Providence, RI---In 1994, University of Utah mathematician Ken Golden
went to the Eastern Weddell Sea for the Antarctic Zone Flux
Experiment. The sea's surface is normally covered with sea ice, the
complex composite material that results when sea water is frozen.
During a powerful winter storm, Golden observed liquid sea water
welling up and flooding the sea ice surface, producing a slushy
mixture of sea water and snow that freezes into snow-ice. With his
mathematician's eyes he observed this phenomenon and said to himself:
"That's percolation!"
Golden is an expert in mathematical models of percolation, a physical
process in which a fluid moves and filters through a porous solid.
Soon after the 1994 trip he started trying to understand how the
mathematics of percolation could describe aspects of the formation and
behavior of sea ice. His results appeared in a landmark paper in
Science in 1998, written with co-authors S. F. Ackley and V. I. Lytle.
Ever since then, Golden has been a leader in the international effort
to model polar climate dynamics and has brought a new level of rigor
and precision to this area of research.
Golden describes the mathematics he and collaborators have developed
in "Climate Change and the Mathematics of Transport in Sea Ice", which
will appear this month in the Notices of the American Mathematical
Society. His article marks Mathematics Awareness Month, celebrated
each year in April. For 2009, the theme of Mathematics Awareness
Month is "Mathematics and Climate". Golden is serving as Chair of the
Mathematics Awareness Month Committee this year.
Sea ice is very different from icebergs, glaciers, and ice sheets, all
of which originate on land. Sea ice is a polycrystalline composite of
pure ice with liquid brine inclusions, plus air pockets and solid
salts. As the boundary layer between the ocean and atmosphere in the
polar regions, sea ice functions as both ocean sunscreen and blanket,
playing a key role as both an indicator and agent of climate change.
Golden discovered that, as a percolation phenomenon, sea ice has
similarities to compressed powders used in the development of stealthy
(or radar-absorbing) composites. He was able to build on existing
models developed for these powders to create a percolation-based model
for sea ice. His model captured one of the key features of sea ice:
When the volume of brine is under about 5 percent, the sea ice is
impermeable to fluid flow. But when the brine volume passes that
critical 5-percent threshold, the sea ice suddenly becomes permeable
to fluid flow. This 5-percent threshold corresponds to a critical
temperature of -5 degrees Celsius for a typical bulk salinity of 5
parts per thousand. At first Golden did not quite realize what a
breakthrough this work represented. "It was just a cool observation,
with the comparison to stealthy materials," he remarked. "I didn't
realize how important it was at the time." But today, polar
scientists routinely refer to the "rule of fives" that emerged from
Golden's work.
One of the reasons the work was so important, Golden explained, is
that the permeability of sea ice is at the heart of a range mechanisms
that control the dynamics of polar climate: the formation of snow-ice,
the evolution of surface melt ponds that determine how much solar
radiation sea ice reflects or absorbs, gas and thermal exchange
processes, and more. The permeability also controls nutrient
replenishment and other processes critical to the biology of algal and
bacterial communities living in the brine inclusions of sea ice, which
support the rich food webs of the polar oceans. "You name it, and
permeability and percolation play a key role," he said. "But before
our work there was no theoretical basis to support this
understanding."
In recent years, with Hajo Eicken of the University of Alaska
Fairbanks and other colleagues, Golden has developed a whole host of
mathematical approaches to understanding and predicting changes in the
permeability of sea ice. These include establishing rigorous
mathematical bounds on fluid permeability. Such bounds had been found
almost 100 years ago for the effective electrical conductivity of
composites. But, Golden noted, "the analogues for bounds on fluid
transport were found 100 years later partly because the fluid problem
is more difficult." He has also developed multigrid and inverse
methods and drawn on techniques from complex analysis and functional
analysis. "We have tried to cover all the bases to predict the
permeability of sea ice," Golden said.
Golden has also capitalized on his research to bring exciting
opportunities to undergraduate students. Over the past several years,
six students have accompanied him on research trips to the Arctic.
One of the star students has been Amy Heaton, a chemistry major who as
a 17-year-old took a calculus class with Golden. In her sophomore
year she helped Golden present their joint work in the US Congress.
In her junior year he sent Heaton to New Zealand to present to a group
of physicists some of the results she and Golden had obtained on
percolation models of sea ice. Heaton just finished a PhD in
chemistry a year ago.
In September and October of 2007 Golden took an outstanding
mathematics student, Adam Gully, to Antarctica on the Australian Sea
Ice Physics and Ecosystem Experiment. They conducted experiments on
fluid and electrical transport in sea ice, making the first-ever
measurements of fluid permeability in Antarctic pack ice, to validate
their mathematical models and observe new phenomena. Gully is
currently working on his Ph.D. in mathematics with Golden.
