Uniform error bounds for fast calculation of approximate Voigt profiles. (August 2021)

• Record Type: Journal Article
• Authors: Nordebo, Sven
• Is Part Of: Journal of quantitative spectroscopy & radiative transfer. Volume 270(2021)
• Publication Date: 2021-08
• Subjects: Radiative transfer in the atmosphere -- Spectral line shapes -- Voigt function -- Faddeeva function -- Uniform approximation; Spectrum analysis -- Periodicals; Radiation -- Periodicals; Analyse spectrale -- Périodiques; Rayonnement -- Périodiques; Radiation; Spectrum analysis; Periodicals; 543.0858
• DOI: 10.1016/j.jqsrt.2021.107715
• Languages: English
• ISSNs: 0022-4073

Abstract

Highlights: Uniform error bounds for approximating the classical Voigt profile are presented which can be useful with the demanding computations of broadband line-by-line analysis of radiative transfer in the atmosphere. The uniform bounds can be used to rigorously determine the domains on which the Voigt profile can be approximated by the corresponding Lorentz pro le to any desired accuracy. The bounds can furthermore be employed to make a fast and efficient estimate of the most significant lines to be included in a subband adaptive line selection strategy. Numerical examples are included showing that the approximation approaches are able to reduce the computational time of the associated line-by-line analysis by several orders of magnitude with little loss of accuracy. Abstract: This paper presents uniform error bounds for fast calculation of approximate Voigt profiles that can be useful with the computationally demanding broadband line-by-line analysis of radiative transfer in the atmosphere. Formal proofs are given and rigorous criteria are provided to determine the domain on which the Voigt profile can be approximated by the Lorentz profile within any required accuracy. The most accurate Voigt-implementation to date can then be used to determine the required threshold parameters. Since most of the broadband radiative transfer calculations in the atmosphere will pertain to far wing computations, the potential saving in time is almost the same as by replacing the Voigt computation for the Lorentzian altogether completely. The error bounds can furthermore be used to derive a simple and efficient subband adaptive line selection strategy which can be used to rigorously exclude lines that will contribute to the resulting absorption coefficient less than any given threshold.