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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 51 to 73 out of 73:

  1. pjcarson2015 @50, you claim the rate of release of geothermal energy varies significantly due to earthquakes and volcanism, but provide no numbers.  Numbers, however, are easy to find.  For example, the largest geologically recent eruption is that of Lake Toba in Indonesia, 74 thousand years ago.  Here is a comparison of ejected lava for Lake Toba compared to other geologically recent volcanoes:

    The Lake Toba erruption was so large that its global impacts may nearly have caused the extinction of the human race.  It errupted with a force of 3.3 x 10^18 Joules, equivalent to 9.15 on the Richter scale.  Despite that, globally and annually averaged, it represents a forcing of just 0.0002 W/m^2.  That is only a 0.2% increase in background geothermal flux, or 0.005% of the forcing from a doubling of CO2.

    Of course, for a change in geothermal flux to significantly effect climate, a 0.2% change for just one year isn't going to do it.  Rather, you would need significantly more than that increase year in and year out over the long term.  So your theory is, not that one Lake Toba erruption equivalent has occurred, but that multiple such eruptions are occuring year in and year out, and we are simply not noticing.  

    Alternatively you might consider the flux to come from increased earthquake activity, and that we are experiencing significantly greater than twenty times the normal rate of magnitude 9+ earthquakes year in, year out without noticing.

    Of course, magnitude 9 earthquakes are fairly noticable, so you may prefer a increase in a lower magnitude quake.  But it takes 52,400 magnitude 6 earthquakes to release the same amount of energy as a Lake Toba erruption (magnitude 9.15 equivalent).  So for a 0.2% increase in the background rate, you have to imagine that the rate of magnitude 6 earthquakes has increased, year in, year out, by 52,400 per annum over their normal background rate.  Unfortunately, the background rate of magnitude 6 earthquakes measured over the twentieth century is 100 to 150 per year.  Ergo your theory requires the rate to have risen to that level from a prior rate of -52,275 magnitude 6 earthquakes a year.

    Quite frankly, all these alternative proposals are ridiculous.

    And what is even more riduculous given that for the change in geothermal flux to be significant relative to the change in heatflow due to the enhanced greenhouse effect, you need a change in the background flux, not of 0.02% but of 10,000%.  Again, we would have noticed.  Indeed, the measurements which determined the current background rate would have picked it up.  The greatest increase in background rate of geothermal flux you can concievably argue for is the current rate of flux of 0.09 W/m^2.  And that is insignificant compared to the change due to the change in greenhouse gases, and relies on the unphysical assumption that there was no geothermal flux prior to about 1850.

    In short, that you provide no numbers in support of your contention is no accident.  That is because if you look at the numbers, you see immediately that your theory cannot be true.

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  2. ..I was of the long held opinion that humanity used about 10 TW of man-made energy: could it be possible that these figures actually be anywhere near approximate from a rational pov?

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  3. I was of course referring to this figure, "..Earth’s 47 TW interior heat..", quoted in comment 50!

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  4. bozza @52 &53, of course the figures are approximate, in the sense that they have error margins. The figure for geothermal flux is plus or minus 4.3%, for example.  Given that, it is quite possible although very improbable that it would change by plus or minus 4% from year to year - an amount so small as to be inconsequential to climate change.  Errors on radiative forcing of greenhouse gases are typically in the plus or minus 10% range.

    With regard to human produced energy, total human energy production by fossil fuel burning and nuclear power stations was 143 x 10^12 Watts as of 2005.  Obviously it has increased since then.  Your 10 TW value is therefore approximately 7% of the actual value.  However, I am not sure I have properly understood what you were saying.

     

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  5. If the moderators will allow it I would like to note for the benefit of pjcarson:

    1)  "sloganeering" is implicitly defined in the updated comments policy, which states:

    "No sloganeering. Comments consisting of simple assertion of a myth already debunked by one of the main articles, and which contain no relevant counter argument or evidence from the peer reviewed literature constitutes trolling rather than genuine discussion. As such they will be deleted. If you think our debunking of one of those myths is in error, you are welcome to discuss that on the relevant thread, provided you give substantial reasons for believing the debunking is in error. It is asked that you do not clutter up threads by responding to comments that consist just of slogans."

