Since many environmental processes such as heat waves or precipitation are
spatial in extent, it is likely that a single extreme event affects several
locations and the areal modeling of extremes is therefore essential if the
spatial dependence of extremes has to be appropriately taken into account.
Although some progress has been made to develop a geostatistic of extremes,
conditional simulation of max-stable processes is still in its early stage.
This paper proposes a framework to get conditional simulations of Brown-Resnick
processes. Although closed forms for the regular conditional distribution of
Brown-Resnick processes were recently found, sampling from this conditional
distribution is a considerable challenge as it leads quickly to a combinatorial
explosion. To bypass this computational burden, a Markov chain Monte-Carlo
algorithm is presented. We test the method on simulated data and give an
application to extreme rainfall around Zurich. Results show that the proposed
framework provides accurate conditional simulations of Brown-Resnick processes
and can handle real-sized problems.