Theory of Radiative Transfer in Inhomogeneous Atmospheres.IV. Application of the Matrix Perturbation Method to a Semi-Infinite Atmosphere

Abstract

view Abstract Citations (4) References (4) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Theory of Radiative Transfer in Inhomogeneous Atmospheres.IV. Application of the Matrix Perturbation Method to a Semi-Infinite Atmosphere Abhyankar, K. D. ; Fymat, A. L. Abstract In order to describe the transfer of partially polarized radiation tbrough an inhomogeneous semi- infinite atmosphere, a matrix N-function has been introduced by considering the limit of the K-function as the optical thickness of a finite atmosphere becomes infinite. The nonlinear singular integral equation satisfied by N is given; it generalizes the scalar H-equation of Sobolev for the fields in which the state of polarization must be taken into account. This equation is solved by our perturbation method in the form of a Neumann series. The region of convergence of this series solution is delimited for the Rayleigh law of scattering. An iteration scheme for computing the solution is described, and, as an illustration, sample computations are presented in which the N-functions for homogeneous Rayleigh nonconservative atmospheres with albedo for single scattering = 0.25 and 0.75 are derived from the N0-function for a reference homogeneous atmosphere with s = 0.5. Comparison of these linear solutions with the exact solutions given earlier demonstrates the effectiveness of the matrix perturbation method; for example, the relative error in the reflected intensity is less than 0.2 percent for = 0.25 and less than 1.9 percent for = 0.75. Publication: The Astrophysical Journal Pub Date: March 1970 DOI: 10.1086/150379 Bibcode: 1970ApJ...159.1019A full text sources ADS |