This means the melting happened from surface ice mass, inland from the coastline, the authors found.
The study, published in Proceedings of the National Academy of Sciences, used data from Nasa's gravity recovery and climate experiment (known as Grace) and Global Positioning System stations scattered across Greenland to analyze changes in ice mass.
The loss of ice mass to the oceans is the second largest contributor to sea level rise. "Only a very small percentage has been lost in the last few decades, but the big worry is that the rate of ice loss in Greenland and Antarctica is accelerating, and the rate of sea-level rise is accelerating", he said.
From 2002 to 2016 Greenland lost 280 billion tons of ice a year, but these losses have been uneven: in 2003-2013, the melting has accelerated nearly four-fold, from 102 to 393 billion tons of ice per year.
Michael Bevis, a professor of geodynamics at The Ohio State University and the lead author of the study, said the research found that humanity may have passed the point of no return when it comes to combating climate change, reported a news agency.
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Antarctica is becoming an increasing concern, however, with ice vanishing at its fastest rate in recorded history.
The effect of this finding is that south-west Greenland, which had not been considered a serious threat, now looks as if it will become a major future contributor to sea-level rise. If all of Greenland's vast ice sheet, 3km thick in places, was to melt, global sea levels would rise by seven meters, or more than 20ft, drowning most coastal settlements.
Prof Bevis said the North Atlantic Oscillation is a natural, if erratic, cycle that causes ice to melt under normal circumstances.
But a team of scientists led by Michael Bevis, lead author and professor of geodynamics at The Ohio State University, made a decision to look at Greenland's less-studied southwest region and found that this region that is devoid of large glaciers has had the largest sustained ice loss from early 2003 to mid-2013. These ice sheets have been melting at an "unprecedented" rate, 50 per cent higher than pre-industrial levels and 33 per cent above 20th-century levels. The freshwater in the salty Atlantic ocean, has found out also an influence on the climate in Europe, researchers have.
Researchers attributed this both to rising global temperatures from climate change, and the North Atlantic Oscillation - a weather phenomenon that causes fluctuations in atmospheric pressure at sea level.
The ice above the Arctic Circle is disappearing far quicker than experts previously thought, and it's feared this will lead to faster sea level rises as Earth's atmosphere continues to warm. "The only thing we can do is adapt and mitigate further global warming, it's too late for there to be no effect", Bevis continued. Data from the satellites showed that between 2002 and 2016, Greenland lost around 280 gigatons of ice per year, equivalent to an annual sea level rise of 0.03 inches. If the ice on the world's largest island is melting more quickly than previous realized, that spells trouble.