Trivariate copulas for characterisation of droughts
Australian agriculture is at serious risk from drought, and water resource infrastructure and management can mitigate the effects. The consequences of droughts depend on their intensity, duration and severity. These variables are correlated and the dependence structure is here described by copulas. Copulas are multivariate uniform distributions which allow for the dependence structure to be modelled independently of the marginal distributions. Trivariate Gaussian and Gumbel copulas are fitted to the data from a rainfall district in NSW. We assess the goodness of fit of the data to the different forms using several criteria. The data are best described by a Gumbel copula and three parameter Weibull marginal distributions. References P. Embrechets, F. Lindskog and A. J. McNeil. Modelling dependence with copulas and applications to risk management. In: Rachev S. T. editor. Handbook of heavy tailed distributions in finance. Amsterdam, North Holland: Elsevier, 2003. A C Favre, S. E. Adlouni, L. Perreault, N. Thiemonge and B. Bobee. Multivariate hydrological frequency analysis using copulas. Water Resources Research 2004, 40 W01101. doi:10.1029/2003WR002456 C. Genest and J. MacKay. The joy of copulas: bivariate distributions with uniform marginals. The American Statistician 1986, 40 (4) 280 283. C. Genest and A C Favre. Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering 2006, 12 (4) 347 368. doi:10.1061/(ASCE)1084 0699(2007)12:4(347) S. Grimaldi and F. Serinaldi. Asymmetric copula in multivariate flood frequency analysis. Advances in Water Resources 2006, 29 1155 1167. doi:10.1016/j.advwatres.2005.09.005 H. Joe. Multivariate models and dependence concepts New York: Chapman and Hall, 1997. T. B. McKee, N. J. Doesken and J. Kliest. The relationship of drought frequency and duration to time scales. In Proceeding of the 8th Conference on Applied Climatology 17 22 January 1993, Anaheim, CA, American Meteorological Society: Boston, MA, USA, 179 184. R Development Core Team. R: A Language and Environment for Statistical Computing R Foundation for Statistical Computing. 2007. http:/www.R project.org J. T. Shiau. Fitting Drought Duration and Severity with Two Dimensional Copulas. Water Resources Management 2006, 20 795 815. doi:10.1007/s11269 005 9008 9 A. Sklar. Fonctions de repartitions a $n$ dimensions et leurs marges. Publications de l'Institut de Statistique de l'Universite de Paris 1959, 8 229 231. The Australian. El Nino bad news for drought stricken east The Australian, 14th September. Accessed 19th September. http:/www.theaustralian.news.com.au/printpage/0,5942,2041027 L. Zhang and V. P. Singh. Bivariate Flood Frequency Analysis using Copula Method. Journal of Hydrologic Engineering 2006, 11 (2) 150 164. doi:10.1061/(ASCE)1084 0699(2006)11:2(150)