On the relationship between radiation and mean daily sunshine

Sunshine data have been collected for longer periods at more locations, and in most cases provide the only historical means of measuring irradiance. The Angstrom radiation/daily-sunshine model has limitations and while an hourly-sunshine model is better, hourly data are not always available. The typical mean daily pattern of sunshine shows a greater concentration about solar noon with a near-symmetric tailing off towards sunrise/sunset. This hourly course of sunshine can be approximated from daily sunshine data using an appropriate bell- or dome-shape sub-model which gives the radiation/daily-sunshine model a stronger physical basis. Applying this pattern to the mean daily fraction of sunshine, F = n(actual)/N(possible), shows how the coefficients of the Angstrom-type equations might be expected to vary with latitude, solar declination and atmospheric transmissivity. As functions of F, the relationships take the approximate module-quadratic form: G(F)/G(1) = [gamma + (1-gamma)FR]/A (Angstrom); G(F)/Q(0) = S[gamma + (1-gamma)FR]/A (Angstrom-Prescott); and Q(F)/Q(0) = S'FR (direct), where G is the mean daily global radiation on a horizontal surface, Q(0) is extraterrestrial daily radiation, gamma is fractional cloud transmission, R = 1 + theta(1 -\1 - 2F\) is the ratio enhancement due to the concentration of F about noon (theta is the fractional increase), A = 1 - rho(1 - F) is an albedo effect due to multiple reflection (rho is the product of earth surface and cloud base albedos), and S, a seasonal atmospheric transmission factor, is the potential fraction of extraterrestrial radiation. S' is the potential fraction for direct radiation (S' < S < 1). The coefficients of these simple relationships between sunshine hours and radiation have a physical meaning which shows realistic behaviour. (C) 1997 Elsevier Science B.V.