Computational aspects of speed-dependent Voigt profiles

- Speed-dependent Voigt is difference of two complex error functions.
- Four digits accuracy for complex error function insufficient for differences thereof.
- A combination of the Humlicek and Weideman rational approximations is fast and accurate.

The increasing quality of atmospheric spectroscopy observations has indicated the limitations of the Voigt profile routinely used for line-by-line modeling, and physical processes beyond pressure and Doppler broadening have to be considered. The speed-dependent Voigt (SDV) profile can be readily computed as the difference of the real part of two complex error functions (i.e. Voigt functions). Using a highly accurate code as a reference, various implementations of the SDV function based on Humlíček׳s rational approximations are examined for typical speed dependences of pressure broadening and the range of wavenumber distances and Lorentz to Doppler width ratios encountered in infrared applications. Neither of these implementations appears to be optimal, and a new algorithm based on a combination of the Humlíček (1982) and Weideman (1994) rational approximations is suggested.