords

Copula; Distributions; Flood frequency analysis; Statistical and graphical tests; Tail dependence

Indexed keywords

CORRELATION THEORY; FLOOD CONTROL; METHOD OF MOMENTS;

COPULA; DISTRIBUTIONS; FLOOD FREQUENCY ANALYSIS; GRAPHICAL TEST; TAIL DEPENDENCE;

FLOODS;

EID: 84920943970     PISSN: 08856087     EISSN: 10991085     Source Type: Journal    
DOI: 10.1002/hyp.10145     Document Type: Article

References (55)

1. Ariff NM, Jemain AA, Ibrahim K, Zin WZW. 2012. IDF relationships using bivariate copula for storm events in Peninsular Malaysia. Journal of Hydrology 470: 158-171. DOI: 10.1016/j.jhydrol.2012.08.045.
2. Ashkar F, Aucoin F. 2011. A broader look at bivariate distributions applicable in hydrology. Journal of Hydrology 405: 451-461. DOI: 10.1016/j.jhydrol.2011.05.043.
3. Bacova-Mitkova V, Onderka M. 2010. Analysis of extreme hydrological events on the danube using the peak over threshold method. Journal of Hydrology and Hydromechanics 58: 88-101. DOI: 10.2478/v10098-010-0009-x.
4. Balistrocchi M, Bacchi B. 2011. Modelling the statistical dependence of rainfall event variables through copula functions. Hydrology and Earth System Sciences 15: 1959-1977. DOI: 10.5194/hess-15-1959-2011.
5. Bardossy A. 2006. Copula-based geostatistical models for groundwater quality parameters. Water Resources Research 42. DOI: 10.1029/2005wr004754.
6. Bezak N, Brilly M, Šraj M. 2014. Comparison between the peaks over threshold method and the annual maximum method for flood frequency analyses. Hydrological Sciences Journal-Journal Des Sciences Hydrologiques. DOI: 10.1080/02626667.2013.831174.
7. Bonacci O, Oskorus D. 2010. The changes in the lower Drava River water level, discharge and suspended sediment regime. Environmental Earth Sciences 59: 1661-1670. DOI: 10.1007/s12665-009-0148-8.
8. Chen L, Singh VP, Guo SL, Hao ZC, Li TY. 2012. Flood coincidence risk analysis using multivariate copula functions. Journal of Hydrologic Engineering 17: 742-755. DOI: 10.1061/(asce)he.1943-5584.0000504.
9. De Michele C, Salvadori G. 2003. A Generalized Pareto intensity-duration model of storm rainfall exploiting 2-Copulas. Journal of Geophysical Research-Atmospheres 108. DOI: 10.1029/2002jd002534.
10. De Michele C, Salvadori G, Canossi M, Petaccia A, Rosso R. 2005. Bivariate statistical approach to check adequacy of dam spillway. Journal of Hydrologic Engineering 10: 50-57. DOI: 10.1061/(asce)1084-0699(2005)10:1(50).
11. Dupuis DJ. 2007. Using copulas in hydrology: benefits, cautions, and issues. Journal of Hydrologic Engineering 12: 381-393. DOI: 10.1061/(asce)1084-0699(2007)12:4(381).
12. Favre AC, El Adlouni S, Perreault L, Thiemonge N, Bobee B. 2004. Multivariate hydrological frequency analysis using copulas. Water Resources Research 40. DOI: 10.1029/2003wr002456.
13. Fisher NI, Switzer P. 1985. Chi-plots for assessing dependence. Biometrika 72: 253-265. DOI: 10.1093/biomet/72.2.253.
14. Fisher NI, Switzer P. 2001. Graphical assessment of dependence: is a picture worth 100 tests? American Statistician 55: 233-239. DOI: 10.1198/000313001317098248.
15. Frahm G, Junker M, Schmidt R. 2005. Estimating the tail-dependence coefficient: properties and pitfalls. Insurance Mathematics & Economics 37: 80-100. DOI: 10.1016/j.matheco.2005.05.008.
16. Ganguli P, Reddy MJ. 2013. Probabilistic assessment of flood risks using trivariate copulas. Theoretical and Applied Climatology 111: 341-360. DOI: 10.1007/s00704-012-0664-4.
17. Gargouri-Ellouze E, Chebchoub A. 2008. Modelling the dependence structure of rainfall depth and duration by Gumbel's copula. Hydrological Sciences Journal-Journal Des Sciences Hydrologiques 53: 802-817. DOI: 10.1623/hysj.53.4.802.
