Surface roughness and three-dimensional heat conduction in thermophysical models

• The first thermophysical model of rough terrain taking 3D heat conduction into account.
• The first investigation of surface temperatures on rough terrains with topography smaller than the thermal skin depth.
• Comparison of surface temperatures between rough and smooth surfaces for various albedo and topography types.

A thermophysical model is presented that considers surface roughness, cast shadows, multiple or single scattering of radiation, visual and thermal infrared self heating, as well as heat conduction in one or three dimensions. The code is suitable for calculating infrared spectral energy distributions for spatially resolved or unresolved minor Solar System bodies without significant atmospheres or sublimation, such as the Moon, Mercury, asteroids, irregular satellites or inactive regions on comet nuclei. It is here used to explore the effects of surface roughness on spatial scales small enough for heat conduction to erase lateral temperature gradients. Analytically derived corrections to one-dimensional models that reproduce the results of three-dimensional modeling are presented. We find that the temperature of terrains with such small-scale roughness is identical to that of smooth surfaces for certain types of topographies and non-scattering material. However, systematic differences between smooth and rough terrains are found for scattering materials, or topographies with prominent positive relief. Contrary to common beliefs, the roughness on small spatial scales may therefore affect the thermal emission of Solar System bodies.