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Assessment of Tikhonov-type regularization methods for solving atmospheric inverse problems

Xu, Jian and Schreier, Franz and Doicu, Adrian and Trautmann, Thomas (2016) Assessment of Tikhonov-type regularization methods for solving atmospheric inverse problems. Journal of Quantitative Spectroscopy and Radiative Transfer, 184, pp. 274-286. Elsevier. doi: 10.1016/j.jqsrt.2016.08.003. ISSN 0022-4073.

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Official URL: http://www.sciencedirect.com/science/article/pii/S002240731630317X


Inverse problems occurring in atmospheric science aim to estimate state parameters (e.g. temperature or constituent concentration) from observations. To cope with nonlinear ill-posed problems, both direct and iterative Tikhonov-type regularization methods can be used. The major challenge in the framework of direct Tikhonov regularization (TR) concerns the choice of the regularization parameter λ, while iterative regularization methods require an appropriate stopping rule and a flexible λ-sequence. In the framework of TR, a suitable value of the regularization parameter can be generally determined based on a priori, a posteriori, and error-free selection rules. In this study, five practical regularization parameter selection methods, i.e. the expected error estimation (EEE), the discrepancy principle (DP), the generalized cross-validation (GCV), the maximum likelihood estimation (MLE), and the L-curve (LC), have been assessed. As a representative of iterative methods, the iteratively regularized Gauss–Newton (IRGN) algorithm has been compared with TR. This algorithm uses a monotonically decreasing λ-sequence and DP as an a posteriori stopping criterion. Practical implementations pertaining to retrievals of vertically distributed temperature and trace gas profiles from synthetic microwave emission measurements and from real far infrared data, respectively, have been conducted. Our numerical analysis demonstrates that none of the parameter selection methods dedicated to TR appear to be perfect and each has its own advantages and disadvantages. Alternatively, IRGN is capable of producing plausible retrieval results, allowing a more efficient manner for estimating λ.

Item URL in elib:https://elib.dlr.de/105814/
Document Type:Article
Title:Assessment of Tikhonov-type regularization methods for solving atmospheric inverse problems
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Xu, Jianjian.xu (at) dlr.deUNSPECIFIED
Schreier, FranzFranz.Schreier (at) dlr.deUNSPECIFIED
Doicu, AdrianAdrian.Doicu (at) dlr.deUNSPECIFIED
Trautmann, ThomasThomas.Trautmann (at) dlr.deUNSPECIFIED
Journal or Publication Title:Journal of Quantitative Spectroscopy and Radiative Transfer
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
DOI :10.1016/j.jqsrt.2016.08.003
Page Range:pp. 274-286
EditorsEmailEditor's ORCID iD
Bernath, PeterOld Dominion University, Norfolk, Virginia, USAUNSPECIFIED
Mishchenko, Michael I.NASA-Goddard Institute for Space Studies, New York, New York, USAUNSPECIFIED
Mengüç, M. PinarÖzyeğin University, Istanbul, TurkeyUNSPECIFIED
Keywords:Atmospheric inverse problems; Direct and iterative Tikhonov-type regularization; Regularization parameter selection methods
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Earth Observation
DLR - Research area:Raumfahrt
DLR - Program:R EO - Earth Observation
DLR - Research theme (Project):R - Vorhaben Spektrometrische Verfahren und Konzepte der Fernerkundung (old), R - Atmospheric and climate research
Location: Oberpfaffenhofen
Institutes and Institutions:Remote Sensing Technology Institute > Atmospheric Processors
Deposited By: Xu, Dr.-Ing. Jian
Deposited On:23 Aug 2016 13:47
Last Modified:23 Jul 2022 13:44

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