Update: Bad Astronomer wrote up an explanation of what you see: slate.com/blogs/bad_astronomy/2012/12/04/time_lapse_video_of_rainbow_as_it_materialize_over_a_hawaiian_canyon.html
Quick attempt at a time lapse movie resulted in incredible luck capturing the formation of a rainbow. Here’s how it happened:
I'm on vacation on Kaua‘i. My friends and I had gone to Barking Sands beach earlier that day, and on our way back to the rental house we decided to make a detour to the top of Waimea Canyon. We were racing the sunset to get there, but managed to arrive before the entire canyon was in shadow.
I bought a GoPro Hero 3 Black Edition the week before the trip (barely; they were very hard to find). I had it set up on a makeshift stand, put it into one second-per-frame time lapse mode, 12 MP images (cropped to 1920x1080 and played back at 30 fps), placed it outside the safety fence at the lookout point (a chilly 3400' above sea level), and pointed it at the canyon. I wanted to capture the last bit of sunlight rising up off the top of the far canyon wall.
I wandered down around the lookout with my iPhone 5, taking photos and panoramas (like this one: flickr.com/photos/jetforme/8230937884/), and generally freezing because I was still in my damp bathing suit from the beach visit earlier. Everyone had their fill of the canyon, I grabbed the GoPro, and headed back to the car to wait for the stragglers in our group. It wasn’t until I got back to the house that I realized what I had captured. I wish I had let the camera run longer.
The Hero 3 field-of-view is rather wide, making the rainbow look more circular than it is.
Technical details: GoPro Hero 3 in time-lapse mode, 12 MP images, bottom portion cropped for 16:9 (1080p) one second-per-frame, 30 fps playback. A bit of color enhancement in Final Cut Pro X (as well as titles).
Great Bad Astronomy article about the video and the formation of rainbows here: slate.com/blogs/bad_astronomy/2012/12/04/time_lapse_video_of_rainbow_as_it_materialize_over_a_hawaiian_canyon.html
Some other press: