  A new characterization of random fields appearing in physical models is
presented that is based on their well-known Homogeneous Chaos expansions. We
take advantage of the adaptation capabilities of these expansions where the
core idea is to rotate the basis of the underlying Gaussian Hilbert space, in
order to achieve reduced functional representations that concentrate the
induced probability measure in a lower dimensional subspace. For a smooth
family of rotations along the domain of interest, the uncorrelated Gaussian
inputs are transformed into a Gaussian process, thus introducing a mesoscale
that captures intermediate characteristics of the quantity of interest.
