In the opinion of some scientists the loss of Arctic summer sea ice (and resulting Arctic amplification) on NH will result in-
Increasing: 

•  climate variability
• weather extremes, including severe prlonged winter cold
• heat waves
• droughts

Recent Research

March 2015 D. Coumou Science. Warming Arctic blamed for worsening summer heatwaves

March 2014 Nature Recent Arctic amplification and extreme mid-latitude weather.

December 2013 Summer Heat Waves May Be Linked To Sea Ice Loss and snow cover decline..

2009 J. Oster Late Pleistocene California droughts during deglaciation and Arctic warming.

Arctic summer wind shift could affect sea ice loss and U.S./European weather, says NOAA-led study

VIDEO LECTURE
Does Arctic amplification
fuel exytreme weather
in miid lattitudes?
Dr J Francis

Scientists call the Arctic snow and summer sea ice albedo cooling efect the 'air conditioner' for the entire northern hemisphere, so the hemispheric climate will change along with further accelerated warming.

"Make no mistake, the Arctic is the Northern Hemisphere’s air conditioner. If the ice starts disappearing in the summer, it will have a significant impact on our climate."
— Dan Satterfield, AGU blog, August 2010

A paper on amplification of planetary waves and recent Northern Hemisphere weather extremes

Dr. Jennifer Francis of Rutgers University, at the AGU meeting in December 2011 (Does Arctic Amplification Fuel Extreme Weather in Mid-Latitudes?), presented new research in review that shows that Arctic sea ice loss may significantly affect the upper-level atmospheric circulation, slowing its winds and increasing its tendency to make contorted high-amplitude loops. Such high-amplitude loops in the upper level wind pattern (and associated jet stream) increase the probability of persistent (that is, longer-duration) weather patterns in the Northern Hemisphere, potentially leading to extreme weather due to longer-duration cold spells, snow events, heat waves, flooding events, and drought conditions.

All of these spell bad news for Northern hemisphere agriculture and therefore world food security.

Research published in 2008 by C. Archer and K. Caldeira reported that the jet stream has moved northwards 270 miles in 22 years, presumably due to global climate change.

 The northern hemisphere is warming faster than the southern hemisphere because there is more land in the north and more water in the south. Midcontental regions tend to warm fastest.

Jennifer A. Francis, Winter Northern Hemisphere weather patterns remember summer Arctic sea-ice extent: , "Mechanisms by which the atmosphere 'remembers' a reduction in summer ice cover include warming and destabilization of the lower troposphere, increased cloudiness, and slackening of the poleward thickness gradient that weakens the polar jet stream. This ice atmosphere relationship suggests a potential long-range outlook for weather patterns in the northern hemisphere."

Effect on the jet stream and planetary weather patterns (http://www.arcticportal.org/effects-of-arctic-sea-ice-reduction):
"Continued loss of Arctic sea ice may dramatically change global weather and precipitation patterns in the decades to come. The jet stream will probably move further north in response to warmer temperatures over the pole, which will bring more precipitation to the Arctic. More frequent and intense droughts over the U.S. and other regions of the mid-latitudes may result from this shift in the jet stream. Changes to the course of the jet stream affect weather patterns for the entire planet, and we can expect impacts on the strength of the monsoons and re-curvature likelihood of hurricanes."

NRDC: Global Warming Puts the Arctic on Thin Ice (www.nrdc.org/globalwarming/qthinice.asp):
"The cold temperatures in the Arctic ... act as a sort of air conditioner for the rest of the world.... The contraction of the Arctic ice cap is accelerating global warming. Snow and ice usually form a protective, cooling layer over the Arctic. When that covering melts, the earth absorbs more sunlight and gets hotter. And the latest scientific data confirm the far-reaching effects of climbing global temperatures.

"A warmer Arctic will also affect weather patterns and thus food production around the world. Wheat farming in Kansas, for example, would be profoundly affected by the loss of ice cover in the Arctic. According to a NASA Goddard Institute of Space Studies computer model, Kansas would be 4 degrees warmer in the winter without Arctic ice, which normally creates cold air masses that frequently slide southward into the United States. Warmer winters are bad news for wheat farmers, who need freezing temperatures to grow winter wheat. And in summer, warmer days would rob Kansas soil of 10 percent of its moisture, drying out valuable cropland."

How much will the loss of Arctic summer sea ice boost the rate of global warming?

There is no published research that answers this question, though for many years scientists have been saying that this will increase the global warming rate.

Professor Peter Wadhams says the loss of all summer Arctic sea ice is equivalent to 20 years of CO2 emissions on global warming.

Sea ice loss is not accounted for in future temperature increase projections by the IPCC. The climate sensitivity used is a single linear metric that does not account for non linear changes in the climate system.