The atmospheric integral transparency coefficient and the Forbes effect

Abstract The Forbes effect (known from 1842) expresses the fact that a total (broadband) direct solar beam becomes increasingly penetrating on its way through the atmosphere – because of changes in its spectral content and loss of less penetrating spectral components. The effect restricts the use of the Bouguer-Lambert law for calculating the characteristics of transparency (or turbidity) of the air. Efforts to overcome this effect and to transform the coefficients of transparency to a given solar elevation have finally met with success, and in this study one of such methods (developed by Murk and Ohvril) is presented in detail. This method is compared with those of Evnevich and Savikovskij. For solar elevations 20°≤ h ≤80° all three techniques are compatible, securing accuracy with an uncertainty below 2.5% with regard to standard values of the coefficient of transparency. Simple transition to the Linke turbidity factor is available. Time courses of mean annual values of the coefficient of atmospheric transparency at solar elevation h =30° and the Linke factor for the last 40 years at an Estonian station at Tiirikoja are given as examples. In the average the multiannual time courses demonstrate an increase of atmospheric turbidity as well as bear evidence of sensitivity to great volcanic eruptions.