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:
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?
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:
Now I do proper 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.
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Jerry Krause
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Hi Zoe,
Have only looked at your first paragraph and the the two images which have nothing to do with the topic of the title. But I am sure you will get there. But the comparison of the two satellites images totally supports my understanding that cloud(s) is the thermostat which constrol the Earth’s energy balance system. For that can be the only thing that limits the radiation lost to space, at the warm (hot) equator, being nealy equal to the radiation lost to space from the cold polar regions.
One must accept what has been plainly observed. The thin cirrus near the cold top of troposphere is scattering the IR radiation form the warm tropical surface back toward these warm surfaces and the the cold tops of these cirrus clouds are emitting IR radiation toward space according to their temperature. Its that simple.
Have a good day, Jerry
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Jerry Krause
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Hi Zoe and PSI Readers,
Have now looked at Zoe’s article. And I see, despite all my common errors, that I was not only correct that the two images had nothing to do with the title but that my unstated assumption, that Zoe’s article would have nothing to do with these two images, was also correct.
Now I have to ask: Did Zoe enclose these two images with the article or did John O’Sullivan (the PSI editor supply these two images? Hopefully, either Zoe or John will.answer my question.
Have a good day, Jerry
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Zoe Phin
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I did not select the image. My post doesn’t have it.
The issue is complicated because there is more geothermal at the equator than poles. This is a result of rotation speed. Venus has low rotation speed, hence little variation between pole and equator geothermal.
We can’t use just the sun and clouds.
This is a complicated topic, which I will address later.
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Zoe Phin
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Jerry,
I agree that John’s image confused the topic greatly. These satellite images have nothing to do with the measured geothermal. He should’ve used this image:
https://agupubs.onlinelibrary.wiley.com/cms/asset/abe094e5-157c-48a2-b7cc-43e0c3a97e7c/ggge20271-fig-0006-m.jpg
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John O'Sullivan
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Hi Zoe, as per your suggestion, have now swapped the image.
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Zoe Phin
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👍👍
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Jerry Krause
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Hi John,
Because I considered the two images, which compared the reflected solar radiation with the IR be emitted from the earth surface toward space as observed from satellite, to be critically important to understand (explain) the earth’s radiation balance system, I would hope you would reinstate them near my comment in hopes some PSI reader might see that to which I was referring.
Have a good day, Jerry.
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Jerry Krause
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Hi Zoe and John and others who may have seen the two images which John removed from Zoe’s article,
I ask: How is it that you seem to be unable to ‘see’ that to which I clearly brought to your attentions? Why no attempt to ‘refute’ that to which I pointed and gave a simple explanation?
And John, the others who have joined this discussion after you removed this two imagines, which allowed one to compare the snapshots of a earth’s hemisphere in the visible solar light and of the same hemisphere in the invisible infrared light (to human eyes), can have no idea of which I have referred and am now again referring. Please reinsert these two images in Zoe’s article.
Have a good day, Jerry
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geran
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Zoe abuses physics much as the GHE practicioners do. She makes mistakes with the equations, then layers on another blog article with more mistakes. Layer upon layer of mistakes becomes pseudoscience.
Earth surface averages about 91 mW/m^2 from core heat. She has that much correct. She should have stopped there.
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Zoe Phin
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The m^2 in geothermal heat flux has nothing to do with the m^2 of Earth’s surface.
The m^2 of geothermal heat flux comes from multiplying (k) by L. L is the DEPTH !!!
IF the geothermal heat flux was 0 W/m^2 from Earth’s core to the surface (a hypothetical), it would imply the surface and core had the same temperature, i.e. 5400C. And the theoretical emission to space from that would be: 58,732,722 W/m^2.
Assuming a given temperature at a given depth, a SMALLER heat flux would yield a
BIGGER emission at the surface. The relationship is inverse.
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geran
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More layers of hilarious pseudoscience from Zoe. She doesn’t understand the relevant physics, and refuses to learn.
It’s the same as we’ve seen for years (decades?) with the GHE fanatics. Zoe is just a “geothermal” fanatic.
Real scientists need not apply…..
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Tom O
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I’m waiting to see your proof that you are right and she is wrong. Anyone can name call, now back your mouth.
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geran
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Tom O, thanks for your interest.
Zoe gets several things wrong. Her easiest-to-understand mistake is: “The m^2 of geothermal heat flux comes from multiplying (k) by L.”
She is multiplying k, which is conductivity, by L, which is “length”, hoping to end up with “area”.
But k has units of Watts/m/K. So, her multiplication results in units of Watts/K, which are not the units for area, which is m^2.
