This work will focus on the modeling of extreme events (possibly attached with a non extremal quantity) over a continuous spatial domain. For instance one may be interested in modeling extreme wind speeds and the associated wind direction over France. The first part of this talk will present a Bayesian hierarchical model which relies on both the extreme value and directional statistical theory. To be more specific, we will make use of a conditional independence assumption to make use of univariate extreme value distribution for the extremal quantity, e.g., wind speed, while preserving spatial dependence through the use of the projected Gaussian process to model the non extremal component, e.g., wind direction. The second part of the talk, more theoretical, will introduce what we shall call an augmented max-stable process which extends the max-stable process to multivariate stochastic processes where some of the components are not extremal. We will explicit some properties of such class of processes and give algorithm for exact unconditional and conditional simulation.