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Mathematicians have solved a puzzle related to sea ice that could potentially reshape climate models.
A newly developed applied mathematical theory could deepen our understanding of sea ice’s impact on global climate, potentially leading to more accurate climate predictions.
The authors of a new paper published in the Proceedings of the Royal Society A on August 28, offer new insights into how heat travels through sea ice, a crucial factor in regulating Earth’s polar climate.
Dr. Noa Kraitzman, Senior Lecturer in Applied Mathematics at Macquarie University and lead author of the study, says the research addresses a key gap in current climate modeling.
“Sea ice covers about 15 percent of the ocean’s surface during the coldest season when it’s at its vast majority,” Dr. Kraitzman says. “It’s a thin layer that separates the atmosphere and the ocean and is responsible for heat transfer between the two.”
Sea ice acts as an insulating blanket on the ocean, reflecting sunlight and moderating heat exchange. As global temperatures rise, understanding how sea ice behaves will become increasingly important for predicting climate change.
New Insights into Sea Ice
The study focuses on the thermal conductivity of sea ice, a critical parameter used in many global climate models. The movement of liquid brine within sea ice, which can potentially increase its heat transport, was not accounted for in previous models.
Dr. Kraitzman says the unique structure of sea ice, along with its sensitive dependence on temperature and salinity, means it is challenging to measure and predict its properties, specifically its thermal conductivity.
“When you look at sea ice on a small scale, what makes it interesting is its complex structure because it’s made up of ice, air bubbles, and brine inclusions.
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“As the atmosphere above the ocean becomes extremely cold, below minus 30 degrees Celsius, while the ocean water remains at about minus two degrees, this creates a large temperature difference, and the water freezes from the top down.
“As the water freezes rapidly, it pushes out the salt, creating an ice matrix of purely frozen water which captures air bubbles and pockets of very salty water, called brine inclusions, surrounded by nearly pure ice.”
These dense brine inclusions are heavier than the fresh ocean water which results in convective flow within the ice, creating big ‘chimneys’ where liquid salt flows out.
Research Developments and Mathematical Proof
The research builds on earlier fieldwork by Trodahl in 1999, which first suggested that fluid flow within sea ice might enhance its thermal conductivity. Dr. Kraitzman’s team has now provided mathematical proof of this phenomenon.
“Our mathematics definitely shows that such an enhancement should be expected once convective flow within the sea ice begins,” Dr. Kraitzman says.
The model also offers a way to relate the sea ice’s thermal properties to its temperature and salt content, allowing theoretical results to be compared with measurements.
Specifically, it provides a tool to be used in large-scale climate models, potentially leading to more accurate predictions of future conditions in the polar regions.
Sea ice in the Arctic has been declining rapidly in recent decades. This loss of ice can lead to a feedback loop: as more dark ocean water is exposed, it absorbs more sunlight, leading to further warming and ice loss.
The loss of sea ice can affect weather patterns, ocean circulation, and marine ecosystems far beyond the polar regions.
Dr. Kraitzman says understanding the thermal conductivity of sea ice is important for predicting its future.
The researchers note that while their model provides a theoretical framework, more experimental work is needed to integrate these findings into large-scale climate models.
Reference: “Homogenization for convection-enhanced thermal transport in sea ice” by Noa Kraitzman, Rebecca Hardenbrook, Huy Dinh, N. Benjamin Murphy, Elena Cherkaev, Jingyi Zhu and Kenneth M. Golden, 1 August 2024, Proceedings A.
DOI: 10.1098/rspa.2023.0747
The study was conducted by mathematicians from Macquarie University in Australia, the University of Utah, and Dartmouth College, New Hampshire in the USA.
It was supported by funding from the US National Science Foundation.
3 Comments
“This loss of ice can lead to a feedback loop: as more dark ocean water is exposed, it absorbs more sunlight, leading to further warming and ice loss.”
This is a Zombie that seems impossible to kill. In the regions of the world where this effect is potentially important, the reflectivity of water changes rapidly with the angle of incidence of sunlight from about 10% at the Arctic Circle to 100% at the North Pole at the Equinoxes. As the tilt increases as the Summer Solstice approaches, the band of total reflection, the terminator, moves farther from the pole on the side opposite the sun. Thus, during the 24 hours that part of the Arctic is illuminated by the sun, some portion receives sunlight with an angle of incidence of 85-90 degrees and open water will reflect sunlight with reflectance equal or greater than old snow. During the Winter Solstice, there is no direct sunlight reaching beyond the Arctic Circle!
https://wattsupwiththat.com/2016/09/12/why-albedo-is-the-wrong-measure-of-reflectivity-for-modeling-climate/
The reason the water is often referred to as “dark” is because with specular reflection (reflection off smooth surfaces) the viewing position is critical as all the light is confined to a sheaf that can only be observed looking towards the sun, at the same angle above the horizon as the sun is. The net effect is complex because it depends on how much ice is present, where it is with relation to the terminator, how abundant ubiquitous clouds are, and where they are with respect to the open water and ice. The quoted general statement oversimplifies reality.
Every model is an over simplification.
Most people who follow climate research are well aware of this elementary fact.
Such articles are written for the lay audience.
What’s your point in going into such detail?
Trying to impress readers with your expertise?
This article does an excellent job pointing out that we don’t know everything about the many various factors that play a role in ice coverage in the polar regions, and that the more we learn about this particular aspect of the behavior of sea ice, the better job we can do of predicting what the climate will be like in the future.
“Every model is an over simplification. ”
Every model is a simplification. That is different from being an over-simplification! An over-simplification implies a “bridge too far.”
That “Most people who follow climate research are well aware of this elementary fact” is not the impression that I’m left with, even reading the journal articles intended for well-educated readers. I see it far too often to suggest that only a minority are unaware of it. However, in fact, there is no mention of ‘dark’ water by the authors in the original paper. It would appear that it was added by someone who prepared a press release, pointing out that some people who have potential influence on what the public believes, holds fallacious views.
Actually, I could have gone into far more detail, but would certainly have lost most of the readers here. The not so subtle insult was uncalled for. The point is that as a former professor, I’m acutely aware that if someone learns something that is wrong, it is very difficult to unlearn it. I’m trying to sensitize both readers and potential authors to the fact that there are common misconceptions in climatology.
I’m completely supportive of the idea that “the more we learn about this particular aspect of the behavior of sea ice, the better job we can do of predicting what the climate will be like in the future.” However, misstatements of fact work in opposition to that. Surely you can see that.