Broadband and luminous extinction coefficients in a clean and dry atmosphere

•Broadband and luminous extinction coefficients in a clean atmosphere are revised.•New generalised solution originates from heuristic analytical derivation.•The analytical formulae are free of any random or systematic errors.•New solution could replace manifold empirical formulae that are currently in use.

The extinction coefficient as a function of optical air mass has been persistently used for many years in order to model both direct normal irradiance and illuminance (DNI). Nevertheless, such a dependence is only approximate, simply a convenient, but inaccurate application in monochromatic radiative transfer theories. The relationship between these characteristics originates from the point source exponential law incorrectly used for broadband radiation and, the set of empirical formulae used for broadband and luminous extinction coefficients have no preferred model. Therefore, in this paper we explain the fundamentals of broadband (ae) and luminous (av) extinction coefficients for a clean and dry atmosphere and introduce general formulae which originate from heuristic analytical derivation that produce exact formulae, free of any random or systematic errors which can arise from numerical integration or processing of experimental data. Another advantage is that each parameter used in new formulae for ae or av has a theoretical base, therefore optimum by delineation. The analytical formulae could replace those routinely used in modelling DNI for broadband spectra (including daylight).