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.
Take care, -Zoe