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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 ISBN 0022-4073 ISSN 0022-4073

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

Abstract

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
Authors:
AuthorsInstitution or Email of AuthorsAuthors 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
Date:2016
Journal or Publication Title:Journal of Quantitative Spectroscopy and Radiative Transfer
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:184
DOI :10.1016/j.jqsrt.2016.08.003
Page Range:pp. 274-286
Editors:
EditorsEmail
Bernath, PeterOld Dominion University, Norfolk, Virginia, USA
Mishchenko, Michael I.NASA-Goddard Institute for Space Studies, New York, New York, USA
Mengüç, M. PinarÖzyeğin University, Istanbul, Turkey
Publisher:Elsevier
ISSN:0022-4073
ISBN:0022-4073
Status:Published
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 - Erdbeobachtung
DLR - Research theme (Project):R - Vorhaben Spektrometrische Verfahren und Konzepte der Fernerkundung (old), R - Vorhaben Atmosphären- und Klimaforschung
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:06 Sep 2019 15:28

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