Relationship between sunshine duration and solar radiation

Abstract

This paper examines the relationship between sunshine duration and solar radiation received on the earth’s surface. Sixty-nine thousand pairs of sunshine–radiation readings from 670 sites were analyzed. A generalization of the Ångström–Prescott equation of the form K¯=K¯clear[β+(1-β)Sγ] was found to most efficiently fit the data and suggests the relationship between the average daily atmospheric transmittance K¯ and the sunshine fraction S is non-linear. The suggested reason for this non-linearity is that a reduced sunshine fraction not only decreases the clear sky radiation duration, but also the radiation transmitted through clouds, i.e. clouds get optically thicker with decreasing S. This finding is supported on theoretical grounds and by analyzing instantaneous solar radiation measurements from Australia and Germany.Representing the sunshine fraction in terms of the proportion of beam radiation reaching the earth’s surface S=H¯b/H¯b,clear leads to a fundamental connection between the monthly average diffuse fraction and the sunshine–radiation relationship. Moreover, it confirms the non-linearity of the latter relationship, which was previously questioned because of limited data and/or poor quality sunshine measurements.