Preprints
https://doi.org/10.5194/egusphere-2023-3112
https://doi.org/10.5194/egusphere-2023-3112
15 Jan 2024
 | 15 Jan 2024

Analytical Approximation of the Definite Chapman Integral for Arbitrary Zenith Angle

Dongxiao Yue

Abstract. This study presents an analytical approximation of the definite Chapman integral, applicable to any zenith angle and finite integration limits. We also present the asymptotic expression for the definite Chapman integral, which enables an accurate and efficient implementation free of numerical overflows. The maximum relative error in our analytical solution is below 0.5 %.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.
Share

Journal article(s) based on this preprint

30 Apr 2024
Analytical approximation of the definite Chapman integral for arbitrary zenith angles
Dongxiao Yue
Atmos. Chem. Phys., 24, 5093–5097, https://doi.org/10.5194/acp-24-5093-2024,https://doi.org/10.5194/acp-24-5093-2024, 2024
Short summary
Download

The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.

Short summary
The stunning colors of the sky and clouds result from light scattering in the atmosphere, whose...
Share