22° Plate Halos by Alan Clark of the University of Calgary, Alberta, Canada. ©Alan Clark, shown with permission.
At top is a sundog, a parhelion, formed in very cold weather by diamond dust crystals. The crystals grew from moisture from the nearby Bow River, Calgary.
The lower image is a 'sub-parhelion' pictured over winter prairie river terrain. "While flying from eastern Canada to Calgary on Jan 1, a thin layer of ice crystals produced a subsun for at least 2 hours, sometimes intermittent, but with intriguing signs of lower tangent arcs and often sub-sun dogs [subparhelia]."
The two halos are related.
Sundogs are formed by rays passing between the side faces of plate crystals inclined 60° to one another. When the sun is near the horizon most rays pass straight across the crystal. As the sun climbs more and more rays reflect internally between the large upper and lower faces.
Rays reflected an EVEN number of times (or not at all) form a sundog.
Rays reflected an ODD number of times form a below-horizon sub-parhelion.