Adjoint perturbation method applied to two-stream radiative transfer

This paper describes a computationally efficient method for solving the plane parallel equation of radiative transfer for the two-stream fluxes based on the adjoint perturbation formulation. Analytical results for the perturbed fluxes are presented for a single layer atmosphere containing both solar and thermal sources. Simple linear and exponential corrections to the base state fluxes are explored. For the solar radiative transfer problem, the exponential form of the perturbation correction can accommodate deviations exceeding 400% in the base state optical properties while maintaining accuracy to within a few percent. For thermal radiative transfer, the linear form of perturbation relation is the more accurate, but unlike the solar problem, deviations from the base state optical properties must remain relatively small (less than 20%) if the errors in the computed fluxes are to remain within a few percent of the true fluxes. The method is applied to the calculation of broadband solar fluxes in a layer of scatterers embedded in an absorbing gas, where the absorption is modeled via the k-distribution method.