Simulating a multivariate sea storm using Archimedean copulas

Coastal Engineering

Volumn 76, Issue , 2013, Pages 68-78

  Corbella, Stefano ^a,b   Stretch, Derek D ^a  

^a UNIVERSITY OF KWAZULU NATAL   (South Africa)

^b EThekwini Municipality   (South Africa)

Author keywords

Copulas; Multivariate statistical models; Sea storms; Waves

Indexed keywords

BIVARIATE ANALYSIS; COPULAS; CORRELATION COEFFICIENT; MATHEMATICAL TRACTABILITY; MULTIVARIATE DISTRIBUTIONS; MULTIVARIATE STATISTICAL MODELS; PHYSICAL CONSTRAINTS; SEA STORM;

STATISTICS; STORMS; WATER LEVELS; WATER WAVES; WAVES;

MULTIVARIANT ANALYSIS;

COASTAL ZONE; COMPUTER SIMULATION; MULTIVARIATE ANALYSIS; OCEAN WAVE; STATISTICAL ANALYSIS; STORM; STORM TRACK; WATER LEVEL; WAVE FORCE;

SOUTH AFRICA;

EID: 84875232655     PISSN: 03783839     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.coastaleng.2013.01.011     Document Type: Article

References (43)

1. Accioly R.S., Chiyoshi F.Y. Modeling dependence with copulas: a useful tool for field development decision process. Journal of Petroleum Science and Engineering 2004, 44:83-91.
2. Boccotti P. Wave mechanics for ocean engineering. Elsevier Oceanography Series 2000, Elsevier Science, Amsterdam.
3. Brechmann E.C., Schepsmeier U. Modeling dependence with C- and D-vine copulas: the R-package CDVine. R Vignette of the R-package CDVine (Version 1.1-4) 2011.
4. Callaghan D.P., Nielsen P., Short A., Ranasinghe R. Statistical simulation of wave climate and extreme beach erosion. Coastal Engineering 2008, 55:375-390.
5. Chakak A., Koehler K.J. A strategy for constructing multivariate distributions. Communications Statistics - Simulation and Computation 1995, 24:537-550.
6. Charpentier A., Segers J. Lower tail dependence for Archimedean copulas: characterizations and pitfalls. Insurance: Mathematics and Economics 2007, 40:525-532.
7. Charpentier A., Segers J. Tails of multivariate Archimedean copulas. Journal of Multivariate Analysis 2009, 100:1521-1537.
8. Chebana F., Ouarda T.B.M.J. Multivariate quantiles in hydrological frequency analysis. Environmetrics 2011, 22(1):63-78.
9. Chini N., Stansby P., Leake J., Wolf J., Roberts-Jones J., Lowe J. The impact of sea level rise and climate change on inshore wave climate: a case study for East Anglia (UK). Coastal Engineering 2010, 57:973-984.
10. Corbella S., Stretch D.D. Predicting coastal erosion trends using non-stationary statistics and process-based models. Coastal Engineering 2012, 70:40-49.
11. Corbella S., Stretch D.D. The wave climate on the KwaZulu-Natal coast of South Africa. Journal of the South African Institution of Civil Engineers 2012, 54(2):45-54.
12. De Michele C., Salvadori G., Passoni G., Vezzoli R. A multivariate model of sea storms using copulas. Coastal Engineering 2007, 54:734-751.
13. Dowd K. Copulas in macroeconomics. Journal of International and Global Economic Studies 2008, 1(1):1-26.
14. Embrechts P., Lindskog F., McNeil A.J. Modelling Dependence with Copulas and Applications to Risk Management http://www.risklab.ch/ftp/papers/DependenceWithCopulas.pdf.
15. Genest C., Rémillard B. Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models. Annales de l'Institut Henri Poincaré - Probabilités et Statistiques 2008, 44(6):1096-1127.
16. Genest C., Rivest L. Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association 1993, 88(423):1034-1043.
17. Goda Y. Random Seas and Design of Maritime Structures 2008, World Scientific Publishing Co. Pte. Ltd., Singapore. 2nd edition.
18. Grimaldi S., Serinaldi F. Asymmetric copula in multivariate flood frequency analysis. Advances in Water Resources 2006, 29:1155-1167.
