I'm having trouble understanding the concept of cresting. A river, let's say, reaches flood stage at 20 feet. How can it crest at 27 feet?

Because flood stage is only an arbitrary designation. The crest of the river is how high it rises, whether above or below flood stage makes no difference. The authorities establish a flood stage for a river at a particular point, but this only tells people that when the river rises to that point things are gonna get rough. The Mississippi has in history crested as 30 feet above flood stage.

In this regard, read Rising Tide, which I am reading now. It's the most fascinating history book I've ever read, dealing with the Mississippi River flood of 1927 and it's aftermath. I cannot recommend this book highly enough, even though I am only half-way through it.

And by all means read the blurb on it at Amazon.com. Two thumbs up for this book.