Equating Perpendicular Planes is Plain Nonsense

Many people believe you can compare the Geothermal Heat Flux to Insolation, see that it’s pitiful and then exclude Geothermal from the energy budget. I have touched on this subject several times: here, here, and here. Today I will again show that this idea is plain nonsense.

Let’s start with the basics of radiation:

Stefan-Boltzmann’s Law

The radiation emerging out of a plane in the (x,y) dimension is proportional to the fourth power of its temperature. The choice of variable names x,y is arbitrary. Now what about conduction?

Conduction through matter

Geothermal Heat Flux has been globally measured to be ~ 91.6 mW/m²; a very small number. Many people claim that you can convert this figure into a value that tells you what the surface temperature would be in the absence of the sun.

What they do is equate the radiation emerging out of a plane with the internal conductive heat flux. In the language of my previous articles, they equate Cold Side Radiation to Conductive Heat Flux: CSR = CHF. Then they solve for T_cold.

This is kind of funny, because even though we have proof that geothermal will deliver ~273 K, they still think geothermal can only deliver ~36 K.

They believe their argument is reasonable because both CSR and CHF are in units W/m², and therefore they can be equated to one another.

What they don’t understand is that the meters squared (m²) are in completely different dimensions.

In radiative flux, the m² comes from the surface plane. But in conductive flux, the m² comes from multiplying thermal conductivity constant (k) by the depth (L).

The depth is orthogonal (perpendicular) to the surface plane!

How much sense does it make to compare emergent radiation to something based on a 90 degree angle to it? None at all.

I derived the proper relationship between CSR and CHF in my previous articles:

Proper relationship between CSR and CHF

Now I do proper dimensional analysis:

Dimensional Analysis

Yes, their idea doesn’t make any sense at all, but it does make for great rhetorical pseudoscience.

Now for some satire …

Question: How much rain falls on a flat roof top?

Answer: It depends on the building material and height of the building.

Normal Person: Say what?

This is the best analogy I could come up with what their idea represents. Maybe someone else could come up with a better one. Main point: they’re 90 degrees wrong.

I hope to repeat this for the last time: the Geothermal Heat Flux is NOT enough information to say what radiation emerges out of the surface. There are many possibilities with the same heat flux value, as shown here. CHF divided by k (thermal conductivity) yields a temperature gradient. A gradient measure tells you nothing about what’s at the top.

Take care, -Zoe

Zoe’s 35th Birthday

16 thoughts on “Equating Perpendicular Planes is Plain Nonsense

  1. Beautifully articulated Zoe. I like the rain roof top analogy too. Better than the one I had of calculating the resultant temp of a length of resistance wire by the wattage of a nanometer of said wire.

    1) Have you explored the implications of your Geothermal Insight for the onset of Ice Ages? I have a bit. It’s profound and provides a far simpler explantion than the cosmic catastrophism, sun, micro nova, proton shower, etc hypotheses of the EU community

    2) Induction as a partial source of geothermal heating? The geology could help explain the Russian anomoly during the last ice age. So very suggestive geology there.

    Again – thank you so much Zoe.

    Liked by 1 person

    1. Thank you, Michael.

      1) Don’t think I have. Tell me more.
      2) Can’t evaluate induction. Remote charging is tricky business. Could be all, could be none, or somewhere in between. I’d hate to speculate.

      I appreciate comments from smart people who get it.

      Since first comment was nice, I included my 35th birthday photo at the end.


      1. I don’t want to front load others suggestions with what I have discovered, but as an entree:

        1) Ice Age onset – in the old model with the Sun providing almost all the heat, the Sun going into dark mode, hibernation, was not even considered as possible, as it would take us down to 35-50 Kelvin only, and that clearly doesn’t occur.

        In your Geothermal theory (far past hypothesis in my assesent), if the Sun goes “dark” (full corona), the earth drops to a minimum low av. of ~ 273K only, and resembles very much what proxy data suggests for the last ice age.

        This is an elegant, simple theory, a fusion of plasmoid earth and EU theories, but without the need for their explicit or implied cyclic catastropes (that is each time, somehow, finely calibrated so as not to destroy all life) to cause the transition in and out of bio-survivable ice ages.