19. Gringorten I.I. A plotting rule for extreme probability paper. Journal of Geophysical Research 1963, 68(3):813-814.
20. Guedes Soares C., Scotto M.G. Application of the r largest-order statistics for long-term predictions of significant wave height. Coastal Engineering 2004, 51:387-394.
21. Hofert M. Sampling Archimedean copulas. Computational Statistics and Data. Analysis 2008, 52:5163-5174.
22. Hofert M. Efficiently sampling nested Archimedean copulas. Computational Statistics and Data Analysis 2011, 55:57-70.
23. Isaacson M.S., MacKenzie N.G. Long-term distributions of ocean waves: a review. Journal of Waterway, Port, Coastal and Ocean Division, ASCE 1981, 107(WW2).
24. Joe H. Multivariate Models and Dependence Concepts 1997, Chapman & Hall, London.
25. Kojadinovic I., Yan J. A goodness-of-fit test for multivariate multiparameter copulas based on multiplier central limit theorems. Statistics and Computing 2011, 21:17-30.
26. Kruger A.C., Goliger A.M., Retief J.V., Sekele S. Strong wind climatic zones in South Africa. Wind and Structures 2010, 13:1.
27. Mendez F.J., Menendez M., Luceno A., Medina R., Graham N.E. Seasonality and duration in extreme value distributions of significant wave height. Ocean Engineering 2008, 35:131-138.
28. Minguez R., Menéndez M., Méndez F.J., Losada I.J. Sensitivity analysis of time-dependent generalized extreme value models for ocean climate variables. Advances in Water Resources 2010, 33:833-845.
29. Nelsen R.B. An introduction to copulas. Springer Series in Statistics 2006, Springer, New York. second edition.
30. Ruggiero P., Komar P.D., Allan J.C. Increasing wave heights and extreme value projections: the wave climate of the U.S. Pacific Northwest. Coastal Engineering 2010, 57:539-552.
31. Salvadori G., De Michele C. Multivariate multiparameter extreme value models and return periods: a copula approach. Water Resources Research 2010, 46:W10501. 10.1029/2009WR009040.
32. Salvadori G.De, Michele C. Statistical characterization of temporal structure of storms. Advances in Water Resources 2006, 29:827-842.
33. Salvadori G., De Michele C., Kottegoda N.T., Rosso R. Extremes in nature. An approach using copulas. Water Science and Technology Library 2007, 56:292. (Springer).
34. Salvadori G.De, Michele C., Durante F. Multivariate design via copulas. Hydrology and Earth System Sciences Discussions 2011, 8:5523-5558.
35. Savu C., Trede M. Hierarchical Archimedean Copulas (2008-11-01). http://www.uni-konstanz.de/micfinma/conference/Files/papers/Savu_Trede.pdf.
36. Savu C., Trede M. Hierarchies of Archimedean copulas. Quantitative Finance 2010, 10(3):295-304.
37. Sorensen R.M. Basic Coastal Engineering 2006, Springer Science and Business Media, Inc., New York. third edition.
38. U.S.Army Corps of Engineers Coastal Engineering Manual, EM 1110-2-1100, Part II: (Chapter 8) 2006, 9-11.
39. van Gent M.R.A., van Thiel de Vries J.S.M., Coeveld E.M., de Vroeg J.H., van de Graaff J. Large-scale dune erosion tests to study the influence of wave periods. Coastal Engineering 2008, 55:1041-1051.
40. van Thiel de Vries J.S.M., van Gent M.R.A., Walstra D.J.R., Reniers A.J.H.M. Analysis of dune erosion processes in large-scale flume experiments. Coastal Engineering 2008, 55:1028-1040.
41. Whelan N. Sampling from Archimedean copulas. Quantitative Finance 2004, 4(3):339-352.
42. Woodroffe C.D. Coasts: Form, Process and Evolution 2003, Cambridge University Press, Cambridge, United Kingdom.
43. Zhang L., Singh V.P. Trivariate frequency analysis using the Gumbel-Hougaard copula. Journal of Hydrologic Engineering 2007, 12(4):431-439.