GLACIAL ICE SHEET, GREENLAND –  Water is seen on part of the glacial ice sheet that covers about 80 percent of Greenland. As the sea levels around the globe rise, researchers affiliated with the National Science Foundation and other organizations are studying the phenomena of the melting glaciers and its long-term ramifications.  (Photo by Joe Raedle/Getty Images)

Scientists have announced a potential solution to a tantalizing puzzle about sea-level rise that’s remained unsolved for more than a decade. In doing so, they’ve helped confirm scientists’ latest estimates of 20th-century glacial melting and our understanding of how sea-level rise fundamentally affects the planet — down to the way it spins on its axis.

At issue is a scientific quandary known as “Munk’s enigma,” which was introduced by famed oceanographer Walter Munk in a 2002 paper published in Proceedings of the National Academy of Sciences. The enigma refers to a key discrepancy between the amount of sea-level rise believed to have occurred during the 20th century and the effects it should have produced on the planet — specifically, on the Earth’s rotation.

The planetary effects of sea-level rise

That’s right — in addition to all the devastating and obvious effects sea-level rise will produce on the planet, such as flooding and erosion, sea-level rise also has the more subtle, but nonetheless mind-boggling ability to alter the way the Earth rotates on its axis.

“If you melt ice sheets or glaciers, which happen to be close to the poles, and all of that mass moves from the poles toward the equators, that movement is very similar [to] a figure skater who puts her arms out,” said the new paper’s lead author, Jerry Mitrovica, a professor of geophysics at Harvard University. “The melting of glaciers acts to slow the spin of the Earth in a measurable way.”

Additionally, glacial melt can also cause the Earth’s rotation to wobble a little, since “the melting of glaciers isn’t perfectly symmetrical, and the water will move more in some parts of the Earth than others,” Mitrovica said.

Theoretically, one should be able to look at calculations of how the Earth’s rotation has changed over the years, compare these changes with the amount of glacial melting believed to have occurred in the same time frame, and find that the two measurements reinforce each other.

This is just what Munk attempted to do. But, as he pointed out in his 2002 paper, the calculations just didn’t add up.

The enigma  

Munk was able to reference both 20th century data and ancient astronomical records for information on how the Earth’s rotation has changed over the years. When trying to determine how much of these changes were caused by 20th-century human-caused sea-level rise, specifically, Munk also had to account for another important factor known as the ice age effect. This is a phenomenon in which massive amounts of glacial melting, which occurred thousands of years ago at the end of the last ice age, can still produce changes on the Earth’s surface — and, thus, affect its rotation — centuries or even millennia after the fact.

This is because the Earth’s interior is viscous, meaning the rocks that make it up tend to flow and reshape themselves very slowly over long periods of time — kind of like clay or putty might spread out very slowly if you were to set it on a table and leave it alone. After the ice age glaciers melted, they left indentations in the Earth’s surface that have been slowly bouncing back ever since, affecting the Earth’s rotation in the process, Mitrovica said. By incorporating an ice age model into his calculations, Munk was able to “correct” for this effect on the Earth’s rotation and see how much room was left over, or how much of a “signal” existed, as the scientists put it, for effects caused by 20th-century sea-level rise.

Herein lies the enigma: While the ice age effect fit the observed rotational changes perfectly, there was no room left to account for 20th-century sea-level rise, which scientists at the time estimated to have occurred at rate of about 1.5 to 2 millimeters per year. In other words, if Munk factored in the rotational changes that should have been produced by modern glacial melting, they suggest a greater effect than has actually been observed. 

It was a true mystery, Mitrovica said. Munk knew that the Earth’s rotation had changed, and he knew that sea-level rise had occurred — he just couldn’t make the two observations match up. In his paper, he proposed a few theories as to what might have gone wrong, including the idea that the ice age model he used was inaccurate or that the estimations of 20th-century sea-level rise were too high.

In any case, Munk noted, figuring out the problem is an important challenge. “Sea level is important as a metric for climate change as well as in its own right,” he wrote in his paper. “We are in the uncomfortable position of extrapolating into the next century without understanding the last.”

