Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 14 6 2007 10.5194/npg-14-789-2007 http://www.nonlin-processes-geophys.net/14/789/2007/ http://www.nonlin-processes-geophys.net/14/789/2007/npg-14-789-2007.html http://www.nonlin-processes-geophys.net/14/789/2007/npg-14-789-2007.pdf 789 797 2007-12-05 Modeling pairwise dependencies in precipitation intensities M. Vrac mathieu.vrac@lsce.ipsl.fr P. Naveau P. Drobinski Laboratoire des Sciences du Climat et de l'Environnement, IPSL-CNRS, Gif-sur-Yvette, France Service d'Aéronomie, IPSL-CNRS, Université Pierre et Marie Curie, Paris, France In statistics, extreme events are classically defined as maxima over a block length (e.g. annual maxima of daily precipitation) or as exceedances above a given large threshold. These definitions allow the hydrologist and the flood planner to apply the univariate Extreme Value Theory (EVT) to their time series of interest. But these strategies have two main drawbacks. Firstly, working with maxima or exceedances implies that a lot of observations (those below the chosen threshold or the maximum) are completely disregarded. Secondly, this univariate modeling does not take into account the spatial dependence. Nearby weather stations are considered independent, although their recordings can show otherwise. <br><br> To start addressing these two issues, we propose a new statistical bivariate model that takes advantages of the recent advances in multivariate EVT. Our model can be viewed as an extension of the non-homogeneous univariate mixture. The two strong points of this latter model are its capacity at modeling the entire range of precipitation (and not only the largest values) and the absence of an arbitrarily fixed large threshold to define exceedances. Here, we adapt this mixture and broaden it to the joint modeling of bivariate precipitation recordings. The performance and flexibility of this new model are illustrated on simulated and real precipitation data. Akaike, H.: A new look at the statistical model identification, IEEE Transactions on Automatic Control, 19, 716&ndash;723, 1974. Beirlant, J., Goegebeur, Y., Segers, J., and Teugels, J.: Statistics of Extremes: Theory and Applications, Wiley Series in Probability and Statistics, 2004. Carreau, J. and Bengio, Y.: A hybrid Pareto model for asymmetric fat-tail data, Technical report 1283, Dept. IRO, Université de Montréal, 2006. Choulakian, V. and Stephens, M. A.: Goodness-of-fit Tests for the Generalized Pareto Distribution, Technometrics, 43, 478&ndash;484, 2001. Coles, S. G.: An introduction to statistical modeling of extreme values, Springer Series in Statistics, 2001. Cooley D., Nychka, D., and Naveau, P.: Bayesian Spatial Modeling of Extreme Precipitation Return Levels, J. Am. Stat. Assoc., 102(479), 824&ndash;840, 2007. De Haan, L. and Ferreira, A.: Extreme Value Theory: An Introduction, Springer Series in Operations Research and Financial Engineering, 2006. Embrechts, P., Klüppelberg, C., and Mikosch, T.: Modelling Extremal Events for Insurance and Finance, Applications of Mathematics, vol 33, Springer-Verlag, Berlin, 1997. Fisher, R. A. and Tippett, L. H. C.: Limiting forms of the frequency distribution of the largest or smallest member of a sample, Proceedings of the Cambridge Philosophical Society, 24, 180&ndash;190, 1928. Frigessi, A., Haug, O., and Rue, H.: A dynamic mixture model for unsupervised tail estimation without threshold selection, Extremes, 5, 219&ndash;235, 2002. Katz, R., Parlange, M., and Naveau, P.: Extremes in hydrology, Adv. Water Resour., 25, 1287&ndash;1304, 2002. Katz, R. W.: Precipitation as a chain-dependent process, J. Appl. Meteorol., 16, 671&ndash;676, 1977. Kotz, S., Balakrishnan, N., and Johnson, N. L.: Continuous multivariate distributions, vol. 1, Models and applications, New York, Wiley, 2000. Naveau, P., Nogaj, M., Ammann, C., Yiou, P., Cooley, D., and Jomelli, V.: Statistical methods for the analysis of climate extremes, C. R. Geoscience, 337, 1013&ndash;1022, 2005. Resnick, S.: Heavy-Tail Phenomena: Probabilistic and Statistical Modeling, Springer Series in Operations Research and Financial Engineering, 2007. Schwarz, G.: Estimating the dimension of a model, Ann. Statist., 6, 461&ndash;464, 1978. Vrac, M. and Naveau, P.: Stochastic downscaling of precipitation: From dry events to heavy rainfalls. Water Resour. Res., 43, W07402, doi:10.1029/2006WR005308, 2007. Vrac, M., Stein, M., and Hayhoe, K.: Statistical downscaling of precipitation through a nonhomogeneous stochastic weather typing approach. Climate Research, 34, 169&ndash;184, doi:10.3354/cr00696, 2007. Wilks, D.: Statistical methods in the atmospheric sciences (second edition), Elsevier, Oxford, 2006.