  We present a new rough-surface thermophysical model (Advanced Thermophysical
Model or ATPM) that describes the observed directional thermal emission from
any atmosphereless planetary surface. It explicitly incorporates partial
shadowing, scattering of sunlight, selfheating and thermal-infrared beaming
(re-radiation of absorbed sunlight back towards the Sun as a result of surface
roughness). The model is verified by accurately reproducing ground-based
directional thermal emission measurements of the lunar surface using surface
properties that are consistent with the findings of the Apollo missions and
roughness characterised by an RMS slope of ~32 degrees. By considering the wide
range of potential asteroid surface properties, the model implies a beaming
effect that cannot be described by a simple parameter or function. It is highly
dependent on the illumination and viewing angles as well as surface thermal
properties and is predominantly caused by macroscopic rather than microscopic
roughness. Roughness alters the effective Bond albedo and thermal inertia of
the surface as well as moving the mean emission away from the surface normal.
For accurate determination of surface properties from thermal-infrared
observations of unresolved bodies or resolved surface elements, roughness must
be explicitly modelled, preferably aided with thermal measurements at different
emission angles and wavelengths.
