In some places the plant ascends almost a foot above the water.
Here's the sort of carpet it makes.
Since posting this eight hours ago I've heard from a dozen people who've identified the plant as Water Hyacinth. It floats on top of the water and is either a pest or a desirable water plant in the south. In the north it dies over the winter and is often sought after in pond gardens. I've heard that at least one southern gardener grows it on purpose and pulls out the surplus to use as daylily mulch!