We have applied the discrete-ordinate method to solve the radiative-transfer problem pertaining to a system consisting of two strata with different indices of refraction. The refraction and reflection at the interface are taken into account. The relevant changes (as compared with the standard problem with a constant index of refraction throughout the medium) in formulation and solution of the radiative-transfer equation, including the proper application of interface and boundary conditions, are described. Appropriate quadrature points (streams) and weights are chosen for the interface-continuity relations. Examples of radiative transfer in the coupled atmosphere–ocean system are provided. To take into account the region of total reflection in the ocean, additional angular quadrature points are required, compared with those used in the atmosphere and in the refractive region of the ocean that communicates directly with the atmosphere. To verify the model we have tested for energy conservation. We also discuss the effect of the number of streams assigned to the refractive region and the total reflecting region on the convergence. Our results show that the change in the index of refraction between the two strata significantly affects the radiation field. The radiative-transfer model we present is designed for application to the atmosphere–ocean system, but it can be applied to other systems that need to consider the change in the index of refraction between two strata.
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