Who is to blame for climate change?

Of course, we all are. If you’ve lived on Earth for even a couple of years, then greenhouse gases—emitted by you or for your benefit—have in some small part helped cause warming temperatures, rising sea levels, and mass extinctions.

It’s that “in some small part” that’s the rub, though. Global warming is a global phenomenon, with millions of victims and billions of culprits. At that kind of scale, how much of that melting ice cap are you responsible for, really?

A new paper provides an answer—at least for one part of the planet. It finds a fundamental linear relationship between the amount of carbon in the atmosphere and the amount of summer sea ice in the Arctic Ocean. For every metric ton of carbon dioxide that enters the atmosphere, 32 square feet of summer sea-ice melts into the Arctic Ocean.

Climate science has few other statistics like this, numbers that immediately link the personal to the planetary. It’s worth dwelling on for a moment.

Americans (and denizens of the rich world, generally) release one ton of carbon dioxide into the atmosphere all the time. If you’re American, you have probably released one ton of carbon into the atmosphere since October 15. About 2,500 miles of highway driving emits that a ton of carbon. Two round-trip flights between Washington, D.C., and San Francisco release one ton of carbon. The average U.S. household is responsible for six tons of atmospheric CO₂ every year through electricity use alone.

Now think of the secondary statistic. Every additional ton is an additional 32 square feet of lost Arctic ice. In other words, every American household melts 200 square feet of the ice cap every year just to keep its lights on and the refrigerator running.

All in all, the average American person reduces the ice cap around the north pole by about 645 square feet (60 square meters) every year. (That’s working from the average U.S. per-capita carbon footprint: about 20 annual tons per capita. If you’re curious, you can estimate your personal carbon footprint using the Nature Conservancy’s calculator.)

The paper is the first to identify a linear relationship between carbon dioxide and Arctic summer sea-ice. That it’s summer ice is crucial, here: The northern ice cap waxes and wanes with the season, receding in the summer and recovering in the winter. Every year, its summer area generally gets smaller and smaller—this year it tied for second-smallest ever—but the nocturnal polar winter allows the ice to post strong recoveries.

This relationship—which is technically 3.0 plus or minus 0.1 square meters per additional ton of carbon—allows the authors to estimate the first year when the Arctic Ocean will lose all of its ice during the summer. They phrase this not in terms of a year, but an amount: When an additional 1,000 gigatons of carbon dioxide are emitted, summer sea ice will vanish.

“At current emissions rates, we will have reached that limit in 25 to 30 years,” says Dirk Notz, an author of the paper and the head of sea-ice research at the Max Planck Institute for Meteorology. “There is not a god-given year, basically, as to when the ice is gone, but it really is this limit of total emissions. So if we emit less, then it will take longer. It’s as simple as that.”

The 2015 summertime minimum of Arctic sea ice was almost 700,000 square miles smaller than the 1981-2010 average, represented above. (NASA / Reuters)

1,000 gigatons is also about how much atmospheric carbon would warm the world by 2 degrees Celsius. Last year, the Paris Agreement set 2 degrees of planetary warming as the maximum amount of climate change that the nations of the world would allow.

“Once we’ve emitted about 1,000 gigatons of CO₂, we’ve reached the two-degree global warming target … and the Arctic is ice free in summer. This suggests the two-degree global-warming target is not sufficient to allow Arctic summer sea ice to survive,” Notz told me.

This chart depicts the annual mean loss of Arctic September sea-ice area caused by the average emissions of each citizen, with emission data taken from 2013. (Science)

Notz and the paper’s other author, Julienne Stroeve, analyzed more than 50 years of observational data and a set of global modeling runs for this study. (Notably, they found that the real Arctic Ocean lost ice faster than the models would predict—in other words, existing models are less sensitive to atmospheric carbon than they should be.) In a similar study last year, Notz and Stroeve identified that global mean temperature and Arctic summer sea-ice maintained a linear relationship. This study advances that work by putting it into individual—even pedestrian—terms.

Cecilia Bitz, a professor of atmospheric sciences at the University of Washington who was not connected to the study, described its findings as “pretty breathtaking.”

“I’ve stood on sea ice, and I feel like when I’m standing on it, I occupy about a square meter of sea ice. To imagine my personal use of fossil fuels is causing about 50 or so square meters to disappear each year… it was very profound,” she told me.

She could not think of another study or statistic that was able to phrase a global change—the diminution of Arctic summer sea ice—in such an intimate way.

How does this clear relationship between global carbon dioxide and Arctic sea ice occur? Researchers still don’t know.

The authors sketch a broad conceptual model in this paper. As rays from the sun and warming rays trapped in the atmosphere heat up the frozen Arctic Ocean, the ice must compensate for the increased warming. It must equalize the system. In other words, it melts, and the ice edge moves further north to where the sun’s rays are less strong.

“You have this increased heat at the ice edge, so the ice will move further north to regain equilibrium, so more CO₂ will push it further north,” says Julienne Stroeve, a professor at University College London and a senior scientist at the National Snow and Ice Data Center.

“Of course it’s established that the Arctic sea ice doesn’t know much about global mean temperature, in the same way that nobody really knows much about global mean temperature—which is what makes it a very hard number to use to communicate anything about global warming,” said Notz. “What the similarity [between the two] implies is that the same mechanisms that determine the global mean temperature—namely, the rise in CO₂ concentration in the atmosphere—are the same mechanisms that also affect Arctic sea ice.”

But other researchers suspect that heat trapped in the oceans might still play some role in sea-ice loss. There’s little evidence that the northern Atlantic or Pacific are warming along the same kind of linear trend as the planet, which lead Notz and Stroeve to reject it as a cause. But Bitz said that might just be a lack of data: Oceanic heat data at high latitudes is still sporadically observed and poorly understood.

Notz and Stroeve’s paper will have two implications for the field. First, it will allow climate modelers to tighten their work on the northern pole. “The observations are over-sensitive compared to models,” Bitz said. “That helps us know how to make models better & how to interpret them now.”

But, second, it also suggests further that if the concentration of atmospheric carbon ever fell, sea ice in the Arctic Ocean could post a good recovery. In another study a few years ago, Notz and Stroeve asked a range of climate models to estimate what would happen if summer sea ice dwindled to nothing. The sea ice still made healthy recoveries in the winter.

“It’s not that once we’ve lost all summer sea ice, the winter sea ice will go automatically,” said Notz. “Winter sea ice will likely stick with us through the end of the century.”

And if humanity manages to limit its emissions, summer sea ice might stick around that long too.