Moonbows, and rainbows in general, have very simple physics which determine where they appear relative to a light source and observer. By knowing where we want the moonbow to appear (the mist of a waterfall) and the known position of the moon, we can determine where and when to position ourselves for the best view. One way to do this is geometrically, by measuring the angle from the viewer to the waterfall mist and then knowing when the moon will subtend an angle of 42 degrees to the mist relative to the viewer. Alternatively, we can determine this computationally, which negates the need to make on-site measurements and alleviates the need for trigonometry . This is the method I have used since 2012.
I use the modeling software, Trimble Sketchup Pro, to import satellite imagery for a 3D reconstruction of Yosemite Valley. I then use TPE to determine the azimuth and elevation of the moon at one hour intervals and create models of the rainbows for those angles. By placing the rainbow models into the model of the valley, I can see precisely where the moonbow will manifest itself at the given times. Based on this information, combined with my past experience of knowing which positions make the best photographs, I select my recommended timeframe for viewing moonbows each night. I also truncate the expected viewing window if it won't be dark enough to view the moonbow or if the moon will be too low to create a moonbow. I do not update the predictions based on weather forecasts or observed conditions. Keep in mind that even slight clouds between the moon and waterfall are enough to diffuse the light and kill the moonbow.
This method of visualizing moonbow position is accurate and versatile. I can try any number of new observation positions just by moving the rainbow model inside the valley model. Over the years, this has helped me visualize the moonbow movements which has made it easier to meet my goals in filming them.
I welcome any questions on this process and if you're really nice to me, I just might share predictions for other interesting locations.