  Several environmental phenomena can be described by different correlated
variables that must be considered jointly in order to be more representative of
the nature of these phenomena. For such events, identification of extremes is
inappropriate if it is based on marginal analysis. Extremes have usually been
linked to the notion of quantile, which is an important tool to analyze risk in
the univariate setting. We propose to identify multivariate extremes and
analyze environmental phenomena in terms of the directional multivariate
quantile, which allows us to analyze the data considering all the variables
implied in the phenomena, as well as look at the data in interesting directions
that can better describe an environmental catastrophe. Since there are many
references in the literature that propose extremes detection based on copula
models, we also generalize the copula method by introducing the directional
approach. Advantages and disadvantages of the non-parametric proposal that we
introduce and the copula methods are provided in the paper. We show with
simulated and real data sets how by considering the first principal component
direction we can improve the visualization of extremes. Finally, two cases of
study are analyzed: a synthetic case of flood risk at a dam (a 3-variable
case), and a real case study of sea storms (a 5-variable case).
