  Spatially isotropic max-stable processes have been used to model extreme
spatial or space-time observations. One prominent model is the Brown-Resnick
process, which has been successfully fitted to time series, spatial data and
space-time data. This paper extends the process to possibly anisotropic spatial
structures. For regular grid observations we prove strong consistency and
asymptotic normality of pairwise maximum likelihood estimates for fixed and
increasing spatial domain, when the number of observations in time tends to
infinity. We also present a statistical test for isotropy versus anisotropy. We
apply our test to precipitation data in Florida, and present some diagnostic
tools for model assessment. Finally, we present a method to predict conditional
probability fields and apply it to the data.
