  H\"usler-Reiss vectors and Brown-Resnick fields are popular models in
multivariate and spatial extreme-value theory, respectively, and are widely
used in applications. We provide analytical formulas for the correlation
between powers of the components of the bivariate H\"usler-Reiss vector, extend
these to the case of the Brown-Resnick field, and thoroughly study the
properties of the resulting dependence measure. The use of correlation is
justified by spatial risk theory, while power transforms are insightful when
taking correlation as dependence measure, and are moreover very suited damage
functions for weather events such as wind extremes or floods. This makes our
theoretical results worthwhile for, e.g., actuarial applications. We finally
perform a case study involving insured losses from extreme wind speeds in
Germany, and obtain valuable conclusions for the insurance industry.
