I think I found the answer. While I was trimming the lawn, I saw a dark brown, mouse-like creature about 2.5" long (not counting the tail) running into a hole at the end of one of the "rivers". After looking up online, it's a vole, and here is a page on voles and their damage to lawns.
http://www.agry.purdue.edu/turf/tips/2007/voles.htm