Natraj, Vijay and Li, King-Fai and Yung, Yuk L. (2009) Rayleigh Scattering in Planetary Atmospheres: Corrected Tables Through Accurate Computation of X and Y Functions. Astrophysical Journal, 691 (2). pp. 1909-1920. ISSN 0004-637X http://resolver.caltech.edu/CaltechAUTHORS:20090827-113208371
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Tables that have been used as a reference for nearly 50 years for the intensity and polarization of reflected and transmitted light in Rayleigh scattering atmospheres have been found to be inaccurate, even to four decimal places. We convert the integral equations describing the X and Y functions into a pair of coupled integro-differential equations that can be efficiently solved numerically. Special care has been taken in evaluating Cauchy principal value integrals and their derivatives that appear in the solution of the Rayleigh scattering problem. The new approach gives results accurate to eight decimal places for the entire range of tabulation (optical thicknesses 0.02-1.0, surface reflectances 0-0.8, solar and viewing zenith angles 0°-88.85°, and relative azimuth angles 0°-180°), including the most difficult case of direct transmission in the direction of the sun. Revised tables have been created and stored electronically for easy reference by the planetary science and astrophysics community.
|Additional Information:||© 2009 The American Astronomical Society. Received 2008 July 7; accepted 2008 October 16; published 2009 February 12. The research described in this paper was performed for the Orbiting Carbon Observatory Project at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. This work was supported in part by NASA grant NAG1–1806. The authors thank Professor Tom Hou for helpful discussions on techniques to solve singular integral equations, Run-Lie Shia for the crucial input on the alternative integro-differential form of the equations for the X and Y functions, and the reviewer for insightful comments.|
|Subject Keywords:||polarization; radiative transfer|
|Official Citation:||Rayleigh Scattering in Planetary Atmospheres: Corrected Tables Through Accurate Computation of X and Y Functions Vijay Natraj, King-Fai Li, and Yuk L. Yung 2009 ApJ 691 1909-1920 doi: 10.1088/0004-637X/691/2/1909.|
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|Deposited By:||Tony Diaz|
|Deposited On:||28 Aug 2009 16:54|
|Last Modified:||26 Dec 2012 11:15|
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