    I have added emphasis to indicate the key sentence which defines "sloganeering" (underlined), and the key feature of sloganeering that makes it mere noise in any attempt at reasonable discussion (bolded).

    In registering with SkS, you agreed to abide by the comments policy when posting, and therefore should have read it.

    2)  By the same token, moderation complaints are also forbidden in the comments policy (the reason your most recent post was deleted).

    3)  For what it is worth, I am not a moderator; but was when the updated comments policy was introduced. 

    4)  If you were to post the substance of your most recent post with actual peer reviewed numbers regarding "the change of heat due to tectonics", it would probably get past the moderators (unless you do something silly like all capitals, etc).  Absent actual peer reviewed numbers, a quick look at your site shows your own calculations to be worthless - something easilly discovered to be the case with regards to your comments on the greenhouse effect in substantially less than eight minutes.  If you want to criticize a scientific theory, it is essential that you actually understand it first, which clearly you do not.  If you want to learn, here is a good starting point.

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  6. For whatever it is worth, I have just posted this comment at pjcarson's website:

    "pjcarson:

    A casual read of your chapter 1 plus annex reveals:
    1) That you have taken purported evidence that CO2 emissions of IR to space come from high in the troposphere (an essential feature of the theory of the greenhouse effect, see https://www.skepticalscience.com/basics_one.html) as a disproof of that theory, thereby showing you do not understand even the basics of the theory you purport to disprove;

    2) That you misread Pierrehumbert (2011)'s explanation of the maths of line by line radiation models as itself an explanation of the greenhouse effect (it is not), thereby showing you have misunderstood even basic level explanations of the evidence;

    3) That you assume in your equation that the AIRS instrument scans the entire visible globe in each frame, whereas it in fact scans an area 1600 km wide, thereby destroying the logical justification of your equation (see http://airs.jpl.nasa.gov/mission_and_instrument/instrument);

    4) That your equation contains no variable for the wavelength or frequency of light, thereby applying equally to all wavelengths. From that it follows that it cannot explain changes in the brightness temperatures at specific wavelengths as is observed in the satellite instrument. Without further need to check the maths, this is sufficient to show your equation does not explain what you claim it to explain.

    5) These very basic errors, discoverable with a very superficial reading, show that you do not bother with basic fact checking, and are out of your depth in logical analysis. That gives sufficient reason to check no further.

    From this, an 8 minute turn around on your submission merely shows the sub-editor had a basic knowledge of climate science, and therefore sufficient knowledge to reject the paper on such a superficial reading."

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  7. Tom. I’m glad you are intrigued. You write, you read my site casually. Consequently you haven’t got anything correct. Try to read it without bias; it’s simply a scientific investigation, not a manifesto. It’s there to be corrected if it’s wrong, but you haven’t done so.

    1. No

    2. No

    3. No. I don’t asume anything about the AIRS instrumentation. You’ve misread again. My diagram actually shows the section of Earth’s surface that is able to direct energy to the satellite. The instrument doesn’t appear in the equation and so the results are independent of the sensor.

    4. The equation is independent of wavelength. Apart from the equation itself, you really should have tweaked IF you really did read my Conclusions …

    “ ALL satellite spectra will need to be adjusted with regard to their measured magnitudes” .

    Your “Without further need to check the maths” suggests you haven’t been able to work out my equation. Although it’s simple, it does require a little trick – changing one’s perspective from Earth’s (first), then to what the satellite sees. Take it as an exercise.

    Anyway, if it’s wrong, how does it get the correct answer?

    5.Try to not make “ad hominem” remarks. You have not shown any errors at all.

    To cap it all off, I’m trying to add another section which explains much more simply why the Greenhouse Effect is minuscule.

    [By trying, I mean working with Wordpress can often be difficult! I’ll get there.]

