Eric Fritch surveyed his 132-acre farm in western Washington on Thursday in the only way possible: by boat.

As waterways in the region rose to historic levels this week, and officials issued urgent evacuation orders to Mr. Fritch and more than 100,000 of his neighbors, the Snohomish River, which runs past his farm, had already submerged his fields and fences, along with his tractor and other equipment, even after he had moved them to higher ground.

He saved the highest spot on the farm for 60 head of cattle, but wasn’t sure they would make it. “They’ve got another foot or two of dry ground,” he said, “so it’s really just a question of what happens in the next day or so.”

That’s the situation across western Washington, where several days of heavy rain have swollen a number of rivers and tributaries. Leaders in the Skagit Valley, roughly halfway between Seattle and the Canadian border, ordered everyone within the 100-year flood plain to evacuate.

“You can stand downtown here and just see whole Doug firs and cottonwood trees coming down the river, like a freight train,” said James Eichner, who sought higher ground in the city of Monroe as floodwaters rose at the Snohomish River farm where he works. “It’s just a giant steamroller.”

Officials were especially concerned about the Skagit and Snohomish Rivers, which reached new heights in places on Thursday, surpassing records set in 1990. State and local leaders warned that levees and dams would remain at risk for days — and people need to be wary even as the waters recede.

“This is a very, very serious situation,” Bob Ferguson, Washington’s governor, said at an afternoon news conference. “If you have instructions to evacuate, please, please, please evacuate.”

Another storm system, albeit not as large as the one this week, is expected to arrive as early as Sunday, with the potential to cause landslides and more flooding on already saturated ground.

The heavy rain is the result of an unusually potent atmospheric river system pulling a plume of moisture off the warm ocean and spreading it across the Pacific Northwest. Its reach has spread flooding to British Columbia, where highways were shut down late Wednesday.

The system’s effects reach as far as the eastern United States, where the moisture in the upper atmosphere is supercharging the chance for heavy snow this week.

Flooding from this sort of weather system unfolds over many days, with rivers rising and falling with the pace of downpours. Many rivers will have crested twice by Friday, and the Puyallup River in Pierce County will have crested three times.

The worst of the flooding has threatened Washington State communities on or close to Puget Sound. Skagit County officials issued what they described as mandatory, immediate evacuation orders for the region’s 100-year flood plain, urging residents, “Do not wait.”

The Los Angeles fires in January forced mandatory evacuation orders for 180,000 people, in a much more heavily populated area.

Hundreds of troops with the Washington National Guard were called up to help with sandbagging efforts as flooding closed schools and shut down public transit in many communities. Flooded roads and washouts made travel treacherous. The police and firefighters repeatedly warned residents not to drive through standing water.

In Mount Vernon, one of the communities most at risk, Mayor Peter Donovan said he was concerned that residents wouldn’t take this emergency seriously. Drills and preparation for flash floods begin every autumn, and locals are used to seeing the Skagit River swell.

“Some people are feeling more comfortable staying at their house, thinking this is just the Skagit River doing what the Skagit River does,” he said. “Maybe you’ve lived through a few of these high-water events, and it hasn’t touched your house. But we’re in uncharted territory.”

Lisa Janicki, a Skagit County commissioner, said officials had seen videos of people driving cars — “Teslas, even,” she said — through standing water, and walking their dogs atop dikes at risk of failing. “Don’t do that,” she said. “Be smart. This is a different situation than what you’ve seen before.”

Road closures and government safety warnings didn’t deter people living near the city of Snohomish from venturing downtown on Thursday to watch the rising river.

“Everyone wants a peek, because it looks so big and scary,” said Jennifer Bynum, the manager at Andy’s Fish House, which sits about 20 feet above the river. “So the coffee shops are popping, and there’s not a parking spot to be had. We’re probably going to sell 50 million gallons of chowder today.”