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Climate Hustle

Heat from the Earth’s interior does not control climate

Posted on 17 September 2011 by Andy Skuce

This blog post is the intermediate-level rebuttal to the climate myth “Underground temperatures control climate”. 

The myth:

"There are other possible causes for climate change which could be associated with solar activity or related to variations in the temperature of the liquid core of the Earth, which is about 5,400 degrees Celsius.  We don't need a high heat flow - just a high temperature for the core to affect the surface climate.  There is massive heat inside the Earth." Link. See here, also.

Consider:

  • The center of the Earth is at a temperature of over 6000°C, hotter than the surface of the Sun.
  • We have all seen pictures of rivers of red-hot magma pouring out of volcanoes.
  • Many of us have bathed in natural hot springs.
  • There are plans to exploit geothermal energy as a renewable resource.

Common sense might suggest that all that heat must have a big effect on climate. But the science says no: the amount of heat energy coming out of the Earth is actually very small and the rate of flow of that heat is very steady over long time periods. The effect on the climate is in fact too small to be worth considering.

The Earth’s heat flow

Where does the heat come from?

  • There are radioactive elements in the Earth, mainly potassium, uranium, and thorium, that have long half-lives. When their nuclei decay, they give off heat, as in a nuclear reactor.  Some researchers say that  "the vast majority of the heat in Earth's interior—up to 90 percent—is fueled by the decaying of radioactive isotopes", while other scientists claim that "heat from radioactive decay contributes about half of Earth’s total heat flux". More here.
  • The Earth is still hot from the time the planet formed from the agglomeration of smaller bits and pieces.  Even more heat was gained as the high-density materials, such as iron and nickel, subsequently separated out and formed the core of the Earth.

The mostly solid, rocky outer layers of the Earth, the crust and mantle, have low thermal conductivity, acting as a thermal blanket slowing down the passage of heat to the surface.  In the very early stages of the Earth’s history, internal temperatures and heat flows were probably much higher than they are today, partly because the planet had only just started to cool, and partly because the energy flow from radioactive decay was much larger then.

How does the heat get to the surface?

According to Stein and Stein (10MByte download) most of the heat energy (about 70%) that makes its way to the surface is transported by the convection of the mantle.  This is the process that drives plate tectonics. Most of the rest of the heat flow, 25%, is by conduction.  The small remainder is transported by mantle plumes, hot spots associated with certain volcanoes.

Figure 1: Showing mantle convection cells, which are responsible for transporting most of the Earth’s heat from the interior to the surface. Wikipedia

Mantle convection cells are the super tankers of global tectonics, transporting vast quantities of hot rock but changing speed and direction only gradually. Conduction of heat through the rocks of the Earth’s continental crust is also an unhurried and stable process; with the supply of heat metered by atomic clockwork. There are a few well-known hot spots around the world, where magma and hot water quickly bring heat to the surface but the energy released at these places does not add up to much in the global scheme of things. The rate of heat escape from the Earth is slow and very steady.

Figure 2: Red indicates the oceanic ridges where mantle convection comes to the surface and where new ocean crust is formed. The colors indicate the age of the oceanic crust, with the purple being the oldest. Source.

How do we measure heat flow?

The temperature gradient in the upper part of the crust is determined by directly measuring temperatures at different elevations in boreholes. On land, temperature measurements are usually made at depths greater than 100 metres to avoid any effect of variable surface temperatures. In the oceans, water temperatures at the sea bed are generally steady; measurements are  made in the uppermost layer of sediments and yield reliable results.  Once the thermal conductivity is known (it can be measured in a laboratory) the heat flow can be calculated using Fourier’s equation:

q = -ku

Where q is the heat flow, k is the thermal conductivity, and u is the temperature gradient.

Figure 3: Heat flow at the surface of the earth, from Davies and Davies (2010).  Heat flow units are in mWm-2. Note how the areas of highest heat flow follow the mid-ocean ridges. The largest areas of measurement uncertainty are along the very crests of the ridges and under the Greenland and Antarctic ice caps. The total heat flow for the planet is 47 TW +/- 2TW, which is equivalent to 0.09Wm-2   (90mWm-2).

Typically, the rate at which temperature increases with depth (the geothermal gradient) is in the range of 25-30°C per kilometer, with higher values at volcanoes, ocean ridges and rifts, and lower values in places that have recently received thick blankets of sediments.  The top several hundred metres of boreholes often show changes in the geothermal gradient that are caused by changes in the surface temperature that have modified the temperature of the rocks at these shallow depths.  These observations can be inverted to reveal paleoclimate information over the past few hundred years; see Huang et al (2000) and Beltrami et al (2011).

How does heat flow from the interior of the Earth compare with other inputs of energy into the climate system?

 

Figure 4: The volumes of the cubes are proportional to the magnitude of the energy flow from various sources. The solar irradiance is the incident energy, averaged over the area of the Earth (divided by four); irradiance varies over 11 year cycles and, at the top of recent cycles, can reach 341.7 Wm-2. The increase in anthropogenic forcing since pre-industrial times comes from the IPCC. The heat flow from the Earth’s interior is the 47 TW figure (see Figure 3 caption) averaged over the surface area.   The energy flow from the human energy production is based on Flanner (2009).  Tidal energy is the total energy input from the gravitational interaction between the Earth, Moon and Sun; a small part of this energy is included in the energy flow from the Earth’s interior (see below for further discussion).

The net increase in the amount of planetary energy flow arising from human activities (mainly the greenhouse effects from emissions of carbon dioxide) since the industrial revolution is more than twenty times the steady-state heat flow from the Earth’s interior.  Any small changes in the Earth’s heat flow over that time period—and there is no evidence for any change at all—would plainly be inconsequential.

Tidal Energy

From the Skeptical Science comments:

"Over the last two weeks I have been doing calculations on borehole data and this very convincingly supports the theory. We see different underground temperatures which are related to latitude, thus confirming that frictional heat (due to the moon) is being generated in the core, more at the equator than at the poles."

