On the proper analytical expression for the sky-view factor and the diffuse irradiation of a slope for an isotropic sky

The contribution raises a question of how good is the standard method for estimating the diffuse irradiation on a tilted surface. This is done with a correction of the diffuse irradiation measurement by a sky-view factor. Many different expressions for the sky-view factor can be found in the literature. According to their definitions, the sky-view factor represents the solid angle of the visible celestial hemisphere normalised by the solid angle of whole celestial hemisphere. It considers only a geometrical aspect of the available sky radiation but does not consider the amount of received irradiation in the proper way. To overcome this deficiency, the diffuse irradiation of the horizontal receiving surface (being normally measured) should be multiplied with the proposed diffuse tilt factor to obtain the irradiation of the tilted surface. Besides the orientation of the tilted surface, the diffuse tilt factor depends on ground reflectivity and the ratio between the diffuse and global irradiation of the horizontal surface.

► Sky-view factor is usually used to correct measured diffuse irradiation on a slope.
► The proposed diffuse tilt factor (DTF) is a more appropriate correction.
► DTF is based on to the slope projected radiance from the sky and the ground.