Analysis of Space Distribution of Scattered Daylight by the Monte Carlo Method Giving Consideration to Atmospheric Particles

—Numerical Simulation of Daylight Scattered in Clouds—

Abstract

Use of the Monte Carlo method to simulate sky luminance and daylight illuminance has led to the following findings.
(1) In the case of a sky with a uniform cloud cover, the sky luminance distribution approaches that in the CIE standard overcast sky as the optical thickness of the clouds grows larger. If the sky luminance (L_m) is given by the equation with clear sky luminance (L_c) and overcast sky luminance (L_o), that is, L_m=e^-AxτL_c+(1-e^-Axτ)L_o (where τ is the optical thickness of the clouds), coefficient A will have a value of 0.16-0.28 when the sun altitude is 30-60 degrees. On the other hand, if the daylight illuminance is given by equation S_r=S_o×e^-Bxτ, coefficient B will have a value of 0.012-0.027. The optical thickness of clouds in a heavily clouded sky is 52-82 when the sun altitude is 30-60 degrees.
(2) In the case of an intermediate sky with separate clouds, the sky luminance L_m is represented by equation L_m=(1-C/10)L_c+(C/10){e^-AxτL_c+(1-e^-Axτ)L_o}, where C is the total cloud amount. With an increase in the total cloud amount, the daylight illuminance averaged on the overall surface decreases, but this is not always so for the maximum and the minimum.