The spinning of the Earth, as well as the rotation of the Moon around the Earth and the orbit of both bodies around the Sun, do indeed have an impact on the energy of the Earth, through tidal friction. The ultimate source of this energy is the Earth’s rotation, to which the Moon and the Sun provide a gentle brake, resulting the generation of frictional heat and the slowing down of the Earth’s rotation (days were two hours shorter 600 million years ago).  The Moon gains some energy from this interaction, being gradually boosted into a higher orbit above the Earth. The total Earth energy flow from tidal effects is about 3.7 TW (0.007 Wm-2 ), of which 95% goes into the familiar ocean tides and some 5% (0.2 TW or 0.0004 Wm-2) goes into Earth tides, which are small deformations of up to a few centimetres that occur on twice-daily or longer timescales.  Earth tides contribute approximately 0.5% to the heat flow of the Earth.

Figure 5: From Munk and Wunsch (1998) showing an “impressionistic” (their word) budget of tidal energy fluxes.

The energy from tides in the oceans is dissipated as heat in marginal areas (shallow waters) and around ocean ridges and seamounts (the “stir sticks” of the oceans). All of this energy is therefore added immediately to the ocean-atmosphere system. As for the Earth tides, the slight flexing of the crust and mantle is dissipated as heat  there. This is a very small amount relative to the heat coming from radioactive decay and from the heat associated with the formation and differentiation of the Earth.

The amount of Earth tide energy flow, 200 gigawatts is miniscule by any planetary standard, it hardly varies at all over periods of millions of years and has no significant effect, globally or regionally, on the energy balance of the climate system.

Science isn’t always common sense

Diagrams such as the one below and its accompanying article make no mention of geothermal heat, tidal energy or “waste” heat from human fossil or nuclear energy use. Is this because its author, Kevin Trenberth, is negligent and unaware how big these sources of energy are?  No, it’s actually because he knows how inconsequential they are.

Figure 6. The global annual mean Earth’s energy budget for 2000 to 2005 (W m–2). The widths of the columns are proportional to the sizes of the energy flows.  From Trenberth et al (2009).

For example, on this figure, a line representing geothermal energy flow would have a thickness of 6 microns, the thickness of a strand of spider-web silk; ocean tidal energy, one-tenth of that; Earth tidal energy less than one-tenth even of that. Our intuitions tell us that earthquakes, volcanoes, geysers and tides are mighty forces of nature and, in relation to a human individual, they are. But compared to the transfers of energy within the climate system, they are too puny to merit consideration.

[Thanks to jg for drafting Figure 4 and to Tom Curtis for helpful comments.]

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Comments

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Comments 1 to 50 out of 70:

  1. One quibble: In the Tidal Energy section, if rotation is being slowed, then day length would have been shorter (not longer) 600 million years ago.
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    Moderator Response: [AS] Indeed! Thanks, I'll correct that.
  2. “Underground temperatures control climate”.

    Next myth:

    Lunar rotation causes tides therefore, it stands to reason, it pulls up on the Earth's crust. Thus the friction caused by the crust being raised by tidal forces causes temperatures to rise.

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  3. villabolo: "tidal forces causes temperatures to rise."

    Since the moon is gradually receding from the earth, tidal forces are growing weaker. That means that the heat from tidal friction is diminishing, leading to an inevitable cooling. With that mechanism, a glacial advance cannot be far off. Global warming? Problem solved!
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  4. The rounded figures are much more comforting. 0.9 of a watt per square meter imbalance does not sound much, yet that tiny imbalance is going to give us so much grief.
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  5. Very nice post, and hope you put Figure 4 in your figures area. One other interesting point you might mention is that about 50% of the total heat flow from the earth is 'primordial', i.e., remaining from the heat generated by gravitational collapse of the proto-planet. See all the articles on geoneutrinos.
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  6. I like the figure.

    A better representation would be 240 W m-2 for the solar figure though, since ~30% is reflected without doing anything. And we're on course to get more like 7 W m-2 from CO2 alone by 2100...
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  7. Where is the cosmic ray cube?
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  8. mlyle@5: I looked at a few references to see what the proportions of heat come from radioactivity compared to the three other proposed sources of heat (initial formstion, gravitational fractionation and latent heat coming from ongoing growth of the solid inner core). The precise numbers seemed to vary considerably, which is why I settled on the imprecise "Most comes from radioactivity". Wikipedia cites 45-90% coming from radioactivity but there's no reference given for the low end of the range. If you, or anyone else, could point me to a definitive reference on geoneutrinos, or a recent review paper on sources of internal heat, I would be most grateful.

    MarkR@6: You're correct about the reflected energy and I thought about including that that in Fig 4. The reflected energy is shown clearly in Figure 6. With all these figures there's a trade-off between getting the basic message across and rigorously including all the factors.

    And yes, we do plan to put Figure 4 in our figures area.
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  9. John Hartz#7: Are you suggesting that cosmic rays are a meaningful source of heat? On the scale of the diagram (fig 4), how big would that cube be?
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  10. Good debunking of yet another climate myth!

    MarkR in #6: You were faster than me with your comment about the 30% of reflected solar energy, the 102 Watts shown to the left in figure 6!

    Something that should put geothermal heat in the correct climate perspective:
    A couple of years ago I debated this issue with a denier on a Norwegian science website. My two central arguments were exactly what is mentioned here: The energy flow from the Earth’s interior is several thousand times smaller than that from the sun, and there are no reasons to believe is has changed much for millions of years. He then claimed that undersea volcanoes are a major heat source and that they can explain the recent warming. After some research on the heat capacity of water and the energy output from volcanoes measured from satellites, I came up with an interesting calculation:

    If 1000 undersea volcanoes, each with the same energy output as Etna in 1992 (12 gigawatts), had continuous eruptions, it would take them about 15,000 years to heat the oceans by 1 K if all that heat stayed in the oceans and wasn’t lost to the atmosphere and space. The heat added to each cubic metre of water every year would equal the body heat from a mouse swimming in that water for a few minutes!
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  11. "The heat added to each cubic metre of water every year would equal the body heat from a mouse swimming in that water for a few minutes! "

    Hmmm...I don't know about you, but I've noticed a substantial increase in mice rummaging through my garden recently.

