Ken Golden is not your "average" mathematician. While he holds a Ph.D. in mathematics and teaches three to four days a week at the University of Utah, he also spends a good deal of his time in the polar regions, studying sea ice—frozen sea water—and the way it moves and melts.
According to Golden, conducting field work is essential to developing relevant mathematics in this area.
"Sea ice is complicated—it does all sorts of things that you wouldn't necessarily expect. It's one thing to sit in your office, but it's another thing to go down there and see it for yourself," he explained.
Notably, he has made 16 voyages to the polar regions. He's been interested in sea ice since he was in high school, studying at the Institute for Arctic and Alpine Research at the University of Colorado, Boulder, through an NSF summer science training program, as well as at NASA/Goddard.
While a freshman at Dartmouth College, he began working with Steve Ackley on radar propagation in sea ice, gauging its thickness, and went on his first Antarctic expedition during his senior year.
After Golden received his B.A. degree in mathematics and physics at Dartmouth, he planned to pursue a Ph.D. degree in mathematics from New York University. Golden thought he would follow a more classical path for a mathematician—perhaps studying differential geometry or quantum field theory—because he wanted to be a "serious" mathematical physicist—and they don't study sea ice.
But then he encountered George Papanicolaou and that all changed.
Papanicolaou, a professor at New York University at the time, was teaching a class on random media and composite materials.
"I have to admit that the moment I first saw 'percolation theory' described at the blackboard, I thought of the brine phase in sea ice," he said. "As I look back now, it was precisely what was needed to revolutionize the study of sea ice and its transport properties" Golden said.
Golden's second published paper included a figure of these brine inclusions coalescing and connecting up to form pathways, which was actually an example of percolation—when fluid can move through a porous solid—although he didn't know it yet.
"The moment I saw George lay out mathematical percolation theory, I was like 'Oh, brine and ice, just like the figure I put in my paper. Again, I had no idea this was important."
Then, in 1994, Golden was in Antarctica for his second trip out, when he saw sea water percolating up and flooding the surface.
"Literally, in one instant, I knew—that's percolation!" he remembers.
And he spent the next few years studying this mystery. As it turns out, he had discovered the on/off switch for fluid flow in sea ice. This "switch" is critical to melt pond evolution and snow-ice formation—key processes that help us to understand the role of sea ice in the climate system.
"It took about 10 years to play out in terms of the mathematics, of actually bringing that one idea to fruition," Golden said. "We published this paper in Science in 1998, and it was probably six, seven years down the road that the sea ice world began to realize the effects. It affected everything. It sort of explained all these processes that they had wondered about for a long time. It was a critical advance when the field work and the theoretical math came together and, ultimately, had a big impact."
This impact continues today, as key discoveries from Golden's research are being used to improve current mathematical models for global warming.
According to Golden, one of the biggest unknowns in the climate world is the sea ice pack's albedo (the ratio of reflected sunlight to incident sun light), which is a critical parameter in climate models, he noted.
"Ice-albedo feedback is one of the key driving mechanisms helping to melt the ice, particularly in the Arctic, at a very fast rate. Ice and snow reflect most of the incoming solar radiation whereas melt water on the surface of the ice or the open ocean absorbs it. The ice protects the ocean below, but if that ice is gone or you've got melt pools on the surface, that radiation is absorbed, which melts the ice even further. The more it melts, the more the solar radiation is absorbed which means the more you melt the system," he explained.
Golden explained that this is a very important nonlinear feedback effect that was not properly incorporated into most existing climate models.
"If you don't properly incorporate ice-albedo feedback and melt ponds into these [climate] models, you can overestimate the volume of ice by a significant amount, almost half. These are real effects that need to be understood and incorporated into these models," Golden said.
The previous generation of global climate models have predicted general declines of summer Arctic sea ice over the 21st century. However, according to Golden, the observed losses have significantly outpaced the predictions of these models.
"We are losing ice really fast. The 21-year average of the September minimum sea ice extent from 1979 to 2000 was about 7 million square kilometers. But now, the record minimum over the satellite era was set on September 13, 2012, when the ice extent on that day was about 3.4 million square kilometers. We can now make the statement that we have lost over half of the summer Arctic sea ice pack. There's obviously something very serious happening here. Our climate really is changing and it's significant," he added.
Kenneth Golden presented "Mathematics and the Melting Polar Ice Caps" as part of the IMA's Public Lecture Series on April 3, 2013.