Linearization of radiative transfer in spherical geometry: an application of the forward-adjoint perturbation theory

The remote sensing of atmospheric constituents with limb-viewing satellite instruments or with nadir viewing instruments at large solar zenith angles requires a forward model that simulates the backscattered radiance taking the spherical shape of the Earth atmosphere into account. In addition, many retrieval schemes are based on a linearization of such a forward model. Whenever it is important to take multiple scattering into account (e.g. due to light scattering air molecules, aerosols and clouds) the linearization of the measurement simulation with respect to the parameters to be retrieved is not trivial. Here, the forward-adjoint perturbation theory provides a general method to linearize radiative transfer. In the first part of this review chapter we provide the theoretical background of the linearization approach for a radiative transfer problem in a spherical model atmosphere which is illuminated by a collimated solar beam. Using an operator formulation of radiative transfer allows one to express the linearization approach in a universally valid notation. Depending on the particular formulation of the radiative transfer problem the perturbation of internal sources has to be taken into account in addition. The needed adjoint calculation corresponds to a so-called searchlight problem that requires the use of three-dimensional radiative transfer simulations in general. Subsequently we show how symmetries of the forward radiation field and a proper choice of the radiation sources can be used to simplify the needed adjoint calculations substantially.