        No need for micronovas, comet impacts, Milankovich cycles, implausibly complex pertubations, etc. Just a quiet, beating heatbeat of the cosmos to induce, and the infrared fire within keeping our blue orb sufficiently warm for life to suvive a vastly diminished solar output until it is pulsed up again 90k years later.

        It also suggests that the Sun could be a metastable entity, with “on” and “off” states, externally induced.

        Hundreds of data points.

        2) valid of course. Nonetheless – you may find it informative to think about the Urals to Lena ice age and magnetic anomolies, and if there is anything in their Large Igneous flood geology and it’s electrical or geothermal properties that might cause chilly Siberia to counterintuitely and uniquely resist glaciation in the northern hemisphere during these hybernating Sun periods.

        Liked by 1 person

  2. Zoe,
    I have had a go at fitting geothermal effects into the energy balance for Earth.
    Given that the incoming solar radiation, the Bond Albedo and the amount of solar radiation that actually reaches the surface are known values the only way to do this is if the Bond Albedo has been miscalculated.
    In other words a misunderstanding of geothermal has resulted in a further misunderstanding of the total amount of energy leaving the Earth. This means that Bond’s Albedo is also misunderstood and is in reality smaller, the geothermal contribution makes it look bigger than it actually is.

    I’ll lay out a speculative set of values:
    For incoming radiation of 340w/m2
    True Albedo 0.11
    Absorbed 303w/m2
    Reflected 37w/m2
    Geothermal 68w/m2

    This gives an apparent reflected value of 68+37=105. This gives an apparent Bond albedo of 105/340=0.31.

    Assuming an emissivity of 0.95 I get
    (303+68) / (0.00000005670373*0.95))^0.25 = 288

    As the solar radiation reaching the surface is 250w/m2 the above means that 53 is absorbed by the atmosphere.

    The “true” value of Bond albedo is therefore close to that of the Moon and Mercury.

    I’d be interested in your thoughts on this.



    1. 105/340 is Shortwave.
      Geothermal is not shortwave, and you can’t add 68 (longwave) to 37 (shortwave).

      Albedo is a geometric phenomena, and 88% of it is due to the atmosphere [Donohoe 2011].


  3. Why can’t you add them? I would have thought that they were both just Watts/m2 as far as far as an energy balance is concerned.

    Also the definition of the Bond albedo is based on all radiation at all angles leaving the body so if there was an extra source of heat from somewhere I’d expect that to create a “false” value for albedo?

    Have you got your own ideas for how the balance works, including both solar and geothermal effects, and if it changes any of the currently accepted values?

    I’ll have a search for your reference. I’m surprised that albedo is thought to be due to the atmosphere as albedos across the solar system don’t seem to bear much relation to the presence of an atmosphere.


    1. You can’t add them, because the albedo is supposed to be the reflected incoming shortwave radiation.

      I have an idea of how things work at the surface. I can explain why the surface temperature is what it is. As for the spread in the atmosphere, that is not complete. When it is, I will post about it.

      I don’t think the albedo is wrong by its own determined standards, it’s a question of how useful it is for the surface energy budget.


      1. In your post above you state that albedo is reflected shortwave. However Bond Albedo is based on the total portion of all reflected radiation, not just shortwave. Sunlight contains a lot of longwave and there would be no way of telling the difference between reflected longwave and emitted longwave.

        Resolving this might involve looking at the methods used to calculate Bond Albedo for Earth. The numbers used for this might actually be proof for your theory, at the least they would give some likely limits for the geothermal effect. The fact that mainstream science rejects internal heating indicates two possibilities:

        That emitted radiation has been incorrectly assessed and included in the reflected category which produces a false high value for Albedo
        That emitted radiation has been correctly assessed and rejected as “not reflected” which implies they know the value of emitted radiation (if you are right they don’t appear to know it or have simply dismissed it as an error).


        1. My definition of shortwave is not visible light and UV, but everything shorter than the Earth’s radiation. If you look at a diagram of solar and earth radiation, everything to the left of Earth, i.e. what the Sun gives, I consider shortwave. A more accurate name would be shorterwave.

