A volcano that rises past the heights of hubris

Byline: | Category: Environment | Posted at: Friday, 27 June 2008

Yesterday Jonah Goldberg pointed to a story about previously unknown volcanoes 13,000 feet beneath the Arctic Ocean and asked:

“am I crazy for wondering why this story doesn’t even address — if only to shoot down — the idea that maybe it’s volcanoes, and not global warming, that are causing the melting ice caps?”

Goldberg isn’t crazy, nor is he the only one wondering such a thing.  In December 2007 Ralph von Frese, an earth sciences professor at The Ohio State University, reported newly discovered volcanic activity beneath the ice sheet that covers nearby Greenland.  His analysis determined that it is possible that recent volcanic activity there might melt enough water at the bottom of the ice sheets to accelerate their flow.  Von Frese concluded that:

The behavior of the great ice sheets is an important barometer of global climate change . . . However, to effectively separate and quantify human impacts on climate change, we must understand the natural impacts, too.

That seems like a rather pragmatic approach, so let’s attempt to quantify the impact of the volcanoes recently discovered at the top of the world.  What the Woods Hole Oceanographic Institute’s researchers found was a series of explosive volcanoes along the Gakkel Ridge, an underwater mountain chain 1,100 miles long.  There, a series of earthquakes in 1999 were the result of volcanic eruptions each “as big as the one that buried Pompeii.”

Geologists tell us that when Mount Vesuvius erupted in 79 AD, burying the ancient Neapolitan city, it launched a cubic mile of molten rock into the atmosphere.  Doing a little bit of math (see below) we find that a single Pompeii-sized eruption would release enough subterranean heat into the Arctic Ocean to put a hole in the polar ice cap the size of Massachusetts. 

Granted, the expanse of the polar ice cap is much greater than the size of the Bay State, but the story says that there was apparently more than one eruption in 1999 when seismologists first learned of the issue.  Climatologists before had barely even considered the effect of undersea volcanoes, whose effects are obviously not insignificant.  The magnitude of the recently discovered eruptions undoubtedly explains some proportion of the melting ice caps that many before have attributed to the effects of man.  As von Frese said, this little understood natural phenomenon deserves more scrutiny.

I say all this to point out what should be obvious but apparently isn’t:  we barely understand the world around us.  In all of recorded history we have only begun to scratch the vast amount of knowledge of the workings of our magnificent planet.  This world is so enormous that we apparently have even missed the existence of one of Earth’s most powerful forces—a volcanic explosion—directly beneath this supposedly well studied area.  For man, who possesses so little knowledge, to conclude that he and he alone is responsible for the changes we now observe around us is the height of hubris.  Volcanoes, it turns out, rise to even higher heights than hubris. 

That “little bit of math” part follows after the jump.

Before the math, I probably need to explain a little bit about enthalpy.  A “little bit” is all I know, since it has been probably two decades since I’ve even said the word “enthalpy.”  Still, the concept is pretty simple.  If it takes a certain amount of heat energy to raise the temperature of a given quantity of something by one degree, it takes ten times that heat energy to raise the temperature of that same quantity by ten degrees.  That simple linear equation holds until you reach the point at which its phase changes.  For example, to raise the temperature of one kilogram of water one degree Celsius you must add 4,186 joules of heat.  That means that to go from 0 degrees to 100 (from the freezing point to the boiling point) requires the addition of 100 times that amount, or 418,600 joules.  However, that’s just the energy required to bring it to the boiling point.  To actually boil the water takes another 2.3 million joules.  That’s why when you heat water on the stove, it warms up quickly, but it always seems to take forever for it to actually boil.

The same works in reverse.  When H2O goes down a phase it gives off the same amount of energy that it took to change into that phase.  It’s not just water that behaves that way; every substance does.  Even rock.

A cubic mile of molten rock, like was launched by Vesuvius on to Pompeii, converts to 4.186 billion cubic meters.  At a density of 3,000 kilograms per cubic meter, that much molten rock works out to be approximately 1.25 x 1013 kg.

Basaltic magma has a specific heat of 1,000 joules per kilogram per degree Celsius.  In other words, a kilogram of magma releases 1,000 joules of heat energy for every degree it cools until it transforms into a solid.  A kilogram of molten rock at 1350 degrees Celsius, therefore gives off 250,000 joules of heat as it cools to its crystallization temperature of 1100 degrees Celsius.  Passing through that phase from liquid to solid, that kilogram releases another 400,000 joules of heat.  Then as the solid rock cools from 1100 degrees to 0 degrees Celsius it releases another 1,400 joules per degree, or 1,540,000 joules.  In total, one kilogram of molten basalt at a temperature of 1,350 degrees releases 2,19 million joules of heat into the surrounding atmosphere.  Multiplying the weight of a cubic mile of lava by the heat energy released per kilogram and we find that a Pompeii-sized underwater eruption releases 2.739 x 1019 joules of heat into the sea.

