Directional Characteristics of Thermal-Infrared Beaming from   Atmosphereless Planetary Surfaces - A New Thermophysical Model
  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. 
Ben Rozitis, Simon F. Green
astro-ph.EP