Drive your car 4000km and its greenhouse gas emissions will melt three square metres of ice on the Arctic Ocean, according to a study that has found a direct link between carbon dioxide and shrinking ice.

Examining long-term trends for ice floating on the ocean since the 1950s, scientists in Germany and the United States projected the ocean around the North Pole would be ice-free in summers by the mid-2040s at current levels of emissions.

In the historical records, they found that every tonne of carbon dioxide emitted to the atmosphere meant on average the loss of three square metres of ice in September, when the ice reaches a minimum extent before expanding in winter.

That made it possible to "grasp the contribution of personal carbon dioxide emissions to the loss of Arctic sea ice," scientists at Germany's Max Planck Institute for Meteorology and the US National Snow and Ice Data Center wrote in the journal Science.

Each passenger taking a return flight from New York to Europe, or driving a car 4000km, would emit about a tonne of carbon dioxide, they estimated.

A long-term retreat of Arctic sea ice is already causing profound changes, disrupting the lives of indigenous peoples while opening the region to more oil and gas exploration and shipping.

Scientists usually deal in more abstract terms such as billions of tonnes of greenhouse gases.