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A general‐purpose extension of the Malkmus band‐model average equivalent width to the case of the Voigt line profile
Author(s) -
Geleyn J.F.,
Bénard P.,
Fournier R.
Publication year - 2005
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1256/qj.04.107
Subject(s) - voigt profile , line (geometry) , function (biology) , computation , term (time) , extension (predicate logic) , table (database) , mathematics , equivalent width , mathematical analysis , computer science , algorithm , physics , geometry , spectral line , quantum mechanics , emission spectrum , evolutionary biology , data mining , biology , programming language
Bypassing the definition of an approximate function with a primitive one for the convoluted Voigt line shape, one may get an accurate and economical analytical approximation of the average equivalent width for an absorption band having the Malkmus‐type statistical distribution of line intensities and a random positioning of those lines. The trick is to start from the well‐known analytical solution of the same problem for the Lorentzian line shape and to identify which term to add to the latter in order to keep the correct asymptotic behaviours. One can then numerically evaluate this unknown term for various values of its two relevant parameters, representative of atmospheric conditions, and make an analytical fit of the resulting table of values. The recombined function, albeit without any inferred line profile, can best be interpreted in terms of a modified amount of absorber, which may lead to the application of the advocated method in many other conditions than in pure band‐model computations. Additionally, one can adapt the classical Curtis–Godson approximation to the resulting new framework in a quite natural way. Copyright © 2005 Royal Meteorological Society.