×

A regionalisation approach for rainfall based on extremal dependence. (English) Zbl 1481.60098

In modelling extreme rainfall events, the article presents a regionalization method that partitions stations into regions of similar extremal dependence using hierarchical clustering with the F-madogram distance and a classification step using a weighted \(k\)-nearest neighbour classifier. To demonstrate the approach, the article considers a study region of a network of daily rainfall stations in Australia and discusses, in detail, the results with respect to known climate and topographic features. Max-stable models are fitted to the observed annual maximal rainfall in each of the regions to visualize and evaluate the effectiveness of the partitioning relative to the full extremal dependence.

MSC:

60G70 Extreme value theory; extremal stochastic processes
62P12 Applications of statistics to environmental and related topics
62G32 Statistics of extreme values; tail inference
62D05 Sampling theory, sample surveys
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Alexander, LV; Arblaster, JM, Historical and projected trends in temperature and precipitation extremes in Australia in observations and CMIP5, Weather Clim. Extrem., 15, 34-56 (2017) · doi:10.1016/j.wace.2017.02.001
[2] Asadi, P.; Engelke, S.; Davison, AC, Optimal regionalization of extreme value distributions for flood estimation, J. Hydrol., 556, 182-193 (2018) · doi:10.1016/j.jhydrol.2017.10.051
[3] Bador, M., Naveau, P., Gilleland, E., Castellà, M., Arivelo, T.: Spatial clustering of summer temperature maxima from the CNRM-CM5 climate model ensembles & E-OBS over Europe. Weather Clim Extrem 9, 17-24 (2015)
[4] Bernard, E.; Naveau, P.; Vrac, M.; Mestre, O., Clustering of maxima: Spatial dependencies among heavy rainfall in France, J. Clim., 26, 7929-7937 (2013) · doi:10.1175/JCLI-D-12-00836.1
[5] Carreau, J.; Naveau, P.; Neppel, L., Partitioning into hazard subregions for regional peaks-over-threshold modeling of heavy precipitation, Water Resour. Res., 53, 4407-4426 (2017) · doi:10.1002/2017WR020758
[6] Castro-Camilo, D.; de Carvalho, M.; Wadsworth, JL, Time-varying extreme value dependence with application to leading European stock markets, Ann. Appl. Stat., 12, 283-309 (2018) · Zbl 1393.62024 · doi:10.1214/17-AOAS1089
[7] Castro-Camilo, D., Huser, R.: Local likelihood estimation of complex tail dependence structures, applied to US precipitation extremes. Journal of the American Statistical Association, 1-29 (2019) · Zbl 1441.62118
[8] Castruccio, S.; Huser, R.; Genton, MG, High-order composite likelihood inference for max-stable distributions and processes, J. Comput. Graph. Stat., 25, 1212-1229 (2016) · doi:10.1080/10618600.2015.1086656
[9] Chamberlain, S.: rnoaa: ‘NOAA’ Weather Data from R. https://CRAN.R-project.org/package=rnoaa, R package version 0.7.0. (2017)
[10] Charrad, M., Ghazzali, N., Boiteau, V., Niknafs, A.: NbClust: An R package for determining the relevant number of clusters in a data set. J. Stat. Softw. 61, 1-36. http://www.jstatsoft.org/v61/i06/ (2014)
[11] Coles, S.: An Introduction to Statistical Modeling of Extreme Values, vol. 208. Springer (2001) · Zbl 0980.62043
[12] Cooley, D., Naveau, P., Poncet, P.: Variograms for spatial max-stable random fields. In: Dependence in Probability and Statistics, pp. 373-390. Springer (2006) · Zbl 1110.62130
[13] Cressie, N.: Statistics for Spatial Data. Wiley, New York (2015) · Zbl 1347.62005
[14] CSIRO and Bureau of Meteorology: Climate Change in Australia Information for Australia’s Natural Resource Management Regions. CSIRO and Bureau of Meteorology, Australia (2015)
[15] Davison, A.C., Padoan, S.A., Ribatet, M., et al.: Statistical modeling of spatial extremes. Stat. Sci. 27, 161-186 (2012) · Zbl 1330.86021
[16] de Haan, L.: A spectral representation for max-stable processes. The Annals of Probability, 1194-1204 (1984) · Zbl 0597.60050
[17] de Haan, L., Ferreira, A.: Extreme Value Theory: An Introduction. Springer Science & Business Media (2006) · Zbl 1101.62002
[18] Dey, D., Yan, J.: Extreme Value Modeling and Risk Analysis: Methods and Applications. CRC Press (2016) · Zbl 1336.62002
[19] Dombry, C.; Eyi-Minko, F., Regular conditional distributions of continuous max-infinitely divisible random fields, Electron. J. Probab., 18, 1-21 (2013) · Zbl 1287.60066 · doi:10.1214/EJP.v18-1991
[20] Dudani, S.A.: The distance-weighted k-nearest-neighbor rule. IEEE Transactions on Systems, Man, and Cybernetics, 325-327 (1976)
[21] Durre, I.; Menne, MJ; Vose, RS, Strategies for evaluating quality assurance procedures, J. Appl. Meteorol. Climatol., 47, 1785-1791 (2008) · doi:10.1175/2007JAMC1706.1
