An efficient analytical approach for calculating line mixing in atmospheric remote sensing applications

Collisional coupling between energy states in a molecule undergoing an optical transition can alter the line shape associated with the transition, an effect known as line mixing. Accounting for this effect in the analysis of remote sensing measurements of Earth's atmosphere by the Atmospheric Chemistry Experiment (ACE) yields reduced residuals, which leads to improved performance in the volume mixing ratio retrievals for some molecules. Analytical expressions are presented for the imaginary components of the polynomial ratios from the Humlicek algorithm, which provides approximate solutions to the complex probability function. These imaginary components are employed in the calculation of line mixing using the Rosenkranz first order approximation. Examples of line mixing in ACE measurements are presented, including a set of CH₄ lines that exhibit both line mixing and speed dependence. An efficient, analytical approach is proposed for calculating line shapes with a combination of line mixing and speed dependence. FORTRAN routines for calculating line mixing effects are provided as a supplement to the paper.