  We consider the Gibbs-measures of continuous-valued height configurations on
the $d$-dimensional integer lattice in the presence a weakly disordered
potential. The potential is composed of Gaussians having random location and
random depth; it becomes periodic under shift of the interface perpendicular to
the base-plane for zero disorder. We prove that there exist localized
interfaces with probability one in dimensions $d\geq 3+1$, in a
`low-temperature' regime. The proof extends the method of
continuous-to-discrete single- site coarse graining that was previously applied
by the author for a double-well potential to the case of a non-compact image
space. This allows to utilize parts of the renormalization group analysis
developed for the treatment of a contour representation of a related
integer-valued SOS-model in [BoK1]. We show that, for a.e. fixed realization of
the disorder, the infinite volume Gibbs measures then have a representation as
superpositions of massive Gaussian fields with centerings that are distributed
according to the infinite volume Gibbs measures of the disordered
integer-valued SOS-model with exponentially decaying interactions.
