2017/12/01 by Kiyoshi Kawabata · 2 citations
Earth and Planetary Sciences · Engineering · Environmental Science · Physics and Astronomy · #Anisotropy #Atmospheric aerosols and clouds #Isotropy #Iterative method #Legendre polynomials #Meteorological Phenomena and Simulations #Phase (matter) #Phase space #Plane (geometry) #Radiative Heat Transfer Studies #Rayleigh scattering #Scattering #astro-ph.IM
paper · pdf · doi:10.1007/s10509-017-3218-5
published as Astrophysics and Space Science January 2018, 363:1 · 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: https://doi.org/10.1007/s10509-017-3218-5. (First Online: 01 December 2017)
openalex publication_date 2017/12/01 · arxiv created 2017/12/12 · arxiv updated 2017/12/14 · openalex created_date 2017/12/22 · openalex updated_date 2026/08/05
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 \varpi0, and 36 values of an angular variable μ(=cos θ), with θ 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.