We consider plane wave time-domain scattering from a fixed target in the presence of a rough (random) surface with application to ground penetrating radar. The timedomain scattering data are computed via a two-dimensional (2-D) finite-difference time-domain (FDTD) algorithm. In addition to examining the statistics of the time-domain fields scattered from such a surface, we investigate subsurface target detection by employing a (commonly used) matched-filter detector. The results of such a detector are characterized by their receiver operating characteristic (ROC), which quantifies the probability of detection and probability of false alarm. Such ROC studies allow us to investigate fundamental assumptions in the matched-filter detector: that the target response is deterministic and the clutter signal stochastic, with the two signals treated as additive and independent. © 1998 IEEE.