Mr. Perez’s wife and father-in-law had urged him not to go to work that day, Chief Acevedo said. “His response was, ‘I’ve got work to do.’” Mr. Perez, who worked in the department’s division of traffic enforcement, was a “sweet, gentle public servant,” the chief added.

Outside Houston’s main shelter, lines formed.

As rain fell in the early afternoon, scores of people waited outside the George R. Brown Convention Center, where more than 9,000 people had already taken shelter. A pile of wet American Red Cross blankets sat near the end of one line.

On Sunday and Monday, evacuees were able to enter the sprawling complex without delay. Buy by Tuesday, while the convention center appeared to be organized, there were some signs of strain. Some people set up bedding in the main corridor, an area that had been mostly empty a day earlier, to get away from the increasingly crowded main dormitory.

Nathan Malbrue, who was sitting on the edge of an inflatable mattress, said he was not bothered by the growing crowd. He said he was in the hallway, near a medical station, because of a heart condition. “Just bring everybody in,” he said. “This is a big building.”

But Cora Watson, 58, feared that the convention center would be overwhelmed. “Move them to hotels or something,” she said, her voice barely audible.

Reservoirs are above capacity in Houston.

Water began flowing over an emergency spillway at a major Houston flood-control reservoir on Tuesday, the Army Corps of Engineers said, adding to flooding in the area about 15 miles west of downtown.

So far the overflow at the Addicks reservoir dam is minor, about 100 cubic feet per second, Edmond Russo Jr., deputy district engineer for the Army Corps’ Galveston district, said at a news conference. But it should rise to about 4,500 cubic feet per second — about 120 million gallons per hour — by Thursday, he said, as the reservoir levels peak.

The rate should decline to current levels two days after that, he said. But the large flow could bring up to 2 feet of water to the streets east of the reservoir. The water will eventually flow into Buffalo Bayou, which passes through downtown.

Dr. Russo said that dam safety operators were monitoring the structure and that it was in no danger.

Levels at a second reservoir nearby, Barker, are increasing as well and its two spillways are expected to overflow starting Saturday, he said.

Water in the two reservoirs, which are normally dry, has risen quickly since Harvey first began inundating the area. Efforts to reduce the levels by controlled releases through gates in both dams have not been sufficient.

In addition to the flooding over the spillway, both reservoirs have been spreading into nearby subdivisions as the water has risen. A spokesman for the Harris County Flood Control District said that about 2,500 homes near Addicks reservoir, and 670 near Barker, have flooded already.

The city also has to worry about having enough potable water. Houston’s Northeast Water Purification Plant, one of three plants that supply water to the city, is flooded. While the system is still working, even with much of its equipment underwater, city officials are worried about their ability to keep it running.

A levee breach threatened a village near Houston.

A levee designed to protect the community of Columbia Lakes, 40 miles southwest of Houston, from the Brazos River was breached, Brazoria County officials said.

Columbia Lakes is a small resort village with a country club and golf course, and is surrounded by levees. Residents were ordered to “GET OUT NOW!!” according to a Twitter message, although many had already left after a mandatory evacuation order was issued Sunday.