The Ångström formula with coefficients having a physical meaning

Abstract

A new method is proposed to evaluate the coefficients a and b of the Ångström formula H H 0 = a + b· s s 0 . Then, a has the physical meaning of the fraction of diffuse radiation, D, to extraterrestrial radiation, H 0, and b has the meaning of the fraction of direct radiation, I(1), to H 0. This is possible at sites where measurements with a shadow band pyranometer are available, in addition to measurements of global radiation, H, and sunshine duration, s. The Ångström formula then gives substantial information about the radiation climate of a site. It is feasible to calculate global radiation, H, on tilted surfaces and planes following the sun's disk, which is essential to evaluate the efficiency of solar energy conversion systems at locations where only measurements of the sunshine duration, s, are available. Thus, it is strongly recommended to replace the regression coefficients a′ and b′ presented in the European Solar Radiation Atlas, which were estimated by least squares approximation. For the site of Hamburg, Germany, it is shown that a ten years interval of data records may be too short to give reliable values of climatological means of D, I(1), H, and s. An increase of direct radiation at Hamburg during the last decade can be detected by the proposed method and may be explained by a decreasing amount of optically active constituents in the air, probable a result of the clean air policy in Germany.