She’s way off, and that’s just the easy-to-understand stuff.
Zoe Phin
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Geran,
Really? That’s your best argument?
I should’ve said multiply k by 1/L. My actual post has it correct. k divided by L.
‘She is multiplying k, which is conductivity, by L, which is “length”, hoping to end up with “area”.’
That’s hilarious! That’s exactly the main point of the post: that OTHERS believe geothermal heat flux describes what can emerge from a surface area.
It does no such thing, and hence can’t be compared to insolation!
Do you actually believe 91 mW/m^2 is what is claimed to emerge from the surface? A quick look at the Davies 2010 or 2013 paper and their data sources should quickly dispell such an absurd notion. They are looking well into the deep, and averaging that worldwide. They don’t claim 91 mW/m^2 is emerging from the surface.
geran
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Zoe responded within 10 minutes! She’s guarding her hilarious pseudoscience like a true fanatic.
She tried to correct her mistake, but only made it worse. k/L still doesn’t results in units of “area”. And her claim that she got it right in the original post is incorrect. She tried to imply that was my “best argument”, when I clearly indicated it was just the easiest-to-understand: “She’s way off, and that’s just the easy-to-understand stuff.”
She’s just shooting in all directions, trying to hit that illusive target.
Zoe Phin
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‘k/L still doesn’t results in units of “area”’
Exactly!
You still get /m^2, and this CAN’T be compared to insolation precisely because it’s NOT an area.
Good boy, geran.
geran
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k/L has units of Watts/m^2/K.
Three strikes in baseball and you’re out. Not sure how many strikes you get in pseudoscience.
Zoe Phin
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Oh, geran, does mommy need to hold your hand?
… then you multiply by the temperature difference between two depths, and you get W/m^2.
The important point is that this m^2 has nothing to do with surface area.
Now that wasn’t hard, was it?
geran
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When Zoe finally realizes she made a mistake, she tries to act like she knew it all along. That’s why it’s such fun to bust her pseudoscience.
And that was only the “easiest-to-understand” mistake that she’d made!
Zoe Phin
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There’s no mistake in the post, geran. Come back when you find something.
geran
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Zoe claimed: “I should’ve said multiply k by 1/L. My actual post has it correct. k divided by L.”
From Zoe’s “actual post”: “In radiative flux, the m^2 comes from the surface plane. But in conductive flux, the m^2 comes from multiplying thermal conductivity constant (k) by the depth (L).”
It’s even more fun when clowns bust themselves!
Zoe Phin
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Ah, so the text is wrong there too. Good catch. Thanks. Why didn’t you say that earlier?
The equations are still correct, and so is the dimensional analysis. Do you disagree?
geran
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Again, Zoe has to admit she’s wrong.
But, in her head, it’s my fault!
Zoe Phin
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geran,
I already said the TEXT was wrong. I also said thanks. I fixed it on my site.
The equations and analysis are correct. Disagree? Make your case.
geran
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No Zoe, the equations and analysis are NOT correct My “case” was made when it took you so long to admit your obvious mistake with a very basic concept–managing units.
You don’t understand the relevant physics, and you refuse learning..
Zoe Phin
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Geran,
The mistake was in the written text. Not in the formulas, not in the diagrams.
You still believe the m^2 of conductive heat flux is a surface area from which radiation can emerge?
geran
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The mistakes were in the written text, AND in the formulas, AND in the diagrams.
You’re wrong because you don’t understand the reletive physics, and can’t learn. It took you a whole day just to admit your units were messed up. It would take you years to even begin to understand your other mistakes.
But science isn’t what you’re about, is it?
Zoe Phin
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Geran,
Where is the mistake in the formulas and diagrams?
The text has been fixed. Thanks.
You believe radiation is based on temperature or conductive hear flux?
You believe conductive heat flux refers to emission surface area?
Make your case. C’mon, let’s hear it, you big bully.
geran
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1) Earth is not a cube, so your made-up equation is invalid. Conductive heat rate for a sphere is:
Q(dot) = 4πk(Th – Tc)(RhRc)/(Rc – Rh)
2) Even with the correct equation, you’re only going to end up with a “ballpark” result. And multiplying that result by a factor of 100 will still be VERY insignificant compared to solar. So, you’re barking up the wrong tree. Learn some physics.
3) You keep claiming that I’m saying things I’m not saying. And, you keep throwing out childish insults. Please clean up your act.