18. Genest C, Boies JC. 2003. Detecting dependence with Kendall plots. American Statistician 57: 275-284. DOI: 10.1198/0003130032431.
19. Genest C, Favre AC. 2007. Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering 12: 347-368. DOI: 10.1061/(asce)1084-0699(2007)12:4(347).
20. Genest C, Remillard B. 2008. Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models. Annales De L Institut Henri Poincare-Probabilites Et Statistiques 44: 1096-1127. DOI: 10.1214/07-aihp148.
21. Genest C, Remillard B, Beaudoin D. 2009. Goodness-of-fit tests for copulas: a review and a power study. Insurance Mathematics & Economics 44: 199-213. DOI: 10.1016/j.insmatheco.2007.10.005.
22. Genest C, Kojadinovic I, Neslehova J, Yan J. 2011. A goodness-of-fit test for bivariate extreme-value copulas. Bernoulli 17: 253-275. DOI: 10.3150/10-bej279.
23. Ghosh S. 2010. Modelling bivariate rainfall distribution and generating bivariate correlated rainfall data in neighbouring meteorological subdivisions using copula. Hydrological Processes 24: 3558-3567. DOI: 10.1002/hyp.7785.
24. Graler B, van den Berg MJ, Vandenberghe S, Petroselli A, Grimaldi S, De Baets B, Verhoest NEC. 2013. Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation. Hydrology and Earth System Sciences 17: 1281-1296. DOI: 10.5194/hess-17-1281-2013.
25. Grimaldi S, Serinaldi F. 2006a. Asymmetric copula in multivariate flood frequency analysis. Advances in Water Resources 29: 1155-1167. DOI: 10.1016/j.advwatres.2005.09.005.
26. Grimaldi S, Serinaldi F. 2006b. Design hyetograph analysis with 3-copula function. Hydrological Sciences Journal-Journal Des Sciences Hydrologiques 51: 223-238. DOI: 10.1623/hysj.51.2.223.
27. Hofert M, Kojadinovic I, Maechler M, Yan J. 2013. Copula: multivariate dependence with copulas. R package version 0.999-7, URL: http://CRAN.R-project.org/package=copula (13.8.2013).
28. Joe H. 1997. Multivariate models and dependence concepts. Chapman & Hall: London, New York; 399.
29. Kao SC, Govindaraju RS. 2010. A copula-based joint deficit index for droughts. Journal of Hydrology 380: 121-134. DOI: 10.1016/j.jhydrol.2009.10.029.
30. Karmakar S, Simonovic SP. 2008. Bivariate flood frequency analysis: Part1. Determination of marginals by parametric and nonparametric techniques. Journal of Flood Risk Management 1: 190-200. DOI: 10.1111/j.1753-318X.2008.00022.x.
31. Karmakar S, Simonovic SP. 2009. Bivariate flood frequency analysis. Part 2: a copula-based approach with mixed marginal distributions. Journal of Flood Risk Management 2: 32-44. DOI: 10.1111/j.1753-318X.2009.01020.x.
32. Kojadinovic I, Yan J, Holmes M. 2011. Fast large-sample goodness-of-fit tests for copulas. Statistica Sinica 21: 841-871.
33. Lee T, Modarres R, Ouarda T. 2013. Data-based analysis of bivariate copula tail dependence for drought duration and severity. Hydrological Processes 27: 1454-1463. DOI: 10.1002/hyp.9233.
34. Liu CL, Zhang Q, Singh VP, Cui Y. 2011. Copula-based evaluations of drought variations in Guangdong, South China. Natural Hazards 59: 1533-1546. DOI: 10.1007/s11069-011-9850-4.
35. Ma MW, Song SB, Ren LL, Jiang SH, Song JL. 2013. Multivariate drought characteristics using trivariate Gaussian and Student t copulas. Hydrological Processes 27: 1175-1190. DOI: 10.1002/hyp.8432.
36. Nelsen RB. 1999. An Introduction to Copulas. Springer: New York; 272.
37. Poulin A, Huard D, Favre AC, Pugin S. 2007. Importance of tail dependence in bivariate frequency analysis. Journal of Hydrologic Engineering 12: 394-403. DOI: 10.1061/(asce)1084-0699(2007)12:4(394).
