http://arxiv.org/abs/1712.04790
We have established an iterative scheme to calculate with 15-digit accuracy the numerical values of Ambartsumian-Chandrasekhar’s H-functions for anisotropic scattering characterized by the four-term phase function: the method incorporates some advantageous features of the iterative procedure of Kawabata (2015) and the double-exponential integration formula~(DE-formula) of Takahashi and Mori (1974), which proved highly effective in Kawabata (2016). Actual calculations of the H-functions have been carried out employing 27 selected cases of the phase function, 56 values of the single scattering albedo $\varpi_0$, and 36 values of an angular variable $\mu(=\cos \theta)$, with $\theta$ being the zenith angle specifying the direction of incidence and/or emergence of radiation.
Partial results obtained for conservative isotropic scattering, Rayleigh scattering, and anisotropic scattering due to a full four-term phase function are presented. As a sample application of the isotropic scattering H-function, an attempt is made in Appendix to simulate by iteratively solving the Ambartsumian equation the values of the plane and spherical albedos of a semi-infinite, homogeneous atmosphere calculated by Rogovtsov and Borovik (2016), who employed their analytical representations for these quantities and the single-term and two-term Henyey-Greenstein phase functions of appreciably high degrees of anisotropy, to find that our results are in satisfactory agreement with theirs.
K. Kawabata
Thu, 14 Dec 17
13/74
Comments: 23 pages including 10 main text pages, 3 pages for Appendix A, 1 page for table and figure captions, 7 tables, and 2 figures. This is a pre-print of an article published in Astrophysics and Space Science, January 2018, 363:1. The final authenticated version is available on line at: this https URL (First Online: 01 December 2017)