Spatial extremes modeling applied to extreme precipitation data in the state of Paraná
R. A. Olinda1, J. Blanchet2, C. A. C. dos Santos3, V. A. Ozaki4, and P. J. Ribeiro Jr.51Department of Statistics, Center for Science and Technology, Paraíba State University – UEPB, Campina Grande, Paraíba, Brazil 2Ecole Polytechnique Fédérale de Lausanne, EPFL-FSB-MATHAA-STAT, Station 8, 1015 Lausanne, Switzerland 3Academic Unit Of Atmospheric Sciences – UACA/CTRN, Federal University of Campina Grande – UFCG, Campina Grande, Paraíba, Brazil 4Department of Exact Sciences, University of São Paulo, School of Agriculture Luiz de Queiroz, 13418-900, Piracicaba, São Paulo, Brazil 5Department of Statistics, Federal University of Paraná, Polytechnic Garden Center of the Americas, 81531-990, Curitiba, Paraná, Brazil
Received: 07 Oct 2014 – Accepted for review: 27 Oct 2014 – Discussion started: 17 Nov 2014
Abstract. Most of the mathematical models developed for rare events are based on probabilistic models for extremes. Although the tools for statistical modeling of univariate and multivariate extremes are well developed, the extension of these tools to model spatial extremes includes an area of very active research nowadays. A natural approach to such a modeling is the theory of extreme spatial and the max-stable process, characterized by the extension of infinite dimensions of multivariate extreme value theory, and making it possible then to incorporate the existing correlation functions in geostatistics and therefore verify the extremal dependence by means of the extreme coefficient and the Madogram. This work describes the application of such processes in modeling the spatial maximum dependence of maximum monthly rainfall from the state of Paraná, based on historical series observed in weather stations. The proposed models consider the Euclidean space and a transformation referred to as space weather, which may explain the presence of directional effects resulting from synoptic weather patterns. This method is based on the theorem proposed for de Haan and on the models of Smith and Schlather. The isotropic and anisotropic behavior of these models is also verified via Monte Carlo simulation. Estimates are made through pairwise likelihood maximum and the models are compared using the Takeuchi Information Criterion. By modeling the dependence of spatial maxima, applied to maximum monthly rainfall data from the state of Paraná, it was possible to identify directional effects resulting from meteorological phenomena, which, in turn, are important for proper management of risks and environmental disasters in countries with its economy heavily dependent on agribusiness.
Olinda, R. A., Blanchet, J., dos Santos, C. A. C., Ozaki, V. A., and Ribeiro Jr., P. J.: Spatial extremes modeling applied to extreme precipitation data in the state of Paraná, Hydrol. Earth Syst. Sci. Discuss., 11, 12731-12764, doi:10.5194/hessd-11-12731-2014, 2014.