AStA Advances in Statistical Analysis

, Volume 97, Issue 2, pp 181–193 | Cite as

Geoadditive modeling for extreme rainfall data

  • Chiara Bocci
  • Enrica Caporali
  • Alessandra Petrucci
Original Paper


Extreme value models and techniques are widely applied in environmental studies to define protection systems against the effects of extreme levels of environmental processes. Regarding the matter related to the climate science, a certain importance is covered by the implication of changes in the hydrological cycle. Among all hydrologic processes, rainfall is a very important variable as it is strongly related to flood risk assessment and mitigation, as well as to water resources availability and drought identification. We implement here a geoadditive model for extremes assuming that the observations follow a generalized extreme value distribution with spatially dependent location. The analyzed territory is the catchment area of the Arno River in Tuscany in Central Italy.


Generalized extreme value distribution Geoadditive model Hydrologic processes 


  1. Burlando, P., Rosso, R.: Effects of transient climate change on basin hydrology. Precipitation scenarios for the Arno river, central Italy. Hydrol. Process. 16, 1151–1175 (2002) CrossRefGoogle Scholar
  2. Caporali, E., Rinaldi, M., Casagli, N.: The Arno river floods. G. Geol. Appl. 1, 177–192 (2005). doi: 10.1474/GGA.2005-01.0-18.0018 Google Scholar
  3. Chavez-Demoulin, V., Davison, A.C.: Generalized additive modelling of sample extremes. Appl. Stat. 54, 207–222 (2005) MathSciNetMATHGoogle Scholar
  4. Coles, S.G.: An Introduction to Statistical Modeling of Extreme Values. Springer, London (2001) MATHGoogle Scholar
  5. Cooley, D., Sain, S.: Spatial hierarchical modeling of precipitation extremes from a regional climate model. J. Agric. Biol. Environ. Stat. 15(3), 381–402 (2010) MathSciNetCrossRefGoogle Scholar
  6. Cooley, D., Nychka, D., Naveau, P.: Bayesian spatial modeling of extreme precipitation return levels. J. Am. Stat. Assoc. 102(479), 824–840 (2007) MathSciNetMATHCrossRefGoogle Scholar
  7. Davison, A.C., Ramesh, N.I.: Local likelihood smoothing of sample extremes. J. R. Stat. Soc. B 62(3), 191–208 (2000) MathSciNetMATHCrossRefGoogle Scholar
  8. Davison, A.C., Padoan, A., Ribatet, M.: Statistical modelling of spatial extremes (with discussion). Stat. Sci. (2012, forthcoming).
  9. Fatichi, S., Caporali, E.: A comprehensive analysis of changes in precipitation regime in Tuscany. Int. J. Climatol. 29(13), 1883–1893 (2009) CrossRefGoogle Scholar
  10. Gelman, A.: Prior distributions for variance parameters in hierarchical models. Bayesian Anal. 1(3), 515–533 (2006) MathSciNetGoogle Scholar
  11. Kammann, E.E., Wand, M.P.: Geoadditive models. Appl. Stat. 52, 1–18 (2003) MathSciNetMATHGoogle Scholar
  12. Katz, R.W., Brown, B.G.: Extreme events in a changing climate: variability is more important than averages. Clim. Change 21, 289–302 (1992) CrossRefGoogle Scholar
  13. Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York (1990) CrossRefGoogle Scholar
  14. Marley, J., Wand, M.P.: Non-standard semiparametric regression via BRugs. J. Stat. Softw. 37(5), 1–30 (2010) Google Scholar
  15. Neville, S.E., Wand, M.P.: Generalised extreme value geoadditive models via variational Bayes. Procedia Environ. Sci. 3, 8–13 (2011) CrossRefGoogle Scholar
  16. Padoan, S.A.: Computational methods for complex problems in extreme value theory. Ph.D. thesis, Ph.D. in Statistical Science, Department of Statistical Science, University of Padova (2008) Google Scholar
  17. Padoan, S.A., Wand, M.P.: Mixed model-based additive models for sample extremes. Stat. Probab. Lett. 78, 2850–2858 (2008) MathSciNetMATHCrossRefGoogle Scholar
  18. Padoan, S.A., Ribatet, M., Sisson, S.A.: Likelihood-based inference for max-stable processes. J. Am. Stat. Assoc. 105(489), 263–277 (2010). doi: 10.1198/jasa.2009.tm08577 MathSciNetCrossRefGoogle Scholar
  19. R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2011). URL ISBN 3-900051-07-0 Google Scholar
  20. Ruppert, D., Wand, M.P., Carroll, R.J.: Semiparametric Regression. Cambridge University Press, Cambridge (2003) MATHCrossRefGoogle Scholar
  21. Sang, H., Gelfand, A.E.: Hierarchical modeling for extreme values observed over space and time. Environ. Ecol. Stat. 16, 407–426 (2009) MathSciNetCrossRefGoogle Scholar
  22. Thomas, A., O’Hara, B., Ligges, U., Sturtz, S.: Making BUGS open. R News 6(1), 12–17 (2006) Google Scholar
  23. World Meteorological Organization: Guide to climatological practices. Tech. Rep. 100, Secretariat of the World Meteorological Organization, Geneva, Switzerland (1983) Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Chiara Bocci
    • 1
  • Enrica Caporali
    • 2
  • Alessandra Petrucci
    • 1
  1. 1.Department of Statistics “G. Parenti”University of FlorenceFirenzeItaly
  2. 2.Department of Civil and Environmental EngineeringUniversity of FlorenceFirenzeItaly

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