  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...
