The American Airlines departure board shows scores of canceled flights on Tuesday at O'Hare. (Credit: Susan Carlson/CBS)

The American Airlines departure board shows scores of canceled flights on Tuesday at O’Hare. (Credit: Susan Carlson/CBS)

Updated 03/05/13 – 1:41 p.m.

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CHICAGO (CBS) — The snow has only just started falling in Chicago, but airlines have already cancelled more than 1,100 flights at Chicago’s two major airports, with up to 10 inches of snow expected to fall by the end of the day.

WINTER STORM WARNING | TRAFFIC | SCHOOL CLOSINGS | FLIGHT DELAYS | RADAR

According to the city’s Aviation Department, approximately 900 flights have been canceled at O’Hare International Airport as of 1:30 p.m.

Another 240 flights have already been canceled at Midway International Airport on the South Side.

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A winter storm warning is in effect until midnight on Tuesday.

A total of 4 to 8 inches of snow is expected–with some localized totals as high as 10 inches.

Snow will begin falling heavily in the afternoon–up to and inch or two an hour–and continue through the afternoon rush hour.

Heavy snow will taper to flurries later in the evening.

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There is a warmup ahead, with temperatures in the 40s by Friday.