HOUSTON - Tropical Storm 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 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 2005's Hurricane Katrina, helicopters landed near flooded freeways, airboats buzzed across submerged neighborhoods, and high-water vehicles plowed through submerged intersections.

Volunteers joined emergency teams to pull people from their homes or from the water, which was high enough in places to gush into second floors. Authorities urged people to get on top of their houses to avoid becoming trapped in attics and to wave sheets or towels to draw attention to their location.

The storm has so far affected about a quarter of the Texas population, or 6.8 million people in 18 counties. It was blamed for at least two deaths.

The National Weather Service issued another ominous forecast: Before the storm that arrived Friday as a Category 4 hurricane is gone, some parts of Houston and its suburbs could get as much as 50 inches (1.3 meters) of rain. That would be the most ever recorded in Texas.

"The breadth and intensity of this rainfall is beyond anything experienced before," the National Weather Service said in a statement.

US President Donald Trump is expected to visit the area on Tuesday.

Up to 1,200 people had to be rescued in Galveston County alone, said Mark Henry, the county judge, the county's top administrative post.

Houston's George R. Brown Convention Center was quickly opened as a shelter. It was also used as a shelter for Katrina refugees in 2005.

Houston Mayor Sylvester Turner said authorities had received more than 2,000 calls for help, with more coming in. He urged drivers to stay off roads to avoid adding to the number of those stranded.

Governor Greg Abbott had urged people to flee from Harvey's path, but the Houston mayor issued no evacuation orders.

"Now is not the time to second-guess the decisions that were made," Abbott said.

The mayor said there was no way to know which parts of the city were most vulnerable. "If you think the situation right now is bad, and you give an order to evacuate, you are creating a nightmare," Turner said.

Ap