Threshold modeling of extreme spatial rainfall

Water Resources Research

Volumn 49, Issue 8, 2013, Pages 4633-4644

  Thibaud, E ^a   Mutzner, R ^a   Davison, A C ^a  

^a EPFL   (Switzerland)

Author keywords

extremes; max stable model; spatial rainfall

Indexed keywords

CATCHMENTS; STABILITY CRITERIA;

CUMULATIVE RAINFALL; EXTREME VALUE THEORY; EXTREMES; HYDROLOGICAL MODELS; LIKELIHOOD FUNCTIONS; PARTIAL DURATION SERIES; SPATIAL RAINFALL; STABLE MODEL;

RAIN;

MUSTELA;

EID: 84879901990     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/wrcr.20329     Document Type: Article

References (66)

1. Banerjee, S., B. Carlin, and, A. Gelfand, (2004), Hierarchical Modeling and Analysis for Spatial Data, Chapman and Hall, New York.
2. Beirlant, J., Y. Goegebeur, J. Teugels, and, J. Segers, (2004), Statistics of Extremes: Theory and Applications, John Wiley, New York.
3. Blanchet, J., and, A. C. Davison, (2011), Spatial modelling of extreme snow depth, Ann. Appl. Stat., 5, 1699-1725, doi: 10.1214/11-AOAS464.
4. Brown, B. M., and, S. I. Resnick, (1977), Extreme values of independent stochastic processes, J. Appl. Probab., 14, 732-739, doi: 10.2307/3213346.
5. Buishand, T. A., (1984), Bivariate extreme-value data and the station-year method, J. Hydrol., 69, 77-95, doi: 10.1016/0022-1694(84)90157-4.
6. Buishand, T. A., L. de Haan, and, C. Zhou, (2008), On spatial extremes: With application to a rainfall problem, Ann. Appl. Stat., 2, 624-642, doi: 10.1214/08-AOAS159.
7. Chandler, R. E., V. S. Isham, E. Bellone, C. Yang, and, P. Northrop, (2006), Space-time modelling of rainfall for continuous simulation, in Statistical Methods for Spatio-Temporal Systems, edited by, B. Finkenstädt, L. Held, and, V. S. Isham, Chapman and Hall, Boca Raton, Fla., doi: 10.1201/9781420011050.ch5.
8. Chavez-Demoulin, V., and, A. C. Davison, (2005), Generalized additive models for sample extremes, Appl. Stat., 54 (1), 207-222, doi: 10.1111/j.1467-9876.2005.00479.x. (Pubitemid 40166931)
9. Chavez-Demoulin, V., and, A. C. Davison, (2012), Modelling time series extremes, REVSTAT-Stat. J., 10, 109-133.
10. Coles, S. G., (1993), Regional modelling of extreme storms via max-stable processes, J. R. Stat. Soc. Ser. B, 55, 797-816.
11. Coles, S. G., (2001), An Introduction to Statistical Modeling of Extreme Values, Springer, London.
12. Coles, S. G., and, J. A. Tawn, (1996), Modelling extremes of the areal rainfall process, J. R. Stat. Soc. Ser. B, 58, 329-347.
13. Cooley, D., D. Nychka, and, P. Naveau, (2007), Bayesian spatial modeling of extreme precipitation return levels, J. Am. Stat. Assoc., 102, 824-840, doi: 10.1198/016214506000000780.
14. Cox, D. R., and, V. S. Isham, (1988), A simple spatial-temporal model of rainfall, Proc. R. Soc. London Ser. A, 415, 317-328, doi: 10.1098/rspa.1988. 0016.
15. Davis, R. A., and, T. Mikosch, (2010), The extremogram: A correlogram for extreme events, Bernoulli, 15, 977-1009, doi: 10.3150/09-BEJ213.
16. Davison, A. C., and, M. M. Gholamrezaee, (2012), Geostatistics of extremes, Proc. R. Soc. London Ser. A, 468, 581-608, doi: 10.1098/rspa.2011. 0412.
17. Davison, A. C., and, N. I. Ramesh, (2000), Local likelihood smoothing of sample extremes, J. R. Stat. Soc. Ser. B, 62, 191-208, doi: 10.1111/1467-9868. 00228.
18. Davison, A. C., and, R. L. Smith, (1990), Models for exceedances over high thresholds (with discussion), J. R. Stat. Soc. Ser. B, 52, 393-442.
19. Davison, A. C., S. A. Padoan, and, M. Ribatet, (2012), Statistical modelling of spatial extremes (with discussion), Stat. Sci., 27, 161-186, doi: 10.1214/11-STS376.
20. Davison, A. C., R. Huser, and, E. Thibaud, (2013), Geostatistics of dependent and asymptotically independent extremes, Math. Geosci., 45 (5), 511-529, doi: 10.1007/s11004-013-9469-y.
21. de Carvalho, M., and, A. Ramos, (2012), Bivariate extreme statistics: II, REVSTAT-Stat. J., 10, 83-107.
