Linearization of a pseudo-spherical vector radiative transfer model

Abstract

We present a linearization of pseudo-spherical vector radiative transfer using the forward-adjoint perturbation theory. The method, which is based on the usual forward and the adjoint formulation of radiative transfer, is extended to radiative transfer problems with internal radiation sources. This allows one to linearize vector radiative transfer in pseudo-spherical approximation. The model PS-LIRA is developed based on this approach. Here, the calculation of the direct beam as well as the integration along the line of sight are performed for a full spherical geometry. The multiply scattered radiation is calculated in a plane-parallel atmosphere. The proposed model provides the intensity vector as well as its derivatives at the top of the atmosphere for solar zenith angles (SZA) up to 90.0° and for off-nadir viewing geometries ranging from limb to limb. In its scalar reduction the developed radiative transfer model is verified with a reference model and shows an accuracy of better than 0.005% in the calculation of the first Stokes parameter. Further, the calculated derivatives are verified with a finite difference method. The comparison shows deviations of less than 0.25% in the calculation of the derivatives. PS-LIRA is then used for a retrieval of atmospheric ozone profiles at large SZA. Subsequently the effect of a pseudo-spherical atmosphere on the retrieval of ozone profiles is investigated for large SZA and large viewing zenith angles.