Efficient calculation of intensity and polarization spectra in vertically inhomogeneous scattering and absorbing atmospheres

We present a method for the efficient calculation of moderate-and high-resolution spectra of intensity and polarization in absorption bands. This linear-k method explicitly accounts for the vertical distribution of the absorption optical thickness by using a linear approximation. It can be applied to any radiative transfer model that calculates the intensity (vector) and its derivatives with respect to the absorption optical thickness in different altitude layers of the model atmosphere. For the three spectral windows of the Orbiting Carbon Observatory (OCO), the error on the modeled intensity introduced by the linear-k method is below 0.13% for the O-2-A band, below 0.06% in the weak CO2 band, and below 0.12% for the strong CO2 band, for an aerosol type dominated by coarse mode particles with an aerosol optical thickness (AOT) of 0.3 at the O-2-A band (the maximum AOT for which OCO retrievals are intended to be performed), and a typical aerosol height distribution with most aerosols located in the boundary layer. For these accuracies the computational effort is reduced by two orders of magnitude compared to line-by-line calculations. A sensitivity study with synthetic OCO measurements shows that the linear-k method introduces a small error of 0.025-0.20 ppm on the retrieved profile weighted mean CO2 mixing ratio, for a boundary layer dominated aerosol distribution, and 0.050-0.50 ppm for an elevated aerosol layer between 5 and 6 km. In most cases the error is considerably smaller than the retrieval noise.