BELLE CHASSE, La.—Isaac dumped more than a foot of rain on parts of the Gulf Coast Wednesday, leaving some residents stranded and hundreds of thousands of homes without power.

A storm surge overtopped a levee in Plaquemines Parish, a rural area southwest of New Orleans with about 25,000 residents, which bore the brunt of Isaac's fury. The surge filled up a neighborhood with as much as 12 feet of water. More than 100 people had to be rescued, some of whom had been stranded in their attics or on their roofs.

Late...