The melting from the mountain glaciers alone raises sea level about 0.7 millimeters a year.

The ice sheets of Antarctica and Greenland together possess about 100 times as much ice as all of the mountain glaciers combined, but contribute only slightly more to the sea level rise: 310 billion tons a year, Dr. Scambos said. That is because most of the mountain glaciers lie in areas where temperatures are closer to the melting point than they are in Greenland or Antarctica, and so slight warming tips them to melting.

Greenland, with 10 percent of the world’s ice, has enough to raise sea level by 23 feet. “I still think Greenland is the most important thing to watch for this century,” Dr. Scambos said.

In 2012, when summer Arctic temperatures were particularly warm, surface melting was observed almost everywhere on Greenland’s glaciers, even in the mountains. That had not happened for decades.

Researchers from Dartmouth found that another side effect from global warming, forest fires, made the melting even worse. Soot from fires elsewhere in the world landed on Greenland snow, making it darker, causing it to absorb more heat.

A new study of Greenland, published Sunday in the journal Nature Geoscience, paints an even bleaker picture. The melting is accelerated because many of the glaciers flow in the warming waters around Greenland. However, scientists had believed that the melting would slow once the bottom of the glaciers melted and they were no longer touching the water.

The new research indicates otherwise. Researchers at the University of California, Irvine, including Eric Rignot, the lead author of one of last week’s papers concluding that the melt in West Antarctica is irreversible, discovered long, deep canyons below sea level and under the ice sheet. So even as the glaciers retreat, they will still be in contact with the encroaching warm water, and as a result, more ice will melt. “They will contribute more to sea level rise,” said Mathieu Morlighem, lead author of the Nature Geoscience paper.

Antarctica is the largest frozen mass on the planet, accounting for about 90 percent of the earth’s ice. Most of it is in East Antarctica, which is generally higher and colder and less likely to melt. By some estimates global warming is leading to increased snowfall there, which is limiting the loss. But as in West Antarctica, some of the ice resides in bowl-shape depressions, which are similarly vulnerable to melting.