The Formation of Parhelia at Higher Solar Elevations

Abstract

The parhelia associated with the 22° halo arise from minimum deviation of light by ice prisms with vertical 60° refracting angles. When the sun is near the horizon, the crystals responsible are thin hexagonal plates, which maintain vertical principal axes while falling under aerodynamic forces in still air. At higher solar elevations simple refraction in such oriented plate crystals cannot produce parhelia (as noted by Bravais in 1851), but an analysis of observations in the Netherlands shows no reduction in parhelion frequency with increasing elevation beyond that which would be expected from other considerations. Attempts to account for higher parhelia can be classified under one of three different optical processes: (i) simple refraction in elongated prisms whose principal axes are maintained vertical by some unspecified mechanism; (ii) refraction accompanied by multiple total internal reflection in plate crystals (Visser); (iii) refraction and one total internal reflection in plate crystals followed by secondary reflection in the horizontal faces of other crystals (Lenggenhager). Using the Stokes vector-Mueller matrix calculus, the polarization forms which would result from each of these processes have been investigated. Observations of parhelia at solar elevations of 0°–34° have shown the light to be very weakly linearly polarized with azimuths that may deviate significantly from the horizontal. These observations are only consistent with Visser’s theory of multiple total internal reflection. Such polarization observations should be useful in clarifying the origins of some of the rarer forms of ice-crystal halos.