Recently, the transformed field expansion (TFE) boundary perturbation method [D. P. Nicholls and F. Reitich, J. Comput. Phys. 170, 276–298 (2001)] has been extended to random rough interfaces using the method of generalized polynomial chaos (gPC) [D. Xiu and J. Shen, Comm. in Comp. Physics 2, 54–72 (2007)] to compute statistics of the scattered field. The TFE boundary perturbation method is similar to the usual small wave height approximation approach, but starts with a coordinate transformation that avoids ill‐conditioning in the perturbation series and maps the original deterministic Helmholtz equation on a random domain to a stochastic Helmholtz equation on a deterministic domain. When dealing with large multiscale rough interfaces like the ocean surface, the number of expansion terms in the gPC representation of the field can grow large. One strategy to keep the number of random variables manageable is to pose the scattering problem in the time domain, allow for the excitation of the rough interface by an impulse, and consider only those random surface features that can be causally linked to the received field. [This work was supported by ONR through NRL.]