And carry a paper map! We were on the Natchez Trace years ago when tornadoes swung through the area. Our weather radio told us which counties were under alert. One was Transylvania County... Where the heck is Transylvania County? After much flipping of pages for adjacent states in our atlas we found it and settled back as it was well North and West of us. The alerts went on for a long time, always somewhere around us. Then they named our specific primitive, unstaffed campground with a fifteen minute warning. We pounded doors (and tents), got everyone into the block bath houses (with 4' skylights) and waited for the storm to rip through. The tornado skimmed over us and touched down a mile away. When we drove out, we could see where they had cleared downed trees off the road. We were very lucky. It was a wide spread, multi-state storm so driving out of it would not have been an option. It would have caught us on the road.
Our weather radio uses rechargeable batteries, can charge off an outlet, from it's little solar panel or by hand crank (lots of cranking). We carry spare batteries and a backup battery like you use for cell phones. Once charged, it can be used to charge your cell phone. Don't count on power from the rig. If you have to run for cover you want that radio, backup power, cell phone and map with you (as well as water, snacks, meds, and other emergency supplies... Pocket knife, matches, flaslight, first aid kit).