Surface Phase Function Behavior and Deviation from Lambertian Across Titan's Tropics

Titan has one of the least understood surfaces in the entire Solar System, due largely to its thick haze-filled atmosphere that is opaque at many wavelengths of light. Some exceptions exist, such as eight spectral windows in the near-infrared through which light passes through the atmosphere with relatively minimal gaseous absorption, but even these clearer wavelengths are subject to the effects of haze scattering.

To combat this complexity, we turn to radiative transfer models of Titan's atmosphere that calculate the influence the atmosphere has on the received signal, allowing for surface effects to be identified. These radiative transfer models depend on accurate knowledge of Titan's atmosphere and are thus most accurate when modeling the equator’s southern spring, since this is when the Huygens probe made in situ measurements critical to capturing the properties of the atmospheric haze. Many surface characterization studies attempting to filter out the influence of the atmosphere have been performed in the past. However, the majority of them make a notable assumption: that the surface behaves as a Lambertian, uniform reflector. Assuming a Lambertian surface is a reasonable first approach, but planetary surfaces across the solar system show decidedly non-Lambertian behavior. For instance, the Moon’s surface shows strong retroreflectivity (opposition surge), and we know the mirror-smooth lakes are decidedly not Lambertian. Therefore, we expect a diversity of surface phase functions on Titan as well. In this work, we seek to demonstrate the degree to which Titan's equatorial surface terrains exhibit non-Lambertian behavior. We compare a Lambertian simulation of Titan to observations of the major equatorial terrain types.

Cassini VIMS acquired spectral mapping cubes of Titan at a variety of viewing geometries. Many non-Lambertian effects manifest most strongly at the extreme viewing angles that plane-parallel-based radiative transfer schemes cannot handle. To gain the useful information contained within observations at non-ideal viewing geometries, the spherical nature of Titan's atmosphere must be accounted for. 

We therefore use SRTC++ (Spherical Radiative Transfer in C++), a Monte Carlo radiative transfer code built to model Titan in full spherical geometry at the infrared wavelengths probed by Cassini's VIMS (Visual and Infrared Mapping Spectrometer) instrument. 

As the equatorial regions are the best characterized atmospherically, we choose to examine various terrain types and the Huygens Landing Site (HLS) across all viewing geometries with observations of sufficient quality across the entire Cassini VIMS dataset. Our results qualitatively validate the SRTC++ simulation against real data and reveal which terrains deviate from Lambertian behavior.