A continuous rainfall model based on vine copulas

Hydrology and Earth System Sciences

Volumn 19, Issue 6, 2015, Pages 2685-2699

  Vernieuwe, H ^a   Vandenberghe, S ^a   De Baets, B ^a   Verhoest, N E C ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS TIME SYSTEMS; STORMS;

CONTINUOUS-TIME; DEPENDENCE STRUCTURES; MULTI DIMENSIONAL; RAINFALL MODELLING; RAINFALL MODELS; RAINFALL SERIES; STATISTICAL COMPARISONS; STORM STRUCTURE;

RAIN;

ANNUAL VARIATION; CLIMATE MODELING; PROBABILITY; RAINFALL; RAINSTORM; SOFTWARE; TIME SERIES;

EID: 84935850181     PISSN: 10275606     EISSN: 16077938     Source Type: Journal    
DOI: 10.5194/hess-19-2685-2015     Document Type: Article

References (61)

1. Aas, K. and Berg, D.: Models for construction of multivariate dependence - a comparison study, Eur. J. Financ., 15, 639-659, 2009.
2. Aas, K., Czado, C., Frigessi, A., and Bakken, H.: Pair-copula constructions of multiple dependence, Insurance: Mathematics and Economics, 44, 182-198, 2009.
3. Bedford, T. and Cooke, R.: Probability density decomposition for conditionally dependent random variables modeled by vines, Ann. Math. Artif. Intel., 32, 245-268, 2001.
4. Bedford, T. and Cooke, R.: Vines - A new graphical model for dependent random variables, Ann. Stat., 30, 1031-1068, 2002.
5. Bonta, J. and Rao, A.: Factors affecting the identification of independent storm events, J. Hydrol., 98, 275-293, 1988.
6. Candela, A., Brigandì, G., and Aronica, G. T.: Estimation of synthetic flood design hydrographs using a distributed rainfallrunoff model coupled with a copula-based single storm rainfall generator, Nat. Hazards Earth Syst. Sci., 14, 1819-1833, doi:10.5194/nhess-14-1819-2014, 2014.
7. Chow, V., Maidment, D., and Mays, L.: Applied Hydrology, McGraw-Hill Book Company, New York, 588 pp., 1988.
8. De Jongh, I., Verhoest, N. E. C., and De Troch, F.: Analysis of a 105-year time series of precipitation observed at Uccle, Belgium, Internat. J. Climatol., 26, 2023-2039, 2006.
9. De Michele, C. and Salvadori, G.: A generalized Pareto intensityduration model of storm rainfall exploiting 2-copulas, J. Geophys. Res., 108, D24067, 2003.
10. De Michele, C., Salvadori, G., Canossi, M., Petaccia, A., and Rosso, R.: Bivariate statistical approach to check adequacy of dam spillway, J. Hydrol. Eng., 10, 50-57, 2005.
11. De Michele, C., Salvadori, G., Passoni, G., and Vezzoli, R.: A multivariate model of sea storms using copulas, Coast. Eng., 54, 734-751, 2007.
12. Demarée, G.: The centennial recording raingauge of the Uccle Plateau: Its history, its data and its applications, La Houille Blanche - Revue International de l'Eau, 4, 95-102, 2003.
13. Evin, G. and Favre, A.-C.: A new rainfall model based on the Neyman-Scott process using cubic copulas, Water Resour. Res., 44, W03433, doi:10.1029/2007WR006054, 2008.
14. Evin, G. and Favre, A.-C.: Further developments of a transient Poisson-cluster model for rainfall, Stoch. Env. Res. Risk A., 27, 831-847, 2013.
15. Favre, A., Adlouni, S. E., Perreault, L., Thiemonge, N., and Bobee, B.: Multivariate hydrological frequency analysis using copulas, Water Resour. Res., 40, W01101, doi:10.1029/2003WR002456, 2004.
16. Ganguli, P. and Reddy, M.: Probabilistic assessment of flood risks using trivariate copulas, Theor. Appl. Climatol., 111, 341-360, 2013.
17. Genest, C.: Frank's family of bivariate distributions, Biometrika, 74, 549-555, 1987.
18. Genest, C., Favre, A., Beliveau, J., and Jacques, C.: Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data, Water Resour. Res., 43, W09401, doi:10.1029/2006WR005275, 2007.
