I have been meaning to draw this for some time. Where I live used to be a rice plantation and the lagoons were rice paddies. This is called a rice trunk and was used to regulate the river water in and out of the largest paddie. I am not sure whether the dam is as old as the rice trunk or whether it was built later to keep the river water out of this ditch. Now there is a pump which regulates the water level in the lagoon as we now call it.
I found the name for them in a book called Very Charleston byDiana Hollingsworth Gessler which is an illustrated journal which is "A Celebration of History, Culture, and Lowcountry Charm." She has also written similar books about California and New Orleans.