    Next climate myth, coming right up! ;-)
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  12. @ muoncounter #9:

    About the size of a pinhead I would imagine.

    My question about cosmic rays was tongue-in-cheek.

    PS -- I'm suffering from Pielke-fatigue syndrom so please forgive me.
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  13. JohnH#12:

    I was hoping you were kidding; it's just so easy to put the blame for all the world's ills on the poor cosmic rays.

    Let's see: LBL's muon page gives an average surface flux of 167 muons per second per sq meter, with an average of 4 GeV each; convert eV per sec to watts; that's a delightfully toasty 10^-7 W/sq meter.
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  14. It looks like a really nice article presentation. However I have to protest the promotion of the idea that radioactive material heats the interior of the Earth. I mean, how do you go about testing this hypothesis? The answer is you cannot. No one knows what is in the center of the Earth. Maybe some people think that this is great since without a means of testing a hypothesis then no one can prove it wrong. But actually this is not good since if a hypothesis cannot be tested then it does not qualify as being a scientific hypothesis. To clarify why this is wrong let me give an example of another untestable hypothesis such as ‘all good people go to heaven after they die’. Untestable hypotheses are not actually science.

    Even without direct evidence, there is still plenty of indirect evidence that strongly weighs in against radioactive heating being correct. For example, if the entire interior of the 4.6 billion year old Earth was filled with radioactive potassium this still would not produce enough heat to account for the heat coming from the Earth’s interior. So there you have it, the radioactive heating claim is preposterous. It is only because so few people are capable of doing the math and / or willing to take the time to do it that the weakness of the radioactive heating claim is not apparent to everyone.

    No doubt it makes us feel good to have answers to life’s questions, but quickly filling every mystery with the first answer that ‘sounds right’ is counterproductive since it brings an end to science inquire. If either one of these propose answers to what heats the Earth’s interior were correct, then they should bring us greater insight into understand our Earth and our solar system. But of course they do not; their purpose is to just to explain away the paradox without concern if the answer is right or wrong. Obviously they are wrong since astronomers have rejected them in their efforts to explain Jupiter’s moon Io is being heated from within. In all likelihood, an answer that explains the heating of one heavenly body should be general such that it works for all the planets and moons of our solar system.

    Astronomers say that tidal heating is what heats Io’s interior. And here is the best part. It can be shown that tidal heating alone can explain the interior heating of all the planets and moons throughout our solar system. The theory correctly predicts which planets should be hot and which ones should not. As an extra bonus, the theory correctly predicts the density of these objects. For example, the Earth has the highest density of all the planets in our solar system due to close proximity of the Moon producing a disproportionally large amount of tidal heating within the Earth.

    One of the biggest problems with science today is that so many people blindly follow science dogma rather than thinking about the new progressive ideas that allow us to understand our reality.

    Read more at http://www.dinosaurtheory.com/hell.html.

    Galileo
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    Response:

    [DB] But then again, one of the biggest problems with science today is that so many people easily reject established science in favor of just about any other alternative that comes along, no matter how tenuous the evidenciary chain that supports it.

  15. From Galileo's website:

    "When scaling, the ratio between the area and volume changes: the area of my kite scaled by a factor of three squared while the volume scaled by a factor of three cubed. I was astonished that the Square-Cube Law was not covered in my grade school science class."

    Someone was asleep in math class ...
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  16. Bizarre claim on Doug Cotton's website:

    "It is the heat flow from the core of the Earth that maintains a "base" temperature simply because the underground conduction rate is far slower than the rate of convection for warm air rising in the atmosphere. Life as we know it would not exist on this planet if the temperature gradient caused by the heat flowing from the core were such that the mean "break out" temperature at the surface were not something like 9 deg.C give or take a few degrees."

    I would put it Doug Cotton that he should consider what the surface temperature of the Earth would be if it had the same solar insolation and same atmosphere, but didn't have a hot centre.

    More to the point, he should calculate what the surface temperature would be if you were able to turn off the sun and let the temperature equilibriate...
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  17. 14, Galileo,

    You make some interesting assertions, but the actual science weighs against you. You say:
    So there you have it, the radioactive heating claim is preposterous.


    The following paper pertains to actual measurements detecting such a source of heat:

    Earth's heat budget: Clairvoyant geoneutrinos (Jun Korenaga, 2011)
    The quantity of heat generated by radioactive decay in Earth’s interior is controversial. Measurements of geoneutrinos emitted from the mantle during this decay indicate that this source contributes only about half of Earth's total outgoing heat flux.


    You said:
    ...this is not good since if a hypothesis cannot be tested then it does not qualify as being a scientific hypothesis.


    And yet it has been tested.

    I'm not going to argue all of the details of a fairly theoretical aspect of science that doesn't entirely interest me, but it is one in which real scientists are now developing ways to actually observe and measure.

    I'm afraid your rather lordly and holy dismissal of the science was a bit premature.
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  18. Stu#16: "Bizarre claim ... Doug Cotton"

    I can't imagine how you could pick out just one bizarre claim, like identifying a single tree in that very large forest.

    For example, his geothermal gradient of 27 deg C/km puts the temperature at the outer core boundary at a mere 79700 C; why worry about an 1800% error?

    But sadly, that's not the most bizarre claim out we're hearing these days.
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  19. Some bizarre claims there #14 Galileo. You claim the radioactive heating hypothesis is preposterous, yet don't tell us why?

    Apart from Sphaerica's excellent point, I might ask you a more philosophical question. If lightning strikes can start forest fires, does that mean that arsonists are incapable of starting forest fires? This is akin to your suggestion that the same single explanation should fully describe the interior states of all the planets in the Solar System.

    You compare Earth to Io, yet one is a planet orbited by a large moon, and the other is a moon orbiting closely to the most massive object apart from the Sun in the Solar System. Io's mass is 1.5% of the Earth's. The objects driving the tides are vastly different - Jupiter's mass is something like 26,000 times that of the Moon, and that mass is driving tides on Io at a similar distance to the lunar tides. Why would the internal processes necessarily have the same origin? Sadly, it's another bizarre claim to add to the increasing list.
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  20. Maybe it's just me, but I felt that Galileo's comment was satire....

