Harvey sent devastating floods pouring into the nation’s fourth-largest city Sunday as rising water chased thousands of people to rooftops or higher ground and overwhelmed rescuers who could not keep up with the constant calls for help.

The incessant rain covered much of Houston in turbid, gray-green water and turned streets into rivers navigable only by boat. In a rescue effort that recalled the aftermath of Hurricane Katrina, helicopters landed near flooded freeways, airboats buzzed across submerged neighborhoods and high-water vehicles plowed through water-logged intersections. Some people managed with kayaks or canoes or swam.