“We are pretty worried, about as worried as you can get,” said Jimmy Barham, a meteorologist at the National Weather Service office in Little Rock, Ark.

• The rain is forecast to persist day after day, with totals well over a foot.
• While the tornado risk was highest on Wednesday, the potential for severe storms that could produce tornadoes will be present through the weekend, primarily in Arkansas and other states across the Deep South.
• The rain falling in the Northeast on Thursday is connected to the same system, which stretches back to Texas.
• Outlooks for high-risk excessive rain — like what is forecast for the Central United States on Thursday and Saturday — are a big deal. Nearly 83 percent of flood-related damage occurs on days when a high risk has been predicted.

“Last night we had two to six inches of rainfall,” Ashton Robinson Cook, a meteorologist at the Weather Prediction Center, said on Thursday morning. Going forward, three-day totals are likely to reach between six and 12 inches, on top of what has already fallen over Arkansas, southeastern Virginia, western Kentucky and western Tennessee.

These amounts are the most likely outcome, bringing total accumulations, including yesterday’s rainfall, to nearly 15 inches. It is possible that some places in this region could receive another foot of rainfall, which would be devastating, and the best case is that these same areas only get four more inches, which would still lead to floods.

“We’re in a persistent pattern where there’s plenty of energy coming in from the Western U.S. and an abundant source of moisture across the southern U.S. that’s kind of interacting with repeat rounds of thunderstorms,” Dr. Robinson Cook said.

On Thursday, one of the biggest risks is to the flatter delta along the Mississippi River in East Arkansas and West Tennessee up into Western Kentucky and Southern Indiana.

“Any location in our area is at risk for flooding, so the threat is widespread,” said Todd Beal, a meteorologist at the National Weather Service office in Memphis.

The ground has soaked up the rain that’s already fallen like a wet T-shirt. Once the ground is saturated like this, it behaves similarly to concrete, where all the water flows off it, Mr. Barham said. This is likely to bring a risk of flash floods even to areas that don’t typically flood.

The more rain, the less the ground can absorb. Mr. Barham explained that at the start of the storm, it took about three inches of rain in three hours for flooding to begin. “Now, we’re down to like one inch in three hours and you get flooding,” he said.

On Friday, the risk will swing slightly back to the west, putting the rounded mountain terrain of the Ozarks, nestled along the border of Arkansas and Missouri, at particular risk. While many of the reservoirs in the region can hold the floodwaters back, there is a risk that some rivers, like the Spring and White, could flood, and that the towns nearby may have to be evacuated, Mr. Barham said.

Another factor to consider is that the stretch of Interstate 40 between Little Rock and Memphis is a major trucking route. It connects deliveries east and west across the country, and it provides a path for trucks going from Dallas north to St. Louis. This farmland around Interstate 40 is known for flooding frequently. Rice fields are typically flooded in the winter, drawing duck hunters. However, too much rain could be a considerable issue.

“Most city systems are not built to take so much rain, so once you get over that threshold there’s nowhere for the water to go, and so that’s when you get water on interstates like I-30 and I-40,” Mr. Beal said.

River flooding will become a growing concern the longer this rainfall lasts. The rain will flow down small streams into larger rivers, which all funnel into the Mississippi.

By Saturday, the concern will shift slightly east, targeting the same region as on Thursday as it brings another rare but persistent risk from Arkansas to Southern Indiana.

“These are widespread and historic amounts of rainfall,” Dr. Robinson Cook said. “It’s not every day that you get a forecast of 10 to 15 inches of rainfall over a four-day period in a local area. That’s just not something that happens commonly.”