A new study, published Monday in the journal Nature Geoscience, uses a new statistical method to analyze the retreat of mountain glaciers all over the world, from Russia to South America. It concludes that their shrinking represents “categorical evidence of climate change.”

“It’s the first time that’s somebody’s done a formal climate change attribution study of mountain glacier length changes,” said Andrew Mackintosh, a glaciology expert at the Victoria University of Wellington in New Zealand who was not involved with the new study.

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Mountain glaciers occur on every inhabited continent except Australia and are important sources of fresh water in many places — yet, worldwide, research suggests that they’re losing ice. But until now, it’s been difficult for scientists to pin the retreat of any individual mountain glacier on the influence of climate change, said Gerard Roe, a glaciology expert at the University of Washington and the new study’s lead author.

In fact, the Intergovernmental Panel on Climate Change (IPCC) has indicated that it’s only “likely” that a substantial amount of the observed mountain glacier retreat has been caused by anthropogenic climate change, a conclusion that the new study’s authors note is “a much weaker attribution than for other metrics of climate change.”

Much of this uncertainty has to do with questions about the way glaciers respond to natural variations in their environments. Mountain glaciers tend to respond to environmental changes over a period of several decades, rather than immediately, Roe said. It can be difficult to parse out whether a glacier’s behavior is due to short-term fluctuations in the climate — “noise,” essentially — or long-term climate change.

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But in the new study, Roe and co-authors Marcia Baker of the University of Washington and Florian Herla of the University of Innsbruck in Austria attempt to address this issue with a new method.

“If you’re going to declare that you’ve detected climate change, then you’ve always got this basic question of how large is the change relative to the basic variability you’d observe anyway,” Roe said. “So that was really our focus in this paper — to estimate the natural variability of glaciers.”

The researchers focused on 37 mountain glaciers around the world. For each one, they compiled information on the glacier’s retreat over the past century or more, as well as its weather and climate history. They then used this information in a series of statistical evaluations aimed at comparing the amount of glacier retreat to the natural weather variations they’d experienced.

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“In every case we find that the retreats are significantly larger, much larger than you can expect [from natural variation alone],” Roe said.

For each glacier, the researchers evaluated the probability that the same changes would have occurred in the absence of climate change. For 21 of the 37 glaciers, they found that it was “virtually certain” that the retreat required climate change, according to IPCC classification criteria. And altogether, for all but one glacier — the Rabots Glacier in northern Sweden — this probability was at least “very likely,” according to the IPCC.

“From a glaciological perspective, we’ve had a sort of strong intuitive sense that that’s how glaciers work for a long time now,” said Mackintosh, the Victoria University of Wellington glacier expert. The new study now provides robust statistical support for the idea, he said.

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The researchers suggest that the behavior of mountain glaciers constitutes one of the clearest signals of climate change on the planet, thanks in part to their decades-long response time when it comes to environmental change.

“It turns out this decades timescale is the sweet spot for detecting climate change,” Roe said. “You get the purest mathematical signal of climate change if you have a timescale of about 20 or 30 years.”

This also means that the statistical method used in this study wouldn’t necessarily work for the iconic glaciers found on the Greenland or Antarctic ice sheets, which can have response times of hundreds or even thousands of years.

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The study’s findings constitute “a significant upgrade to our understanding of the relationship between climate trends and glacier retreat,” Roe said. They may also drive home — yet again — the dramatic influence climate change is already having all over the world.