Assessing conditional extremal risk of flooding in Puerto Rico

We model multivariate hydrological risks in the case that at least one of the variables is extreme. Recently, Heffernan JE, Tawn JA (2004) A conditional approach for multivariate extremes. J R Stat Soc B 66(3):497-546 (thereafter called HT04) proposed a conditional multivariate extreme value model which applies to regions where not all variables are extreme and simultaneously identifies the type of extremal dependence, including negative dependence. In this paper we apply this modeling strategy and provide an application to multivariate observations of five rivers in two clearly distinct regions of Puerto Rico Island and for two different seasons each. This effective dimensionality of ten-dimensions cannot be handled by the traditional models of multivariate extremes. The resulting fitted model, following HT04 model and strategies of estimation, is able to make long term estimation of extremes, conditional than other rivers are extreme or not. The model shows considerable flexibility to address the natural questions that arise in multivariate extreme value assessments. In the Puerto Rico 5 rivers application, the model clearly puts together two regions one of two rivers and another of three rivers, which show strong relationships in the rainy season. This corresponds with the geographical distribution of the rivers.