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How statistical physics illuminates sea ice, a critical piece of Earth’s climate system

Since he began studying polar sea ice at NASA in 1975, mathematician Ken Golden has helped document alarming changes in the seasonally shifting, thin veneers covering the Arctic and Antarctic oceans.

There’s now a lot less ice and the University of Utah scientist has since devoted much of his career to applying statistical mechanics—the physics of phase transitions and complex collective behavior in systems like gases and magnets—to better understand the role of climate change in the disappearance of our polar sea ice covers. The stakes couldn’t be higher as the impacts accelerate. In recent decades, according to Golden, the extent of Arctic sea ice has shrunk by about half.

U mathematician Ken Golden

“Not over the past million years, like on geophysical scales, not over a thousand years, but over the past 30 or 40 years. A couple of months ago, even in Antarctica, we just saw a new record low,” Golden said in his opening remarks at the May 17 Climate Summit hosted by the U College of Science’s Wilkes Center for Climate Science & Policy. “But just like throwing a rock into a pond, there are ripple effects, and the bigger the rock, the bigger the ripples and the further they go. The extent of sea ice we’ve lost in the Arctic is about two-thirds the area of the contiguous United States and is probably the largest change on Earth’s surface due to planetary warming. That’s a big rock.”

The part of Earth’s climate system featuring snow and ice, known as the cryosphere, is experiencing severe disruptions as the planet continues warming. Ice still covers 9% to 15% of Earth’s ocean surface, but the trends are ominous.

PHOTO CREDIT: University of Utah

U mathematician Ken Golden, left, drills into sea ice during a 2014 expedition to the Arctic.

A leading sea ice researcher, Golden co-wrote a viewpoint published this week by Nature, expounding on the physics of the cryosphere. Improving our ability to understand and model the behavior of sea ice is a central problem in the physics of Earth’s climate system, according to Golden, a distinguished professor in the Department of Mathematics who has completed 18 polar research expeditions.

More than just ice

Other than containing water, sea ice floes have little in common with the frozen cubes in your fridge.

“As a material, sea ice is a hierarchical, multiscale composite with complex structure on length scales ranging from tenths of millimeters to tens of kilometers, and it exhibits rich dynamics on the scale of the Arctic Ocean,” Golden wrote in the piece’s leadoff essay published in Nature Reviews Physics. “A principal modeling challenge is how to use data on a smaller-scale structure to find the effective properties of sea ice on larger scales relevant to climate and process models.”

In other words, what can we learn about the planet from examining the minute structures within sea ice? A lot, and not just about climate, Golden believes, but all sorts of other areas of science and engineering where the math is similar, such as in bones, medical imaging, carbon sequestration, semiconductors and even high-tech composites with exotic properties.

Sea ice serves as a robust habitat for creatures ranging from apex predators and birds all the way down to algae living inside the brine inclusions of sea ice, that feed off the nutrient-laden seawater coursing through the brine channels and pathways that can permeate the ice.

How sea ice affects climate

It also plays a crucial role in regulating the climate system because it affects ocean currents and reflects solar radiation back into space, which is measured by a property known as albedo. While ice reflects this energy, seawater as well as meltwater ponds on top of sea ice, absorb it. That means the planet could warm even faster as sea ice shrinks, exposing more absorptive, watery surface, and reducing the planet’s albedo, according to Golden.

“It forms the very thin frozen boundary layer between the two principal geophysical fluids on the Earth—the ocean and the atmosphere,” he said at a 2021 Frontiers of Science lecture. “And as such, it mediates the exchange of heat, gases, and momentum between them. Both the melting and the freezing of sea ice play a very important role in global ocean circulation and form principal pathways by which the polar regions communicate with the rest of the world’s ocean system, as well as the global climate system.”

What’s special about five?

Golden is well-known for developing a mathematical theory he calls the “Rule of Fives,” which was the first application of a classical model in statistical mechanics to the physics of sea ice – to identify and predict an “on-off” switch for how fluids flow through the ice. Based on a percolation model used in the development of stealthy coatings that make aircraft invisible to radar, the rule holds that fluid can move vertically when the brine volume fraction exceeds the percolation threshold of 5%, which corresponds to a critical temperature of –5 °C for a typical bulk salinity of five parts per thousand.

PHOTO CREDIT: University of Utah

Ken Golden, a U mathematician who studies sea ice, applies a green dye to an ice floe during a 2014 expedition to the Arctic.

Golden wants to see the far-reaching and broadly applicable ideas of statistical mechanics put to greater use for exploring the cryosphere.

“Statistical physics has seen widespread success and become a key branch of modern physics,” Golden wrote in his essay. “Yet even though it provides such a natural framework for formulating and addressing key questions in the physics of sea ice, and opens up a broad array of powerful ideas and methods, it has been used in only a few contexts, albeit with unusual success.”

The other contributors are Alison Banwell of the Cooperative Institute for Research in Environmental Sciences (CIRES), physicist Justin Burton of Emory University, Claudia Cenedese of the Woods Hole Oceanographic Institution and Jan Åström of Åbo Akademi University in Finland.

Cendese’s piece illuminates iceberg calving; Banwell looks at how surface meltwater triggers ice-shelf collapses; Åström examines catastrophic ice disintegration; and Burton discusses “ice mélange,” a floating assemblage of broken icebergs that can clog fjords and waterways, and affect sea level rise.

Read more about Golden’s sea ice research