Big trees in a levee can be a big problem. You are going to need to dig the stumps out completely with an excavator.
-HH
X2 - as the roots rot they create voids that would very easily provide a path for water to take. I believe the rule of thumb is that if the tree is larger than 4 inches in diameter you need to remove the stump and repack the hole, but others more knowledgeable than I will jump in and provide more details.