19. Gräler, B.: Modelling skewed spatial random fields through the spatial vine copula, Spatial Statistics, 10, 87-102, 2014.
20. Gräler, B., van den Berg, M. J., Vandenberghe, S., Petroselli, A., Grimaldi, S., De Baets, B., and Verhoest, N. E. C.: Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation, Hydrol. Earth Syst. Sci., 17, 1281-1296, doi:10.5194/hess-17-1281-2013, 2013.
21. Grimaldi, S. and Serinaldi, F.: Design hyetograph analysis with 3-copula function, Hydrolog. Sci. J., 51, 223-238, 2006.
22. Gyasi-Agyei, Y.: Copula-based daily rainfall disaggregation model, Water Resour. Res., 47, W07535, doi:10.1029/2011WR010519, 2011.
23. Gyasi-Agyei, Y. and Melching, C.: Modelling the dependence and internal structure of storm evens for continuous rainfall simulation, J. Hydrol., 464, 249-261, 2012.
24. Hobæk Haff, I., Aas, K., and Frigessi, A.: On the simplified paircopula construction - Simply useful or too simplistic?, J. Multivariate Anal., 101, 1296-1310, 2010.
25. Huff, F.: Time distribution of rainfall in heavy storms, Water Resour. Res., 3, 1007-1019, 1967.
26. Joe, H.: Multivariate Models and Dependence Concepts, Chapman and Hall, 399 pp., 1997.
27. Kao, S. and Govindaraju, R.: Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas, Water Resour. Res., 44, W02415, doi:10.1029/2007WR006261, 2008.
28. Katz, R. and Parlange, M.: Overdispersion phenomenon in stochastic modeling of precipitation, J. Climate, 11, 591-601, 1998.
29. Kavvas, M. and Delleur, J.: A stochastic cluster model of daily rainfall sequences, Water Resour. Res., 17, 1151-1160, 1981.
30. Kurowicka, D. and Cooke, R.: Sampling algorithms for generating joint uniform distributions using the vine-copula method, Comput. Stat. Data An., 51, 2889-2906, 2007.
31. Ma, M., Song, S., Ren, L., Jiand, S., and Song, J.: Multivariate drought characteristics using trivariate Gaussian and Student t copulas, Hydrol. Process., 27, 1175-1190, 2013.
32. Menabde, M. and Sivapalan, M.: Modeling of rainfall time series and extremes using bounded random cascades and Levy-stable distributions, Water Resour. Res., 36, 3293-3300, 2000.
33. Mendes, B. and Accioly, V.: Robust Pair-Copula based forecasts of realized volatitiliy, Applied Stochastic Models in Business and Industry, 30, 183-199, 2014.
34. Nelsen, R.: An Introduction to Copulas, in: Lecture Notes in Statistics, edited by: Bickel, P., Diggle, P., Fienberg, S., Krickeberg, K., Olking, I., Wermuth, N., and Zeger, S., pp. 216, Springer-Verlag, New York, 2006.
35. Nikololoupoulos, A., Joe, H., and Li, H.: Vine coplas with asymmetric tail dependence and applications to financial return data, Computational Statistics and Data Analysis, 56, 3659-3673, 2012.
36. Ntegeka, V. and Willems, P.: Trends in 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, 2008.
37. Onof, C., Chandler, R., Kakou, A., Northrop, P., Wheater, H., and Isham, V.: Rainfall modelling using Poisson-cluster processes: a review of developments., Stoch. Env. Res. Risk A., 14, 384-411, 2000.
38. Pan, M., Yuan, X., and Wood, E. F.: A probabilistic view on drought recovery., Geophys. Res. Lett., 40, 3637-3642, 2013.
39. Pham, M. T., Vanhaute, W. J., Vandenberghe, S., De Baets, B., and Verhoest, N. E. C.: An assessment of the ability of Bartlett-Lewis type of rainfall models to reproduce drought statistics, Hydrol. Earth Syst. Sci., 17, 5167-5183, doi:10.5194/hess-17-5167-2013, 2013.
40. Restrepo-Posada, P. and Eagleson, P.: Identification of independent rainstorms, J. Hydrol., 55, 303-319, 1982.
