Abstract
This paper is devoted to a prototype of max-stable models called the storm process. At first its spatial distribution is given in association with different observation supports. Then the compatibility relationships between extremal coefficients at various supports are completely characterized. Particular attention is paid to the special case where the storms are indicator functions of Poisson polytopes. Explicit formulae are found for the extremal coefficients with finite or convex supports. A new algorithm for exactly simulating the Poisson storm process in continuous space is also provided. Overall, the storm process can be used as a benchmark for comparing the performances of several estimators of extremal coefficients, or for model selection.