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Irradiance during total lunar eclipses is simulated using a pinhole model. The Moon is illuminated by direct sunlight that is refracted into the Earth’s shadow as it passes through the atmosphere at the terminator but is depleted by scattering by molecules, extinction by aerosol particles, absorption by ozone, and obstruction by clouds and elevated land. On a spherical, sea-level Earth, and a cloudless, molecular atmosphere with no ozone, the eclipsed Moon appears red and calculated irradiance at the center of the umbra is reduced by a factor of about 2400 from direct moonlight. Selective absorption mainly of light around 600 nm by stratospheric ozone turns the periphery of the umbra pale blue. Typical distributions of aerosol particles, ozone, mountains, and clouds around the terminator reduce irradiance by an additional factor of the order of 100.
© 2008 Optical Society of America
Irradiance and color during the total lunar eclipses of 2007 and 2008 are simulated using a ray tracing model that includes refraction, scattering by molecules, and observed or climatological distributions of aerosols, ozone, clouds, and topography around the terminator. Central portions of the umbra appear deep red for almost all eclipses due to preferential removal of short wavelengths in the spectrum of sunlight by scattering in the lower troposphere. The fringe of the umbra appears turquoise or blue due to selective removal of wavelengths around 600 nm by the Chappuis absorption bands of ozone in the stratosphere. Asymmetric distributions of clouds and aerosols, particularly for the 2008 eclipse, produce minimum calculated irradiance up to 17 arc min from the umbra center, while high ozone content over the arctic makes the northern edge of the umbra deepest blue.
© 2008 Optical Society of America
We present simple radiative transfer models for the radiance and color of atmospheric optical phenomena. Skylight, halos, and rainbows are treated as singly scattered sunlight that is depleted by scattering as it passes through a plane-parallel atmosphere and a vertical rain shaft or a geometrically thin cloud layer. Skylight in a molecular atmosphere grades from deep blue at the zenith to pale blue near the horizon whenever the solar zenith angle sun ≤ 80°. Skylight near the horizon is orange resulting from wavelength-dependent scattering by air molecules and aerosol particles through a long oblique path through the atmosphere when the sun is low in the sky (sun ≥ 85°). Halos (and coronas) seen through clouds facing the sun are brightest for cloud optical depth τcld ≈ cos(sun), and fade to obscurity for τcld ≥ 5. Rainbows (and glories), seen by light that is backscattered from clouds, also appear most dramatic when 0.2 ≤ τcld ≤ 1, but remain visible even in the thickest clouds.
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, β≈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, ϕsun , increase. At ϕsun=60° it appears most striking when the cloud is optically thick, β≈5 , and the beam width Δx≈1000 m . In these cases, increasing aerosol radius, raer , to about 1000 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 β−1≪1 . In all cases, the brightest rays occur when sunlight passes through an optical thickness of atmosphere, τ≈O(1) .
© 2011 Optical Society of America