Heng, Kevin; Malik, Matej; Kitzmann, Daniel (2018). Analytical Models of Exoplanetary Atmospheres. VI. Full Solutions for Improved Two-stream Radiative Transfer, Including Direct Stellar Beam. Astrophysical journal - supplement series, 237(2), p. 29. Institute of Physics Publishing IOP 10.3847/1538-4365/aad199
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Two-stream radiative transfer is used frequently in Earth, planetary, and exoplanetary sciences due to its simplicity and ease of implementation. However, a longstanding limitation of the two-stream approximation is its inaccuracy in the presence of medium-sized or large aerosols. This limitation was lifted by the discovery of the improved two-stream technique, where the accuracy of the scattering greenhouse effect is matched to that of multi-stream calculations by construction. In this study, we derive the full solutions for improved two-stream radiative transfer, following its introduction by Heng & Kitzmann, and include contributions from the direct stellar beam. The generalization of the original two-stream flux solutions comes in the form of a correction factor, traditionally set to unity, which is the ratio of a pair of first Eddington coefficients. We derive an analytical expression for this correction factor and also provide a simple fitting function for its ease of use by other workers. We prove that the direct stellar beam is associated with a second Eddington coefficient that is on the order of unity. Setting this second Eddington coefficient to 2/3 and 1/√3 reproduces the Eddington and quadrature closures, respectively, associated with the direct beam. We use our improved two-stream solutions for the fluxes to derive two-stream source function solutions for both the intensity and fluxes.
Item Type: |
Journal Article (Original Article) |
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Division/Institute: |
10 Strategic Research Centers > Center for Space and Habitability (CSH) 08 Faculty of Science > Physics Institute > Space Research and Planetary Sciences 08 Faculty of Science > Physics Institute 08 Faculty of Science > Physics Institute > NCCR PlanetS |
UniBE Contributor: |
Kitzmann, Daniel |
Subjects: |
500 Science > 520 Astronomy 100 Philosophy 500 Science > 530 Physics |
ISSN: |
0067-0049 |
Publisher: |
Institute of Physics Publishing IOP |
Language: |
English |
Submitter: |
Danielle Zemp |
Date Deposited: |
03 Jun 2019 10:39 |
Last Modified: |
05 Dec 2022 15:26 |
Publisher DOI: |
10.3847/1538-4365/aad199 |
BORIS DOI: |
10.7892/boris.126823 |
URI: |
https://boris.unibe.ch/id/eprint/126823 |
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