  An efficient method to compute accurate polarized solar radiance spectra
using the (three-dimensional) Monte Carlo model MYSTIC has been developed. Such
high resolution spectra are measured by various satellite instruments for
remote sensing of atmospheric trace gases. ALIS (Absorption Lines Importance
Sampling) allows the calculation of spectra by tracing photons at only one
wavelength: In order to take into account the spectral dependence of the
absorption coefficient a spectral absorption weight is calculated for each
photon path. At each scattering event the local estimate method is combined
with an importance sampling method to take into account the spectral dependence
of the scattering coefficient. Since each wavelength grid point is computed
based on the same set of random photon paths, the statistical error is the
almost same for all wavelengths and hence the simulated spectrum is not noisy.
The statistical error mainly results in a small relative deviation which is
independent of wavelength and can be neglected for those remote sensing
applications where differential absorption features are of interest.
  Two example applications are presented: The simulation of shortwave-infrared
polarized spectra as measured by GOSAT from which CO$_2$ is retrieved, and the
simulation of the differential optical thickness in the visible spectral range
which is derived from SCIAMACHY measurements to retrieve NO$_2$. The
computational speed of ALIS (for one- or three-dimensional atmospheres) is of
the order of or even faster than that of one-dimensional discrete ordinate
methods, in particular when polarization is considered.
