A physical rationale for generalized Ångström–Prescott regression

The transparency of the terrestrial atmosphere has been related to the relative sunshine duration ever since the seminal work of Ångström [Ångström, A., 1924. Solar and terrestrial radiation. Q. J. Roy. Meteor. Soc. 50, 121–126]. Modified by Prescott [Prescott, J.A., 1940. Evaporation from water surface in relation to solar radiation. Trans. Roy. Soc. Austr. 40, 114–116], linear Ångström–Prescott regression has seen world-wide application in investigations concerned with solar irradiance of the surface at specific sites. Extensions of the linear formula to higher orders have been suggested as better suited in certain cases. A drawback of this kind of regressional modeling has been the lack of a clear link between the empirical formulae and the theory of radiative transfer. The coefficients involved are usually interpreted on an ad hoc basis. In the present work, a rationale for deriving and interpreting a polynomial relation between ground-level solar irradiance and relative sunshine duration is proposed.