    As for Cotton's stuff, apparently the Earth, like Venus (which is heating due to an internal source too, dontchaknow) has a blue supergiant star instead of a ball of solid nickel-iron for a core. Don't ask why we don't weigh a lot more, why the Sun doesn't orbit around the Earth, how the Earth's crust is solid, how life evolved in a barrage of radiation that doesn't exist, etc.

    I know - Romulan force field, augmented with Borg technology. Oh, wait, Romulans use captured miniature black holes for their warp drives, not blue supergiant stars. OH! Maybe that's it, then!

    Oh, Doug, I've got a new idea for you....
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  21. Angliss @20:

    I sincerely doubt that Galileo #14 was merely satire. Only he can confirm or deny your interpretation.
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  22. #14: "there is still plenty of indirect evidence ... if the entire interior of the 4.6 billion year old Earth was filled with radioactive potassium this still would not produce enough heat"

    I'm not sure how this unsubstantiated hypothetical qualifies as 'evidence.'

    However, here is some actual evidence: Radioactive potassium may be major heat source in Earth's core

    "Our new findings indicate that the core may contain as much as 1,200 parts per million potassium - just over one tenth of one percent," Lee said. "This amount may seem small, and is comparable to the concentration of radioactive potassium naturally present in bananas. Combined over the entire mass of the Earth's core, however, it can be enough to provide one-fifth of the heat given off by the Earth."

    "the Earth has the highest density of all the planets in our solar system due to close proximity of the Moon producing a disproportionally large amount of tidal heating"

    The moon's proximity is the reason earth's density (5.52) is as high as it is? Then please explain the densities of Venus (5.2) and Mercury (5.6), all relative to water=1. Where are their close proximity moons? Why would more tidal heating result in higher density? And isn't 5.6 > 5.52?

    Funny thing about the real Galileo; he was right. I fear what we have here is an example of it's turtles all the way down.
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  23. I have found a few references on the radioactive contribution to heat flow. This one, which describes how geoneutrinos are measured and how they may provide constraints on the quantity of radioactive heating in the solid Earth. That reference led to this recent paper on the same subject, which reports that "heat from radioactive decay contributes about half of Earth’s total heat flux". The original statement in the blog post "Most of the heat that flows to the surface comes from this source" therefore needs to be amended, which I will do.

    Lord Kelvin did some calculations in 1864 on the thermal age of the Earth that neglected entirely any contribution from radioactive decay, which had not been discovered at that time. The text of some of the paper and be seen here and images of the original article can be viewed here. Kelvin came up with an age of the Earth on the range of 20-400 million years, but he later leaned more to the low side of this range. These figures were disputed by contemporary geologists and by supporters of Charles Darwin, who believed that much more time was required to account for geological and biological evolution. Of course, the natural philosophers eventually won that particular dispute with the physicists.
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  24. It's just comical (albeit predictable) to see skeptics even tried this one. I think the next one has to be:

    "Heat Release From Bioluminescent Sea Animals The Real Cause For Ocean Heating."
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  25. I'm a bit late, but I'd like to take issue with the statement about heat from the Earth's core: "The effect on the climate is in fact too small to be worth considering."

    Net solar heat flow is 341.3 - 101.9 - 238.5 = 0.9 W/m2
    Heat flow from the core is 0.09 W/m2. That's 10% of the net heat flow. That's significant.

    Net gain from solar and core together is 0.99 W/m2.
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  26. Martin @25:

    It is wrong to call all that "solar", the 238.5 number you provide must be IR losses to space, not solar.

    When it comes to climate change, you need to focus on radiation change. The net IR change related to doubling CO2 is about 4 W/m^2. How much do you think the 0.09 W/m^2 geothermal heat flux has changed? How important is that compared to 4?
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  27. The hypothesis of earth core heat affecting sea temperature and atmosphere should be taken more seriously. NASA takes it seriously enough to research it. Here is a link to their 2011 study which shows significant correlation but inconclusive in the end. Maybe  the variable to consider is not overall increased heat but movement of the heat source which changes exposure to different areas.

    http://climate.nasa.gov/news/489/

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  28. Maark @27, that hypothesis faces several major obstacles.  First is the claim that it accounts for plus or minus 0.2 C in the Earths Global Mean Surface Temperature (GMST).  In terms of power, that requires fluctuations of 0.8 W/m^2, or approximately 9 times the average energy flow from the Earth's interior.  That is implausible on the positive side, but absurd on the negative side (where it would require the energy to be flowing into the interior rather than out of it).

    Second, such a large change in energy flow would be evident in borehole temperature reconstructions, but is not:

     

    Third, and on their own evidence, the theory fails to match observations prior to 1900:

    So, at best they show an emperical fit over one cycle length, but a complete mismatch prior to that one cycle.  That is hardly compelling evidence.

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  29. I should add to my comment @28 that the NASA scientists involved are arguing for a correlation between temperature as adjusted to remove anthropogenic influences, and the Length Of Day (LOD).  They are not arguing, as Maark does, that this effect is brougth about by fluctuations in geothermal heat.  Ergo only my third point is directly relevant to their actual theory.

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  30. Maark,

    The concluding aragraph of your reference reads:

    "Regardless of the eventual connections to be established between the solid Earth and climate, Dickey said the solid Earth's impacts on climate are still dwarfed by the much larger effects of human-produced greenhouse gases. "The solid Earth plays a role, but the ultimate solution to addressing climate change remains in our hands," she concluded."

    My emphasis.  The scientists involved think the correlation they found is interesting but Humans cause AGW.

