Equilibrium Temperatures and Directional Emissivity of Sunlit Airless Surfaces With Applications to the Moon. Issue 6 (9th June 2020) - Rubanenko, L.
Abstract: Solar irradiance dominates the heat flux incident on airless planetary bodies. In thermal equilibrium, surface roughness affects the temperature distribution by changing the incidence angle local to each slope. In order to simulate temperatures and thermal emissions at different phase angles, existing thermophysical models usually employ computationally expensive techniques such as ray tracing. Here we derive the equilibrium surface temperature distribution of sunlit Gaussian rough surfaces, providing an exact solution for the Sun at the zenith and an approximate solution for the general case. We find that although the slope distribution of realistic airless surfaces is often non‐Gaussian, their temperature distribution is well modeled assuming a Gaussian slope distribution. We additionally present closed‐form expressions that describe the radiation emitted from rough surfaces at different emissions angles and employ them to radiometrically estimate the roughness of the lunar surface using measurements obtained by Lunar Reconnaissance Orbiter (LRO) Diviner. Our model may also be applied to studying the roughness of resolved and unresolved surfaces on other airless planetary bodies. Plain Language Summary: The thermal radiation emitted from the lunar surface is affected by roughness on scales much smaller than the scale of topographic features currently resolved by remote sensing instruments. Here we derive equations to predict the temperature distribution of airless surfaces and the infrared brightness they emit at different observation angles. Using our model, we probe the surface roughness of the Moon on centimeter lateral scales, revealing notable differences between the lunar maria and highlands regions. Our model may also be applied to study the roughness of other unresolved planetary bodies, such as asteroids. Key Points: We derive equations to calculate the equilibrium temperature distribution of illuminated rough Gaussian surfaces Using our model, we estimate the surface roughness of the Moon at ∼1 cm lateral scales Our model may be used to measure small‐scale surface roughness on airless planetary bodies, such as small moons and asteroids