The photos look to the east-northeast. The rainbow occurs in a storm that is receding and drifting to the east and has just passed Sawmill Canyon in the foreground. The mountain ridge on the photo is called Timber Ridge, and most of the heavier rainfall is on the other side of that. The much finer, mist-like droplets near the trailing end of the storm are still falling in the canyon and create a rainbow that has a smaller radius and is a little wider than an 'ordinary' bow that occurs in larger raindrops. The effect is very obvious but requires a fairly specific landscape setting to be seen.
The photos were taken on July 27, 2009 using a Nikon D700 camera. Times below are local time (MDT).
Photo 1: The effect is just beginning to occur. 18:37:50 pm, 36 mm focal length, ISO 800, 1/160 sec at f/6.3.
Photo 3: The rainbow in canyon is disappearing and still shows a discontinuity. Also note that the 'foot' of the rainbow beyond the canyon is not following the circle but appears to kink - i.e. the radius is getting larger at lower altitude - maybe due to drops coalescing and increasing in size as they fall? 18:45:11 pm, 48 mm focal length, 200 ISO, 1/125 sec at f/5.6.
All three photos have not been cropped, modified or enhanced in any way.