HOUSTON (AP) -- Rising floodwaters from the remnants of Hurricane Harvey chased thousands of people to rooftops or higher ground Sunday in Houston, overwhelming rescuers who fielded countless desperate calls for help.
A fleet of helicopters, airboats and high-water vehicles confronted flooding so widespread that authorities had trouble pinpointing the worst areas. Rescuers got too many calls to respond to each one and had to prioritize life-and-death situations.
The turbid water rose high enough to begin filling second floors -- a highly unusual sight for a city built on nearly flat terrain. Authorities urged people to get on top of their homes to avoid becoming trapped in attics and to wave sheets or towels to draw attention to their location.
Harris County Sheriff Ed Gonzalez used Twitter to field calls for assistance. Among those seeking help was a woman who posted: "I have 2 children with me and the water is swallowing us up."
Some people used inflatable beach toys, rubber rafts and even air mattresses to get through the water to safety. Others waded while carrying trash bags stuffed with their belongings and small animals in pet carriers.
Houston Mayor Sylvester Turner said authorities had received more than 2,000 calls for help and would be opening the city's main convention center as a shelter. He urged drivers to stay off flooded roads to avoid adding to the number of those stranded.
"I don't need to tell anyone this is a very, very serious and unprecedented storm," Turner told a news conference. "We have several hundred structural flooding reports. We expect that number to rise pretty dramatically."
The mayor defended his decision not to ask residents to evacuate before the heavy rain from Harvey swamped roads and neighborhoods across the nation's fourth-largest city. He said there was no way to know which neighborhoods would be most vulnerable.
"If you think the situation right now is bad and you give an order to evacuate, you are creating a nightmare," he said, citing the risks of sending the city's 2.3 million inhabitants onto the highways at the same time.
Rainfall of more than 4 inches per hour resulted in water levels higher than in any recent floods and higher than during Tropical Storm Allison in June 2001, said Jeff Linder of flood control district in Harris County, which includes Houston.
The latest forecasts showed that 15 to 25 more inches (38 to 63 centimeters) was possible over the next several days, with some places getting as much as 50 inches (127 centimeters) total, the National Hurricane Center announced.
Rescue came by land, water and air.
On Interstate 45 south of downtown, television video showed people climbing over concrete dividers to get to a high-wheel dump truck that appeared to be wheels-deep in water on a service road. They clambered up the side of the truck to get into the dump box.
In Friendswood near Houston, authorities asked people with flat-bottomed airboats or fuel for them to help rescue people.
Jesse Gonzalez, and his son, also named Jesse, used their boat to rescue people from a southeast Houston neighborhood. Asked what he had seen, the younger Gonzalez replied: "A lot of people walking and a lot of dogs swimming."
"It's chest- to shoulder-deep out there in certain areas," he told television station KTRK as the pair grabbed a gasoline can to refill their boat.
The Coast Guard, which received more than 300 requests for help, deployed five helicopters and asked for additional aircraft from New Orleans.
Staff at a Houston television station broadcasting live coverage of the floods had to evacuate after water from the nearby Buffalo Bayou started to gush into the building. The anchors and news operations at KHOU-TV moved first to a second floor before finally abandoning the station.
The director of the Federal Emergency Management Agency, Brock Long, said the government expected to conduct a "mass care mission" and predicted that the aftermath of the storm would require FEMA's involvement for years.
"This disaster's going to be a landmark event."
President Donald Trump tweeted Sunday morning that he would visit Texas.
"I will be going to Texas as soon as that trip can be made without causing disruption," the president posted on Twitter. "The focus must be life and safety."
The rescues unfolded a day after the hurricane settled over the Texas coastline. It was blamed for killing at least two people and injuring up to 14.
Anxiety ran high throughout the region between Corpus Christi and Houston because some of the areas with the greatest hurricane damage were inaccessible to rescuers.
One person was killed in Aransas County when in a fire at home during the storm, county Judge C.H. "Burt" Mills Jr. said.
Another person -- a woman who tried to get out of her vehicle in high water -- died in flooding in Harris County, where Houston is located, , though authorities had not confirmed a cause of death, said Gary Norman, a spokesman for the Houston emergency operations center.
Meanwhile, rainfall totals climbed by the hour. By midday, South Houston had received nearly 25 inches (63 centimeters) and the suburbs of Santa Fe and Dayton got 27 inches (69 centimeters).
The fiercest hurricane to hit the U.S. in more than a decade came ashore late Friday about 30 miles (48 kilometers) northeast of Corpus Christi as a mammoth Category 4 storm with 130 mph (209 kph) winds.
Harvey weakened Saturday to a tropical storm. By Sunday morning the system was centered about 65 miles southeast of San Antonio, with maximum sustained winds of about 45 mph (72.42 kph), according to the hurricane center, which described the flooding as "catastrophic."
Harvey arrived as the fiercest hurricane to hit the U.S. in 13 years and the strongest to strike Texas since 1961's Hurricane Carla, the most powerful Texas hurricane on record.