Uniform error bounds for fast calculation of approximate Voigt profiles

TL;DR

This paper introduces uniform error bounds for approximating Voigt profiles, enabling faster atmospheric radiative transfer calculations with minimal accuracy loss, by combining a new 'full' Voigt profile and adaptive line selection strategies.

Contribution

It presents a novel method for calculating uniform error bounds for Voigt profile approximations and introduces a new 'full' Voigt profile combining Faddeeva evaluations.

Findings

Reduces computational time by several orders of magnitude

Maintains high accuracy with the approximation methods

Enables efficient adaptive line selection in radiative transfer

Abstract

The broadband line-by-line analysis of radiative transfer in the atmosphere is extremely demanding with regard to computational resources. As a remedy, we present here the calculation of uniform error bounds for approximating the classical Voigt profile. A new "full" Voigt profile, which can be expressed as a combination of two Faddeeva evaluations, is also presented and included in the analysis. The uniform bounds can be used to rigorously determine the domains on which the Voigt profiles can be approximated by the corresponding Lorentz profiles 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. By using a realistic numerical example of radiative transfer in the atmosphere, we demonstrate that these 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.