MINNEAPOLIS (AP) — The upper Midwest was in the deep freeze Tuesday, with the arctic air expected to shift eastward and affect millions of people as the week wears on.

The National Weather Service posted advisories for the Dakotas and Minnesota on Tuesday, with wind chills from 10 to 20 below zero. Wind chill is the combination of air temperature and wind, and forecasters say wind chills this cold can cause frostbite to exposed skin in as little as 30 minutes.

Dense morning fog over much of Texas on Tuesday slowed the commute for motorists and delayed flights at Dallas-area airports. Fog also impaired visibility in the Austin, Houston and San Antonio regions, and the National Weather Service issued a dense fog advisory for many parts of the state.

In Indiana, snow falling at rates of more than an inch per hour on Tuesday caused poor travel conditions, including along the Interstate 70 corridor. The state Department of Transportation deployed nearly 500 snowplows and trucks statewide.

The cold will affect parts of the northern and eastern U.S. later this week and into the weekend, with frigid temperatures expected in the Great Lakes, Mid-Atlantic and Northeast regions, according to Climate Prediction Center forecaster Stephen Baxter.

Below-normal temperatures are expected this weekend and into Monday across the entire northern half of the country, from the Pacific Northwest to Maine and as far south as Oklahoma, Arkansas and Virginia, according to the Climate Prediction Center.

Up to half a foot of snow also could fall from the Upper Mississippi Valley to the Northeast on Friday and Saturday, and areas east of the Appalachian Mountains could see freezing rain and sleet on Saturday.

Another arctic air mass on the heels of this cold front is expected to bring temperatures to the northern Plains over the weekend and into early next week that will be as much as 24 degrees below normal, according to Baxter.

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