This video demonstrates digital media that emulates the original design shown below.

The projections rely on a set design that allows the sky to be visible in every setting.

The original design that I did for this show combined traditional cyc lighting, gobos, projected clouds, and shadow play. The balloon shadow shown here was a plywood cutout that traveled behind the cyclorama. In the media, it has been replaced with a digital silhouette.
The image shown in the foreground in the video demonstration above is from a 2012 production.
There were traps in the floor into which the company lowered themselves for the tornado. This was a minimalist way of creating storm cellars. Other than benches and very simple props, no other scenery was brought on stage.
The digital media maintains the original atmospheric mix of layers of clouds with stars and sunset effects.
You can see many more photos from the original design on this page.