A comparative copula-based bivariate frequency analysis of observed and simulated storm events: A case study on Bartlett-Lewis modeled rainfall

Water Resources Research

Volumn 47, Issue 7, 2011, Pages

  Vandenberghe, S ^a   Verhoest, N E C ^a   Onof, C ^b   De Baets, B ^a  

^a GHENT UNIVERSITY   (Belgium)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIVARIATE; DEGREE OF ASSOCIATION; EXTREME RAINFALL; EXTREME VALUE ANALYSIS; FREQUENCY ANALYSIS; INTER-ARRIVAL TIME; MODEL PERFORMANCE; POINT PROCESS; RAINFALL MODELS; RAINFALL SIMULATIONS; RETURN PERIODS; SIMULATED RAINFALL; SIMULATED STORMS; STORM VARIABLES; TEMPORAL STRUCTURES; UNIVARIATE;

COMPUTER SIMULATION; DISTRIBUTION FUNCTIONS; RAIN; STOCHASTIC MODELS; STORMS; TIME SERIES;

TIME SERIES ANALYSIS;

COMPARATIVE STUDY; HISTORICAL PERSPECTIVE; HYDRAULIC STRUCTURE; HYDROLOGICAL MODELING; RAINFALL; STOCHASTICITY; STORM SURGE; TIME SERIES; VOLUME;

EID: 79960739155     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2009WR008388     Document Type: Article

References (57)

