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

ALIS: An efficient method to compute high spectral resolution polarized solar radiances using the Monte Carlo approach