Kenneth Golden, a mathematician at the University of Utah, was reading pictures of Arctic sea ice when he noticed a pattern that seemed familiar to him. Seen from above, the melting sea-ice looked like a white-speckled field with dark spots in which the ice had turned into liquid. For Golden, it seemed terribly similar to the arrangement of the atoms in a magnetic material. There is no obvious reason why magnets have a relationship to aerial photographs of ice, but the thought remained with him. More than a decade later, this intuition has finally become a model that better predicts the impact of climate change on the sea ice.
Melting ponds are exactly what they sound like: pools of water forming on them. Sea ice when the top layer of ice melts in spring and summer. The ponds are important because they change the reflectivity of ice. Ice has a high albedo, which means that it reflects most of the sunlight that hits it. However, water has a low albedo and absorbs a large portion of the sunlight as heat. This results in a feedback loop: As ice melts into smelting ponds, a higher percentage of the ice surface absorbs sunlight as heat, which melts even more ice and creates more larger smelting ponds.
Knowing what percentage of the ice surface is made up of melting ponds is therefore crucial to knowing the speed with which Arctic ice melts, contributing to the global climate. However, since the Arctic is so large and satellite images have only a limited resolution, measuring the total area of molten ponds is a difficult problem. This is where Golden comes into play.
Golden began to major in mathematics at Dartmouth College to study sea ice and, in his last year, even traveled to Antarctica. He concentrated his career on more theoretical mathematics, but ten years after his first Antarctic expedition, he received a call from his research consultant, who invited him to join a major polar research project with the US Navy.
The project was to characterize the sea ice from satellite data, and the team needed someone like Golden to develop an algorithm that understood its optical properties. Over the next few years, Golden embarked on several expeditions to the Antarctic and Arctic with "real sea-ice inhabitants," as he said, researchers wading ankle-deep or knee-deep in icy puddles. He also analyzed images of these smelting ponds coming from helicopters, and found that in their patterns he recognized a ferromagnetic model from his physics class: the Ising model.
The model named after Ernst Ising began as a problem that Ising was given by his dissertation consultant in the 1
Magnets work because single atoms can be considered as minimagnets with north and south poles. The direction of its north pole is called the magnetic moment, and because atoms are inherently quantum, they have only two directional options: spin-up or spin-down. When all the atoms of a piece of material align their magnetic moments, the entire material becomes a magnet. This is the configuration with the lowest energy that the atoms can accept. "When I was hanging out with these people in melting ponds and seeing all these pictures, I noticed that they look like images I saw from the Ising model," says Golden.
In this model, magnetic moments are arranged in a grid in which the moment of each atom can only interact with and possibly change the moment of a neighbor. This causes patches of atoms with the same spin to form in the material. When Golden leafed through photos of the melting ponds, he noticed that they interacted with the surrounding ice in much the same way.
Golden began to play with Ising model simulations out of curiosity and tried to figure out how to combine these seemingly disparate ideas. It started with a random topography of ice, an uneven surface with pits and hills, and allowed the ice to melt – meaning the magnetic spins began to tip over. The resulting images of the simulations show dark or light islands for atoms with spin up or down, water or ice whose edges are jagged and fractal. He showed the result of such a simulation to a colleague who analyzed pictures of melting ponds, and the colleague initially thought Golden would show him one of his own pictures.
"Not only are ponds made with the right geometry, but they really look like ponds," says Golden. To verify his results, Golden compared the model's predicted distribution of pond areas and perimeters with those observed in nature. They were in close agreement with the distribution of natural smelting ponds, and the model was published in the New Journal of Physics.
The realism of such a simple model, often referred to by scientists as a "toy model", is limited. Golden therefore plans to consider the effects of the Arctic winds that can alter the edges of the ponds. He can not explain every facet of the real world, but the yardstick in Golden's model of about a meter is already much smaller than those used in typical climate models.
"These are big global models," says Elizabeth Hunke, lead developer for the Los Alamos Sea Ice Model. "We use lattices that are more than one kilometer from one side, and these smelting ponds are much smaller than these lattice cells, so we have to somehow describe which part of the lattice cell is covered by smelting ponds." Goldens model, she says: "Provides a statistical method that represents the essential dynamics."
Donald Perovich, a geophysicist at Dartmouth College who is familiar with Golden's research, saw an immediate opportunity to link the model to his own upcoming Arctic work. "This model helps us to inform what types of observations we are making, and these observations can then be used to rate that model."
In addition to its applicability, Perovich also finds a deeper value in the model. "I find it rather amazing how mathematics provides a window to understand the world around us," he says.
For Golden, who spent his career at the interface of theory and reality, the idea is a natural one. "Mathematics is the operating system of the sciences," he says.
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