Analysis of Atmospheric Turbidity for Daylight Calculations

A large set of illuminance and irradiance data has been collected for four years at 15-minute intervals in San Francisco. This data set has been used to investigate the impact of atmospheric turbidity on daylight calculations. Existing predictive formulae for Linke turbidity, TL, provide moderate agreement to measured values of TL when using nominal design values for the Angstrom scattering coefficient, B, and precipitable water vapor, w. When average measured values for B and w are used, the agreement improves. We suggest the use of an illuminance turbidity, Til, to calculate direct normal illuminance directly. We derive a simple approximate solution, Til = 1 + 21.6 B. Til appears to be a better parameter to describe atmospheric conditions since, unlike TL, it is insensitive to air mass and thus solar altitude or time of day. We present and compare plots of Ti, and TL vs. solar altitude, time of day, and month. Finally, we examine and compare several alternative pathways to derive direct normal illuminance from irradiance and luminous efficacy (dependent on B and w), or directly from B.