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A mathematical method for accurately determining the upper and lower diffuse-fraction (kd) limits that divide the sky into clear, intermediate, and overcast is developed. Fourteen sites around the world are selected for demonstrating the methodology. The upper and lower kd values for these sites are determined from scatter plots of direct-normal solar radiation vs. kd pairs over the typical meteorological year of each site. They vary between 0.73 and 0.80 for the upper and between 0.24 and 0.27 for the lower kd limits. Plots of sunshine duration (SSD) vs. kd are prepared for 12 of the 14 sites. These plots show a decreasing trend in SSD with increasing values of kd, as anticipated. According to local climatology, the number of the SSD values in each sky-condition classification varies from site-to-site.

Mathematical Determination of the Upper and Lower Limits of the Diffuse Fraction at Any Site