Articles | Volume 24, issue 8
https://doi.org/10.5194/acp-24-5093-2024
https://doi.org/10.5194/acp-24-5093-2024
Research article
 | 
30 Apr 2024
Research article |  | 30 Apr 2024

Analytical approximation of the definite Chapman integral for arbitrary zenith angles

Dongxiao Yue

Related subject area

Subject: Gases | Research Activity: Atmospheric Modelling and Data Analysis | Altitude Range: Stratosphere | Science Focus: Physics (physical properties and processes)
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Cited articles

Bauer, S. J. and Lammer, H.: Radiation and Particle Environments from Stellar and Cosmic Sources, in: Planetary Aeronomy, Phys. Earth Space Env., Springer, Berlin, Heidelberg, 3–30, https://doi.org/10.1007/978-3-662-09362-7_2, 2004. a
Brasseur, G. and Solomon, S.: Aeronomy of the Middle Atmosphere, Atmospheric and Oceanographic Sciences Library, Vol. 32, Springer, Boulder, Colorado, https://doi.org/10.1007/1-4020-3824-0_4, 2005. a
Chapman, S.: The absorption and dissociative or ionizing effect of monochromatic radiation in an atmosphere on a rotating earth part II. Grazing incidence, Proc. Phys. Soc., 43, 483–501, https://doi.org/10.1088/0959-5309/43/5/302, 1931. a, b
Chapman, S.: Note on the grazing-incidence integral ch(x,χ) for monochromatic absorption in an exponential atmosphere, Proc. Phys. Soc. B, 66, 710–712, https://doi.org/10.1088/0370-1301/66/8/411, 1953. a
Engel, W.: GPU Pro 360 Guide to Rendering, 1st Edn., A. K. Peters, Ltd., USA, ISBN 0815365519, 2018. a
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The stunning colors of the sky and clouds result from light scattering in the atmosphere, whose density changes with height. Previously, calculating these colors involves costly, sometimes inaccurate methods. This paper presents a silver bullet: a single elegant formula that simplifies these complex calculations. What is the result? We have faster, more precise predictions of atmospheric colors, from Earth's blue skies and red sunsets to Venus's golden hues.
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