Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Mathematics and Climate Change

14.04.2009
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 http://www.ams.org/notices/tx090500562p.pdf.

Additional information is available at the Mathematics Awareness Month web site, http://www.mathaware.org.

A hi-res image of Golden drilling in the Antarctic is available upon request from paoffice@ams.org.

For further information contact: Professor Kenneth M. Golden Phone: (801) 581-6176 Email: golden@math.utah.edu http://www.math.utah.edu/~golden

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:
http://www.mathaware.org
http://www.math.utah.edu/~golden
http://www.ams.org/notices/tx090500562p.pdf

More articles from Earth Sciences:

nachricht International team reports ocean acidification spreading rapidly in Arctic Ocean
28.02.2017 | University of Delaware

nachricht Secrets of the calcerous ooze revealed
28.02.2017 | Washington University in St. Louis

All articles from Earth Sciences >>>

The most recent press releases about innovation >>>

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

Im Focus: Safe glide at total engine failure with ELA-inside

On January 15, 2009, Chesley B. Sullenberger was celebrated world-wide: after the two engines had failed due to bird strike, he and his flight crew succeeded after a glide flight with an Airbus A320 in ditching on the Hudson River. All 155 people on board were saved.

On January 15, 2009, Chesley B. Sullenberger was celebrated world-wide: after the two engines had failed due to bird strike, he and his flight crew succeeded...

Im Focus: Breakthrough with a chain of gold atoms

In the field of nanoscience, an international team of physicists with participants from Konstanz has achieved a breakthrough in understanding heat transport

In the field of nanoscience, an international team of physicists with participants from Konstanz has achieved a breakthrough in understanding heat transport

Im Focus: DNA repair: a new letter in the cell alphabet

Results reveal how discoveries may be hidden in scientific “blind spots”

Cells need to repair damaged DNA in our genes to prevent the development of cancer and other diseases. Our cells therefore activate and send “repair-proteins”...

Im Focus: Dresdner scientists print tomorrow’s world

The Fraunhofer IWS Dresden and Technische Universität Dresden inaugurated their jointly operated Center for Additive Manufacturing Dresden (AMCD) with a festive ceremony on February 7, 2017. Scientists from various disciplines perform research on materials, additive manufacturing processes and innovative technologies, which build up components in a layer by layer process. This technology opens up new horizons for component design and combinations of functions. For example during fabrication, electrical conductors and sensors are already able to be additively manufactured into components. They provide information about stress conditions of a product during operation.

The 3D-printing technology, or additive manufacturing as it is often called, has long made the step out of scientific research laboratories into industrial...

Im Focus: Mimicking nature's cellular architectures via 3-D printing

Research offers new level of control over the structure of 3-D printed materials

Nature does amazing things with limited design materials. Grass, for example, can support its own weight, resist strong wind loads, and recover after being...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Booth and panel discussion – The Lindau Nobel Laureate Meetings at the AAAS 2017 Annual Meeting

13.02.2017 | Event News

Complex Loading versus Hidden Reserves

10.02.2017 | Event News

International Conference on Crystal Growth in Freiburg

09.02.2017 | Event News

 
Latest News

New technology offers fast peptide synthesis

28.02.2017 | Life Sciences

WSU research advances energy savings for oil, gas industries

28.02.2017 | Power and Electrical Engineering

Who can find the fish that makes the best sound?

28.02.2017 | Information Technology

VideoLinks
B2B-VideoLinks
More VideoLinks >>>