41. Rodriguez-Iturbe, I., Cox, D., and Isham, V.: Some models for rainfall based on stochastic point processes, Proc. R. Soc. Lon. Ser.- A, 410, 269-288, 1987a.
42. Rodriguez-Iturbe, I., Febres de Power, B., and Valdés, J.: Rectangular pulses point process models for rainfall: analysis of empirical data, Geophys. Res., 92, 9645-9656, 1987b.
43. Salvadori, G. and De Michele, C.: Analytical calculation of storm volume statistics involving Pareto-like intensityduration marginals, Geophys. Res. Lett., 31, L04502, doi:10.1029/2003GL018767, 2004.
44. Salvadori, G. and De Michele, C.: Statistical characterization of temporal structure of storms, Adv. Water Resour., 29, 827-842, 2006.
45. Salvadori, G. and De Michele, C.: On the use of copulas in hydrology: theory and practice, J. Hydrol. Eng., 12, 369-380, 2007.
46. Serinaldi, F. and Grimaldi, S.: Fully nested 3-copula: procedure and application on hydrological data, J. Hydrol. Eng., 12, 420-430, 2007.
47. Sklar, A.: Fonctions de répartition á n dimensions et leurs marges., Publications de l'Institut de Statistique de l'Université de Paris, 8, 229-231, 1959.
48. Song, S. and Singh, V.: Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data, Stoch. Env. Res. Risk A., 24, 425-444, 2010.
49. Vaes, G., Willems, P., and Berlamont, J.: 100 years of Belgian rainfall: Are there trends?, Water Sci. Technol., 45, 55-61, 2002.
50. Vandenberghe, S., Verhoest, N. E. C., Buyse, E., and De Baets, B.: A stochastic design rainfall generator based on copulas and mass curves, Hydrol. Earth Syst. Sci., 14, 2429-2442, doi:10.5194/hess-14-2429-2010, 2010a.
51. Vandenberghe, S., Verhoest, N. E. C., and De Baets, B.: 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, 2010b.
52. Vandenberghe, S., Verhoest, N. E. C., Onof, C., and De Baets, B.: A comparative copula-based bivariated frequency analysis of observed and simulated storm evens: a cast study on Bartlett-Lewis modeled rainfall, Water Resour. Resear., 47, W07529, doi:10.1029/2009WR008388, 2011.
53. Vanhaute, W. J., Vandenberghe, S., Scheerlinck, K., De Baets, B., and Verhoest, N. E. C.: Calibration of the modified Bartlett-Lewis model using global optimization techniques and alternative objective functions, Hydrol. Earth Syst. Sci., 16, 873-891, doi:10.5194/hess-16-873-2012, 2012.
54. Verhoest, N., Troch, P., and De Troch, F.: On the applicability of Bartlett-Lewis rectangular pulses models in the modeling of design storms at a point, J. Hydrol., 202, 108-120, 1997.
55. Verhoest, N. E. C., Vandenberghe, S., Cabus, P., Onof, C., Meca-Figueras, T., and Jameleddine, S.: Are stochastic point rainfall models able to preserve extreme flood statistics?, Hydrol. Process., 24, 3439-2445, 2010.
56. Viglione, A., Castellarin, A., Rogger, M., Merz, R., and Blöschl, G.: Extreme rainstorms: Comparing regional envelope curves to stochastically generated events, Water Resour. Res., 48, W01509, doi:10.1029/2011WR010515, 2012.
57. Willems, P.: A spatial rainfall generator for small spatial scales, J. Hydrol., 252, 126-144, 2001.
58. Wong, G., Lambert, M., Leonard, M., and Metcalfe, A.: Drought Analysis using trivariate copulas conditional on climatic states, J. Hydrol. Eng., 15, 129-141, 2010.
59. Xiong, L., Yu, K., and Gottschalk, L.: Estimation of the distribution of annual runoff from climatic variables using copulas, Water Resour. Res., 50, 7134-7152, 2014.
60. Zhang, D.: Vine copulas and applications to the European Union sovereign debt analysis, International Review of Financial Analysis, 36, 46-56, 2014.
61. Zhang, L. and Singh, V.: Gumbel-Hougaard copula for trivariate rainfall frequency analysis, J. Hydrol. Eng., 12, 409-419, 2007.