One kilogram of ice at 0 degrees Celsius requires the addition of 333,550 joules of heat energy to turn it into a liquid.  Dividing that number into the quantity of joules of heat released by the volcano that we calculated above, we find that the cubic mile of magma can melt roughly 82 trillion kilograms of ice.  A cubic meter of ice at 0 degrees weighs 917 kilograms, so that works out to roughly 90 billion cubic meters of ice melted by our undersea volcano.

Because of the shifting currents beneath the North Pole, the sea ice there is only two to three meters thick.  Dividing 3 meters into the volume of ice that our volcano melted, we find that it would cover an area of just under 30 billion meters square, or a little less than 30 thousand square kilometers.  Convert that into English, and it works out to 11,532 square miles of ice three meters thick, or an area about 10% larger than the state of Massachusetts.

Obviously, I’ve made some simplifications, like ignoring whatever effects the pressure of 13,000 feet of sea might have on the equation, and I haven’t taken into account the change in melting point as a result of the salinity of the ocean.  But this is probably close enough to demonstrate that Jonah Goldberg’s original question is worthy of much more analysis. 

In short: how much polar ice is melted by an undersea volcano?  A whole lot.

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6 Responses to “A volcano that rises past the heights of hubris”

  1. Conrad Says:

    You took 2.739 x 10^19 joules of heat from your hypothetical volcano and applied it directly to the ice… ignoring the small matter of the Arctic Ocean which happens to lie between the volcano and the ice.

    That ocean has a volume of about 14 million kilometres cubed… and thus a mass of about 14 quadrillion kilograms. 2.739 x 10^19 joules of heat applied to 14 quadrillion kilograms of water raises the temperature of that water by about 0.47 degrees celsius.

    That less than half a degree would then radiate into the water of the surrounding oceans, the air, and yes the ice. By itself it wouldn’t melt anything. If it happened during the Winter the ice would stay frozen. If it happened during the Summer it would briefly contribute to the much greater melting caused by the multiple degree Summer heat increase from the Sun.

    Further… these volcanos have ALWAYS been under the North Pole and haven’t caused it to melt out before.

    And… the most recent eruption they found evidence of was ten years ago, which therefor clearly had nothing to do with the record melt last year.

    In short: how much polar ice is melted by an undersea volcano? Not much.

  2. Brian Dodge Says:

    How much Arctic ice melted last year? Approximately 7.72 million km2. A whole lot.
    How big is the 110% of the state of Massachusetts?
    approximately 23 thousand km2. NOT a whole lot.
    How many Vesuvius scale eruptions would it take to melt 7.72 million km2? 373
    How much Arctic ice melting isn’t explained by one undersea eruption?
    Approximately 7.7 million km2, or 99.7%.
    Volcanic explanation for Arctic ice melting -99.7% BS.

  3. Wildmonk Says:

    Conrad makes the same kind of error that he accuses Bob of making. First, he makes a very good point regarding the fact that Bob left out the warming required of the ocean. Ignoring this means that Bob is certainly incorrect about the total amount of ice actually melted. However, Conrad then goes on to dilute the heat flow by the total volume of the Arctic Ocean. That is a bit like saying that the water on the stove will never boil because it will take too long for the stove to heat all of the air in the room so that it is hot enough to boil the water.

    Surely you know better than that. The effects will be focused on the area where prevailing currents (ocean or glacial melting) take this energy.

    Furthermore, you and Brian both miss the point. Bill isn’t saying “this one volcano explains the recent retreat in Arctic ice.” He’s saying, “this system has some complications we don’t understand.” He’s couched his point in caveats so that people won’t walk away thinking he’s really trying to explain the “hole” thing (sorry for the pun). Furthermore, he’s made it clear that he isn’t talking about a single volcano but a “string” of them whose total output isn’t clear.

    It may well be that the volcanos have nothing to do with recent ice cover retreats because, as Conrad says, they may well have contributed this same energy in the past when the ice *wasn’t* retreating. But don’t we owe it to ourselves to try to look into this further? Not as a way to put off conversion to greener fuels, mind you, but simply to ensure that we truly understand the foundations on which we are proposing radical changes in the technological foundations of our civilization.

  4. bob Says:

    My analysis was not to say that this is how much ice is melted by a volcano (there are more than one beneath the Arctic Ocean), but to give an equivalent amount of ice that could be melted by the heat released by one such volcano. But your larger point, which flew totally by the previous two commenters, is my own: we don’t know enough and need to study more. To profess otherwise is the height of hubris.

  5. streiff Says:

    pinched your headline. Great story


  6. GREG ARCHER Says: