Application and evaluation of the small-angle approximation on forward radiative transfer model

• Published in: Journal of quantitative spectroscopy & radiative transfer 2020-05, Vol.246, p.106937, Article 106937
• Main Authors: Sun, Bingqiang, Ding, Shouguo
• Format: Article
• Language: English
• ISSN: 0022-4073; 1879-1352
• DOI: 10.1016/j.jqsrt.2020.106937

•The correction vector radiative transfer equation is explicitly given to evaluate the cross terms associated with decomposition and the second-order approximated solution is obtained. The equation can be used in any radiative transfer method.•The radiative transfer equation associated with particle scattering is solved by combining the small-angle approximation (SAA) and the adding-doubling method (ADM).•The line-by-line method (LBLRTM) is used to compute the molecular optical depth and corresponding Rayleigh extinction. The LBLRTM+SAA+ADM are combined together as the forward radiative transfer model.•The combined model is verified using the line-by-line method (LBLRTM) and the straightforward adding-doubling method (SAD). Six standard atmospheric models are used as the atmospheric profiles and great agreement is reached between the LBLRTM+SAA+ADM and the LBLRTM+SAD. The small-angle approximation is used in solving the radiative transfer equation when the single-scattering phase function has a strong forward peak. The original vector radiative transfer equation is decomposed into three equations: the forward, the regular, and the correction ones. The forward equation can be efficiently solved using the small-angle approximation. The solution of the regular equation is given by the adding-doubling method in this study. The correction equation including cross terms between the forward and the regular quantities is given and analyzed. The combined model associated with the forward and regular equations is further verified in the forward radiative transfer model, where the molecular absorptions with respect to the standard atmospheric profiles are taken into consideration using the line-by-line method. Great agreements are given between the combined model and the model using the straight adding-doubling method.