Radiative transfer in the atmosphere-ocean system: the finite-element method

The finite-element method has been applied to solving the radiative-transfe r 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 bidirectional refle ctivity, and refraction and reflection at the interface between the media w ith different refractive properties. The incident radiation is a parallel f lux on the top boundary that is characteristic of illumination of the atmos phere by the Sun in the UV, visible, and near-IR regions of the electromagn etic spectrum. The necessary changes, compared with the case of a uniformly refracting layered medium, are described. An energy-conservation test has been performed on the model. The algorithm has also been validated through comparison with an equivalent backward Monte Carlo code and with data taken from the literature, and optimal agreement was shown. The results show tha t the model allows energy conservation independently of the adopted phase f unction, 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 docu mented and is available for applications. (C) 1999 Optical Society of Ameri ca.