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Regularized inverse algorithms for temperature and absorbing constituent profiles from radiance spectra

Retrieving of temperature profiles from radiance data obtained by interferograms is an important problem in remote sensing of atmosphere. The great amount of data to process and the ill-conditioning of the problem demand objective procedures able to reduce the error of the retrieval. In this paper we use Generalized Singular Value Decomposition (GSVD), which is able to deal with deficient-rank smoothing functionals in order to regularize the problem and the L-Curve criterion for choosing the optimal regularization parameter and then the proper amount of smoothing. Some test problems of temperature inversion are carried out to examine the effectiveness of the methods considered; to this purpose we use some indicators based on the bias and variance of the output temperature. We show that the objective L-Curve criterion does not perform fully satisfactory in estimating the optimal regularization parameter and then in reducing output error at best. In any case GSVD plus L-Curve criterion prove effective in reducing output error (with respect to the ordinary least squares method). In particular, reduction of variance over troposphere and stratosphere is high for all tested cases; reduction of bias depends on the first-guess profile. An important role in the latter is played by the choice of deficient-rank smoothing functional.