Numerical and analytical study of high-resolution limb spectral radiance from nonequilibrium atmospheres

Abstract Emission line shapes are calculated numerically for isolated optically thick infrared lines in the earthlimb as a function of tangent height using a general nonlocal thermodynamic equilibrium (non-LTE), upper-atmospheric line-by-line radiation transport code. It is shown that the exact integral form of the transport equation can be written in a form that is easily amenable to analytical approximation of high accuracy. In this form, the limb spectral radiance Iv appears as a weighted average of nu/nl, the ratio of upper-state to lower-state population density, multiplied by the absorptivity 1 - exp[-τ(v)], where τ(v) is the total optical path along the line of sight. In the wings the variation of Iv is governed by the absorptivity; in the core of the optically thick line, Iv is determined by the averaged population ratio. The analytical forms enable us to calculate all of the important features of the self-absorbed line and agree remarkably well with more time-intensive numerical calculation. These results are illustrated by calculations on the 15-μm CO2 v2 (0110-0000) vibrational transition for tangent heights ranging through the mesosphere and lower thermosphere. Even though the collision linewidth is less than 1% of the Doppler width at these altitudes, it is shown that it is essential to use the Voigt line profile in this calculation rather than the Doppler profile. Failure to do so leads to a total band radiance that is in error by up to a factor of three, as well as incorrect band shapes and line shapes.

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