The upper Midwest is in the deep freeze, with the arctic air expected to shift eastward as the week wears on.

The National Weather Service posted advisories for the Dakotas and Minnesota 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.

Climate Prediction Center forecaster Stephen Baxter says the cold will affect parts of the northern and eastern U.S. late this week and into the weekend, with much-below-normal temperatures expected in the Great Lakes, Mid-Atlantic and Northeast regions.

Up to half a foot of snow also could fall from the Upper Mississippi Valley to the Northeast Friday and Saturday.

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