1. Bárdossy, A., and G. G. S. Pegram (2009), Copula based multisite model for daily precipitation simulation, Hydrol. Earth Syst. Sci., 13(12), 2299-2314.
2. Burton, A., C. G. Kilsby, H. J. Fowler, P. S. P. Cowpertwait, and P. E. O'Connell (2008), RainSim: A spatial-temporal stochastic rainfall modelling system, Environ. Modell. Software, 23(12), 1356-1369, doi:10.1016/j.envsoft. 2008.04.003.
3. Cameron, D., K. Beven, and J. Tawn (2000), An evaluation of three stochastic rainfall models, J. Hydrol., 228(1-2), 130-149. (Pubitemid 30156972)
4. Cowpertwait, P. S. P. (1995), A generalized spatial-temporal model of rainfall based on a clustered point process, Proc. R. Soc. London, Ser. A, 450(1938), 163-175. (Pubitemid 26439501)
5. Cowpertwait, P. S. P. (1998), A Poisson-cluster model of rainfall: Highorder moments and extreme values, Proc. R. Soc. London, Ser. A, 454(1971), 885-898. (Pubitemid 128733181)
6. Cowpertwait, P. S. P. (2004), Mixed rectangular pulses models of rainfall, Hydrol. Earth Syst. Sci., 8(5), 993-1000. (Pubitemid 40294959)
7. Cowpertwait, P. S. P., C. G. Kilsby, and P. E. O'Connell (2002), A spacetime Neyman-Scott model of rainfall: Empirical analysis of extremes, Water Resour. Res., 38(8), 1131, doi:10.1029/2001WR000709.
8. Cowpertwait, P. S. P., V. Isham, and C. Onof (2007), Point process models of rainfall: Developments for fine-scale structure, Proc. R. Soc. London, Ser. A, 463(2086), 2569-2587, doi:10.1098/rspa.2007.1889.
9. De Jongh, I. L. M., N. E. C. Verhoest, and F. P. De Troch (2006), Analysis of a 105-year time series of precipitation observed at Uccle, Belgium, Int. J. Climatol., 26(14), 2023-2039. (Pubitemid 44823234)
10. Demaree, G. (2003), The centennial recording raingauge of the Uccle Plateau: Its history, its data and its applications, Houille Blanche, 4, 95-102. (Pubitemid 37190250)
11. De Michele, C., and G. Salvadori (2003), A generalized Pareto intensityduration model of storm rainfall exploiting 2-copulas, J. Geophys. Res., 108(D2), 4067, doi:10.1029/2002JD002534.
12. De Michele, C., G. Salvadori, M. Canossi, A. Petaccia, and R. Rosso (2005), Bivariate statistical approach to check adequacy of dam spillway, J. Hydrol. Eng., 10(1), 50-57. (Pubitemid 40102822)
13. Evin, G. (2008), Nouveaux développements du processus de Neyman- Scott. Introduction d'une dépendance entre l'intensité et la dureé des cellulces pluvieuses et non-stationnarité, Ph.D. thesis, Univ. du Québec, Quebec, Ont., Canada.
14. Evin, G., and A. C. Favre (2008), A new rainfall model based on the Neyman-Scott process using cubic copulas, Water Resour. Res., 44, W03433, doi:10.1029/2007WR006054. (Pubitemid 351628562)
15. Favre, A. C., S. E. Adlouni, L. Perreault, N. Thiemonge, and B. Bobee (2004), Multivariate hydrological frequency analysis using copulas, Water Resour. Res., 40, W01101, doi:10.1029/2003WR002456.
16. Frahm, G., M. Junker, and R. Schmidt (2005), Estimating the taildependence coefficient: Properties and pitfalls, Insur. Math. Econ., 37(1), 80-100. (Pubitemid 41110158)
17. Genest, C., and A. C. Favre (2007), Everything you always wanted to know about copula modeling but were afraid to ask, J. Hydrol. Eng., 12(4), 347-368. (Pubitemid 47023282)
18. Genest, C., and J. Segers (2009), Rank-based inference for bivariate extreme-value copulas, Ann. Stat., 37(5B), 2990-3022, doi:10.1214/ 08-AOS672.
19. Genest, C., A. C. Favre, J. Beliveau, and C. Jacques (2007), Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data, Water Resour. Res., 43, W09401, doi:10.1029/2006WR005275. (Pubitemid 350058437)
20. Genest, C., B. Rémillard, and D. Beaudoin (2009), Goodness-of-fit tests for copulas: A review and a power study, Insur. Math. Econ., 44(2), 199-213, doi:10.1016/j.insmatheco.2007.10.005.
21. Grimaldi, S., and F. Serinaldi (2006a), Asymmetric copula in multivariate flood frequency analysis, Adv. Water Resour., 29(8), 1155-1167. (Pubitemid 44089287)
22. Grimaldi, S., and F. Serinaldi (2006b), Design hyetograph analysis with 3-copula function, Hydrol. Sci. J., 51(2), 223-238.
23. Islam, S., D. Entekhabi, R. L. Bras, and I. Rodriguez-Iturbe (1990), Parameter-estimation and sensitivity analysis for the modified Bartlett- Lewis rectangular pulses model of rainfall, J. Geophys. Res., 95(D3), 2093-2100.
24. Kao, S. C., and R. S. Govindaraju (2007), A bivariate frequency analysis of extreme rainfall with implications for design, J. Geophys. Res., 112, D13119, doi:10.1029/2007JD008522. (Pubitemid 47408367)
25. Kao, S. C., and R. S. Govindaraju (2008), Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas, Water Resour. Res., 44, W02415, doi:10.1029/2007WR006261. (Pubitemid 351442493)
26. Kwiatkowski, D., P. C. B. Phillips, P. Schmidt, and Y. C. Shin (1992), Testing the null hypothesis of stationarity against the alternative of a unit-root. How sure are we that economic time-series have a unit-root?, J. Econ., 54(1-3), 159-178.
27. Lennartsson, J., A. Baxevani, and D. Chen (2008), Modelling precipitation in Sweden using multiple step Markov chains and a composite model, J. Hydrol., 363(1-4), 42-59, doi:10.1016/j.jhydrol.2008.10.003.
28. Nelsen, R. B. (2006), An Introduction to Copulas, Springer, New York.
