With more dark, open water in the summer, less of the sun’s heat is reflected back into space. So the entire Earth is absorbing more heat than expected, according to a study published Monday in the Proceedings of the National Academy of Sciences.

That extra absorbed energy is so big that it measures about one-quarter of the entire heat-trapping effect of carbon dioxide, said the study’s lead author, Ian Eisenman, a climate scientist at the Scripps Institution of Oceanography in California.

The Arctic grew 8 percent darker between 1979 and 2011, Eisenman found, measuring how much sunlight is reflected back into space.

“Basically, it means more warming,” Eisenman said in an interview.

The North Pole region is an ocean that mostly is crusted at the top with ice that shrinks in the summer and grows back in the fall. At its peak melt in September, the ice has shrunk on average by nearly 35,000 square miles — about the size of Maine — per year since 1979.