This version of the CIE distribution uses illuminance turbidity as a parameter. The original CIE formulation gives 2 separate equations which correspond to Til =2.45 and Til =5.5, for clean and industrial atmospheres respectively.
An alternative luminance distribution formula was developed by Nagata(3,4,5) from luminance measurements made in Japan. This formula gives absolute luminance values with a distribution similar to the CIE equation. It may be used to predict zenith luminance with atmospheres of given turbidity.