On limb radiance calculations and convergence of relaxation type retrieval algorithms

Several approaches to the solution of the radiative transfer equation assume either Curtis-Godson average or linear change of the source function across grid segments. When such solutions are used for calculating limb radiances, the peak radiance response to the source function perturbation at tangent point i is displaced down to the tangent point i+1. This effect is explained through a geometric argument. Temperature profile retrievals performed by applying the ratio of signals at level i+1 for correcting temperature at level i demonstrate dramatic convergence acceleration of the iterative relaxation scheme.