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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
Abstract
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/ | |||||||||||||||
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| Document Type: | Article | |||||||||||||||
| Title: | A review of the matrix-exponential formalism in radiative transfer | |||||||||||||||
| Authors: |
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| Date: | 2017 | |||||||||||||||
| 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: | 196 | |||||||||||||||
| DOI : | 10.1016/j.jqsrt.2017.02.015 | |||||||||||||||
| Page Range: | pp. 17-45 | |||||||||||||||
| Editors: |
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| Publisher: | Elsevier | |||||||||||||||
| ISSN: | 0022-4073 | |||||||||||||||
| Status: | Published | |||||||||||||||
| 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 - Erdbeobachtung | |||||||||||||||
| 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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- A review of the matrix-exponential formalism in radiative transfer. (deposited 12 Apr 2017 12:06) [Currently Displayed]
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