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Phase functions have been calculated usingthe Monte Carlo/geometric ray tracing method for single hexagonal pyramidal icecrystals (such as solid and hollow bullets) randomly oriented in space andhorizontal plane, in order to study the concentric halo formations. Results fromthree dimensional model calculations show that 9° halo can be as bright as thecommon 22° halo for pyramidal angle of 28°, and the 18°, 20°, 24° and 35°halos cannot be seen due to the strong 22° halo domination in the scatteringphase function between 18° and 35°. For solid pyramidal ice crystals randomlyoriented horizontally, the 35° arc can be produced and its intensity depends onthe incident ray solar angle and the particle aspect ratio

Pyramidal ice crystal scattering phase functions and concentric halos