22. de Haan, L., (1984), A spectral representation for max-stable processes, Ann. Probab., 12, 1194-1204, doi: 10.1214/aop/1176993148.
23. de Haan, L., and, A. Ferreira, (2006), Extreme Value Theory: An Introduction, Springer, New York.
24. de Haan, L., and, T. T. Pereira, (2006), Spatial extremes: Models for the stationary case, Ann. Stat., 34, 146-168, doi: 10.1214/009053605000000886. (Pubitemid 43836797)
25. Diggle, P. J., and, P. J. Ribeiro, (2007), Model-Based Geostatistics, Springer, New York.
26. Dombry, C., F. Éyi-Minko, and, M. Ribatet, (2013), Conditional simulation of max-stable processes, Biometrika, 100 (1), 111-124, doi: 10.1093/biomet/ass067.
27. Feng, S., S. Nadarajah, and, Q. Hu, (2007), Modeling annual extreme precipitation in china using the generalized extreme value distribution, J. Meteorol. Soc. Jpn., 85, 599-613.
28. Fisher, R. A., and, L. H. C. Tippett, (1928), Limiting forms of the frequency distribution of the largest or smallest member of a sample, Math. Proc. Cambridge Philos. Soc., 24 (2), 180-190, doi: 10.1017/S0305004100015681.
29. Hall, P., and, N. Tajvidi, (2000), Nonparametric analysis of temporal trend when fitting parametric models to extreme-value data, Stat. Sci., 15, 153-167, doi: 10.1214/ss/1009212755.
30. Huser, R., and, A. C. Davison, (2013a), Composite likelihood estimation for the Brown-Resnick process, Biometrika, 100, 511-518, doi: 10.1093/biomet/ass089.
31. Huser, R., and, A. C. Davison, (2013b), Space-time modelling of extreme events, J. R. Stat. Soc. Ser. B, in press.
32. Ingelrest, F., G. Barrenetxea, G. Schaefer, M. Vetterli, O. Couach, and, M. Parlange, (2010), SensorScope: Application-specific sensor network for environmental monitoring, ACM Trans. Sens. Network, 6, 17:1-17:32, doi: 10.1145/1689239.1689247.
33. Kabluchko, Z., M. Schlather, and, L. De Haan, (2009), Stationary max-stable fields associated to negative definite functions, Ann. Probab., 37, 2042-2065, doi: 10.1214/09-AOP455.
34. Katz, R. W., M. B. Parlange, and, P. Naveau, (2002), Statistics of extremes in hydrology, Adv. Water Resour., 25, 1287-1304, doi: 10.1016/S0309-1708(02)00056-8. (Pubitemid 35465151)
35. Langbein, W. B., (1949), Annual floods and the partial-duration flood series, Trans. AGU, 30 (6), 879-881.
36. Ledford, A. W., and, J. A. Tawn, (1996), Statistics for near independence in multivariate extreme values, Biometrika, 83, 169-187, doi: 10.1093/biomet/83.1.169.
37. Lindsay, B., (1988), Composite likelihood methods, Contemporary Math., 80, 221-239.
38. Madsen, H., P. S. Mikkelsen, D. Rosbjerg, and, P. Harremoës, (2002), Regional estimation of rainfall intensity-duration-frequency curves using generalized least squares regression of partial duration series statistics, Water Resour. Res., 38 (11), 1239, doi: 10.1029/2001WR001125.
39. Northrop, P. J., and, P. Jonathan, (2011), Threshold modelling of spatially dependent non-stationary extremes with application to hurricane-induced wave heights (with discussion), Environmetrics, 22, 799-809, doi: 10.1002/env.1106.
40. Padoan, S. A., M. Ribatet, and, S. A. Sisson, (2010), Likelihood-based inference for max-stable processes, J. Am. Stat. Assoc., 105, 263-277, doi: 10.1198/jasa.2009.tm08577.
41. Pickands, J. I., (1975), Statistical inference using extreme order statistics, Ann. Stat., 3, 119-131, doi: 10.1214/aos/1176343003.
42. R Development Core Team (2012), R: A Language and Environment for Statistical Computing, R Found. for Stat. Comput., Vienna.
43. Ramesh, N. I., and, A. C. Davison, (2002), Local models for exploratory analysis of hydrological extremes, J. Hydrol., 256 (1-2), 106-119, doi: 10.1016/S0022-1694(01)00522-4. (Pubitemid 34134667)
44. Renard, B., (2011), A Bayesian hierarchical approach to regional frequency analysis, Water Resour. Res., 47, W11513, doi: 10.1029/2010WR010089.
45. Rodriguez-Iturbe, I., D. R. Cox, and, V. S. Isham, (1987), 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)
