Using a hit-and-miss Monte Carlo method, we followed many paths of Sun rays through a layer of hexagonal ice crystals. The angle of scattering by a single crystal is determined by tracing the path of the Sun rays through the crystal with its particular orientation. In this way we produced point plots of the intensity of the scattered sunlight for a specified population of crystals. By comparing the intensity patterns from single and multiple scattering, we looked for additional effects caused by multiple scattering. Several new secondary structures appear; however, their intensities are significant only when they result from spotlike primary structures. It appears that secondary structures from two combinations should be observable: from thick-plate crystals, the sun dogs of the sun dogs; and for long-column crystals in the Parry-arc orientation, the subsun of the lower tangent arc for Sun elevations around 15°. We show that multiple scattering is essential to explain the Saskatoon display.
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