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  31. I prepared the following in response to a post by Nick on another thread.  The contents of that post relevant to this topic have since been (deservedly) deleted, but as it has been an intention of mine to determine and post this list at sometime, here are nearly all energy sources that contribute to the Earth's Global Means Surface Temperature (GMST):

    Heating SourceW/m^20K
    Solar240255.06
    Cosmic Background Radiation3.13E-62.73
    Starlight6.91E-63.32
    Cosmic Rays3.2E-6

    2.74

    Meteorites2.27E-80.80
    Combined off planet sources240255.06
    Geothermal0.0935.49
    Tidal0.0118.74
    Geothermal &Tidal0.136.17

    Total Energy Sources

    240.1255.09
    CO2

    30.21

    151.93
    Greenhouse Feedbacks128.79218.31
    Total Greenhouse159230.12
    Total399.1289.65

    Observed Surface Energy

    398

     
    Observed Surface Temperature 287.15

     The most important factor not shown is albedo, which is included within the solar value for convenience.  I have also ignored industrial waste heat, and the effects of emissivity (which increases the effective temperature) and uneven surface temperatures (which decrease it).  Also not shown is seismic energy.  The reason it is missing is that the vast majority of seismic energy is dissipate as heat deep within the Earth's surface, where it contributes to geothermal energy.  Including it as a seperate item would have merely been double counting.  Likewise, volcanic energy is included with geothermal energy, and so not shown as a seperate item.

    The most important thing to notice is that the smaller items on the list are almost completely irrelevant.  Based on caculations above, for example, we can determine that if the Earth floated far from any sun in galactic space, it would still maintain a surface temperature of around 36-37 oK.  That represents the combined energy effects of geothermal heat (35.5 oK by itself), the cosmic background radiation, starlight, and cosmic rays.  Assuming it orbited a dark star, providing the the further effects of tides and meteors, that would raise the temperature to 37-38 oK.  But adding all these factors to the effect of sunlight would only raise the GMST by 0.03 oK, significantly less than the observational error of the Earths absolute GMST.  Their contribution becomes even less when the greenhouse effect is also included.

    The second most important thing to notice is that, despite their inclusion on the table, the greenhouse effect does not represent an additional source of energy.  That is because for every joule returned to the Earth's surface by the greenhouse effect, an additional joule leaves the Earth's surface by means of radiation, increase convection or increased evaporation or transpiration.  The greenhouse effect only makes the existing energy sources more efficient at heating the surface by recycling the energy.  In that way, greenhouse gases act like blankets (an analogy which is exactly correct with reference to the thermodynamics, although completely inaccurate with regard to mechanism).  The values shown for the greenhouse effect on the table, therefore, are best understood as the amount of additional energy from other sources that the Earth's surface would need to maintain the same GMST without a greenhouse effect.

    Finally, every now and again, somebody will pop up and insist that geothermal energy or some other equally obscure source of heating is the primary driver of GMST.  Such theories fail absolutely once the relative energy inputs are calculated (something they never do).  The theories are complete drivel on the same level as those of Flat Earth Society.

    Sources:  

    Solar and Total GHE -  IPCC AR5 Fig 2-11

    CO2 proportion of GHE - Schmidt et al (2010)

    Cosmic Background Radiation - Calculated from temperature

    Starlight and Cosmic Rays - Bowen et al (1933)

    Meteorites - Lovel, Geophysics II, p. 452

    Geothermal and Tidal - Skeptical Science

    Observed Surface Energy - IPCC AR5 Fig 2-11

    Observed absolute GMST - IPCC AR5 Fig 9-08

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  32. Tom, a few questions from a layman;

    1. Where are the other greenhouse gases? In the 'CO2' line (CO2 equivalent?) or lumped in with 'Greenhouse Feedbacks'? I know most of them have little impact, but water vapor at least is significant.
    2. The degree Kelvin figures don't add (i.e. 35.49 Geothermal and 18.74 Tidal, but only 36.17 Geothermal & Tidal combined). I assume this is because each degree of temperature increase requires more 'incoming energy' than the last (i.e. diminishing returns due to increasing outgoing energy). Correct?
    3. The computed energy & temperature are higher than the observed values. Is this due to the 'Greenhouse Feedbacks' line projecting future impacts?
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  33. CBDunkerson @32:

    1)  essentially the greenhouse effect comes from condensing and non-condensing gases.  The non-condensing gases (CO2, CH4, NO2, O3, etc) have concentrations that do not primarilly depend on GMST, although they are influenced by them.  Of them only CO2 and CH4 had appreciable effects in the 1980s, ie, the time period covered by Schmidt et al, and in that period CH4 represented only 1% of the total greenhouse effect.  As the vast majority of that 1% came from anthropogenic emissions from 1750-1980, I decided it was easier to just ignore it, and fold it and the other minor non-condensing greenhouse gases in with the condensing gases.

    The vast majority of the "greenhouse feedback" represent the greenhouse effect from water vapour and clouds.  These are the condensing greenhouse gases, where temperature very tightly controlls concentration.  As a result, there presense in the atmosphere is always a feedback on other energy sources plus the CO2 greenhouse effect.  In particular, absent the solar energy input, the greenhouse feedback would be zero; and absent the CO2 greenhouse effect, it would be substantially less (Lacis et al, 2010).  I put it as a seperate item because its behaviour is so different at temperature consistent with solar input.

    It is, of course, not intended to indicate feedbacks only from the greenhouse effect, or all feedbacks from the greenhouse effect.

    2)  I thought I had already clarrified this point in the paragraph starting, "The most important thing...".  In all cases the temperature response to a given factor is:

    T = (j*/σ)^0.25, where j* is the energy input in W/m^ and σ is the Stefan-Boltzman constant 

    For j*= 0.09 W/m^2, T = 35.49 oK

    For j* = 240 W/m^2, T = 255.06 oK

    But for j* = 240.09, T = 255.09 oK

    The crux is that the relationship between energ input and temperature is far from linear, so any energy input with a big impact at low temperatures has negligible impact at high temperatures.

    3)  No.  Values are effectively for 2010 in that I used the IPCC AR5 value for total greenhouse effect.  As such, these values include an anthropogenic forcing larger than any of the non-solar energy impacts.

    The two major sources of inaccuracy in determining the GMST from a given energy input are the assumption that the Earth is a black body (emissivity = 1), and the assumption that the Earth has a constant temperature at all locations.  (I mentioned these briefly among the missing factors.)  Of these, the fact that the Earth's emissivity is slightly less than 1 will increase the GMST by about 2 to 8 oK depending by how much the emissivity is overstated.  Probably closer to 2 than 8, but absent a global radiation budget model I cannot determine the exact value.  

