We study coherent wave scattering through waveguides with a step-like surface
disorder and find distinct enhancements in the reflection coefficients at
well-defined resonance values. Based on detailed numerical and analytical
calculations, we can unambiguously identify the origin of these reflection
resonances to be higher-order correlations in the surface disorder profile
which are typically neglected in similar studies of the same system. A
remarkable feature of this new effect is that it relies on the longitudinal
correlations in the step profile, although individual step heights are random
and thus completely uncorrelated. The corresponding resonances are very
pronounced and robust with respect to ensemble averaging, and lead to an
enhancement of wave reflection by more than one order of magnitude
