On the relationship between duration of sunshine and solar radiation on the earth's surface: Angstrom's equation revisited

The paper presents a relationship between the relative sunshine duration and solar irradiation on the earth's surface, Following a review of the literature on Angstrom's equation and the properties of instantaneous solar radiation. the sunshine-radiation relationship is derived from monthly average values of daily beam radiation which are used as a measure for the fraction of clear sky, f(clear) = (H) over bar(b)/(H) over bar(b,clear). The resulting (non-linear) relationship, f(clear) = ((K) over bar/(K) over bar(clear))(2), unlike the Angstrom-Prescott relation, does not contain empirical constants and only requires the monthly average clear sky atmospheric transmittance to account for the climate of a particular location ((K) over bar(clear) is typically between 0.65 to 0.75). The relationship is verified for monthly intervals for Perth and Townsville. Australia and compared to existing Angstrom-Prescott equations for a wide range of climates and locations. The excellent agreement of the proposed relationship with the average value of data in the latter comparison suggests that it may be universally valid and that the Angstrom-Prescott equation is a local (linear) approximation of the derived relationship. For daily time intervals the sunshine-radiation relationship changes to f(clear) = (K/K-clear)(3). The paper closes with a discussion on applications of the new relationship including the performance prediction of solar energy systems. (C) 2000 Elsevier Science Ltd. All rights reserved.