Sky luminance/radiance model with multiple scattering effect

Angular distribution of the diffuse light essentially varies with the physical state of a disperse media. The main factors influencing the optical behaviour of the Earth’s atmosphere are the total optical thickness, the scattering ability of atmospheric layers, and also the reflectance of underlying surface. Any model aspiring to be more universal and still satisfactory accurate must at least account for these quantities. The paper presents the theoretically derived equation simulating the sky luminance/radiance under various meteorological conditions. Because the radiative transfer equation in plan-parallel atmosphere is solved exactly, the proposed approximation formula is physically well-founded. Compared with other, predominately empirical models, the presented approach accepts the basic principles of light scattering in a turbid environment and the model is spectral in its nature (contrary to empirical models in current use). In addition, the contribution of multiple scattering is taken into account. A set of free parameters, otherwise used as weighting factors for individual optical effects, makes the model easily scalable and applicable for a wide range of optical states of the atmosphere.