Atmospheric transmittance of an absorbing gas: a computationally fast and accurate transmittance model for absorbing gases with constant mixing ratios in inhomogeneous atmospheres

At a given pressure level the atmospheric transmittance for an absorbing gas with a constant mixing ratio varies only with the temperature profile of the atmosphere. A simple transmittance model based on temperature differences is derived for monochromatic radiation. This model then is extended to the more important case of polychromatic radiation through the use of scaling approximations. The resulting algorithm for calculating transmittances for an arbitrary temperature profile is simple to use, accurate, and computationally fast because only arithmetic operations are required. In fact, resulting transmittances agreed with line-by-line calculations to within 0.0031 for the cases tried. Details for calculating the expansion coefficients are provided.