Abstract
By investigating the long-term observations at Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP), we find that the routinely used Beer-Bouguer-Lambert law and the models that empirically separate direct normal irradiance (DNI) from measurements of global horizontal irradiance (GHI) have dramatic and unexpected bias in computing cloudy-sky DNI. This bias has led to tremendous uncertainty in estimating the electricity generation by solar energy conversion systems. To effectively reduce the bias, this study proposes a physical solution of all-sky DNI that computes solar radiation in the infinite-narrow beam along the sun direction and the scattered radiation falls within the circumsolar region. In sharp contrast with the other DNI models, this method uses a finite-surface integration algorithm that computes solar radiation in differential solid angles and efficiently infers its contribution to a surface perpendicular to the sun direction. The new model substantially reduces the uncertainty in DNI by a factor of 2-7.