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A review of the matrix-exponential formalism in radiative transfer

Efremenko, Dmitry and Molina García, Víctor and Gimeno García, Sebastián and Doicu, Adrian (2017) A review of the matrix-exponential formalism in radiative transfer. Journal of Quantitative Spectroscopy and Radiative Transfer, 196, pp. 17-45. Elsevier. doi: 10.1016/j.jqsrt.2017.02.015. ISSN 0022-4073.

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Official URL: http://dx.doi.org/10.1016/j.jqsrt.2017.02.015


This paper outlines the matrix exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the matrix exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the matrix operator method, and the matrix Riccati equations method is proved rigorously by means of the matrix exponential formalism. For optically thin layers, approximate solution methods relying on the Padé and Taylor series approximations to the matrix exponential, as well as on the matrix Riccati equations, are presented. For optically thick layers, the asymptotic theory with higher-order corrections is derived, and parameterizations of the asymptotic functions and constants for a water-cloud model with a Gamma size distribution are obtained.

Item URL in elib:https://elib.dlr.de/111872/
Document Type:Article
Title:A review of the matrix-exponential formalism in radiative transfer
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Efremenko, Dmitrydmitry.efremenko (at) dlr.deUNSPECIFIED
Molina García, Víctorvictor.molinagarcia (at) dlr.deUNSPECIFIED
Doicu, Adrianadrian.doicu (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.2017.02.015
Page Range:pp. 17-45
EditorsEmailEditor's ORCID iD
Bernath, PeterOld Dominion University, Norfolk, Virginia, USAUNSPECIFIED
Mengüç, M. PinarÖzyeğin University, Istanbul, TurkeyUNSPECIFIED
Mishchenko, Michael I.NASA-Goddard Institute for Space Studies, New York, New York, USAUNSPECIFIED
Keywords:Matrix-exponential; Discrete ordinate method; Matrix operator method; Matrix Riccati equations; Asymptotic theory
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)
Location: Oberpfaffenhofen
Institutes and Institutions:Remote Sensing Technology Institute > Atmospheric Processors
Deposited By: Efremenko, Dr Dmitry
Deposited On:12 Apr 2017 12:06
Last Modified:06 Sep 2019 15:28

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