At one point this summer, 97 percent of the surface of Greenland’s massive ice sheet was melting. At current rates, Arctic waters could be ice-free in summer by the end of the decade, scientists say.

“Things are happening much faster than what any scientific model predicted,” said Dr. Morten Rasch, who runs the Greenland Ecosystem Monitoring program at Aarhus University in Denmark.

Ownership of the Arctic is governed by the United Nations Convention of the Law of the Sea, which gives Arctic nations an exclusive economic zone that extends 200 nautical miles from land, and to undersea resources farther away so long as they are on a continental shelf. The far northern Arctic Ocean belongs to no country, and conditions there are severe. In a place where exact boundaries were never much of a concern, haggling over borders has begun among the primary nations — between Canada and Denmark, and the United States and Canada, for example.

The United States has been hampered in the current jockeying because the Senate has refused to ratify the Convention of the Law of the Sea, even though both the Bush and Obama administrations have strongly supported doing so. This means the United States has not been able to formally stake out its underwater boundaries. “We are being left behind,” Deputy Secretary Nides said.

But experts say boundary disputes are likely to be rapidly resolved through negotiation, so that everyone can get on with the business of making money. There is “very little room for a race to grab territory, since most of the resources are in an area that is clearly carved up already,” said Kristofer Bergh, a researcher at the Stockholm Institute.

Even so, Arctic nations and NATO are building up military capabilities in the region, as a precaution. That has left China with little choice but to garner influence through a strategy that has worked well in Africa and Latin America: investing and joining with local companies and financing good works to earn good will. Its scientists have become pillars of multinational Arctic research, and their icebreaker has been used in joint expeditions.

And Chinese companies, some with close government ties, are investing heavily across the Arctic. In Canada, Chinese firms have acquired interests in two oil companies that could afford them access to Arctic drilling. During a June visit to Iceland, Premier Wen Jiabao of China signed a number of economic agreements, covering areas like geothermal energy and free trade.