Towards a comprehensive model of Earth's disk-integrated Stokes vector

Abstract

A significant body of work on simulating the remote appearance of Earth-like exoplanets has been done over the last decade. The research is driven by the prospect of characterizing habitable planets beyond the Solar System in the near future. In this work, I present a method to produce the disk-integrated signature of planets that are described in their three-dimensional complexity, i.e. with both horizontal and vertical variations in the optical properties of their envelopes. The approach is based on pre-conditioned backward Monte Carlo integration of the vector Radiative Transport Equation and yields the full Stokes vector for outgoing reflected radiation. The method is demonstrated through selected examples inspired by published work at wavelengths from the visible to the near infrared and terrestrial prescriptions of both cloud and surface albedo maps. A clear advantage of this approach is that its computational cost does not appear to be significantly affected by non-uniformities in the planet optical properties. Earth's simulated appearance is strongly dependent on wavelength; both brightness and polarisation undergo diurnal variations arising from changes in the planet cover, but polarisation yields a better insight into variations with phase angle. There is partial cancellation of the polarised signal from the northern and southern hemispheres so that the outgoing polarisation vector lies preferentially either in the plane parallel or perpendicular to the planet scattering plane, also for non-uniform cloud and albedo properties and various levels of absorption within the atmosphere. The evaluation of circular polarisation is challenging; a number of one-photon experiments of 1E9 or more is needed to resolve hemispherically-integrated degrees of circular polarisation of a few times 1E-5. Last, I introduce brightness curves...