    In contrast, unequal temperatures (which certainly exist) will reduce the estimated GMST.  In an extreme case where the Earth has a permanently sunlit hemisphere, and a permanently dark hemisphere with constant temperature in each hemisphere, but no energy shared between hemispheres so that the dark hemisphere is much cooler than the sunlit hemisphere, the GMST would fall to 181.31 oK, a drop of 108.33 oK.  That is an interesting case in that it approximates to conditions on the Moon.  It also shows how large an effect unequal temperatures can have.  The Earth certainly has unequal surface temperatures, and they are even unequal at the tropopause from which most IR radiation escapes.  Therefore this reduction in expected temperature certainly is a factor.  However, again without a complex and accurate model, it is impossible to determine how much of a factor.  Indeed, in this case you would need a full climate model, as temperature variation also varies with time of day and season.

    Given these two significant, and opposite effect factors which cannot easilly be determined, it is surprising the above calculations are as accurate as they are.  Certainly the minor inaccuracy is nothing to be concerned about against that backdrop.  In fact, the errors in calculated values from observed values are less than the range of errors between different estimates of the observed values.

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  34. Tom Curtis - That's an excellent summary of relative energy magnitudes. I'll add that anthropogenic waste heat (link here), another source bandied about sans evaluation as a primary driver of climate, represents a contribution of perhaps 0.028 W/m2. That's 1/4th of geothermal contributions, 1/100th the contributed energy of post-Industrial CO2 emissions, and an even tinier and less significant fraction of the total greenhouse effect. 

    Numbers are oh so important. 

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  35. The effective thermal IR emissivity of the Earth to space, assuming a balance of 240 W/m2 incoming and outgoing and a surface temperature of ~15C, is about 0.614; that is 61% as effective a radiator as a theoretic black-body. 

    Varying temperatures are effectively emissivity increases (incorporated in that value), as a warmer region will contribute more outgoing energy (based on the Stephan-Boltzmann equation and the nonlinear T4 relationship) than equally cooler regions will decrease it, radiating more total energy than a thermally homogenous Earth would. 

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  36. KR @34, thanks for the link.  Part of my reason for placing the comment on this page was the presence of jg very useful figure in the OP:

    It shows not only the approximate value of industrial waste heat (red) but also the change in forcing from anthropogenic factors (orange) and the full solar input with no adjustment for albedo.  (Note again, the forcing is not literally an energy input to the Earth, although it does represent an increased energy flux at the surface matched at equilibrium by an equal increase in the outward flux.)  One advantage of jg's figure is that it includes every energy flux that could reasonably be supposed to have an impact on the Earth's climate, the others being several orders of magnitude smaller.  Of course, of the anthropogenic fluxes, only the anthropogenic forcing is large enough to have a measurable impact on GMST.

    @35, I agree that the greenhouse effect can be approximated at the simplest level by treating the Earth as having a relatively low emissivity (0.614 rather than the actual value which is greater than 0.9, and probably greater than 0.95).  I think that simplicity is bought at the risk at too many potential misunderstandings, a point I know we will have to agree to disagree on :)

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  37. Tom Curtis - "...a point I know we will have to agree to disagree on :)"

    Fair enough - we do tend to focus on the accuracy of different regimes of the climate discussion. But for completeness an even simpler derivation of effective emissivity to space is the ~240 W/mm2 emitted to space divided by the ~396 W/m2 emitted from the ground, or ~0.601. Which can also be obtained by looking at the integrated emission spectra observed at the top of the atmosphere versus the blackbody thermal radiation at Earth surface temperature - again a ratio of ~0.601. 

    Overall I'm very glad we're not redundant commentors - I would just feel silly otherwise :)

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  38. vesuvian7 @here

    An estimate of the heat content of the earth was reported by Dickson & Fanelli (2004) thus:-

    It has been estimated that the total heat content of the Earth, reckoned above an assumed average surface temperature of 15 °C, is of the order of 12.6 x 1024 MJ, and that of the crust is of the order of 5.4 x 1021 MJ (Armstead, 1983).

    This seems perhaps low to me but the original reference isn't apparent on-line to check. Taking the 12.6e24 figure, I reckon that amount of heat would raise the oceans by 2,100ºC.

    Your question about how big a fissure would be required to heat the oceans 1ºF in 100 years is not really answerable. Rather, let's stick with how much rock would need to erupt into the oceans with the heat content equal to the task. (Adding in the fissure size required with your time limit of 100 years would embroil you in some serious modeling and a mass of assumptions, so I wouldn't expect anything sensible on that score.)

    If lava has a heat capacity one fifth that of water and arrives at a temperature of, say 1,800 °F, and if the oceans are 360 million sq km and 4km deep, then you'd need 4 million cu km of the stuff which is indeed rather a lot. Krakatoa ejected 25 cu km. Supervolcanoes are classified as those ejecting more than 1,000 cu km (VEI>8) with the largest estimated as "well over 15,000 km³" (see Wiki here). So I reckon that demonstrates that the actual heat coming out from volcanoes has not been a significant player in global climate for billions of years.

    The earth's store of internal energy is remarkably constant. The temperature gradient through the crust has even been used in attempts to provide a record of past surface temperature.

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  39. In order for subaerial volcanoes to warm the ocean, they would have to be erupting on orders of magnitude larger than observed. This also would be affecting the acidification of the ocean, which we know is derived from human FF usages. Per Gerlach 2011:


    "To create more than 35 gigatons per year of volcanic CO2 would require that magma across the globe be produced in amounts exceeding 850 cubic kilometers per year, even for magma hypothetically containing 1.5-weight-percent CO2. It is implausible that this much magma production—more than 40 times the annual midocean ridge magma supply—is going unnoticed, on land or beneath the sea. Besides, the release of more than 35 gigatons per year of volcanic CO2 into the ocean would overwhelm the observed acid-buffering capacity of seawater and contradict seawater’s role as a major sink for atmospheric CO2 [Walker, 1983; Khatiwala et al., 2009]. In short, the belief that volcanic CO2exceeds anthropogenic CO2 implies either unbelievable volumes of magma production or unbelievable concentrations of magmatic CO2. These dilemmas and their related problematic implications corroborate the observational evidence that volcanoes emit far less CO2 than human activities.