Solving the riddle  

“Over the years, this was one of those papers that just kept coming back and coming back, and there was a group of us who realized that this is really an issue, here,” Mitrovica said. In a new paper, Mitrovica and an interdisciplinary team of colleagues claim to have resolved the enigma by pointing out a few key flaws in Munk’s original calculations.

First, they say, the estimates of 20th-century sea-level rise used by Munk were too high. More recent estimates put the rate at between 1 and 1.5 millimeters per year, Mitrovica said. Additionally, he and his colleagues argue that the model Munk used to correct for the ice age effect was inaccurate.

“What Munk didn’t realize at the time…is that the model he used for the ice age made a very significant error about the Earth’s internal structure,” Mitrovica said, suggesting that the model Munk used didn’t accurately reflect how viscous the Earth’s internal structure actually is. He and his colleagues proposed a new model, one that estimates viscosity differently.

Even with the new model and the updated sea-level rise estimates, however, the calculations didn’t quite fit with historical astronomical records. It looked as though there was one last missing piece — and the authors believe it has to do with the way motion in the Earth’s core affects the planet’s rotation. This is a factor that Munk failed to take into account entirely, said Sabine Stanley, a professor of physics at the University of Toronto and one of Mitrovica’s co-authors.

“The earth itself is made up of a solid layer with this liquid core inside,” Stanley said. “Whenever motion occurs in one layer, that’s going to affect the other layer.” She likened this “coupling effect” to a hamster running in a wheel — as the hamster runs in one direction, it causes the wheel to spin in the opposite direction.

“We know that there have been changes in the magnetic field to suggest changes in the core’s rotation, and that means changes in the way we see things on the surface,” Mitrovica said. When the scientists added the coupling effect to their calculations, suddenly everything snapped together — the calculations fit the observed astronomical data, and there was enough rotational “signal” left over to account for 20th-century sea-level rise.

A controversy continued

But the mystery may not be quite resolved, according to some. William Richard Peltier, a professor of physics at the University of Toronto, takes issue with some of the paper’s key points. Peltier was not involved with this paper, but is familiar with much of the work that went into it — Mitrovica was one of his doctoral students, and some of Peltier’s own work was incorporated into Munk’s original calculations.

Peltier’s main issue with the argument in the paper has to do with the new viscosity model — the model of the way the Earth flows — that the authors used to help account for the ice age effect. Previous research has suggested that this model does not match up with observed data on the way the Earth’s geology actually behaves, Peltier said. In essence, he claims, this aspect of the paper is “absolutely incorrect.”

Peltier does note that the authors’ inclusion of the coupling influence — that hamster-wheel effect described by Stanley — is “the really interesting and innovative comment in the paper.” However, taken as a whole, he said the proposal is a “nice try, but no cigar.”

So, it seems, there’s still a debate to be had here. Mitrovica insists that the striking thing about this paper is how neatly all the calculations line up at the end. “The general framework for solving the enigma is done now, and happily that framework shows that there is a signal left over when you correct for the ice age,” he said, noting that “the signal is precisely what it has to be” to account for the estimated 20th-century sea-level rise. To Mitrovica, that’s no coincidence.

Reinforcing modern climate science  

The findings “lend support to our confidence in recent estimates of sea level rise and the increasing ice sheet contribution,” said Michael Oppenheimer, the Albert G. Milbank professor of geosciences and international affairs at Princeton University’s department of geosciences, in an email to The Post.

Indeed, Mitrovica said, exploring climate change’s more subtle effects — such as its ability to affect the planet’s rotation — is an important way for scientists to back up the existing climate science. “Yes, this is a subtle effect; yes, we don’t like talking about it, because it’s so subtle,” Mitrovica said. “[But] it sort of adds to the credibility of the scientific consensus by saying even the most subtle effects that we might predict from global climate change are consistent with the scientific consensus.”

And, more simply, the paper helps reinforce the awe-inspiring power of climate change to produce global-scale effects, changing the planet’s very rotation. While this effect might be tiny from a human perspective, “the amazing thing is that we can observe these things,” Mitrovica said. “The effects are very small, but hidden in them are very large changes in the Earth’s system.”

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