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Polarized Radiative Transfer of a Cirrus Cloud Consisting of Randomly Oriented Hexagonal Ice Crystals: The 3 x 3 Approximation for Non-Spherical ParticlesThe reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.
Document ID
20170003715
Acquisition Source
Goddard Space Flight Center
Document Type
Reprint (Version printed in journal)
Authors
Stamnes, S.
(NASA Langley Research Center Hampton, VA United States)
Ou, S. C.
(California Univ. Los Angeles, CA, United States)
Lin, Z.
(Stevens Inst. of Tech. Hoboken, NJ, United States)
Takano, Y.
(California Univ. Los Angeles, CA, United States)
Tsay, S. C.
(NASA Goddard Space Flight Center Greenbelt, MD United States)
Liou, K.N.
(California Univ. Los Angeles, CA, United States)
Stamnes, K.
(Stevens Inst. of Tech. Hoboken, NJ, United States)
Date Acquired
April 20, 2017
Publication Date
July 9, 2016
Publication Information
Publication: Journal of Quantitative Spectroscopy & Radiative Transfer
Publisher: Elsevier
Volume: 193
ISSN: 0022-4073
Subject Category
Geophysics
Report/Patent Number
GSFC-E-DAA-TN41851
Distribution Limits
Public
Copyright
Other
Keywords
Polarization
Cirrus clouds

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