Paranthelion

Haloes are not all that common around Kootenay Lake—at least when it is compared with other places I have lived. Further, of all the many haloes that can be seen, the paranthelion is sufficiently uncommon that I cannot recall having seen one here before.

halo: rings, arcs or spots of light in the sky caused by ice crystals.
22° halo: circle centred on Sun having an angular radius of 22°.
parhelion: [lit. beside sun] coloured spots adjacent to a halo at the solar elevation. 
paranthelion: [lit. beside the point opposite the Sun] a colourless spot 120° degrees from the Sun.
parhelic circle: white line around the sky at the solar elevation.
• The Kootenay Lake website offers more pictures of haloes.

The first thing I noticed as the radiation fog was clearing Sunday morning was an unusually bright parhelion (also called a sundog because it dogs the Sun). The parhelion is the coloured spot near the center of this picture. The parhelion and the 22° halo (the nearly vertical line on the left) are both explained by the refraction of sunlight through plate-like hexagonal ice crystals. The difference is that the halo results from smaller tumbling crystals, while the parhelion is from larger horizontally oriented ones. These larger crystals will fall almost like (hexagonal) dinner plates spread out on a table. As the Sun rises above the horizon (here its elevation is 34°), sunlight passing through the horizontally oriented plates takes a skewed path. This shifts the parhelion outside the halo. Also seen in the picture is the parhelic circle—the white horizontal line.

The scene kept changing as cirrus drifted across the sky. This wider-angle view was taken a short time after the first picture. It shows parhelia on either side of the Sun, a portion of an upper tangential arc above the Sun and bits and pieces of the parhelic circle. The departing fog can be seen over the Lake in the lower right.

Finally, here is a nearly half-sky panorama. The 22° halo and its two parhelia are on the left, the parhelic circle extends across much of the sky, and the paranthelion is near the right edge of the picture. As this diffuse bright spot sits 120° from the Sun, it is also known as the 120° parhelion. The parhelic circle is explained by a single reflection of sunlight off the vertical sides of the hexagonal ice crystals. The paranthelion has a slightly more complex explanation. Sunlight enters the top of the crystal, is internally reflected in succession off adjacent sides of the crystal and exits the crystal bottom. The adjacent vertical sides of the crystal form a corner reflector with an internal angle of 120° and this deviates the light by the observed 120°. When parhelia are particularly bright, it is a good time to look for a paranthelion.