A new multi-layer discrete ordinate approach to radiative transfer in vertically inhomogeneous atmospheres

Mathematics

Scientific paper

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Atmospheric Physics, Discrete Functions, Radiative Transfer, Anisotropic Media, Approximation, Inhomogeneity, Matrices (Mathematics), Program Verification (Computers)

Scientific paper

A recently developed matrix formulation of the discrete ordinate method is extended for application to an inhomogeneous atmosphere. The solution yields fluxes, as well as the complete azimuthal dependence of the intensity at any level in the atmosphere. The numerical aspects of the solution are discussed and numerical verification is provided by comparing computed results with those obtained by other methods. In particular, it is shown that a simple scaling scheme, which removes the positive exponentials in the coefficient matrix when solving for the constants of integration, provides unconditionally stable solutions for arbitrary optical thicknesses. An assessment of the accuracy to be expected is also provided, and it is shown that low-order discrete ordinate approximations yield very accurate flux values.

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