Computation of Synthetic Spectra for a Semi-Infinite Atmosphere

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Abstract
The computation of absorption spectra in a model planetary atmosphere is shown to be feasible using the Neumann series (successive orders of scattering) solution to the equation of radiative transfer for semi-infinite atmospheres. The method may be applied for arbitrary single scattering albedo and phase function. For orders of scattering n ≫ 1, the terms of the Neumann series assume an asymptotic form. With the aid of this asymptotic form, simple expressions are given for the reflection function of the layer and the mean number of scatterings in the atmosphere. Computations illustrating the approach to the asymptotic form, the shape of a Lorentz-broadened absorption line, the mean number of scatterings in an atmosphere, and the equivalent width of a Lorentz line are presented graphically for both isotropic scattering and phase functions typical of clouds and hazes. Abstract The computation of absorption spectra in a model planetary atmosphere is shown to be feasible using the Neumann series (successive orders of scattering) solution to the equation of radiative transfer for semi-infinite atmospheres. The method may be applied for arbitrary single scattering albedo and phase function. For orders of scattering n ≫ 1, the terms of the Neumann series assume an asymptotic form. With the aid of this asymptotic form, simple expressions are given for the reflection function of the layer and the mean number of scatterings in the atmosphere. Computations illustrating the approach to the asymptotic form, the shape of a Lorentz-broadened absorption line, the mean number of scatterings in an atmosphere, and the equivalent width of a Lorentz line are presented graphically for both isotropic scattering and phase functions typical of clouds and hazes.

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