Geospatial–temporal dependence among weekly precipitation extremes with applications to observations and climate model simulations in South America

A quantification of the spatio-temporal dependence among precipitation extremes is important for investigating the properties of intense storms as well as flood or flash-flood related hazards. Extreme value theory has been widely applied to the hydrologic sciences and hydraulic engineering. However, rigorous approaches to quantify dependence structures among extreme values in space and time have not been reported in the literature. Previous researchers have quantified the dependence among extreme values through the concept of (pairwise bivariate) tail dependence coefficients. For estimation of the tail dependence coefficients, we apply a recently developed method [Kuhn G. On dependence and extremes. PhD thesis (Advisor: C. Klüppelberg), Munich University of Technology, 2006] which utilized the multivariate tail dependence function of a subclass of elliptical copulas. This study extends the previous approach in the context of space and time by considering pairs of spatial grids in South America and quantifying the dependence among precipitation extremes based on the time series at each spatial grid. In addition, Kendall’s τ is used to estimate the pairwise copula correlation (for an elliptical copula) of precipitation between all grids in South America. The geospatial–temporal dependence measures are applied to precipitation observations from 1940 to 2005 as well as simulations from the Community Climate System Model version 3 (CCSM3) for 1940–2099. New insights are obtained regarding the spatio-temporal dependence structures for precipitation over South America both with regard to correlation as well as tail dependence.