Abstract
Novel mathematical procedures for the efficient calculation of weighting functions inside finite differencing radiative transfer models are presented. Linearization of the radiative transfer equation allows to compute the weighting functions directly without the use of numerical perturbation schemes. The methods developed have been implemented in the finite-differencing model GOMETRAN. Validation of the quasi-analytical computations of the weighting functions has been achieved by comparison with results using numerical perturbation methods from finite-differencing and doubling-adding. An interpretation of the weighting functions is presented and outlines their relationship with air mass factors. Finally, the weighting function technique is applied to the retrieval of ozone and temperature vertical profiles from satellite measurements.
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