WASHINGTON — Driving a gas-powered car about 90 miles – the distance between New York and Philadelphia – melts about a square foot of Arctic sea ice in the critical month of September, according to a new study that directly links carbon pollution to the amount of ice that’s thawing.

At current carbon emission levels, the Arctic will likely be free of sea ice in September around mid-century, which could make weather even more extreme and strand some polar animals, a study published Thursday in the journal Science finds. The study calculates that for every ton of carbon dioxide put in the air, there’s 29 square feet less of sea ice during the crucial month when the Arctic region is least frozen. Using observations, statistics and 30 different computer models, the authors show heat-trapping gases cause the melting of sea ice in a way that can be translated into a simple mathematical formula.

There’s “a very clear linear relationship” between carbon dioxide emissions and sea ice retreat in September, especially at the southern boundary edges, said study lead author Dirk Notz, a climate scientist at Max Planck Institute for Meteorology in Germany.

“It’s very simple. Those emissions from our tailpipes and our coal-fired power plants are all going into the atmosphere,” said co-author Julienne Stroeve, a climate scientist at both the National Snow and Ice Data Center in Boulder, Colorado, and University College, London. “It just increases the warming at the surface. So the ice is going to respond to that. The only way it can do that is to move farther north.”

Rutgers University marine scientist Jennifer Francis said the link is so direct that “we know beyond a shadow of a doubt that Arctic sea ice is disappearing because of increased carbon dioxide.”