Unpacking Polar Sea Ice with Math

Newswise — Polar sea ice is ever-changing. It shrinks, expands, moves, breaks apart, reforms in response to changing seasons, and rapid climate change. It is far from a homogenous layer of frozen water on the ocean’s surface, but rather a dynamic mix of water and ice, as well as minute pockets of air and brine encased in the ice.

New research led by University of Utah mathematicians and climate scientists is generating fresh models for understanding two critical processes in the sea ice system that have profound influences on global climate: the flux of heat through sea ice, thermally linking the ocean and atmosphere, and the dynamics of the marginal ice zone, or MIZ, a serpentine region of the Arctic sea ice cover that separates dense pack ice from open ocean.

In the last four decades since satellite imagery became widely available, the width of the MIZ has grown by 40% and its northern edge has migrated 1,600 kilometers northward, according to Court Strong, a professor of atmospheric sciences.

“It has also shifted toward the pole while the size of the sea ice pack has declined,” said Strong, a co-author on one of two studies published by U scientists in recent weeks. “Most of these changes have happened in the fall, around the time when sea ice reaches its seasonal minimum.”

A tale of two studies, one north and one south

This study, which adapts a phase transition model normally used for alloys and binary solutions on laboratory scales to MIZ dynamics on the scale of the Arctic Ocean, appears in Scientific Reports. A second study, published in the Proceedings of the Royal Society A and based on field research in the Antarctic, developed a model for understanding the thermal conductivity of sea ice. The issue cover featured a photo exposing regularly spaced brine channels in the bottom few centimeters of Antarctic sea ice. 

Ice covering both polar regions has sharply receded in recent decades thanks to human-driven global warming. Its disappearance is also driving a feed-back loop where more of the sun energy’s is absorbed by the open ocean, rather than getting reflected back to space by ice cover.

Utah mathematics professors Elena Cherkaev and Ken Golden, a leading sea ice researcher, are authors on both studies. The Arctic study led by Strong examines the macrostructures of sea ice, while the Antarctic study, led by former Utah postdoctoral researcher Noa Kraitzman, gets into its micro-scale aspects.

Sea ice is not solid, but rather is more like a sponge with tiny holes filled with salty water, or brine inclusions. When the ocean water below interacts with this ice, it can set up a flow that allows heat to move more quickly through the ice, just as when you stir a cup of coffee, according to Golden. Researchers in the Antarctic study used advanced mathematical tools to figure out how much this flow boosts heat movement.

The thermal conductivity study also found that new ice, as opposed to the ice that remains frozen year after year, allows more water flow, thereby enabling greater heat transfer. Current climate models could be underestimating the amount of heat moving through the sea ice because they don’t fully account for this water flow. By improving these models, scientists can better predict how fast sea ice melts and how this affects the global climate.

While the aspects of ice investigated in the two studies are quite different, the mathematical principles for modeling them are the same, according to Golden.

“The ice not a continuum. It’s a bunch of floes. It’s a composite material, just like the sea ice with the tiny brine inclusions, but this is water with ice inclusions,” said Golden, describing the Arctic’s marginal ice zone. “It’s basically the same physics and math in a different context and setting, to figure out what are the effective thermal properties on the big scale given the geometry and information about the floes, which is analogous to giving detailed information about the brine inclusions at the sub-millimeter scale.”

Golden is fond of saying what happens in the Arctic does not stay in the Arctic. Changes in the MIZ are certainly playing out elsewhere in the world in the form of disrupted climate patterns, so it is critical to understand what it’s doing. The zone is defined as that part of the ocean surface where 15% to 80% is covered by sea ice. Where the ice cover is greater than 80% it is considered pack ice and less than 15% it’s considered to be the outer fringes of open ocean.

A troubling picture from space

“The MIZ is the region around the edge of the sea ice, where the ice gets broken into smaller chunks by waves and melting,” Strong said. “Changes in the MIZ are important because they affect how heat flows between the ocean and atmosphere, and the behavior of life in the Arctic, from microorganisms to polar bears, and navigating humans.”

With the advent of quality satellite data beginning in the late 1970s, scientific interest in the MIZ has grown, since now its changes are easily documented. Strong was among those who figured out how to use imagery shot from space to measure the MIZ and document alarming changes.

“Over the past several decades, we’ve seen the MIZ widen by a dramatic 40%,” Strong said.

For years, scientists have scrutinized sea ice as a so-called “mushy layer.” As a metal alloy melts or solidifies from liquid, either way it passes through a porous or mushy state where the liquid and solid phases coexist. Freezing salt water is similar, resulting in a pure ice host with liquid brine pockets, which is particularly porous or mushy in the bottom few centimeters nearest the warmer ocean, with vertical channels called “chimneys” in mushy layer language.

Strong’s team tested whether previously modeled mushy layer physics could be applied to the vast reaches of the MIZ. According to the study, the answer is yes, potentially opening a fresh look at a part of the Arctic that is in constant flux.

In short, the study proposed a new way of thinking about the MIZ, as a large-scale phase transition region, similar to how ice melts into water. Traditionally, melting has been viewed as something that happens on a small scale, like at the edges of ice floes. But when the Arctic is viewed in its entirety, the MIZ can be seen as a broad transition zone between solid, dense pack ice and open water. This idea helps explain why the MIZ is not just a sharp boundary, but rather a “mushy” region where both ice and water coexist.

“In climate science, we often use very complex models. This can lead to skillful prediction, but can also make it difficult to understand what’s happening physically in the system,” Strong said. “The goal here was to make the simplest possible model that can capture the changes we’re seeing in the MIZ, and then to study that model to gain insight into how the system works and why it’s changing.”

The focus in this study was to understand the MIZ’s seasonal cycle. The next step will be applying this model to better understand what drives MIZ trends observed over the past few decades.

The study “Homogenization for convection-enhanced thermal transport in sea ice” appeared Aug. 28 in the journal Proceedings of the Royal Society A. Co-authors include Rebecca Hardenbrook of Dartmouth University and Huy Dinh, N. Benjamin Murphy, Elena Cherkaev and Jingyi Zhu of the U’s Department of Mathematics. The Arctic study titled, “Multiscale mushy layer model for Arctic marginal ice zone dynamics,” appeared Sept. 3 in Scientific Reports. Funding for this research came from the National Science Foundation and the U.S. Office of Naval Research.