29. Ntegeka, V., and P. Willems (2008), Trends and multidecadal oscillations in rainfall extremes, based on a more than 100-year time series of 10 min rainfall intensities at Uccle, Belgium, Water Resour. Res., 44, W07402, doi:10.1029/2007WR006471.
30. Onof, C., and H. S. Wheater (1993), Modeling of British rainfall using a random parameter Bartlett-Lewis rectangular pulse model, J. Hydrol., 149(1-4), 67-95.
31. Onof, C., and H. S. Wheater (1994), Improvements to the modeling of British rainfall using a modified random parameter Bartlett-Lewis rectangular pulse model, J. Hydrol., 157(1-4), 177-195. (Pubitemid 279828)
32. Onof, C., R. E. Chandler, A. Kakou, P. Northrop, H. S. Wheater, and V. Isham (2000), Rainfall modelling using Poisson-cluster processes: A review of developments, Stochastic Environ. Res. Risk Assess., 14(6), 384-411.
33. Poulin, A., D. Huard, A. C. Favre, and S. Pugin (2007), Importance of tail dependence in bivariate frequency analysis, J. Hydrol. Eng., 12(4), 394-403. (Pubitemid 47023285)
34. Restrepo-Posada, P. J., and P. S. Eagleson (1982), Identification of independent rainstorms, J. Hydrol., 55, 303-319.
35. Rodriguez-Iturbe, I., D. R. Cox, and V. Isham (1987a), Some models for rainfall based on stochastic point processes, Proc. R. Soc. London, Ser. A, 410, 269-288, doi:10.1098/rspa.1987.0039. (Pubitemid 17599343)
36. Rodriguez-Iturbe, I., B. Febres De Power, and J. B. Valdés (1987b), Rectangular pulses point process models for rainfall: Analysis of empirical data, J. Geophys. Res., 92(D8), 9645-9656.
37. Rodriguez-Iturbe, I., D. R. Cox, and V. Isham (1988), A point process model for rainfall: Further developments, Proc. R. Soc. London, Ser. A, 417, 283-298, doi:10.1098/rspa.1988.0061.
38. Salvadori, G. (2004), Bivariate return periods via 2-copulas, Stat. Methodol., 1, 129-144. (Pubitemid 43339379)
39. Salvadori, G., and C. De Michele (2004), Frequency analysis via copulas: Theoretical aspects and applications to hydrological events, Water Resour. Res., 40, W12511, doi:10.1029/2004WR003133.
40. Salvadori, G., and C. De Michele (2006), Statistical characterization of temporal structure of storms, Adv. Water Resour., 29(6), 827-842.
41. Salvadori, G., C. De Michele, N. Kottegoda, and R. Rosso (2007), Extremes in Nature: An Approach Using Copulas, Springer, New York.
42. Serinaldi, F. (2009), Copula-based mixed models for bivariate rainfall data: An empirical study in regression perspective, Stochastic Environ. Res. Risk Assess., 23(5), 677-693, doi:10.1007/s00477-008-0249-z.
43. Serinaldi, F., and S. Grimaldi (2007), Fully nested 3-copula: Procedure and application on hydrological data, J. Hydrol. Eng., 12(4), 420-430. (Pubitemid 47023288)
44. Shiau, J. T. (2003), Return period of bivariate distributed extreme hydrological events, Stochastic Environ. Res. Risk Assess., 17(1-2), 42-57. (Pubitemid 36922606)
45. Sklar, A. (1959), Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Stat. Univ. Paris, 8, 229-231.
46. Stephens, M. A. (1974), EDF statistics for goodness of fit and some comparisons, J. Am. Stat. Assoc., 69(347), 730-737.
47. Sun, T. (2008), Modeling of multivariate rainfall data with autocorrelated discrete-continuous mixture margins using copulas, Ph.D. thesis, York Univ., Toronto, Ont., Canada.
48. Tawn, J. A. (1998), Bivariate extreme value theory: Models and estimation, Biometrika, 75(3), 397-415.
49. Vaes, G., P. Willems, and J. Berlamont (2002), 100 years of Belgian rainfall: Are there trends?, Water Sci. Technol., 45(2), 55-61. (Pubitemid 34182853)
50. Vandenberghe, S., N. E. C. Verhoest, and B. De Baets (2010a), Fitting bivariate copulas to the dependence structure between storm characteristics: A detailed analysis based on 105 year 10 min rainfall, Water Resour. Res., 46, W01512, doi:10.1029/2009WR007857.
51. Vandenberghe, S., N. E. C. Verhoest, E. Buyse, and B. De Baets (2010b), A stochastic design rainfall generator based on copulas and mass curves, Hydrol. Earth Syst. Sci. Discuss., 7(3), 3613-3648, doi:10.5194/hessd-7- 3613-2010.
52. Van Gelder, P. H. A. J. M., W. Wang, and J. K. Vrijling (2007), Statistical estimation methods for extreme hydrological events, in Extreme Hydrological Events: New Concepts for Security, NATO Sci. Ser., IV, vol. 78, edited by O. F. Vasiliev, P. H. A. J. M Van Gelder, E. J. Plate, and M. V. Bolgov, pp. 199-252, Dordrecht, Netherlands.
53. Velghe, T., P. A. Troch, F. P. De Troch, and J. Van De Velde (1994), Evaluation of cluster-based rectangular pulses point process models for rainfall, Water Resour. Res., 30(10), 2847-2857. (Pubitemid 287997)
54. Verhoest, N., P. A. Troch, and F. P. De Troch (1997), On the applicability of Bartlett-Lewis rectangular pulses models in the modeling of design storms at a point, J. Hydrol., 202(1-4), 108-120. (Pubitemid 28118038)
55. Yue, S., and P. Rasmussen (2002), Bivariate frequency analysis: Discussion of some useful concepts in hydrological application, Hydrol. Processes, 16(14), 2881-2898.
56. Zhang, L., and V. P. Singh (2007a), Bivariate rainfall frequency distributions using Archimedean copulas, J. Hydrol., 332(1-2), 93-109. (Pubitemid 44937315)
57. Zhang, L., and V. P. Singh (2007b), Gumbel-Hougaard copula for trivariate rainfall frequency analysis, J. Hydrol. Eng., 12(4), 409-419. (Pubitemid 47023287)