I just captured the following two pictures. Straight above me, almost directly above, was a rainbow, about 120 degrees of it were visible.

The thing is, the sun was completely out, low on the horizon and not centred. What explains this? My understanding was that the refraction at specific angles was what made the colour separate in a specific pattern. The angles didn't match, here.

Location: Montreal, ~15 minutes ago, unseasonably warm.

enter image description here

In the portrait picture, the sun is in the very bottom, on the left side: enter image description here

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    $\begingroup$ Search term: circumzenith arc. A nice reference site is atoptics.co.uk. $\endgroup$ – rob Jun 8 at 22:25
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    $\begingroup$ I'm guessing aliens. $\endgroup$ – Steeven Jun 9 at 8:16
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    $\begingroup$ @Steeven fabulous aliens $\endgroup$ – Michael Jun 9 at 22:39

As pointed out in the comment by @Rob, this is called a Circumzenithal Arc or colloquially, an "upside-down rainbow". Different to usual rainbows (which appear on the opposite side of the sky from the sun), a circumzenithal arc is centered around the zenith of the sky (directly above), and can only appear if the sun's angle is less than $\approx 30°$ to the horizontal.

In order for a circumzenithal arc to form, small ice crystals need to be positioned high in the sky in order to create a field of tiny prisms. Then the sun's rays will enter these ice crystals and refract through them therefore projecting an arc in the sky. If this projection was complete (a full $360°$), it would completely encircle the sky's zenith - hence the term circumzenithal.

Completely circular circumzenithal arcs do occur but are very rare, so most of them only take up a section of the sky. The circumzenithal arc remains until the sun's angle exceeds $\approx 30°$ to the horizontal.

Note also how the colors of a circumzenithal arc are also reversed compared to a rainbow. The violet end is closer to the sky's zenith and the red end is closest to the horizon.

In most cases, a circumzenithal arc will last 30 minutes to an hour (sometimes more). They are most common in colder climates (I assume in Montreal - where you took these images - it is fairly cool), where ice crystals abundantly tend to collect in the sky (they can be sometimes be seen in mild temperature zones as well during winter, or periods of cooler weather).

The above link (which pretty much explains the phenomena in detail) has more technical details:

The circumzenithal arc, also called the circumzenith arc (CZA), upside-down rainbow, and the Bravais arc,is an optical phenomenon similar in appearance to a rainbow, but belonging to the family of halos arising from refraction of sunlight through ice crystals, generally in cirrus or cirrostratus clouds, rather than from raindrops. The arc is located at a considerable distance (approximately $46°$) above the observed Sun and at most forms a quarter of a circle centered on the zenith. It has been called 'a smile in the sky', its first impression being that of an upside-down rainbow. The CZA is one of the brightest and most colorful members of the halo family. Its colors, ranging from violet on top to red at the bottom, are purer than those of a rainbow because there is much less overlap in their formation.

The intensity distribution along the circumzenithal arc requires consideration of several effects: Fresnel's reflection and transmission amplitudes, atmospheric attenuation, chromatic dispersion (i.e. the width of the arc), azimuthal angular dispersion (ray bundling), and geometrical constraints. In effect, the CZA is brightest when the Sun is observed at about $20°$.

  • $\begingroup$ > "it is fairly cool." 30 celsius today! Altitude I guess... $\endgroup$ – Jeffrey Jun 9 at 2:17
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    $\begingroup$ @Jeffrey - "generally in cirrus or cirrostratus clouds" - those wispy clouds nicely visible in your second picture do look like part of a cirrostratus sheat $\endgroup$ – Filip Milovanović Jun 9 at 12:23
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    $\begingroup$ A couple of corrections: the Circumzenithal arc is never a complete circle. There are complete circles that can form at the zenith, but they are (as you say) almost impossible rare. The complete circular "Kern arc" is formed by light taking a different route through the ice crystals from the circumzenithal arc. atoptics.co.uk/halo/cza.htm Secondly the temperature at ground level has little to do with the presence of ice crystals at altitude. It is always cold enough at 6000-10000m that cirrostratus clouds form. $\endgroup$ – James K Jun 9 at 19:48
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    $\begingroup$ "Note also how the colors of a circumzenithal arc are also reversed compared to a rainbow" It's obviously a "how you think about it" thing, but I don't "see" the colours as reversed (red is still "on the outside"), just that the rainbow is upside down. $\endgroup$ – TripeHound Jun 9 at 21:46
  • $\begingroup$ @TripeHound Yes. I agree with you. $\endgroup$ – joseph h Jun 12 at 5:10

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