    It is informative to calculate volcanic analogs that elucidate the size of humanity’s carbon footprint by scaling up volcanism to the hypothetical intensity required to generate CO2 emissions at anthropogenic levels. For example, using the 2010 ACM factor of 135 (Figure 1) to scale up features of present-day volcanism, Kilauea volcano scales up to the equivalent of 135 Kilauea volcanoes; scaling up all active subaerial volcanoes evokes a landscape with the equivalent of about 9500 active present-day volcanoes [Siebert et al., 2010]. Similarly, the seafloor mid-ocean ridge system scales up to the equivalent of 135 such systems. Of particular interest, though, is the roughly 4 cubic kilometers per year of current global volcanic magma production [Crisp, 1984], which would scale up to about 540 cubic kilometers per year. This significantly exceeds the estimated average magma output rates of continental flood basalt volcanism [Self, 2010], which range from about 10 to 100 cubic kilometers per year. Thus, annual anthropogenic CO2 emissions may already exceed the annual CO2 emissions of several continental flood basalt eruptions, consistent with the findings of Self et al. [2005]."


    http://volcanoes.usgs.gov/hazards/gas/climate.php

    Tom Curtis further unpacks this topic very clearly in a comment here.

    It's not subaerial volcanoes.

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  40. Thanks for this very thorough article as well as the discussion .

    I have run into a few other denier hypotheses; 1. That the weakening of the earth’s electromagnetic field is causing climate change. 2. That it is from HAARP. 3. That it is from climate warfare. 4. That it is caused by reduction in cloud cover. 5. That it is caused by chem-trails. Most of the above is easy to ignore.


    Here’s part of my response to the cloud cover and chem-trail hypotheses:

    Here is some science and math related to the purpose and weather out-comes from chem-trails. It also documents increased rather than decreased cloud cover: http://meteora.ucsd.edu/~jnorris/presentations/Caltechweb.pdf

    See:
    Page 19 for a chart that shows the type of clouds that reduce the green house effect.
    Page 29 for a discussion of anthropogenic effects that make clouds more reflective.
    Pages 30 and 31--charts that explain the above.
    Page 64 --last statement: "Cloud changes since 1952 have had a net cooling effect on the earth."
    (Of course we know that the net cooling the clouds are providing is not enough to offset global warming.)
    Important— on page 59 he states that the increase in the types of clouds which are reducing the effects of climate change cannot solely be attributed to anthropogenic sources.

    ~~~

    Thanks again, just thought if you hadn't seen this link or these hypotheses you might find the interesting.

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  41. I will pose this as a question because I am not an advanced scientist, just a college student in some basic environmental classes. If the earth's record shows 7 cycles of heat/cooling in past 650,000 years, then we should ask what is the common factor in all of these events. It is possible atmospheric C02 was the source, but then humans were not the source of the C02. Another common factor was the Earth's core and its heat. It is simple to observe earth's heat on any day in winter in our North American climate. When I pour concrete I must keep the ground below the concrete from freezing. We construction workers pile hay or straw in the ground and in a couple of days it is unfrozen. Does anyone disagree that there is constant heat radiating up from the earth core? This is basic right?

    My hypothesis, after reading the very basics of plate techtonics, is that warmer plates move closer to the surface heating water and soil. It is a fact that the plates are constantly moving so shouldn't this be considered? Where could I find evidence from core drill temperatures? Are there records kept as in sea temperatures?

    Some arguments above negate the potential for core heat to radiate this strongly on the basis that the change in temperature would need to be drastic. But my science book is saying that if air temperatures increase just one degree the results are drastic. Well then if an area under the Atlantic 1,000- square miles warmed by 4 degrees and the ocean conveyor belt brought that warm water to the equator it would certainly affect our huricane season and El Nino. It would also affect the glaciers. This hypothesis is at least consistent with warming in the pre-human historic past.

    If you have a simple expaination I sincerely want to know before I embarrass myself in class. Thanks

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  42. Maaark

    Use the search option at the top of the page to search for informaton about 'Milankovitch Cycles'.

    Essentially cyclical changes in Earths orbit and axial tilt that cause small fluctuations in how much sunlight is received by different parts of the Earth at different times of the year.

    This provides a small warming and cooling impetus. This then is magnified by changes in CO2 levels in the atmosphere as the oceans warm and cool, changes in methane levels in different climates and expansion/contraction of land and sea ice, altering how much sunlight the earth reflects to space.

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  43. Maark @41, you should more carefully read the post above as it contains enough information to refute your theory as is.  Further information is available here.  On top of that, the rate of spread over time at ocean ridges is well known by dating the ocean floor.  That rate of spread is in turn correlated with amount of magma ejected, and hence the rate of heat flux at the ocean ridge.  This data does not support your theory.

    Finally, looking at things differently, the key question is not the absolute rate of energy release from the interior, but the rate of change in that energy release.  That allows us to consider the direction of that change by considering the sources of geohysical heat, which are two fold: friction from tidal interactions, and heat from radioactive decay.  The later necessarilly decreases with time because the radioactive elements are in fact decaying, ie, becoming inert elements by various combinations of radioactive emissions.  The rate at which that occurs is slow, being dominated by elements with half lifes in the billions of years - but it is one way.  The process cannot reverse itself.  Likewise, over time tidal forces reduce as tidal friction moves the interacting bodies further apart.  Again this is very slow.  There is a slight possibility of variation in that different continental configurations will result in more or less tidal friction, and hence more or less geothermal heat from tidal forces.  As it happens, the current continental configuration represents a near peak for tidal friction, but that peak will have been declining since the closing of the isthmus of panama as Australia, South America and Africa continue to drift north (thereby reducing friction by opening up the gap to Antarctica.  In any event, any change form this will represent a very small fraction of total geothermal heat over intervals of 100s of thousands of years.

    There is simply no physical basis to think geothermal heat could be increasing on a global level, and if anything it will be declining, at a far slower than glacial rate.

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  44. Glen and Tom thank you both. I think that my hypothesis may be over simplified. I am not addressing the possibilty of the tidal energy. That discussion may be valid for some but that is far removed from my points so I will state very slowly.

