Rayleigh-scattering calculations for the terrestrial atmosphere

TLDR

The study computes wavelength‑dependent Rayleigh‑scattering cross sections and volume‑scattering coefficients for standard air, derives analytic formulas, and uses them to calculate optical depths for the 1962 U.S. Standard Atmosphere and five supplementary models.

Abstract

Rayleigh-scattering cross sections and volume-scattering coefficients are computed for standard air; they incorporate the variation of the depolarization factor with wavelength. Rayleigh optical depths are then calculated for the 1962 U.S. Standard Atmosphere and for five supplementary models. Analytic formulas are derived for each of the parameters listed. The new optical depths can be 1.3% lower to 3% higher at midvisible wavelengths and up to 10% higher in the UV region compared with previous calculations, in which a constant or incorrect depolarization factor was used. The dispersion of the depolarization factor is also shown to affect the Rayleigh phase function slightly, by approximately 1% in the forward, backscattered, and 90° scattering-angle directions.