What Ångström—Prescott equation tells us about the cloud and clear-sky climatologies?

The Ångström–Prescott equation defines generically the relationship between solar energy available at ground level and sunshine duration. From the very beginning in the history of the solar energy converters, the equation was extensively used to estimate the amount of collectable solar energy. In the present paper, we propose a different way of looking to the Ångström–Prescott equation, namely, to use it for the estimation of cloud and clear sky atmospheric transmittances. The key tools are the mathematical expressions which give the clear sky and cloud transmittances in terms of the Ångström–Prescott empirical coefficients. The theory is verified by comparing the mean all-sky atmospheric transmittance (innovatively inferred from the cloud and clear sky atmospheric transmittances) with the measured clearness index. Reasonably good concordance between the two quantities has been found. It was shown that the best performance is obtained with the linear Ångström–Prescott equation. Higher-order polynomial equations tend to overfit the measurements. Examples are also shown about how to use the linear Ångström–Prescott equation to obtain information about the time series stationarity and the seasonal sensitivity of the cloud and clear-sky transmittances. The present point of view gives the perspective to estimate past cloud and clear-sky climatology in places where the Ångström–Prescott equation has been fitted to the sunshine data.