When taking trips to the national parks, I like to plan some of my photos shoots. I do some internet research of the location and usually purchase a photography book specific to the park. For my most recent trip to Yellowstone, I purchased Gustav Verderber's "Photographing Yellowstone National Park: Where to Find Perfect Shots and How to Take Them". This is one in a series of books that covers several national parks. I've used these books for Death Valley, Great Smoky Mountains, Everglades and Glacier National Parks as well.
I found Verderber's book for Yellowstone to be particularly helpful. He advises the photographer to "be at Artist Point Overlook on a clear morning at precisely 9:45 am. At that exact moment, the cloud of mist at the bottom of the falls turns luminous as though lit from within by the northern lights...by 9:55, the mist at the foot of the Lower Falls has become a complete, shimmering rainbow!" He also provides time spans for the rainbow from some other vantage points including Uncle Tom's Overlook and Lookout Point.
Using this information, I positioned myself at the Artist Point Overlook one morning and the Lookout Point the next morning at the recommended times. As promised, the rainbow arrived right on schedule!
Sometimes, it pays to do a little research!