Mathematical insights into sea ice

EurekAlert: 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 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."…

Melt ponds atop sea ice in Baffin Bay (NASA)