pieces of an urgent puzzle posed by global warming. Can the continuing slow increase in worldwide temperatures touch off abrupt climate upheavals?

Each piece of the puzzle is a dynamic and complicated body of water. One, the North Atlantic, is some two miles deep and liquid. The other, this ice cap, is two miles high and solid. For scale, think of it as a freshwater Gulf of Mexico that has been frozen, inverted and plunked atop the world's largest island.

Experts have reported a series of observations in recent months that show that the ice and the waters here are in a state of profound flux. If the trends persist, they could mean higher sea levels and widespread coastal flooding. There is also a small chance that the changes could lead to a sharp cooling in parts of the Northern Hemisphere.

Although nobody expects shifts as rapid or cataclysmic as portrayed in the new movie "The Day After Tomorrow," the cooling could disrupt the relatively stable climatic conditions in which modern human societies have evolved.

In the last few years, Greenland's melt zone, where summer warmth turns snow on the edge of the ice cap into slush and ponds of water, has expanded inland, reaching elevations more than a mile high in some places, said Dr. Konrad Steffen, a glaciologist at the University of Colorado.

Recent measurements by NASA scientists show that such melting can have outsize effects on the ice sheet. Meltwater formed on the surface each summer percolates thousands of feet down through fissures, allowing the ice to slide more easily over the bedrock below and accelerating its slow march to the sea.

Some jutting tongues of floating ice, where riverlike glaciers protrude into the sea, are rapidly thinning. Measurements this year by Dr. Steffen and others on the Petermann Glacier in northern Greenland show that more than 150 feet of thickness melted away under that tongue in the last year. Such melting can speed the seaward movement of ice in the same way that removing a doorstop lets a door swing freely.

As Dr. Steffen settled in with three colleagues for weeks of grueling research at this half-buried wind-tattered camp 4,000 feet up the flanks of the ice cap, he described how other Greenland glaciers were speeding their discharge of icebergs into the sea.

"If other ice streams start to react in a similar way," he said, "then we will actually produce much more fresh water."

This influx of fresh water could block North Atlantic currents that help moderate the weather of the Northern Hemisphere. "If that feedback kicks in," he said, "then the average person will worry."

Some oceanographers say global warming may already be pushing the North Atlantic toward instability. In less than 50 years, waters deep in the North Atlantic and Arctic have become significantly fresher, matched by growing saltiness in the tropical Atlantic. Worldwide, seas have absorbed enormous amounts of heat from the warming atmosphere. A big outflow of water from Greenland could take the system to a tipping point, some say.

In past millenniums when such oceanic breakdowns occurred, the climate across much of the Northern Hemisphere jumped to a starkly different state, with deep chills and abrupt shifts in patterns of precipitation and drought from Europe to Venezuela. Some changes persisted for centuries.

But whether something similar is likely to result from the new melting in Greenland is far from clear. The forces that caused abrupt climate change in the past, like monumental floods released from collapsing ice-age glaciers, are different from the much slower ones being measured today.

Gaps in understanding are enormous. Scientists have been unable to devise computer simulations that consistently replicate past jolts to the climate, leaving intellectual heartburn about the future.

"The models are not nearly as sensitive as the real world," Dr. Richard B. Alley, an expert at Penn State on Greenland's climate history, said. "That's the kind of thing that makes you nervous."