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

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.