    However, its essence is

    All the above is true and accepted by all, but embarrassingly, what has been forgotten is that radiation is but one method of transferring energy, the other two being conduction and convection, and it is principally using these processes that Earth heats its atmosphere.”

    You say you left a message. My site hasn’t registered any comments from you.

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    Moderator Response:

    [DB] Inflammatory and argumentative snipped.

  8. pjcarson @57, I was in no way intrigued by your 'analysis'.  That sort of flat earther level denialism is a dime a dozen.  Because it is premised on not undersanding the science it criticizes, its criticizisms cannot be interesting.  I made the comment only because I thought my 8 minute comment meant I owed you that much.  So, I have delivered.  You have responded with flat denial and more nonsense.  So, you won't learn hence there is no point my trying to teach you.  End of conversation.

    (If any readers want more details on why pjcarson's website is nonsense, I will be happy to do so on a more appropriate thread, but he himself at this stage can only escape the charge of dishonesty by pleading idiocy, given his response.  Horse, water, etc.)

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  9. Tom Curtis @58.

    The link to pjcarson's 'grand work' has been moderated away and it should be reinstated to allow understanding of this interchange.

    I do sympathise with you in trying to correct his thesis. And we are off topic on this thread, but where do you start on something so heavily loaded with nonsensical assertions. For instance, that equation he presents is simply the diameter in degrees of the planetary disc visible from the satellite divided by 360 degrees. It is obviously wrongly applied but his description of what he thinks it represents is simply nonsensical.

    I think myself I would make a start at unravelling his lunacy at the beginning by asking for clarification of his opening statement:-

    "IR properties have been somewhat neglected, eg in the thousands of pages churned out by IPCC, very few refer to IR – and even these are of dubious scientific character."

    I am not familiar with any parts of IPCC ARs that could be described as being "of dubious scientific character." I consider it quite outrageous for someone to make such an statement entirely unsupported.

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  10. #59 MA Rodger.
    1. If my simple equation is incorrect, why does it give the correct answer!? [The equation is simple, isn't it!] It does show why I regard IPCC's IR badly.

    2. Please give quantitative answers to show my lunacy.

    3. No ad hominem! It only degrades its user.

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    Moderator Response:

    [DB]  Argumentative, baiting and inflammatory snipped.

  11. MA Rodger.

    1. #38 You do a calculation to show how much lava is required to heat the whole ocean. OK, so why do you not also consider the same when dealing with the Greenhouse” effect which you reckon is so much larger?
    Simply, the whole of the oceans are NOT warmed. As it’s the air near the surface that’s measured (WMO), it is only necessary that the top of the oceans (and the land) are warmed to change measured Global Warming.

    2. I started here with comment #48 concerning geothermal heat. I responded (#50) to Tom Curtis’ #49 comment about Greenhouse gases’ relative size, but later comments, until #57, were “moderated”.

    However, I’m glad you took the time to derive the equation. Perhaps you can help Tom as he seems unable to do so?

     

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    Moderator Response:

    [DB] Inflammatory snipped.

  12. pjcarson @60/61.

    So you tell me @60 that if an equation happens to give the hoped-for answer, then the equation can be considered to be correct. Are you serious? (I'm not sure here how the IPCC fit into the issue. Do they use a different equation? Or is it that they obtain a different answer, one you disagree with?)

    And if that is not enough to provide a measure of the lunacy of you spout, do note that if, as you argue, all the IR that leaves the surface of a planet emerges after a few adventures at the top of the atmosphere and then shoots off into space; if this were true, how can CO2 (or for that matter, any other gas in the atmosphere) be acting as a greenhouse gas? The very notion that GHGs can operate without creating back-radiation is pure thermodynamical nonsense!!

    And you may be glad to learn that a quick back-of-fag-packet calculation of you geometric explanation for a change in 'fantasy-total-globe' satellite radiation measurement due to different heights of emission suggests the % of the Earth visible from the satellite drops by 1.5% for an increase of 10km in height (~65K temperature drop) but due to the inverse square law having twice the opposite effect, the radiation measurement at the satellite would actually rise with increased in height. So you also supply a goodly quantity of geometrical nonsense.

