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    The very weird physics of sea-level changes

    Obervers stood in 2013 above melting water on part of the glacial ice sheet that covers about 80 percent of Greenland.
    Getty Images
    Obervers stood in 2013 above melting water on part of the glacial ice sheet that covers about 80 percent of Greenland.

    As the earth’s climate warms, everyone wants to know how high sea levels are going to rise. It might seem like a simple calculation, but groundbreaking research by a geophysicist at Harvard University has demonstrated that accurately measuring sea levels is surprisingly complicated — and turns on some strange though ultimately intuitive ways in which parts of the earth are interconnected.

    Most people think (incorrectly) of the earth’s oceans as a bathtub, Jerry Mitrovica explains. In this view, when any of the big ice sheets melt (Greenland, Antarctica), you’d imagine sea levels would rise around the globe, just as a bath would rise uniformly if you were to add a bucket of water.

    This isn’t at all how it actually works, though. Massive ice sheets, like the one in Greenland, exert a gravitational pull on the surrounding water. When ice from the sheet melts, it adds water to the world’s oceans, yes, but the melting also reduces the mass of the ice sheet, which reduces its gravitational pull. As a result, water flows away from the diminished ice sheet, which actually leads to sea levels falling in the exact place where the ice melted.

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    “If an ice sheet melts, water moves away from the location of the ice sheet and you pay the price farther away,” Mitrovica says.

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    There’s another even more unexpected effect. Ice sheets sit on land, weighing it down. When ice melts, there’s less weight pressing down on the land, which allows the land to rise slightly. As the land rises, it effectively pushes “nearby” water away from it, compounding the effects of the reduced gravitational pull. To picture how this works, instead of a bathtub, picture a waterbed.

    “Sit on it, and it sinks beneath you and bulges up around you as your behind forces water to the sides,” writes Richard Alley, a geologist at Penn State University, in an e-mail. “Stand up, and it goes back to the original shape.”

    For people wanting to know what these various effects mean for their own stretch of shoreline, it’s important to define what it means for a melting ice sheet to be “nearby.” Mitrovica explains that the threshold is about 1,200 miles — places within that distance of the melting ice will see sea levels fall and places farther away will see sea levels rise (in both cases, effects taper as you get farther from the melting). To put some numbers on this, if the Greenland ice sheet were to melt enough to raise average global sea levels by a meter, in Boston Harbor, which is relatively close to Greenland, sea levels would rise by only about 0.7 meters. Conversely, melting from the more distant Antarctic ice sheet would disproportionately affect Boston and other places in the northern hemisphere. This means every locale has its own problem ice sheets to keep an eye on.

    “I was just talking to some people in Holland,” Mitrovica says, “and I told them that if the Greenland ice sheet melts, they have nothing to worry about, but if the Antarctic melts, they’re in trouble.”

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    The idea that gravitational forces affect sea level is not new. It was in the air in the 1800s, but largely forgotten afterward. Mitrovica says he “reacquainted” the scientific community with these factors with an article he published in Nature about a decade ago. Today they are fully accepted. Alley describes Mitrovica’s work modeling the forces that affect sea-level as “fascinating, visionary, reliable, and important.”

    They are also useful in order to “fingerprint,” as Mitrovica calls it, sources of global melting.

    The idea is to combine all the so-called isostatic forces that influence sea levels into a single model. These forces include gravitational effects, the changing contours of the earth’s crust as ice melts, and other complicating forces, like the fact that water expands as it warms. With a model like this in place, it’s possible to measure sea-level rise in different parts of the earth and infer backwards which ice sheets must have melted, and by how much, to produce those measurements. This approach can be more accurate than trying to measure the melting of ice sheets directly. The technique is also responsible for a change in research emphasis among earth scientists.

    “No one talks about global average sea levels anymore,” says Mitrovica. “The real focus is on fingerprinting sources.”

    Kevin Hartnett is a writer in South Carolina. He can be reached at kshartnett18@gmail.com.

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