A Theoretical Study of a Vector Radiative Transfer Equation for Atmosphere and Ocean Medium

Abstract

Radiative transfer plays a fundamental role in several disciplines of sciences and engineering. For certain applications in turbid media, such as atmosphere or ocean, due to the polarization effect of light, the vector radiative transfer equation (VRTE) rather than the scalar radiative transfer equation must be adopted. Although there have been numerous discussions on the application and numerical simulations of the VRTE, a rigorous theoretical analysis of the equation is still needed. This letter provides a well-posedness analysis of the VRTE. Under some assumption on the combined size of the single-scattering albedo and the scattering phase matrix of the medium, existence and uniqueness of a solution are proved for the VRTE supplemented with a boundary condition. The solution is shown to be Lipschitz continuous dependent on the source function and the boundary condition function.