Two-stream, second-order, probabilistic radiative transfer

Mathematics – Probability

Scientific paper

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Diffuse Radiation, Flow Equations, Probability Theory, Radiative Transfer, Stellar Atmospheres, Boundary Conditions, Energy Conservation, Radiation Distribution

Scientific paper

An extension of second-order probabilistic radiative transfer that treats the diffuse radiation field as composed of two oppositely directed streams is presented. These new equations are shown to have wider applicability and greater accuracy than current published two-stream equations and to reduce to the widely used one-stream second-order probabilistic equation. The present two-stream equations also suggest natural and numerically efficient boundary equations that compare favorably in accuracy to the energy conservation boundary condition for one-stream transfer. The two-stream solutions are shown to be within 20 percent of the exact solution throughout the atmosphere, and to be significantly better than the first-order solutions. A derivation of an expression for the radiative force accurate to first-order in the gradient of the source function is also presented.

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