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This research is a part of the work devoted on the application of analytical Discrete Ordinate (ADO) method to the polarized monochromatic radiative transfer equation undergoing anisotropic scattering with source function matrix in a finite coupled Atmosphere -Ocean media having flat interface boundary conditions involving specular reflection and transmission matrix. Discontinuities in the derivatives of the Stokes vector with respect to the cosine of the polar angle at smooth interface between the two media with different refractive indices (air and water) is tackled by using a suitable quadrature scheme devised earlier. Atmosphere and ocean are assumed to be homogeneous. No stratification is adopted in the two media. Exact expression for the emergent radiation intensity vector from the top of the atmosphere is derived. Exact expressions for the emergent polarized radiation intensity vector from the air-water interface as well as from any point of the two medium in any direction can also be derived in terms of eigenvectors and eigenvalues. Keywords: Polarized Radiative transfer, Eigenvectors, Eigenvalues, Green function, specular.

iosr journal of mathematics

Exact Analytical Expression for Outgoing Intensity from the Top of the Atmosphere in a Flat Homogeneous Atmosphere–Ocean System using Analytical Discrete Ordinate method for the Solution of Polarized Radiation Transfer Equation.