46. Rodriguez-Iturbe, I., D. R. Cox, and, V. S. 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.
47. Salvadori, G., and, C. D. Michele, (2010), Multivariate multiparameter extreme value models and return periods: A copula approach, Water Resour. Res., 46, W10501, doi: 10.1029/2009WR009040.
48. Sang, H., and, A. Gelfand, (2010), Continuous spatial process models for spatial extreme values, J. Agric. Biol. Environ. Stat., 15 (1), 49-65, doi: 10.1007/s13253-009-0010-1.
49. Schlather, M., (2002), Models for stationary max-stable random fields, Extremes, 5 (1), 33-44, doi: 10.1023/A:1020977924878.
50. Schlather, M., and, J. A. Tawn, (2003), A dependence measure for multivariate and spatial extreme values: Properties and inference, Biometrika, 90, 139-156, doi: 10.1093/biomet/90.1.139. (Pubitemid 39047187)
51. Shang, H., J. Yan, and, X. Zhang, (2011), El Niño-Southern Oscillation influence on winter maximum daily precipitation in California in a spatial model, Water Resour. Res., 47, W11507, doi: 10.1029/2011WR010415.
52. Simoni, S., S. Padoan, D. F. Nadeau, M. Diebold, A. Porporato, G. Barrenetxea, F. Ingelrest, M. Vetterli, and, M. B. Parlange, (2011), Hydrologic response of an alpine watershed: Application of a meteorological wireless sensor network to understand streamflow generation, Water Resour. Res., 47, W10524, doi: 10.1029/2011WR010730.
53. Tawn, J. A., (1988), Bivariate extreme value theory: Models and estimation, Biometrika, 75, 397-415, doi: 10.1093/biomet/75.3.397.
54. Tobin, C., B. Schaefli, L. Nicotina, S. Simoni, G. Barrenetxea, R. Smith, M. Parlange, and, A. Rinaldo, (2013), Improving the degree-day method for sub-daily melt simulations with physically-based diurnal variations, Adv. Water Resour., 55, 149-164, doi: 10.1016/j.advwatres.2012.08.008.
55. Todorovic, P., and, J. Rousselle, (1971), Some problems of flood analysis, Water Resour. Res., 7 (5), 1144-1150, doi: 10.1029/WR007i005p01144.
56. Todorovic, P., and, E. Zelenhasic, (1970), A stochastic model for flood analysis, Water Resour. Res., 6 (6), 1641-1648, doi: 10.1029/WR006i006p01641.
57. Van de Vyver, H., (2012), Spatial regression models for extreme precipitation in Belgium, Water Resour. Res., 48, W09549, doi: 10.1029/2011WR011707.
58. Varin, C., and, P. Vidoni, (2005), A note on composite likelihood inference and model selection, Biometrika, 92 (3), 519-528, doi: 10.1093/biomet/92.3.519. (Pubitemid 41241590)
59. Varin, C., N. Reid, and, D. Firth, (2011), An overview of composite likelihood methods, Stat. Sin., 21, 5-42.
60. Villarini, G., J. A. Smith, M. L. Baeck, T. Marchok, and, G. A. Vecchi, (2011), Characterization of rainfall distribution and flooding associated with U.S. landfalling tropical cyclones: Analyses of Hurricanes Frances, Ivan, and Jeanne (2004), J. Geophys. Res., 116, D23116, doi: 10.1029/2011JD016175.
61. Vrac, M., and, P. Naveau, (2007), Stochastic downscaling of precipitation: From dry events to heavy rainfalls, Water Resour. Res., 43, W07402, doi: 10.1029/2006WR005308.
62. Wadsworth, J. L., and, J. A. Tawn, (2012), Dependence modelling for spatial extremes, Biometrika, 99 (2), 253-272, doi: 10.1093/biomet/asr080.
63. Westra, S., and, S. A. Sisson, (2011), Detection of non-stationarity in precipitation extremes using a max-stable process model, J. Hydrol., 406, 119-128, doi: 10.1016/j.jhydrol.2011.06.014.
64. Wilks, D. S., and, R. L. Wilby, (1999), The weather generation game: A review of stochastic weather models, Prog. Phys. Geogr., 23, 329-357, doi: 10.1177/030913339902300302. (Pubitemid 30005514)
65. Yang, C., R. E. Chandler, V. S. Isham, and, H. S. Wheater, (2005), Spatial-temporal rainfall simulation using generalized linear models, Water Resour. Res., 41, W11415, doi: 10.1029/2004WR003739.
66. Zheng, X., and, R. W. Katz, (2008), Simulation of spatial dependence in daily rainfall using multisite generators, Water Resour. Res., 44, W09403, doi: 10.1029/2007WR006399.