Geothermal energy

I’m currently away from my office, waiting for a meeting that will start in about an hour. I don’t really have anything particular to say, but thought I would write about something that I was considering yesterday. There’s been suggestions by some that the increase in the deep ocean heat content could be due to the release of geothermal energy from undersea volcanoes. This seemed a little unlikely, so I thought I would see if it made any sense. An approximation for the amount of internal energy in the earth is
E = G M2/R,
which is 4 x 1032 J. If this were to be released at a constant rate over a 10 billion year timescale, it would release 4 x 1022 J every year. The deep ocean (700 – 2000 m) heat content has increased by about 5 x 1022 J in the last 40 years. I was surprised that the amount of geothermal energy could be this large. Admittedly, my assumptions were very simplistic as it isn’t actually released at a constant rate (faster when the Earth is young), and this also ignores energy generated by radioactive decay.

I looked into this a bit more and it turns out that the oceanic crust releases 101 mJ per square metre per second. The ocean covers 70% of the Earth’s surface, so this is 3.6 x 1013 W. This means that it is releasing 1.13 x 1021 J every year, or 4.5 x 1022 J every 40 years. Therefore it seems that if all this energy remained in the deep ocean, it could explain the rise in deep ocean heat content. This seems unlikely and so it doesn’t seem as though the rise in deep ocean heat content can be explained via the release of geothermal energy.

However, there is one other obvious problem with the suggestion that it is geothermal energy that is heating the deep ocean. There is no evidence to suggest that the rate of geothermal energy release has changed in the last century. If anything, it is probably decreasing slowly (although, probably on a very long timescale). The geothermal energy has therefore always been included in the Earth’s energy budget. One would therefore expect to reach some kind of equilibrium in which the energy is transported through the oceans to the surface to be radiated through the atmosphere and into space. Even if it is geothermal energy that is heating the deep oceans (and – as shown above – this would require all of the geothermal energy), what has changed in the last 40 years that has caused this energy to remain in the deep ocean and hence increase the deep ocean heat content?

Anyway, I was just a little surprised that there was so much geothermal energy. It does appear as though the amount of geothermal energy released in the last 40 years is almost the same as the increase in deep ocean heat content (5 x 1022 J). It might be attractive to suggest that this then explains the increase in deep ocean heat content. There are, however, two main issues with this. One is that it would require a 100% retention of this energy in the deep ocean – which seems unlikely. The other is that one has to explain why the deep ocean hasn’t reached some kind of equilibrium in which the energy going into the deep ocean (from geothermal activity) is balanced by energy leaving the deep ocean and eventually being lost to space. It may well be that this energy is contributing to the heating of the deep ocean, but this isn’t inconsistent with it being a consequence of an energy imbalance that’s driving global warming.

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8 Responses to Geothermal energy

  1. bg says:

    would be interesting to have terms in equation defined an/or reference to it.

  2. Yes, indeed. I would normally do that fairly religiously. So G is the gravitational constant, M is the mass of the Earth, and R is the radius of the Earth.

  3. Rachel says:

    I think I read somewhere that scientists used to think Earth got its warmth from the core. That was before the greenhouse theory was posited. One of the problems with the theory that warmth came from the Earth itself – from what I understand – was that there wasn’t enough heat to generate current surface temperatures.

  4. Yes, I think that is the point. The Earth gets it’s internal energy from accretion (i.e., the material that collides to make it), from differentiation, and from radioactive decay. The calculation I did at the beginning of this post was basically only for the energy from accretion. Differentiation should not add much, but radioactive decay can be substantial but still isn’t enough to explain our enhanced temperature. A quick calculation I’ve just done suggests that the internal heat could have kept us 30 degrees warmer than our non-greenhouse temperature for about 150 million years, so clearly not enough.

    It was also the case that 19th century scientists thought that the Sun got its energy in the same way. However, when Darwin showed that the Earth was much older than originally thought, this created a problem because the Sun should only have been able to exist for a few 10s of millions of years, given its internal energy. They realised that if the Earth and Sun were billions of years old, it would require some other (as yet unkown) energy source in the Sun. It was only when nuclear fusion was discovered that it explained the Sun’s energy source.

  5. bg says:

    That is correct. That is essentially the finding of the paper published by Fourier in 1828, which is considered by most to be the first of the fundamental papers on global warming. See for example “The Warming Papers,” edited by Arched and Pierrehumbert.

  6. bg says:

    Ooops, should be Archer.

  7. bg says:

    Well, that is what I would have guessed, guess now I’ll have to go figure out why that represents the energy stored.

  8. That’s relatively straightforward. If you consider building the Earth by accreting objects (called planetesimals with mass m) that fall from a large distance, then the change in gravitational potential energy is (GMm/R1 – GMm/R2) where R1 is the original large distance, R2 is the radius of the object being built and M is the mass of the object being built. This energy will be converted from potential to kinetic which, in this case, would typically be in the form of heat. If R1 is very large you can ignore it. If you add up all the energy you get something close to GM^2/R (I think strictly speaking it is actually 3/5 GM^2/R). If you wanted to do it properly, you would need to integrate from M’ = 0 to M’ = M and also include that the radius changes as the object grows, but I think the estimate here is pretty close. As I say below, this ignore internal energy that comes from radioactive decay and energy from differentiation.

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