38. Reddy MJ, Ganguli P. 2012a. Application of copulas for derivation of drought severity-duration-frequency curves. Hydrological Processes 26: 1672-1685. DOI: 10.1002/hyp.8287.
39. Reddy MJ, Ganguli P. 2012b. Bivariate flood frequency analysis of upper Godavari River flows using archimedean copulas. Water Resources Management 26: 3995-4018. DOI: 10.1007/s11269-012-0124-z.
40. Renard B, Lang M. 2007. Use of a Gaussian copula for multivariate extreme value analysis: some case studies in hydrology. Advances in Water Resources 30: 897-912. DOI: 10.1016/j.advwatres.2006.08.001.
41. Salvadori G, De Michele C. 2004. Frequency analysis via copulas: theoretical aspects and applications to hydrological events. Water Resources Research, 40. DOI: 10.1029/2004wr003133.
42. Salvadori G, De Michele C, Kottegoda NT, Rosso R. 2007. Extremes in Nature an Approach using Copulas. Springer: Dordrecht; 292.
43. Salvadori G, De Michele C, Durante F. 2011. On the return period and design in a multivariate framework. Hydrology and Earth System Sciences 15: 3293-3305. DOI: 10.5194/hess-15-3293-2011.
44. Serinaldi F, Grimaldi S. 2011. Synthetic design hydrographs based on distribution functions with finite support. Journal of Hydrologic Engineering 16: 434-446. DOI: 10.1061/(asce)he.1943-5584.0000339.
45. Singh VP, Zhang L. 2007. IDF curves using the Frank Archimedean copula. Journal of Hydrologic Engineering 12: 651-662. DOI: 10.1061/(asce)1084-0699(2007)12:6(651).
46. Sklar A. 1959. Fonction de re'partition a' n dimensions et leurs marges, vol. 8. Publications de L'Institute de Statistique, Universite' de Paris: Paris; 229-231.
47. Šraj M, Bezak N, Brilly M. 2012. The influence of the choice of method on the results of frequency analysis of peaks, volumes and durations of flood waves of the Sava River in Litija. Acta Hydrotehnica 25: 41-58. (In Slovenian).
48. Vandenberghe S, Verhoest NEC, De Baets B. 2010. Fitting bivariate copulas to the dependence structure between storm characteristics: a detailed analysis based on 105 year 10 min rainfall. Water Resources Research, 46. DOI: 10.1029/2009wr007857.
49. Vandenberghe S, Verhoest NEC, Onof C, De Baets B. 2011. A comparative copula-based bivariate frequency analysis of observed and simulated storm events: a case study on Bartlett-Lewis modeled rainfall. Water Resources Research 47. DOI: 10.1029/2009wr008388.
50. Wong G, Lambert MF, Leonard M, Metcalfe AV. 2010. Drought analysis using trivariate copulas conditional on climatic states. Journal of Hydrologic Engineering 15: 129-141. DOI: 10.1061/(asce)he.1943-5584.0000169.
51. Wong G, van Lanen HAJ, Torfs P. 2013. Probabilistic analysis of hydrological drought characteristics using meteorological drought. Hydrological Sciences Journal-Journal Des Sciences Hydrologiques 58: 253-270. DOI: 10.1080/02626667.2012.753147.
52. Yue S, Rasmussen P. 2002. Bivariate frequency analysis: discussion of some useful concepts in hydrological application. Hydrological Processes 16: 2881-2898. DOI: 10.1002/hyp.1185.
53. Zhang L, Singh VP. 2006. Bivariate flood frequency analysis using the copula method. Journal of Hydrologic Engineering 11: 150-164. DOI: 10.1061/(asce)1084-0699(2006)11:2(150).
54. Zhang L, Singh VP. 2007a. Bivariate rainfall frequency distributions using Archimedean copulas. Journal of Hydrology 332: 93-109. DOI: 10.1016/j.jhydrol.2006.06.033.
55. Zhang L, Singh VP. 2007b. Trivariate flood frequency analysis using the Gumbel-Hougaard copula. Journal of Hydrologic Engineering 12: 431-439. DOI: 10.1061/(asce)1084-0699(2007)12:4(431).