Spatial modeling of extremes and an angular component

Many environmental processes such as rainfall, wind or snowfall are inherently spatial and the modeling of extremes has to take into account that feature. In addition, environmental extremes are often attached with an angle, e.g., wind gusts and direction or extreme snowfall and time of occurrence. This article proposes a Bayesian hierarchical model with a conditional independence assumption that aims at modeling simultaneously spatial extremes and angles. The proposed model relies on the extreme value theory as well a recent development for handling directional statistics over a continuous domain. Starting with sketches of the necessary elements of extreme value theory and directional statistics, the model is motivated. Working within a Bayesian setting, a Gibbs sampler is introduced and whose performances are analyzed through a simulation study. The paper ends with an application on extreme snowfalls in the French Alps. Results show that, the most severe events tend to occur later in the snowfall season for high elevation regions than for lower altitudes.