Reflection Rainbows
These may be refered to as "double rainbows" like secondary rainbows often are, but while secondary rainbows are relatively common, these are much rarer.
Oikofuge - Converging Rainbows - rainbow reflected by body of water into air above normal rainbow
Reflection Rainbows
APOD Sep 7, 2007 - NASA (cropped and annotated)
These are not the reflection of rainbows in water, but rainbows created by the reflection of light from a body of water.
RainbowSpec
Sunlight hits a still body of water, reflects off of the surface, and then enters the raindrops, forming another rainbow. The center of the reflection rainbow is above the primary antisolar point.Reflection Rainbows - AtOpt
The reason the reflection antisolar point is not opposite of the real sun is because of the direction of the light when it enters the drop. If we extend the entering light path past the body of water, we can imagine a fake sun that could have made the same path but straight, without reflecting. The reflection antisolar point is opposite of this imaginary sun.
The fake sun is a mirror image of the real sun, reflected directly across the horizon, so since the horizon is perfectly in the middle of the suns, it is in the middle of the antisolar points, thus the rainbow and the reflection rainbow intersect at the horizon. As the sun sets and the antisolar point also gets closer to the horizon, the primary rainbow and the reflection rainbow become closer together. Conversely, the higher the sun, the further ppart the primary and reflection rainbows will be.Reflection Rainbows - AtOpt When the horizon intersects the sun in half, the mirrors sun will be in the same place, as will the antisolar points, creating a single rainbow again.
Speculation
Considering as the sun rises, the anti-solar point of the reflection rainbow also rises, I suspect it is possible to see a reflection rainbow when the sun is too high to see a regular rainbow (when the ground normally obscures the rainbow cone). This rainbow could be high in the sky, its full circle visible. If the sun were precisely in the middle of the sky and a body of water directly under it, the mirror sun would be exactly opposite of it. Said mirror sun's antisolar point would be opposite of it, thus in the middle of the real sun, forming a rainbow around the real sun. This of course is just speculation, I have not seen any evidence of this occuring.
Note that the source of water is typically behind the viewer (much like the sun is behind the viewer). Reflection Rainbows - AtOpt The light could also reflect off of wet land like wet sand.
Secondary rainbows can also have reflection versions!
Most "quadrupal" rainbows will be because of reflection rainbows; the primary and its secondary, plus the reflection rainbow and its own secondary.
Next Page: Split Rainbows