  The effects of lunar surface roughness, on both small and large scales, on
Askaryan radio pulses generated by particle cascades beneath the lunar surface
has never been fully estimated. Surface roughness affects the chances of a
pulse escaping the lunar surface, its coherency, and the characteristic
detection geometry. It will affect the expected signal shape, the relative
utility of different frequency bands, the telescope pointing positions on the
lunar disk, and most fundamentally, the chances of detecting the known UHE
cosmic ray and any prospective UHE neutrino flux. Near-future radio-telescopes
such as FAST and the SKA promise to be able to detect the flux of cosmic rays,
and it is critical that surface roughness be treated appropriately in
simulations. of the lunar Askaryan technique. In this contribution, a facet
model for lunar surface roughness is combined with a method to propagate
coherent radio pulses through boundaries to estimate the full effects of lunar
surface roughness on neutrino-detection probabilities. The method is able to
produce pulses from parameterised particle cascades beneath the lunar surface
as would be viewed by an observer at Earth, including all polarisation and
coherency effects. Results from this calculation are presented for both
characteristic cosmic ray and neutrino cascades, and estimates of the effects
mentioned above - particularly signal shape, frequency-dependence, and
sensitivity - are presented.