[22] Durre, I.; Menne, MJ; Gleason, BE; Houston, TG; Vose, RS, Comprehensive automated quality assurance of daily surface observations, J. Appl. Meteorol. Climatol., 49, 1615-1633 (2010) · doi:10.1175/2010JAMC2375.1
[23] Grose, MR; Barnes-Keoghan, I.; Corney, SP; White, CJ; Holz, GK; Bennett, J.; Gaynor, SM; Bindoff, NL, Climate Futures for Tasmania: General Climate Impacts Technical Report Cooperative Research Centre (2010), Tasmania: Hobart, Tasmania
[24] Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning. Springer (2009) · Zbl 1273.62005
[25] Haylock, M., Nicholls, N., et al.: Trends in extreme rainfall indices for an updated high quality data set for Australia, 1910-1998. Int. J. Climatol. 20, 1533-1541 (2000)
[26] Hosking, J., Wallis, J.: Regional Frequency Analysis. An Approach Based on L-moments. Cambridge University Press Cambridge (1997)
[27] Huser, R.; Genton, MG, Non-stationary dependence structures for spatial extremes, J. Agric. Biol. Environ. Stat., 21, 470-491 (2016) · Zbl 1347.62246 · doi:10.1007/s13253-016-0247-4
[28] Huser, R.; Dombry, C.; Ribatet, M.; Genton, MG, Full likelihood inference for max-stable data, Stat, 8, e218 (2019) · doi:10.1002/sta4.218
[29] Jones, DA; Wang, W.; Fawcett, R., High-quality spatial climate data-sets for Australia, Austral. Meteorol. Oceanograph. J., 58, 233 (2009) · doi:10.22499/2.5804.003
[30] Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley (1990) · Zbl 1345.62009
[31] Min, SK; Cai, W.; Whetton, P., Influence of climate variability on seasonal extremes over Australia, J. Geophys. Res. Atmosph., 118, 643-654 (2013) · doi:10.1002/jgrd.50164
[32] Murtagh, F., A survey of recent advances in hierarchical clustering algorithms, Comput. J., 26, 354-359 (1983) · Zbl 0523.68030 · doi:10.1093/comjnl/26.4.354
[33] Murtagh, F., Legendre, P.: Ward’s hierarchical agglomerative clustering method: Which algorithms implement Ward’s criterion? J. Class. 31, 274-295 (2014) · Zbl 1360.62344
[34] Naveau, P.; Guillou, A.; Cooley, D.; Diebolt, J., Modelling pairwise dependence of maxima in space, Biometrika, 96, 1-17 (2009) · Zbl 1162.62045 · doi:10.1093/biomet/asp001
[35] Oesting, M.; Schlather, M.; Friederichs, P., Statistical post-processing of forecasts for extremes using bivariate brown-resnick processes with an application to wind gusts, Extremes, 20, 309-332 (2017) · Zbl 1373.86016 · doi:10.1007/s10687-016-0277-x
[36] Padoan, SA; Ribatet, M.; Sisson, SA, Likelihood-based inference for max-stable processes, J. Am. Stat. Assoc., 105, 263-277 (2010) · Zbl 1397.62172 · doi:10.1198/jasa.2009.tm08577
[37] Queensland Floods Commission of Inquiry: Queensland Floods Commission of Inquiry: Final Report. Queensland Floods Commission of Inquiry (2012)
[38] Resnick, SI, Extreme Values Point Processes and Regular Variation (1987), New York: Springer, New York · Zbl 0633.60001 · doi:10.1007/978-0-387-75953-1
[39] Ribatet, M.: SpatialExtremes: Modelling Spatial Extremes. https://CRAN.R-project.org/package=SpatialExtremes, R, package version 2.0-2 (2015)
[40] Risbey, JS; Pook, MJ; McIntosh, PC; Wheeler, MC; Hendon, HH, On the remote drivers of rainfall variability in Australia, Mon. Weather. Rev., 137, 3233-3253 (2009) · doi:10.1175/2009MWR2861.1
[41] Rohrbeck, C., Tawn, J.A.: Bayesian spatial clustering of extremal behaviour for hydrological variables. Journal of Computational and Graphical Statistics, pp 1-38 (2020)
[42] Samworth, RJ, Optimal weighted nearest neighbour classifiers, Ann. Stat., 40, 2733-2763 (2012) · Zbl 1373.62317
[43] Saunders, K., Stephenson, A.G., Taylor, P.G., Karoly, D.: The spatial distribution of rainfall extremes and the influence of El Nino Southern Oscillation. Weather and Climate Extremes (2017)
[44] Saunders, K.: An Investigation of Australian Rainfall Using Extreme Value Theory. Ph.D. thesis, University of Melbourne (2018)
[45] Schlather, M., Models for stationary max-stable random fields, Extremes, 5, 33-44 (2002) · Zbl 1035.60054 · doi:10.1023/A:1020977924878
[46] Smith, R.L.: Max-Stable Processes and Spatial Extremes. Unpublished manuscript, Univer (1990)
[47] Stern, H.; de Hoedt, G.; Ernst, J., Objective classification of Australian climates, Aust. Meteorol. Mag., 49, 87-96 (2000)
[48] Tibshirani, R.; Walther, G.; Hastie, T., Estimating the number of clusters in a data set via the gap statistic, J. R. Stat. Soc. Ser. B (Stat. Methodol.), 63, 411-423 (2001) · Zbl 0979.62046 · doi:10.1111/1467-9868.00293
[49] Westra, S.; Alexander, LV; Zwiers, FW, Global increasing trends in annual maximum daily precipitation, J. Clim., 26, 3904-3918 (2013) · doi:10.1175/JCLI-D-12-00502.1
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.