          The visual geometric albedo is reflected sun light in the visible light spectrum.
          The bond albedo is the portion of solar radiation that is reflected: UV, Light, Near Infrared, etc.


  4. Zoe I think you will find this discussion at Judith Curry’s blog of interest.


    I spent a lot of time caving in WVA during my years at UVA. They are warm in the winter and cool in the summer. About 55 degrees in most WVA caves. How can this not have translate into an impact on surface temperatures.

    The contribution of geothermic heat to ocean heat content has puzzled me for some time. The above blog post and its comments provide some useful data.

    I think you should put together a post and submit it to Judith for publication at her site. I think the comments would be interesting.

    I wonder if there is a spherical instrument that can continuously measure radiation across all wave lengths at all points on the sphere. The energy budget graphs with up and down arrows just weird me out.

    You have to wonder about the effects we will observe if the earth’s magnetic field continues to weaken. My guess is that geothermic activity will rise.

    You should watch the movie 2012. It a great disaster movie that is driven by solar flares heating up the earths mantle.

    Liked by 1 person

  5. Your final sentence in your last reply to me contains an important point.

    The key word is “reflected”. There is no fundamental difference between radiation that is incident, transmitted, reflected or absorbed, it is just radiation. Regarding long or short the sun outputs across the entire range of wavelengths and the usual calculation of Bond Albedo includes all wavelengths.

    Consequently there is a big assumption in there that mainstream science might have missed. The assumption is that they know the value going in and that they know the value “reflected” purely because they assume all outgoing radiation from Earth is “reflected”. Your theory implies that a significant portion of outgoing radiation is not reflected, it has in fact been incorrectly assigned as such when it is actually emitted geothermal.

    I have been thinking how to resolve this. If the actual numbers and method for calculating the Earth’s albedo could be established they could be checked for different assumptions for reflected and emitted to see what range of values fits your theory. This in turn would give the likely range for the geothermal contribution. This would be an interesting inquiry to see as you are not the first person to propose a theory that Bond Albedo might be wrong or not applicable.


    1. Radiation is waves. Waves have wavelengths. Wavelengths are subjected to the peculiarities of molecular dimensions and space in between. Some go through the medium of molecules, others do not.

      Bond Albedo is not calculated, but measured by satellite. If ~340 W/m^2 was supposed to return, but ~240 W/m^2 did, then albedo is ~0.3.

      What is returned to space is not 1 minus what arrives at the surface. The atmosphere absorbs an additional ~0.22 of solar radiation, and this does not reach the satellite. It’s below its view, so to speak.

      We can’t count solar spectrum atmospheric absorption as part of albedo, nor can we add it to surface absorption.

      I think the Bond Albedo is fine by its standards. It’s not guaranteed to tell you how much radiation reaches the surface. If there is no atmosphere, then obviously it does.


      1. Are you proposing a different definition of Albedo? Your post suggests that you separate Bond Albedo into atmospheric and surface values. There was a discussion on another forum some years ago regarding assuming black body behaviour (Albedo=0) for worlds with atmospheres. You seem to be heading in a parallel direction, towards a different treatment for this parameter.

        The commonly used definition of Bond Albedo is reflected/Incoming. The “reflected” radiation isn’t sorted into atmospheric and surface, its an aggregate result. So the common definition includes absorption and reflection at all levels of the atmosphere, surface and water as far as radiation penetrates. If the assumption in the measurements and final calculation is that all outgoing radiation is reflected then any geothermal would skew the Bond Albedo result.

        This gives us:
        Mainstream Bond Albedo = 0.3, assumes all outgoing radiation is reflected, no geothermal
        Zoe’s theory corrected Bond Albedo = 0.1-0.2???, takes into account that some outgoing is not reflected but is geothermal in origin

        I did look for papers showing the calculation of Bond albedo from multiple satellite measurements and there seems to be wide variation across the Earth’s surface. I’d expect that combining this into a single value would give plenty of chance for a wrong assumption to be hidden in the error bars.

        There is a paper that revises the Bond Albedo for Jupiter from 0.34 to 0.50 and to maintain the energy balance this demanded that the value for internal heat was also revised.


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