Global Warming: A Human Perspective

According to most climate experts, anthropogenic greenhouse gases add about 2 watts per square-meter of radiative forcing to earth’s environment. This is roughly the power used by a small Christmas tree lamp. In more personal terms, the human body generates approximately 100 watts of power and has a surface area of around 2 square-meters. Assuming that the sole of the average foot has an area of about 200 square-centimeters, it would emit 1 watt of power. Both feet, applied to a surface, would add 2 watts to that surface. Applied to a square-meter, that would be equivalent to the anthropogenic greenhouse effect.

If we could cover every square meter of the Greenland ice cap with a barefoot human — a magical, never frostbitten human willing to stand, day after day, pumping his 2 watts into the ice — would we expect the ice to melt?

The answer is “eventually.” A back-of-the-envelope calculation* suggests that it would take about 10,000 years, assuming an average ice depth of 2 kilometers. In light of this, Al Gore’s threat to invoke the wrath of Gaia to bring about a complete meltdown in 60 years seems off by a couple of orders of magnitude — unless, of course, he is willing to acknowledge the possibility that the warming we observe is due to a so-far unmeasurable anthropogenic effect superimposed on a poorly understood natural warming process that began when Abraham Lincoln was a baby, long before carbon dioxide levels changed.

Such an admission, however, might be inconvenient.

*2 Watts = 172800 Joules/day
333700 Joules melts 1 kg of ice
Therefore 2 watts melts 172800/333700=0.52 kg/day
1 kg = 1000 cubic centimeters of ice (yes, I know its really a bit more because of expansion)
Distributed over 1 square meter, this equals a depth of 0.1 cm
But our feet can melt only 0.52 kg/day, so a hotfooted human would melt a depth of (0.52)X 0.1 cm / day = 0.05 cm/day (half a millimeter)
THUS, the heat from a person’s feet would melt (distributed over a square meter), a depth of:
0.05 cm/day
1 meter/2000 days (call it 5 years)
2000 meters in 10,000 years (This surprised even me, so I’d appreciate a check of this reasoning by more arithmetically adept readers).

NB: Junk Science has a detailed discussion of how to evaluate anthropogenic radiative forcing .

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Quest for a New Earth

If our civilization survives for another decade or two, we may get our first glimpse of a planet remarkably like Earth. The red dwarf star Gliese 581 is about 20.5 light years away, practically next door. Last year, two planets were discovered orbiting it. Both are giant worlds like Jupiter, detected by the subtle wobble they produced in their “sun” as they tug it slightly to and fro with their gravitational fields. Last month, astronomers announced the discovery of a third planet, dubbed GL 581 c. Two things about it are intriguing: Its mass is only about 5 times greater than Earth’s (as opposed to Jupiter’s 300 times greater heft), making it one of the smallest extrasolar planets yet detected. If it is made of rocky material like earth, it would be only about 75 percent larger than our world. The second interesting thing is its orbit, which places it squarely in its parent star’s “Goldilocks Zone,” where it is neither too hot nor too cold to sustain liquid water. This is the first planet we’ve found that could conceivably look something like Earth, with white swirling clouds and vast oceans.

We should be reluctant to draw a graph using two data points, however, and all we know about this world is its mass and orbit. Be cautioned that all that follows is speculation. Gliese 581 shines with only 1.3 percent of the Sun’s luminosity, so a planet would have to orbit 14 times closer than Earth orbits the Sun in order to receive the same amount of heat. GL 581 c does this, in fact, giving it a “year” that is only 13 earth-days long. In such a close orbit Gliese 851c has probably become tidally locked, so that its rotation period matches its orbital period. This means that the same hemisphere would always be turned toward its star. Our own moon does this, so that we see only one side of it.

Such a situation could make for an interesting climate. Any ocean in the subsolar region of GL 581 c might simmer under a perpetual hood of steam. If the atmosphere is dense enough, convection might carry heat away to the dark side, possibly preventing it from freezing in its eternal night. The most habitable place might be the “Twilight Zone” near the boundary between night and day. Any creatures living in this temperate band would see their sun as a bloated orange orb — a dozen times larger than our sun looks to us — poised always on the horizon. Plants, questing for light, would tumble over themselves, trying to grow ever-sunward. I imagined a situation like this back in 1980, and have updated my painting of this “Marching Forest” to suit the GL 581 c scenario.

So far, no telescope has been able to photograph a planet orbiting another star, but with any luck, sophisticated satellites planned for the next decade may obtain spectrographic data that could tell us something about the compositions of the atmospheres of these distant worlds. GL 581 c is close enough that, should its atmosphere contain oxygen — almost certainly proof of life because it is so unlikely to remain unbound for long — we would have the first evidence that earthlike worlds abound.

Whether that realisation does anything to improve behavior on this planet is anyone’s guess. A sense that there is still wonder and mystery in the universe might kindle hope in those parts of the world where there currently doesn’t seem to be much, this side of Paradise.

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