Mathematical Model of Sky Radiation Reflection by Lambert Underlying Surface

The solar radiance diffused by a randomly-rough underlying surface might lead to increase sky radiance. The computation of sky radiance resulted from the earth's diffuse reflection is studied based on a hypothesis that a underlying surface is randomly rough. The paper gives an analysis of the method to calculate the reflectivity, average hemisphere reflectivity, and transmission in virtue of the reciprocity law from the earth's surface to the top of the atmosphere. The calculation of the effect of different albedo of underlying surface on sky radiance is made at different viewing zenith angles and compared with the experimental result. The results show that sky radiance rises rapidly as the albedo of the earth's surface becomes big while viewing zenith angle is close to 90°.