ACPD Atmospheric Chemistry and Physics Discussions ACPD 1680-7375 Copernicus GmbH Göttingen, Germany 10.5194/acpd-9-25663-2009 Technical Note: Variance-covariance matrix and averaging kernels for the Levenberg-Marquardt solution of the retrieval of atmospheric vertical profiles Ceccherini S. 1 Ridolfi M. 2 Istituto di Fisica Applicata "Nello Carrara" (IFAC) del Consiglio Nazionale delle Ricerche (CNR), Firenze, Italy Dipartimento di Fisica, Università di Bologna, Bologna, Italy 30 11 2009 9 6 25663 25685 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.atmos-chem-phys-discuss.net/9/25663/2009/acpd-9-25663-2009.html The full text article is available as a PDF file from http://www.atmos-chem-phys-discuss.net/9/25663/2009/acpd-9-25663-2009.pdf

The variance-covariance matrix (VCM) and the averaging kernel matrix (AKM) are widely used tools to characterize atmospheric vertical profiles retrieved from remote sensing measurements. Accurate estimation of these quantities is essential for both the evaluation of the quality of the retrieved profiles and for the correct use of the profiles themselves in subsequent applications such as data comparison, data assimilation and data fusion. We propose a new method to estimate the VCM and AKM of vertical profiles retrieved using the Levenberg-Marquardt iterative technique. We apply the new method to the inversion of simulated limb emission measurements. Then we compare the obtained VCM and AKM with those resulting from other methods already published in the literature and with accurate estimates derived using statistical and numerical estimators. The proposed method accounts for all the iterations done in the inversion and provides the most accurate VCM and AKM. The method can be easily implemented in any Levenberg-Marquardt iterative retrieval scheme, either constrained or unconstrained, without significant computational overhead.

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