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Ken Golden's magic number is five. The University of Utah math professor has spent three decades applying the power of numbers to understand sea ice, which he says begins to percolate when temperatures and salinity levels involve the number five.
To learn what this means for global climate change, Golden regularly leads polar research expeditions funded by the National Science Foundation. Golden's ongoing research has shown that microstructures within sea ice, which allow for the movement of water, play a crucial role in how sea ice forms and behaves.
Understanding these dynamics will improve the models scientists use to predict how quickly sea ice will succumb to global warming, says Golden, who recently returned from a two-week sojourn on Antarctica's McMurdo Sound.
From this frozen plain off Ross Island, he and U. electrical engineers pulled cylinders of ice to measure their temperature, salinity and electrical properties. He has completed six expeditions to the Antarctic and five to the Arctic, with another scheduled this summer.
"I like to say I'm bipolar," Golden jokes.
But the implications of his research are no joking matter, with the future of our warming planet at stake. That's because pack ice, the thin, frosty barrier between polar seas and the atmosphere, is a crucial indicator — and amplifier — of climate change.
A hot topic
Sea ice reflects solar radiation, while the open ocean absorbs it, says Don Perovich, a geophysicist with the U.S. Army's Cold Regions Research and Engineering Laboratory in New Hampshire (CRREL), who studies the reflective properties of ice and snow, known as albedo. Shrinking sea ice results in greater warming of the ocean, triggering a positive feedback loop that could hasten the disappearance of the polar ice caps with massive environmental impacts.
In 1980, the Arctic ice cap at its summer minimum was about the size of the continental United States. Around 2005 to 2007, the polar cap suddenly shrunk to its smallest size in recorded history, about half of what it was in 1980.
"That got a lot of attention," says Perovich, who roamed Alaska with Golden on previous expeditions. "The models were shown to be too conservative."
Confounding our understanding of how sea ice behaves are so-called "melt ponds," pools of water forming on top of sea ice that reduce the albedo of the ice.
"We can't predict the evolution of the ponds and that's where Ken's work is critical in understanding percolation," Perovich says. "You have an intricate dance between how much melt there is and how much percolation there is."
Sea ice has little in common with the stuff in your freezer. It's not even frozen salt water, because the crystalline structure of ice rejects the mineral content of sea water. Think of it as a composite material, laced with tiny "inclusions" of brine.
"Because of the chemistry and physics, you get these dendritic structures, pure ice platelets growing down into the ice vertically and the salty water gets trapped between the platelets," Golden says. "The inclusions occupy 3 to 15 percent, depending on the temperature of the ice. [The brine] is liquid and that's why it's so fascinating."
This permeability allows sea ice to harbor the algae and bacteria that form the base of the food chain.
The inclusions grow as temperatures rise, particularly above minus 5 centigrade, and when they reach 5 percent by volume they become an interconnecting lattice that renders the ice permeable, Golden says. This finding was the basis for his "rule of fives," which he first published in 1998 as a theoretical framework for understanding sea ice dynamics.
Brine conducts electricity, while the near-pure frozen water is an insulator, so when the inclusions link up they act as a conduit for not just water but also electricity.
Golden's latest research seeks to relate the flow of electricity to the flow of fluid through the ice.
The valley of ice
Golden pursued degrees in math and science at Dartmouth College, and then worked under Stephen Ackley, a world authority on ice, at CRREL. Golden taught at Princeton University until 1991, when he migrated to the U., drawn by Utah's mountains and skiing.
His previous Antarctic trips were aboard ice breakers at sea. On his most recent trip he took a passenger jet from Christchurch, New Zealand, to a portable outpost on the ice, 12 miles from Scott Base. Joining him were Cynthia Furse, a professor of electrical engineering; undergraduate student David Lubbers; Joyce Lin, a mathematics post-doctoral research fellow; and a team of New Zealand physicists.
"I became an engineer because I wanted to change the world," says Furse, who also serves the U. as associate vice president for research. "If you want to make a difference, one clear issue is climate change: Are we contributing to it, can we control it, what can we do to change it?"
Using a high-torque, low-speed drill, they removed meter-long ice cores, sticking them with electrodes and probes, before crushing them for salinity surveys. They lost track of time while the bright sun rounded the horizon with the approach of the Antarctic summer solstice. McMurdo Sound felt like a flat, empty valley of uninterrupted white hemmed by volcanoes.
"With the sun never going down, it had a timelessness to it," Lubbers says. "And there's no point of reference between you and the volcanoes, so they seem a lot closer than they really are."
Their outpost consisted of nine "wannigans," metal sheds on runners the scientists used for sleeping and labs.
"We worked a lot, the whole time, but we had a lot of fun," says Lin, describing the parasail-pulled sled the engineers rigged from a tarp and other items at the outpost; the companionship of their New Zealand colleagues added to their enjoyment.
Golden had learned from experience that he needed to back up his gear because the failure of one little device can undermine the success of the entire trip. So he brought three thermistors and two salinometers, and even then the team narrowly averted disaster.
On the second day, two of his three thermistors were on the fritz, making it impossible to achieve quick temperature profiles of the ice cores. His electrical engineering colleagues had no trouble diagnosing the problem — salt water had infiltrated the device, creating additional electrical connections — and fixing it.
Furse solved another problem having to do with measuring the speed by which 6-foot bore holes filled with water. Her low-tech solution was to rig a plastic bottle as a float; a tent-pole inside the bottle rose above the ice along with the water.
"This is Home Depot science, but it worked beautifully," Golden says.
Polar sea ice, by the numbers
Sea ice is full of tiny brine "inclusions" that allow water to percolate at certain temperatures and salinity levels, according to U. mathematician Ken Golden. He is developing a theoretical model that will improve predictions of how sea ice will respond to planetary warming. Golden's team recently returned from Antarctica, where they studied ice cores.