Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:


Mathematics and Climate Change

Kenneth Golden, an expert in mathematical models of percolation in sea ice, is 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. A forthcoming article describes the mathematics he and collaborators have developed to study sea ice.

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.

An advance copy of Golden's article "Climate Change and the Mathematics of Transport in Sea Ice" is available to reporters at the non-public URL

Additional information is available at the Mathematics Awareness Month web site,

A hi-res image of Golden drilling in the Antarctic is available upon request from

For further information contact: Professor Kenneth M. Golden Phone: (801) 581-6176 Email:

Founded in 1888 to further mathematical research and scholarship, today the American Mathematical Society has more than 32,000 members. The Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.

| Newswise Science News
Further information:

More articles from Earth Sciences:

nachricht NASA finds newly formed tropical storm lan over open waters
17.10.2017 | NASA/Goddard Space Flight Center

nachricht The melting ice makes the sea around Greenland less saline
16.10.2017 | Aarhus University

All articles from Earth Sciences >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Neutron star merger directly observed for the first time

University of Maryland researchers contribute to historic detection of gravitational waves and light created by event

On August 17, 2017, at 12:41:04 UTC, scientists made the first direct observation of a merger between two neutron stars--the dense, collapsed cores that remain...

Im Focus: Breaking: the first light from two neutron stars merging

Seven new papers describe the first-ever detection of light from a gravitational wave source. The event, caused by two neutron stars colliding and merging together, was dubbed GW170817 because it sent ripples through space-time that reached Earth on 2017 August 17. Around the world, hundreds of excited astronomers mobilized quickly and were able to observe the event using numerous telescopes, providing a wealth of new data.

Previous detections of gravitational waves have all involved the merger of two black holes, a feat that won the 2017 Nobel Prize in Physics earlier this month....

Im Focus: Smart sensors for efficient processes

Material defects in end products can quickly result in failures in many areas of industry, and have a massive impact on the safe use of their products. This is why, in the field of quality assurance, intelligent, nondestructive sensor systems play a key role. They allow testing components and parts in a rapid and cost-efficient manner without destroying the actual product or changing its surface. Experts from the Fraunhofer IZFP in Saarbrücken will be presenting two exhibits at the Blechexpo in Stuttgart from 7–10 November 2017 that allow fast, reliable, and automated characterization of materials and detection of defects (Hall 5, Booth 5306).

When quality testing uses time-consuming destructive test methods, it can result in enormous costs due to damaging or destroying the products. And given that...

Im Focus: Cold molecules on collision course

Using a new cooling technique MPQ scientists succeed at observing collisions in a dense beam of cold and slow dipolar molecules.

How do chemical reactions proceed at extremely low temperatures? The answer requires the investigation of molecular samples that are cold, dense, and slow at...

Im Focus: Shrinking the proton again!

Scientists from the Max Planck Institute of Quantum Optics, using high precision laser spectroscopy of atomic hydrogen, confirm the surprisingly small value of the proton radius determined from muonic hydrogen.

It was one of the breakthroughs of the year 2010: Laser spectroscopy of muonic hydrogen resulted in a value for the proton charge radius that was significantly...

All Focus news of the innovation-report >>>



Event News

ASEAN Member States discuss the future role of renewable energy

17.10.2017 | Event News

World Health Summit 2017: International experts set the course for the future of Global Health

10.10.2017 | Event News

Climate Engineering Conference 2017 Opens in Berlin

10.10.2017 | Event News

Latest News

Osaka university researchers make the slipperiest surfaces adhesive

18.10.2017 | Materials Sciences

Space radiation won't stop NASA's human exploration

18.10.2017 | Physics and Astronomy

Los Alamos researchers and supercomputers help interpret the latest LIGO findings

18.10.2017 | Physics and Astronomy

More VideoLinks >>>