Abstract

Model simulations of laboratory-generated and natural crepuscular rays are presented. Rays are created in the laboratory with parallel light beams that pass through artificial fogs and milk–water solutions. Light scattered by $90°$ in a dilute mixture of whole milk first increases in intensity with distance from the source to a maximum as a result of multiple scattering by mainly small angles before decreasing exponentially due to extinction as distance continues to increase. Crepuscular rays are simulated for three cloud configurations. In case 1, the Sun at the zenith is blocked by a cloud with an overhanging anvil. The rays appear white against blue sky and are brightest when atmospheric turbidity, $\mathit{\beta }\approx 11$. Shading by the anvil separates maximum brightness from apparent cloud edge. In case 2, a ray passes through a rectangular gap in a cloud layer. The ray is faint blue in a molecular atmosphere but turns pale yellow as β and solar zenith angle, ${\mathit{\varphi }}_{\text{sun}}$, increase. At ${\mathit{\varphi }}_{\text{sun}}=60°$ it appears most striking when the cloud is optically thick, $\mathit{\beta }\approx 5$, and the beam width $\mathrm{\Delta }\mathit{x}\approx 1000\mathrm{m}$. In these cases, increasing aerosol radius, ${\mathit{r}}_{\text{aer}}$, to about $1000\mathrm{nm}$ brightens, narrows, and shortens rays. In case 3, the twilight Sun is shaded by a towering cloud or mountain. The shaded rays are deeper blue than the sunlit sky because the light originates higher in the atmosphere, where short waves have suffered less depletion from scattering. The long optical path taken by sunlight at twilight makes color and lighting contrasts of the rays greatest when the air is quite clean, i.e., for $\mathit{\beta }-1\ll 1$. In all cases, the brightest rays occur when sunlight passes through an optical thickness of atmosphere, $\mathit{\tau }\approx O(1)$.

© 2011 Optical Society of America

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