Modeling the Lunar Thermal Emission Phase Function With the Diviner Lunar Radiometer

The lunar thermal emission phase function (EPF) describes the anisotropic variation in observed infrared emission and brightness temperature with illumination and viewing geometry. The EPF is caused by small‐scale surface roughness below the resolution of current orbital data sets. Accounting for the EPF is critical for interpreting off‐nadir remote sensing data and for modeling the effect of topographic emission on surface temperatures, especially at high latitudes and polar regions where illumination conditions are more extreme. We develop a semi‐analytical model that uses small‐scale bowl‐shaped craters to simulate daytime surface temperature distributions and directional emission. Our model is validated by the novel Diviner EPF data set, which covers a wider range of targets, illumination and viewing geometries than previous lunar thermal data sets, enabling this model to predict the EPF more accurately than previous studies. Since the EPF is caused by sub‐pixel surface roughness, the model can be used to derive root‐mean‐square (RMS) slopes for the lunar surface at thermally relevant spatial scales. Using Diviner EPF data from typical highlands and mare targets, adirectional RMS slopes were derived as ∼32° for highlands and ∼31° for mares. These are consistent with previous studies and correspond to millimeter spatial scales when compared to a multi‐scale RMS slope data set. This implies that the level of roughness is generally similar across the lunar surface at thermally relevant scales. This EPF model provides a critical correction for high‐resolution 3D thermophysical models, which is essential for accurate prediction of surface temperatures in grazing illumination and volatile stability at the poles.