    (Note - I would attempt to find a more appropriate thread for this comment but the scope of argument being addressed defies easy categoraisation.)

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  13. MA Rodger.

    1. #38 You do a calculation to show how much lava is required to heat the whole ocean. OK, so why do you not also consider the same when dealing with the Greenhouse” effect which you reckon is so much larger?
    Simply, the whole of the oceans are NOT warmed. As it’s the air near the surface that’s measured (WMO), it is only necessary that the top of the oceans (and the land) are warmed to change measured Global Warming.

    2. I started here with comment #48 concerning geothermal heat. I responded (#50) to Tom Curtis’ #49 comment about Greenhouse gases’ relative size, but later comments, until #57, were “moderated”.

    However, I’m glad you took the time to derive the equation. Perhaps you can help Tom as he seems unable to do so?

     

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    Moderator Response:

    [DB]  Please note that posting comments here at SkS is a privilege, not a right.  This privilege can and will be rescinded if the posting individual continues to treat adherence to the Comments Policy as optional, rather than the mandatory condition of participating in this online forum.

    Moderating this site is a tiresome chore, particularly when commentators repeatedly submit offensive, off-topic posts or intentionally misleading comments and graphics or simply make things up. We really appreciate people's cooperation in abiding by the Comments Policy, which is largely responsible for the quality of this site.
     
    Finally, please understand that moderation policies are not open for discussion.  If you find yourself incapable of abiding by these common set of rules that everyone else observes, then a change of venues is in the offing.

    Please take the time to review the policy and ensure future comments are in full compliance with it.  Thanks for your understanding and compliance in this matter, as no further warnings shall be given.

  14. pjcarson @63:

    "Perhaps you can help Tom as he seems unable to do so?"

    As you insist on niggling...

    The formula being discussed is the found on pjcarsons's addendum to his 'chapter one'.  He attempts to explain the CO2 notch seen in IR spectra for Venus, Earth and Mars, as shown in Pierrehumbert (2011):

    pjcarson follows Pierrehumbert in calling it a 'dip'.

    pjcarson conjectures that:

    "The experimental relative dip (eg from figure 6 or 8) is the ratio (measured IR) / (hypothetical directly transmitted IR, ie black body curve)."

    (My emphasis)

    Note carefully that it is the measured IR, not the IR that strikes the satellite.  Measured IR can only be that observed by the instrument itself.  It follows that in calculating the ratio of the area above the limb of the planet (approx: horizon) for the satellite to a sphere with a radius equal the the satellite limb distance, he is calculating an irrelevant quantity.  Much of that radiation falls on the outershell of the satellite, or other instruments, and not the AIRS instrument that did the observing (for Earth).

    If we look at the description of the AIRS instrument we read:

    "AIRS looks toward the ground through a cross-track rotary scan mirror which provides +/- 49.5 degrees (from nadir) ground coverage along with views to cold space and to on-board spectral and radiometric calibration sources every scan cycle. The scan cycle repeats every 8/3 seconds. Ninety ground footprints are observed each scan. One spectrum with all 2378 spectral samples is obtained for each footprint. A ground footprint every 22.4 ms. The AIRS IR spatial resolution is 13.5 km at nadir from the 705.3 km orbit."

    Plus or minus 49.5 degrees turns out to be approximately 77% of the limb to limb angle, meaning pjcarson's formula (if it were the correct formula) would significantly overestimate the ratio of " (measured IR) / (hypothetical directly transmitted IR".  Worse, that arc is not what is observed in a single spectrum.  Rather, there is one spectrum per footprint, with a resolution of 13.5 km, so each spectrum as in panel a in the figure above represents the IR radiation from an area just 13.5 km wide (unless explicitly stated to be a composite spectrum).  That is, pjcarsons formula (if it were correct) would overestimate incoming radiation by a factor of 116 or so.

