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There have been some claims made (example) that global warming had something to do with why the 2013-2014 winter was so cold in the Midwest area of America.

If this is true then how did global warming make the winter so cold? Shouldn't it make the temperature rise in all parts of the world, during all seasons?

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    $\begingroup$ Not really sure why this question got downvoted so hard. With the changes Siv suggested, it's a great question (albeit one with some misconceptions, but those can be dealt with in the answers/comments). Voting to re-open, and editing in context. $\endgroup$ – naught101 Sep 10 '14 at 7:41
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I bet you live on the eastern half of North America, which had a cold winter of 2013-2014, Europe and Alaska had a very warm winter, and China had its second warmest January.

Jennifer Francis of Rutgers has been advocating the Arctic or Polar Amplification theory (Wikipedia). In which she hypothesises that warming of the Arctic has been greater than lower latitudes, and this lowers the temperature contrast between the poles and the equator. This in turn weakens the jet stream which becomes slow and meandering. This weakened and meandering jet stream then is less able to hold back cold polar air, the so called "polar vortex" which can then bring outbreaks of cold air from the poles to the mid latitudes.(BBC Article outlining the theory)

However, the theory is not without some problems...

One problem is that the changes in atmospheric thickness and wind speed observed have become apparent only since the mid-1990s, which gives fewer than 20 years of data to work with. Another difficulty concerns the blocking patterns. Dr Francis’s theory suggests there will be more of them in future, as the world warms. But climate models unanimously disagree, saying that global warming will produce fewer of them...(The Economist)

and...

Tim Woollings, an atmospheric dynamics researcher at Oxford University pointed out in an email exchange that over the Atlantic the jet stream was stuck, but was not meandering or slowed, however he did concede that the jet stream over the Pacific did match the hypothesis.(Yale Environment 360) The jet stream over the Atlantic reached sustained speeds over 230 miles per hour (370 km/h) during the winter,(Liam Dutton) reaching 275 miles per hour (443 km/h) on 22 December 2013. 30% stronger than the normal jet stream.

So yes, there is a theory which describes how warming can bring locally colder winters, but also, the science isn't exactly settled yet.

Addendum: here's a link to a good blog post on the matter Polar Amplification, Vortex Disruption to Set off Extreme Weather Events For US, UK Yet Again

An overview of the debate as of 2016:Wapo 2016

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