I’ve never seen a full-circle rainbow, but I did once see one of about 190 degrees, dipping into Yellowstone Canyon. Then, a few years after that, conditions were just right that I was able to see a 270-degree one from my ninth-floor apartment. In both cases, the non-sky portions were very faint, because there wasn’t very much depth of rain between me and the ground, but there was enough to be visible.
Yup, along with sundogs, vertical bright yellowish bands on either side of the Sun.
Sundogs are actually caused by the same ice crystals that form that halo, but when they fall they are oriented by aerodynamic forms so that the axis is vertical. Hence, you only get that portion of the halo to the right or left of the sun.
How the sundog appears depends upon the size of the crystal. If the crystals are small, then the sundogs do indeed appear as yellowish-brownish blobs of light. In that case diffraction effects act counter to the prismatic effects of the crystals and re-combine the colors that the prismatic effect spreads out.
But if the crystals are large, then the sundogs can look spectacular, with rainbow separations of color that can extend horizontally for quite a distance.
Incidentally, sundogs are extremely common. They’re about 10 times as common as rainbows. It’s just that most people don’t know about them and don’t look for them, even when they’re multicolored. I’ve had to point them out to people who were oblivious to them. But a lot of the time the crystals are small, and the sundogs aren’t all that prominent.
Sundogs are only visible, by the way, up to a solar height of about 40 degrees, and they get less likely the higher the sun gets. Your best chance of seeing one is in the morning or evening, near sunrise or sunset. And at such times they can be spectacular indeed.