    You can see this mismatch of pjcarson's concept of the resolution of the instrument and the actual resolution from some of the AIRS products:

    The images on the right show a 13km resolution within a single scan path.  Where pjcarson's model of how the instrument operated correct, there could be no resolution of details across the width of the scan path, and the width of the pass would be wider.

    When confronted with this essential fact above, pjcarson responded that:

    "The instrument doesn’t appear in the equation and so the results are independent of the sensor."

    As he is attempting to explain properties of the measured results (ie, the actual IR spectrum) his claim that the results are independent of the sensor are absurd.  Apparently, in his world, the mission planers could have greatly reduced the budget by simply leaving the instrument on the ground, given that the "measured results" are "independent of the sensor".

    Pressing on, pjcarson then shows a diagram essentially similar to this one from wikipedia:

    The only significant differences are some difference in the labelling and the fact that he shows the reflection around the R,h axis.  He then states:

    " Then the calculated relative dip is the ratio ≈ (planet sector area exposed to satellite) / (satellite-centred sphere area) = 2* sin-1 (R/(R+h)) / 360".

    sin^-1(R/(R+h)) is the inverse sine of the opposite (R) over the hypotenuse of the included angle for line segments d and h.  It returns the value of that angle.  Multiplying by 2 gives the included angle from limb to limb from the satellite.  Dividing by 360 gives the ratio of that included angle to the number of degrees in a circle.  At this point, pjcarson simply assumes that that ratio is also the ratio of area between the "planet sector area exposed to satellite" and the "satellite-centred sphere area".  If the angles were dividing the sphere in a manner similar to the quarts of an orange, it would be.  But the "planet sector area exposed to satellite" is not analogous to a quart of an orange.  Rather it is a spherical cap.  Therefore the formula pjcarson should in fact be using if his premises were sound (though we know they are not), is the ratio of the area of a spherical cap of the earth for the included angle γ, relative to 4*pi*d^2 (ie, the area of the satellite centered sphere, with radius equal to the satellite to limb distance).

    As it turns out, for a satellite altitude of 700 km, for the Earth, that ratio is 0.035.  pjcarson, by using the wrong formula, has overestimated the value he purports to find by a factor of approximately 10.

    That it was the wrong forumla, that the principles used to invoke the formula, and that the formula even as concieved cannot explain the selective dip only at certain wavelengths given that the formula contains no variable for wavelength can all be seen at a glance by somebody who knows the topic.  It take rather longer to explain it to people who are less familiar, and it cannot be effectively explained to somebody who will not learn.  

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  15. Correction to my post @65.

    I made an error in my spreadsheet that resulted in a significant error in calculating the ratio (planet sector area exposed to satellite) / (satellite-centred sphere area).  Correcting that error gives a correct value of approximately 0.214.  That is much greater than the incorrect value of 0.035 cited above, and means pjcarson's incorrect formula overstates the value by about 66%.

    In double checking the formula, I noticed that, counter-intuitively the ratio approaches 0.25 as you approach 0 Km altitude.  That is not a mistake, and is a consequence of the fact that the visible area of the surface approaches the shape of a circle (area = pi*r^2) rather than a sphere (area = 4*pi*r^2).  It does mean that pjcarson would probably prefer to state his ratio in terms of the area of the occluded part of the sphere with radius d centered on the satellite relative to the area of the full sphere.  So calculated, the value for the satellite bearing the airs instrument is approximatly 0.283.  Even thus reduced, pjcarson's formula overstates the value by about 26%.

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  16. And you spent all that time getting everything wrong!?

    My simple equation is correct, as shown such diverse atmospheres as Earth Venus and Mars. The equation simply shows how much energy is re-radiated from any planet’s surface to a point at a height h in its sky. It’s independent of sensors as it only deals with energy flows. Each satellite has different sensors.

