Visualization of the twilight sky is a good representation for the tasks of the meteorological conditions analysis, astronomical observations, navigation, driving conditions, some tasks of the lighting engineering and lighting design. A qualitative solution for this problem requires the calculation of the distribution of color coordinates, one of the main components of which is lightness. If for the daytime sky the modeling of this component is recognized as sufficiently good and does not have any particular difficulties, then for the twilight environment a reliable mathematical model based on the real physical characteristics of the atmosphere requires significant computational resources. The problem here is that the Independent Pixel Approximation (IPA) method and the simplification of the model to a flat layered medium for the twilight zone becomes inaccurate due to the peculiarities of the direction of incidence of the rays to the boundary of the atmosphere and the entry of radiation into a special region where it is necessary to consider its spherical shape, i.e., accurate 3D atmosphere model. A solution to this problem is proposed by extracting the anisotropic part based on a small-angle modification of the spherical harmonics method and solving the smooth part in diffusion approximation in the Comsol Multiphysics environment. The obtained picture of the luminance distribution visualization coincides qualitatively with G.V. Rosenberg's monograph “Twilight” data.

Twilight, luminance distribution visualization, radiative transfer, quasi-diffusion approximation, Comsol Multiphysics

Budak Vladimir Pavlovich,  ,  orcid.org/0000-0003-4750-0160,  Moscow Power Engineering Institute

Smirnov Pavel Alexandrovich,  ,  orcid.org/0009-0000-1971-7157,  Moscow Power Engineering Institute