Providence, RI---In 1994, University of Utah mathematician Ken Goldenwent to the Eastern Weddell Sea for the Antarctic Zone FluxExperiment. The sea's surface is normally covered with sea ice, thecomplex composite material that results when sea water is frozen.During a powerful winter storm, Golden observed liquid sea waterwelling up and flooding the sea ice surface, producing a slushymixture of sea water and snow that freezes into snow-ice. With hismathematician's eyes he observed this phenomenon and said to himself:"That's percolation!"
Golden is an expert in mathematical models of percolation, a physicalprocess in which a fluid moves and filters through a porous solid.Soon after the 1994 trip he started trying to understand how themathematics of percolation could describe aspects of the formation andbehavior of sea ice. His results appeared in a landmark paper inScience in 1998, written with co-authors S. F. Ackley and V. I. Lytle.Ever since then, Golden has been a leader in the international effortto model polar climate dynamics and has brought a new level of rigorand precision to this area of research.
Golden describes the mathematics he and collaborators have developedin "Climate Change and the Mathematics of Transport in Sea Ice", whichwill appear this month in the Notices of the American MathematicalSociety. His article marks Mathematics Awareness Month, celebratedeach year in April. For 2009, the theme of Mathematics AwarenessMonth is "Mathematics and Climate". Golden is serving as Chair of theMathematics Awareness Month Committee this year.
Sea ice is very different from icebergs, glaciers, and ice sheets, allof which originate on land. Sea ice is a polycrystalline composite ofpure ice with liquid brine inclusions, plus air pockets and solidsalts. As the boundary layer between the ocean and atmosphere in thepolar 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 hassimilarities to compressed powders used in the development of stealthy(or radar-absorbing) composites. He was able to build on existingmodels developed for these powders to create a percolation-based modelfor 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 isimpermeable to fluid flow. But when the brine volume passes thatcritical 5-percent threshold, the sea ice suddenly becomes permeableto fluid flow. This 5-percent threshold corresponds to a criticaltemperature of -5 degrees Celsius for a typical bulk salinity of 5parts per thousand. At first Golden did not quite realize what abreakthrough this work represented. "It was just a cool observation,with the comparison to stealthy materials," he remarked. "I didn'trealize how important it was at the time." But today, polarscientists routinely refer to the "rule of fives" that emerged fromGolden's work.
One of the reasons the work was so important, Golden explained, isthat the permeability of sea ice is at the heart of a range mechanismsthat control the dynamics of polar climate: the formation of snow-ice,the evolution of surface melt ponds that determine how much solarradiation sea ice reflects or absorbs, gas and thermal exchangeprocesses, and more. The permeability also controls nutrientreplenishment and other processes critical to the biology of algal andbacterial communities living in the brine inclusions of sea ice, whichsupport the rich food webs of the polar oceans. "You name it, andpermeability and percolation play a key role," he said. "But beforeour work there was no theoretical basis to support thisunderstanding."
In recent years, with Hajo Eicken of the University of AlaskaFairbanks and other colleagues, Golden has developed a whole host ofmathematical approaches to understanding and predicting changes in thepermeability of sea ice. These include establishing rigorousmathematical bounds on fluid permeability. Such bounds had been foundalmost 100 years ago for the effective electrical conductivity ofcomposites. But, Golden noted, "the analogues for bounds on fluidtransport were found 100 years later partly because the fluid problemis more difficult." He has also developed multigrid and inversemethods and drawn on techniques from complex analysis and functionalanalysis. "We have tried to cover all the bases to predict thepermeability of sea ice," Golden said.
Golden has also capitalized on his research to bring excitingopportunities 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 asa 17-year-old took a calculus class with Golden. In her sophomoreyear 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 groupof physicists some of the results she and Golden had obtained onpercolation models of sea ice. Heaton just finished a PhD inchemistry a year ago.
In September and October of 2007 Golden took an outstandingmathematics student, Adam Gully, to Antarctica on the Australian SeaIce Physics and Ecosystem Experiment. They conducted experiments onfluid and electrical transport in sea ice, making the first-evermeasurements of fluid permeability in Antarctic pack ice, to validatetheir mathematical models and observe new phenomena. Gully iscurrently working on his Ph.D. in mathematics with Golden.
Source: American Mathematical Society