    The dip is supposed by St P to represent an extra amount that CO2 can absorb (because it is “unsaturated”). But one can easily see, for a species such as CO2 that’s already absorbed all Earth’s re-radiated IR in its wavelength and then re-radiates it in all directions, that there must be a dip of at least 50% (because at least 50% is directed away from the satellite).

    Your analysis of the derivation of my equation fails. You worry about the Earth surface bending the wrong way, ie bends towards the satellite, however, from the satellite’s perspective, it makes no difference which way the surface bends as the area “cut out” from the sphere centred on the satellite is the same.

    I’d be interested in seeing what you get wrong with Chapter 1B newly on my site.

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    Moderator Response:

    [DB] Multiple instances of sloganeering snipped.  Simply declaring a dog's tail to be a 5th leg does not make it so.  Similarly, handwaving away the explicit analysis of another that demonstrates your specific errors as being "wrong" without any subsequent analysis of your own to rebut it is also wrong and is sloganeering.

    Either step up, do the hard work and analysis to support your position, replete with citations to credible sources, or cede the point and move on.

    That is what an actual skeptic would do.

  17. I note that pjcarson having been comprehensively proved wrong on one lie (that I could not derive his simplistic equation) immediately launches another.  IMO, his latest comment, as many before it, contains no substantive argument and should be considered sloganeering only.  Given the absurd nature of his claims, and his repeated failure to present substantive argument in favour of his views, I further suggest a high bar be set to establish that he is not sloganeering.  

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  18. The publication date of pjcarson's latest efforts, his Chapter 1B, was April Fool's Day. If it had any other author, it would be treated as an April Fool wheeze. But for somebody who has exhibited such egregious stupidity as pjcarson, I feel this is for real.

    pjcrson's latest contribution to the blog-o-sphere turns on its head his previous assertion that there is a greenhouse effect from CO2 (but no AGW) and makes the following incredible pronouncements. (Excuse my while I stifle a guffaw.)

    (1) CO2 can only contribute to the usually accepted GHG effect of +33°C in proportion to its concentration within the atmosphere, that is 0.04% of it. (2) The thermal mass of air tells us that N2 & O2 are "the real Greenhouse molecules" . (3) "The size of Greenhouse heating (blanketing) is constant" and determined by the number of molecules within the atmosphere. So burning FF which converts O2 into CO2 has zero effect. (4) The greenhouse effect is constant over 100,000s of years and is "degrees less" than +33°C.

    All this remains off-topic on this thread. I do not see pjcarson clearing the bar suggested by Tom Curtis @68. Moderators please moderate away to restore the sanity.

     
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    Moderator Response:

    [DB] Inflammatory snipped.  Please, all participants, keep it clean.

  19. I took a quick look at pjcarson2015's blog - in his screed on CO2 there is no mention of the lapse rate, the tropopause, 'top of the atmosphere', pressure, effective radiating altitude, etc. A word search of his 'Chapter 1' fails to find any of those terms. 

    As a result it's clear that pjcarson doesn't understand how increasing CO2 raises the altitude where emitted IR can escape, the altitude of effective emission to space, which due to the lapse rate means radiating from a cooler parcel of gas. This reduces the rate of radiation with respect to the ground temperature, requiring a warmer surface to balance energy flows - the very core of the radiative greenhouse effect. Failing to understand the basics, pjcarsons blog is simply D-K nonsense, and a waste of time and mental energy. 

    Pjcarson - educate yourself.  Until you learn some of the basics you have no chance of relevance. 

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    Moderator Response:

    [JH] You and other responder to pjcarson2015 are now skating on the thin ice of dogpiling, which is prohibited by the SkS Comments Policy

    Since most of what pjcarson2015 has posted to date is unsubstantiated personal opinion, there is no need for more than one or two people to respond to his/her future posts.

  20. KR @69, it always stuns me when climate change deniers makes statements such as:

    "All the above is true and accepted by all, but embarrassingly, what has been
    forgotten is that radiation is but one method of transferring energy, the other two
    being conduction and convection, and it is principally using these processes that
    Earth heats its atmosphere."