    Premise #1: if earth has a history of heating/cooling cycles then we should be seeking a pattern that explains those and also is somehow connected with today's situation. Example: I have had 7 migrane headaches in the last month. Today I ate icecream so that must be the source of my headaches = poor science. Good science would seek to find a common factor in all 7 headaches. Therefore we should find common patterns in the previous cycles. Does anyone agree? Are there theories on past cycles?

    If greehouse gases were the causes before fine, but we should see some science on this. There are some books that speculate that one cycle may have been triggered by an asteroid in the Yucatan area of Mexico.

    I do not propose that earth's core is increasing in heat. So I accept what Tom says but it does not adress my question.

    Hypothesis: I propose that due to continual movements of tectonic plates areas of the upper mantle engage the crust as the lithospheric plates move allowing variations in the way that heat reaches the surface. In a very primitive example it would be like sliding a pan over the stove burner so different parts of the pan are exposed and heated even though the burner itself is constant. The plates are constantly moving some diverging down to be reheated while others move nearer to the surface.
    Maybe a constant temperature is maintaned because while some submerge others emerge in equilibrium. However, what if there are cycles where large portions of hot mantle emerge under large portions of the sea? This hypothesis would at least be reconciable with cycles prior to human contributions.

    It seems prudent that NASA and NOA should place thermometers a couple meters deep incrementally across our seas to monitor changes in crust temperatures.

    Thanks for your patience gentlemen. I should learn to explain myself in my best scientific language in this type of setting. Please address both issues: premise of cycles and plate tectonics as related to heat movement.

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  45. Maaark,

    This web site has all the information that you ask about.  It is not the responsibility of posters here to spoonfeed you the answer to your questions.  It is your responsibility to look for it and inform yourself.  

    I typed "climate in the past has changed before"  into the search box above and got this post which addresses your first question.  Please read that post and then follow up with questions there where they will be on topic.

    The OP here addresses your other question.  It states:

    "The net increase in the amount of planetary energy flow arising from human activities (mainly the greenhouse effects from emissions of carbon dioxide) since the industrial revolution is more than twenty times the steady-state heat flow from the Earth’s interior. Any small changes in the Earth’s heat flow over that time period—and there is no evidence for any change at all—would plainly be inconsequential."

    If you have a question that is not addressed by this quote about mantle heat you need to be more specific about the changes you suggest which would increase heat flow by a factor of 20 without anyone noticing.  The method of measuring the heat flow is described in the OP, it is not necessary for NOAA to install additional thermometers.

    If heat from the mantle was warming the ocean, the ocean would warm from the bottom up.  Extensive data shows clearly that the ocean is warming from the top down which contradicts your hypothesis.

    Please make use of the search box, your questions will be better after you read more.

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  46. Even doubling crustal heat flow is utterly insignificant compared to other climate forcings. Changes in heat flow leave their mark and are a critical input to petroleum models used to determine when and where sediments heat to the point that oil and gas are expelled. (I maintain one of these models). At least over the last 180million years, there is no evidence for any cycle or significant change in these heat flows, let alone something that could have climatic effect. Because of the importance of heat flow to petroleum, measurement and analysis is ongoing throughout the world.

    I also do not see any period in earth climate history over last 500my where change cannot be explained by the existing well-understood physics.

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  47. Thanks

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  48. Figure 6 diagram is repeated everywhere, in fact I think it’s the only one I’ve seen. It glosses over the fact that the final output results from the difference between 2 large numbers, both of which are known only approximately, being zero when Earth is neither heating nor cooling, and approximately balances otherwise. In these circumstances, compared to a mean of zero, the 47 TW released by Earth, and perhaps even the 3.75 TW of tidal energy, is no longer “puny”.

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  49. pjcarson2015 @48, had you read the original paper from which that diagram it taken, you would notice that the error margins in the absolute values of the "two large quantities" was so large as to not narrow down the difference at all (and would have indicated a much larger difference taken at face value).  Consequently the authors used reanalysis products to narrow down difference in the values.  More recently, the principle of conservation of energy has been used in conjunction with the much better known increase in surface heat content (mostly in the form of Ocean Heat Content) to constrain the difference between the values.

    More importantly, the 47 TerraWatts is a product of radioactive decay and tidal stresses.  The tidal energy is also the product of tidal stresses.  Absent a major change in the relative orbits of the Earth, Moon and Sun (which has not occurred at any time over the last 4.5 billion years), and/or radical change over time of the fundamental physical constants, these cannot increase over the long term.  Indeed, both will gradually decrease over the long term as the amount of radioactive material decreases, and as the Moon gradually moves further from the Earth (reducing tidal stress).  In the geologically short term, tidal stresses will change at a rate proportional to continental drift as different configurations of continents induce more or less tidal friction.  At the moment the northward migragion of Africa, India, Australia and South America are (very gradually) reducing tidal stress, not increasing it, and the slowness of the process will not result in changes detectable on a centenial scale.  In like manner, there has been no new formation of large ignious provinces, or rapid acceleration of continental drift that would be necessary to increase heat flow from the interior (but not heat generation in the interior that necessarilly decreases).

    In short, theories that the rapid recent rise in temperatures is primarilly due to factors other than the increase in greenhouse gases suffer the same impediment as another famous 'theory':

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  50. Planet Earth does its own (analog) calculations which it always gets right. It doesn’t have error bars. (Man is playing catch up in the calculation stakes.) Earth’s input and output energy always balance to zero when the Earth’s temperature is at equilibrium. As I wrote previously, this is the circumstance when Earth’s 47 TW interior heat comes into significance.

    As you say, the rate of Earth’s heat production is a very slowly changing property – too slow to be of any significance in these discussions – but its rate of release does vary significantly, principally with earthquakes and volcanism, both of which known to change.

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    Moderator Response:

    [PS] Please note the Comments Policy statement on "No sloganeering". If you wish to make assertions about "Planet Earth does its own calculations",  or that geothermal rate can change in a way that could be significant to climate, then you must back your assertions with data and/or papers. You beliefs fly in the face of known data and laws of physics. Please provide the basis for such beliefs.

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