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The finite element method has been applied to solve the radiative transfer equation in a layered medium with a change in the refractive index, such as the atmosphere-ocean system. The physical processes that are included in the algorithm are multiple scattering, bottom boundary bi-directional reflectivity refraction and reflection at the interface between the medias with different refractive properties. The incident radiation is a parallel flux on the top boundary that is characteristic for illumination of the atmosphere by the sun in the UV, vizible and near-infrared regions of the electromagnetic spectrum. The necessary changes, as compared with the case of a uniformly layered medium, are described. An energy conservation test has been performed on the model. The algorithm has been also validated through the comparison with an equivalent backward Monte Carlo code and with data taken from literature, showing optimal agreement. The results show that the model allows energy conservation independently of the adopted phase function, the number of grid points and the relative refractive index. The radiative-transfer model can be applied to any other layered system with a change in the refractive index. The FORTRAN code for this algorithm is documented and is available for applications.

Additional information

Authors: BULGARELLI B, SAI Ispra (IT);KISSELEV B V, Saint Petersburg Institute (RU);ROBERTI L, Politecnico di Torino, Torino (IT)
Bibliographic Reference: Article: Applied Optics, 1998, 1-36
Record Number: 199910365 / Last updated on: 1999-03-12
Original language: en
Available languages: en
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