High water need not impede your trip as shown by these photos from 1979.
Tow Boat Sucked Under a Bridge - Survives
These are real pictures of an incident that took place at Rooseter Bridge on the Tombigbee River in southwest Alabama in 1979. The photos were taken by a photographer for the Linden Democrat-Reporter.
Scenario plays out like this. The captain was dropping 2 of his 4 barges through the east span of the Rooster Bridge, with the intent of running around through the lift span, and then catching the barges below. The captain underestimated the current and got too close the the bridge. He wasn't able to avoid a collision. Through a series of complicated events (read about them here), he was turned sideways, sucked under the bridge, and popped out and righted on the other side, with the boat still running. He was even able to meet up the the barges he had already sent through.
Don’t try this at home!