Ångström–Prescott equation: Physical basis, empirical models and sensitivity analysis

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 converters, the equation was extensively used to estimate the amount of collectable solar energy. In this paper the Ångström–Prescott equation is reviewed from three different perspectives: (1) the physical basis, (2) the accuracy of the empirical models and (3) the sensitivity to geographical and seasonal factors. A mathematical derivation of the Ångström–Prescott equation is performed, showing the approximations behind it and the physical meaning of the coefficients. A number of 33 empirical Ångström–Prescott equations of different degrees of complexity and originated from different location around the world are being analyzed and tested against data recorded at 59 European stations. No model is ranked as the best, but the specific situations when a model performs better than others are discussed. A comparative study on the influence of different parameters (latitude, altitude, season, local climatology) on the performance of the Ångström–Prescott equations is presented. It is shown that an Ångström–Prescott equation having relative sunshine, altitude and the month index as input parameters can explain roughly 90% of the variability in the data from the entire database considered in this paper.