Is it the Rogue River or the Rouge River?

Here in Oregon, we spell our whitewater rafting river R-o-g-u-e. In Canada, they spell their river, R-O-U-G-E. And to make matters even more confusing, in the great state of Michigan, there is a Rogue River and a Rouge River! Whew. Almost too much Rogueness (or should we say Rougeness?).
Interestingly, both the Rogue River in Oregon and the Rouge River in Canada, each tout themselves as "one of the best whitewater rafting excursions in America, offering first class rapids throughout summer." Hmmm...it wouldn't be such a bad summer adventure plan--rafting both the Rogue and the Rouge--and then deciding for yourself which you like the best! Whichever river (or spelling) you choose...you're sure to have a top-notch whitewater rafting experience!