There’s news about glaciers, and it’s grim.

Regardless of climate mitigation strategies, the world’s glaciers are on track to shrink significantly over hundreds of years, according to new study published on Thursday. They’re locked in to losing ice.

Even if global temperatures stayed where they are today for the next thousand years, essentially an impossibility, glaciers outside of ice sheets would lose roughly one-third of their mass, researchers estimated.

But there’s still hope to avoid the most severe losses, the assessment said. Limiting warming to 1.5 degrees Celsius, or 2.7 degrees Fahrenheit, above the preindustrial average could save about twice as much ice in a millennium than if the planet warmed by 2.7 degrees Celsius, the trajectory the world is currently on for 2100, according to the study.

“Every tenth of a degree less of warming will help preserve glacial ice,” said Lilian Schuster, a glacial modeler at the University of Innsbruck in Austria who helped lead the research, which was published in the journal Science. “With ambitious climate measures, we can save a lot of ice.”

The massive ice sheets that cover Antarctica and Greenland get a lot of attention in the climate change discussion; if they melted, sea levels would rise more than 200 feet, flooding coastal cities around the world.

But glaciers found in mountains and near the margins of ice sheets play a small but significant role in the climate change story, too. They make up less than half of 1 percent of the world’s ice and, if they melt, they would contribute about a foot to global sea level rise.