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Bayesian comparison of different rainfall depth-duration-frequency relationships. (English) Zbl 1169.62397
Summary: Depth-duration-frequency curves estimate the rainfall intensity patterns for various return periods and rainfall durations. An empirical model based on the generalized extreme value distribution is presented for hourly maximum rainfall, and improved by the inclusion of daily maximum rainfall, through the extremal indexes of 24 hourly and daily rainfall data. The model is then divided into two sub-models for the short and long rainfall durations. Three likelihood formulations are proposed to model and compare independence or dependence hypotheses between the different durations. Dependence is modelled using the bivariate extreme logistic distribution.
The results are calculated in a Bayesian framework with a Markov Chain Monte Carlo algorithm. The application to a data series from Marseille shows an improvement of the hourly estimations thanks to the combination between hourly and daily data in the model. Moreover, the results are significantly different with or without dependence hypotheses: the dependence between 24 and 72 h durations is significant, and the quantile estimates are more severe in the dependence case.

62P12 Applications of statistics to environmental and related topics
62F15 Bayesian inference
62G32 Statistics of extreme values; tail inference
65C40 Numerical analysis or methods applied to Markov chains
86A10 Meteorology and atmospheric physics
Full Text: DOI
[1] Ancona-Navarrete, MA; Tawn, JA, A comparison of methods for estimating the extremal index, Extremes, 3, 5-38, (2000) · Zbl 0965.62044
[2] Bacro, JN; Chaouche, A., Incertitude d’estimation des pluies extrêmes du pourtour méditerranéen: illustration par les données de Marseille, Hydrol Sci J, 51, 389-405, (2006)
[3] Beirlant J, Goegebeur Y, Segers J, Teugels J (2004) Statistics of extremes, theory and applications
[4] Bernard, MM, Formulas for rainfall intensities of long durations, Trans ASCE, 96, 592-624, (1932)
[5] Borga, M.; Vezzani, C.; Dalla Fontana, G., Regional rainfall depth-duration-frequency equations for an alpine region, Nat Hazards, 36, 221-235, (2005)
[6] Burlando, P.; Rosso, R., Scaling and multiscaling models of depth-duration-frequency curves for storm precipitation, J Hydrol, 187, 45-64, (1996)
[7] Capéraà, P.; Fougères, AL; Genest, C., A non-parameteric estimation procedure for bivariate extreme value copulas, Biometrika, 84, 567-577, (1997) · Zbl 1058.62516
[8] Chaouche, K.; Hubert, P.; Lang, G., Graphical characterization of of probability distribution tails, Stochastic Environ Res Risk Assess, 16, 342-357, (2002) · Zbl 1037.62117
[9] Chow VT, Maidment DR, Mays LW (1988) Applied hydrology. McGraw-Hill
[10] Coles S (2001) An introduction to statistical modeling of extreme values. Springer, London · Zbl 0980.62043
[11] Coles, S.; Pericchi, L., Anticipating catastrophes through extreme value modelling, J R Stat Soc. Series C: Appl Stat, 52, 405-416, (2003) · Zbl 1111.62366
[12] Coles, S.; Pericchi, L.; Sisson, S., A fully probabilistic approach to extreme rainfall modelling, J Hydrol, 273, 35-50, (2003)
[13] Dubuisson B, Moisselin JM (2006) Evolution des extrêmes climatiques en France à partir des séries observées, Colloque SHF, Lyon, France
[14] Garcia-Bartual, R.; Schneider, M., Estimating maximum expected short-duration rainfall intensities from extreme convective storms, Phys Chem Earth, Part B: Hydrol Oceans Atmos, 26, 675-681, (2001)
[15] Gelman A, Carlin JB, Stren HS, Rubin DB (1997) Bayesian Data analysis. Oxford, London
[16] Gumbel EJ (1958) Statistics of Extremes. Columbia University Press, New York
[17] Hershfield DM (1961) Rainfall frequency atlas of the United States for durations from 30 min to 24 h and return periods from 1 to 100 years. U. S. D. o. C. Weather Bureau Technical Paper 40. Washington DC
[18] Hosking, J.; Wallis, J.; Wood, E., Estimation of the generalized extreme value distribution by the method of probability-weighted moments, Technometrics, 27, 251-261, (1985)
[19] Kendall MG (1975) Rank correlation methods. Griffin, London
[20] Kieffer Weisse A (1998) Etude des précipitations exceptionnelles de pas de temps court en relief accidenté (Alpes françaises). Méthode de cartographie des précipitations extrêmes. Ph. D. Mécanique des milieux géophysiques et Environnement. Grenoble, Institut National Polytechnique de Grenoble
[21] Koutsoyiannis, D., Statistics of extremes and estimation of extreme rainfall. I. Theoretical investigation, Hydrol Sci J, 49, 575-590, (2004)
[22] Koutsoyiannis, D., Statistics of extremes and estimation of extreme rainfall. II. Empirical investigation of long rainfall record, Hydrol Sci J, 49, 591-610, (2004)
[23] Koutsoyiannis, D.; Baloutsos, G., Analysis of a long record of annual maximum rainfall in Athens, Greece, and design rainfall inferences, Nat Hazards, 22, 31-51, (2000)
[24] Koutsoyiannis, D.; Kozonis, D.; Manetas, A., A comprehensive study of rainfall intensity-duration-frequency relationships, J Hydrol, 206, 118-135, (1998)
[25] Leadbetter, MR, Extremes and local dependence in stationary sequences, Zeit Wahrscheinl -theorie, 65, 291, (1983) · Zbl 0506.60030
[26] Lima, MIP; Grasman, J., Multifractal analysis of 15-min and daily rainfall from a semi-arid region in Portugal, J Hydrol, 220, 1-11, (1999)
[27] Llasat, MC, An objective classification of rainfall events on the basis of their convective features. Application to rainfall intensity in the north-east of Spain, Int J Climatol, 21, 1385-1400, (2001)
[28] Mann, HB, Nonparametric tests against trend, Econometrica, 13, 245-259, (1945) · Zbl 0063.03770
[29] Montfort, MAJ, Concomitants of the Hershfield factor, J Hydrol, 194, 357-365, (1997)
[30] Nadarajah, S.; Anderson, CW; Tawn, JA, Ordered multivariate extremes, J R Stat Soc B, 60, 473-496, (1998) · Zbl 0910.62054
[31] Pickands J (1981) Multivariate extreme value distributions. Bulletin of the International Statistical Institute. In: Proceedings of the 43rd Session, Buenos Aires
[32] Pickands J (1989) Multivariate negative exponential and extreme value distributions. Extreme value theory. In: Proceedings, Oberwolfach · Zbl 0672.62065
[33] Renard B, Garreta V, Lang M (2006) An empirical comparison of MCMC methods used in bayesian inference. Application for regional trend detection. Water Resour Res (in press)
[34] Robinson, ME; Tawn, JA, Extremal analysis of processes sampled at different frequencies, J R Stat Soc Ser B Stat Meth, 62, 117-135, (2000) · Zbl 0976.62093
[35] Sisson, SA; Pericchi, LR; Coles, SG, A case for a reassessment of the risks of extreme hydrological hazards in the Caribbean, Stochastic Environ Res Risk Assess, 20, 296-306, (2006)
[36] Veneziano, D.; Furcolo, P., Multifractality of rainfall and scaling of intensity-duration-frequency curves, Water Resour Res, 38, 421-4212, (2002)
[37] Weiss, LL, Ratio of true to fixed-interval maximum rainfall, J Hydraul Div ASCE, 90, 77-82, (1964)
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