Zoe Phin
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Geran,
You’re correct that Earth is not a cube. You are so smart. I never knew that. That is such an important point, that I now have to concede everything. Oh wait …
Your equation still shows that m^2 will come from k and delta R. R is a depth! Depth is orthogonal to surface area.
You fail again on the important point.
P.S. I don’t care about the small error from not using conics. The fact that it’s more accurate seldom matters to the main point. I want my argument simple enough for grandma to understand!
geran
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Zoe, you are the one confused about conduction and emission. That’s probably why you are making up stuff.
We’ve seen it before. First there was “heat creep” down from the atmosphere. Now, you’ve come up with “heat creep” from the center of Earth!
Learn some physics.
Herb Rose
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Hi Geran,
You can’t argue with Zoe she majored in economics (a real science). Ask her to explain why gravity preferentially works on denser objects.
Herb
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lifeisthermal
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But the surface emits ~390W/m^2, and according to Prevost and Planck all of the emission depends on the internal state of the emitter. So all of the 390W comes from within the surface, 91mW is only the heat flow between two points close to each other in the thin crust. If you boil a pot of water on the stove, you´ll have a very small heat transfer between two points inside the boiling water, but you´ll have a much larger heat flow from the stove through the water.
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Zoe Phin
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I’m glad someone has a brain 🙂
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Alan
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This is just nonsense, including the references. It takes a textbook example of steady state heat conduction through a material, where there is a constant energy flow through the material, Q. The heat flow in is equal to the heat flow out and the heat flow through the material. It is the assumed flow of energy by radiation from the low temperature side that creates the error, and it is that conservation of energy applies, and it does not in this example.
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Zoe Phin
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Alan,
Then you will have no problem producing a textbook example showing I’m wrong. An actual example! Not misused formulas based on theorizing.
Boltzmann and Planck both said radiation is based solely on TEMPERATURE (and emissivity), not conductive heat flow!!!
You can learn more here:
http://phzoe.com/2020/02/20/two-theories-one-ideological-other-verified/
See 2 examples at the end.
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TL Winslow
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[[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).]]
No. KISS. What comes out of the surface plane is what comes out of the surface plane, which is what started at the Earth’s interior. The internal thermal conductiivity and depth are irrelevant because the heat flow out of the surface is the net result of the conduction, which has a steady state value equal to the internal thermal heat generation, i.e. all of the internal heat makes it to the surface. Thus the Earth’s surface emits a steady state power equal to the internal geothermal power of 47 TW, and since the Earth’s surface area is 510 Tm^2, the average power per meter squared would be 47/510 = .092 W/m^2, and the S-B Law can be used to give a surface temperature of 35.65K as long as you junk the fake physics CO2 back radiation hoax.
“Thermal conduction is defined as the transport of energy due to random molecular motion across a temperature gradient.” – https://en.wikipedia.org/wiki/Thermal_conductivity
”Estimates of the total heat flow from Earth’s interior to surface span a range of 43 to 49 terawatts (TW) (a terawatt is 1012 watts).[10] One recent estimate is 47 TW, equivalent to an average heat flux of 91.6 mW/m2, and is based on more than 38,000 measurements. The respective mean heat flows of continental and oceanic crust are 70.9 and 105.4 mW/m2.]] – https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget
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Zoe Phin
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“Thus the Earth’s surface emits a steady state power equal to the internal geothermal power of 47 TW”
No, it doesn’t. The geothermal heat flux has nothing to do with what is emitted at the surface. What is emitted at the surface is based on temperature (and emissivity), not the conductive heat flux.
My whole article is exactly a refutation of what you just said. I have more explanation and two experiments, here:
http://phzoe.com/2020/02/20/two-theories-one-ideological-other-verified/
I think lifeisthermal did a good job summarizing:
“91mW is only the heat flow between two points close to each other in the thin crust. If you boil a pot of water on the stove, you´ll have a very small heat transfer between two points inside the boiling water, but you´ll have a much larger heat flow from the stove through the water.”
Indeed. And that is what experiment shows, obviously.
IF the geothermal heat flux was 0 W/m^2 from Earth’s core to the surface (a hypothetical), it would imply the surface and core had the same temperature, i.e. 5400C. And the theoretical emission to space from that would be: 58,732,722 W/m^2.
5400C would CERTAINLY not produce 0 W/m^2 of radiation just because the conductive heat flux was 0 W/m^2.
Conservation of Heat Flow is not a thing in real physics. Conservation of Energy IS!
And 5400C worth of energy (emis=1) will produce 58,732,722 W/m^2 not 0 W/m^2.
QED
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Max Polo
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Zoe is brilliant as usual. Thanks for the great discussion.
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