    (From pjcarsons Chapter 1B, emphasis in original)

    That was a fair criticism of climate science prior to 1964.  In 1964, however, Manabe and Strickland published their landmark paper, Thermal Equilibrium of the Atmosphere with a Convective Adjustment.  We are less than a fortnight from the 52nd anniversary of the acceptance of that paper, and 3 month from the 52nd anniversary of its publication - so to say that climate science has "forgotten is that radiation is but one method of transferring energy" is to forget nearly all the history of climate science.  Manabe and Strickland used a specified, convection induced lapse rate, but certainly by 1981 models were determining the lapse rate by analyzing the combined radiative and convective energy flux.  Modern models also include latent heat, and have for decades.  All of that science is just scrubbed from the record for deniers, at best, because they are two lazy to read the actual science.

    From the earliest such analysis it was shown that the effect of convection was to cool the atmosphere relative to the temperature it would have been with radiative heat transfers alone:

       

    Thus while convection dominates in determing the thermal structure of the lower atmosphere (troposphere), it is untrue to say that "conduction and convection" are the principle means of heating the atmosphere.  

    PJCarson goes on to say:

    "Radiation does transfer energy by far the quickest – equilibrium is achieved in tiny fractions of a second – compared to convection and conduction which vary considerably depending on the circumstances. "

    Contrary to pjcarsons supposition convective equilibrium is achieved much more rapidly (within hours) than radiative equilibrium, which as can be seen above takes almost a year to achieve equilibrium.  That is why convection dominates the troposphere's thermal structure. 

    Of course, fundamentally, the greenhouse effect does not depend on how the thermal gradient in the atmosphere is established, only that it exist.

    In the end, that pjcarson and his like get the minor details wrong is immaterial.  The fundamental claim is what is extraordinary.  It is comparable to criticizing Newton's theory of gravity for not taking into account the inverse square law.

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  21. Please explain if my analogy incorrect. There is a home, all the windows and doors are closed. There is a Stove on in the Kitchen. Isn't if fair to say that while the Stove can't heat the rest of the house to the Stove Temperature, if the Stove is perpetually on, at some point it will have an affect on the overall temperature of the home, no?

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  22. 71 @PetroCurious

    "if the Stove is perpetually on, at some point it will have an affect on the overall temperature of the home, no?"

    Your question is not quite defined enough as you need to state more precisely what you mean and the starting conditions. What do you mean by "affect" the temperature? Go up? Go down? Stay the same? All are possible in the scenario you have described. 

    Perhaps what you are thinking is the temperature will go up? That depends on the starting temperature and the rate of loss of the heat from the house. There is a theoretical equilibrium point where the heat being lost is equal to the heat the stove is providing. The house will reach this equilibrium temperature eventually. 

    Or are you suggesting the house does not lose any heat because the "windows and doors are closed"? It will still lose heat through radiation.

    Does that answer your question?

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  23. PetroCurious @71,

    The centre of the earth is incredibly hot but this is achieved because it is well insulated rather than being supplied with a big power input. So think 'candle' rather than 'stove'. And the 'home' has no windows to let warming sunlight in - it is a concrete bunker, well insulated and very very hot inside.

    But we are concerned with the outside surface temperature of the bunker, heated by the sun. Even without a mechanism analagous to the GHG effect, the average temperature of the outer skin of the bunker will be about 250K due to the sunlight heating the outside, although on the outside surface the nights will be cold without a GHG effect, heated only by the warmth left from the day within the concrete, and not forgetting that candle.

    The candle, while it raises the interior of the bunker to fantastical temperatures because of the insulating concrete, is only supplying 80W which at the surface of a 10 metre cubes bunker is only 0.1W/sq m, enough if the sun stopped-for-ever to heat the outer skin of the concrete to just 36K above absolute zero. But with the T^4 relationship in:-

    Radiate energy = (Emissivity) * (Stefan-Boltzmann constant) * (Temperature)4 * (Area),

    with the sun heating the skin, the candle only raises the average outer temperature from 250K to 250.02K, a trivial increase.

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